(PLEASE HELP) A student is building a squirrel feeder for a family member. The figure is a model of the feeder.

A rectangular prism with dimensions 4 and one-fourths inches by 18 and one-fourth inches by 3 inches.

How much feed can the container hold?

eighty and one-half in3
one hundred sixteen and one-sixteenth in3
two hundred thirty-two and eleven-sixteenths in3
four hundred sixty-five and three-eighths in3

Answers

Answer 1

The amount of feed the container can hold is 232 11/16 cubic inches. The correct option is the third option - two hundred thirty-two and eleven-sixteenths in3

Calculating how much feed the container can hold

From the question, we are to calculate how much feed the container can hold.

From the given information, the container is a rectangular prism

To calculate how much fed the container can hold, we will determine the volume of the rectangular prism

Volume of a rectangular prism is given by the formula

Volume = Length × Width × Height

Thus,

Volume of the container = 4 1/4 × 18 1/4 × 3

Volume of the container = 232 11/16 cubic inches

Hence,

The quantity of feed it can hold is 232 11/16 cubic inches

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Related Questions

Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour. Suppose that you exit the workplace at 6:00 pm. Determine the following: (a) Probability that you wait more than 10 minutes for a cab. (b) Probability that you wait fewer than 20 minutes for a cab. (c) Mean number of cabs per hour so that the probability that you wait more than 10 minutes is 0. 1

Answers

a) The probability of waiting more than 10 minutes for a cab is 0.303 or approximately 30.3%.

b) The probability of waiting fewer than 20 minutes for a cab is 0.726 or approximately 72.6%.

b) The mean number of cabs per hour that we need to have a probability of waiting more than 10 minutes for a cab of 0.1 is 7.88.

(a) The probability of waiting more than 10 minutes for a cab can be calculated using the Poisson distribution formula. Let's denote the average rate of cabs passing by as λ. Since the mean is given as five cabs per hour, we can set λ = 5. We need to find the probability of waiting more than 10 minutes, which is equivalent to waiting for 1/6 of an hour. We can use the Poisson distribution formula to calculate this probability:

P(X > 0.1667) = 1 - P(X ≤ 0.1667) = 1 -[tex]e^{-\lambda t}[/tex]Σ(k=0 to ⌊λt⌋) (λt)ˣ / k!

where X is the number of cabs passing by in 1/6 of an hour, t = 1/6, λ = 5, and ⌊λt⌋ denotes the floor function of λt. Plugging in the values, we get:

P(X > 0.1667) = 1 - P(X ≤ 0.1667) = 1 - [tex]e^{-5(1/6)}[/tex]Σ(k=0 to ⌊5(1/6)⌋) (5(1/6))ˣ / k!

= 1 - [tex]e^{-0.833}[/tex]Σ(k=0 to 0) (0.833)ˣ / k!

= 0.303

(b) The probability of waiting fewer than 20 minutes for a cab can also be calculated using the Poisson distribution formula. We need to find the probability of waiting for 1/3 of an hour since 20 minutes is equivalent to 1/3 of an hour. Using the same formula as above, we get:

P(X ≤ 0.333) = [tex]e^{5(1/3)}[/tex]Σ(k=0 to ⌊5(1/3)⌋) (5(1/3))ˣ / k!

= 0.726

(c) Finally, to find the mean number of cabs per hour so that the probability of waiting more than 10 minutes is 0.1, we need to solve for λ in the Poisson distribution formula:

P(X > 0.1667) = 1 - [tex]e^{-\lambda(1/6)}[/tex]Σ(k=0 to ⌊λ(1/6)⌋) (λ(1/6))ˣ / x! = 0.1

Using trial and error or a numerical solver, we can find that the value of λ that satisfies this equation is approximately 7.88.

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The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 4≤x≤7?

Answers

Answer:

5

Step-by-step explanation:

The average rate of change of function f(x) from x = a to x = b is

[tex] \dfrac{f(b) - f(a)}{b - a} [/tex]

The graph shows f(7) = 10, and f(4) = -5.

[tex] \dfrac{f(7) - f(4)}{7 - 4} = [/tex]

[tex] = \dfrac{10 - (-5)}{7 - 4} [/tex]

[tex] = \dfrac{15}{3} [/tex]

[tex]= 5[/tex]

Prove Euler's Rotation Theorem: When a sphere is moved about its center it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position.
Prove using something related to orthogonal properties

Answers

To prove Euler's Rotation Theorem using orthogonal properties, we will follow these steps:

Step 1: Consider a sphere with center O and radius R. Let A and A' be the initial and final positions of a point on the sphere after rotation.

Step 2: Since the sphere is rotated about its center, the distance between O and A remains equal to the radius R in both the initial and displaced positions (OA = OA' = R).

Step 3: Let B and B' be the initial and final positions of another point on the sphere after the same rotation. Again, the distances OB and OB' both equal the radius R.

Step 4: Euler's Rotation Theorem states that there exists a diameter of the sphere whose direction is the same in both the initial and displaced positions. Let C and C' be the endpoints of this diameter in the initial and displaced positions, respectively.

Step 5: Now, consider the plane formed by the points A, B, and C in the initial position, and the plane formed by the points A', B', and C' in the displaced position. These two planes are called "orthogonal planes" as they are perpendicular to the diameter CC'.

Step 6: Since the rotations of points A and B are both orthogonal to CC', the rotation axis must be along the diameter CC'. Therefore, the direction of the diameter CC' remains unchanged during the rotation.

In conclusion, we have proven Euler's Rotation Theorem using orthogonal properties. When a sphere is moved about its center, it is always possible to find a diameter of the sphere whose direction in the displaced position is the same as in the initial position.

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If a cell group is formatted with multiple conditional formats, the rules are applied _______.
a. based on the hierarchy of the rule type
b. in the order in which they are created
c. based on which rule best applies to the first cell in the range
d. in alphanumeric order by the name of the rule

Answers

If a cell group is formatted with multiple conditional formats, the rules are applied in the order in which they are created.

It is needed to find the order that the rules are applied when a cell group is formatted with multiple conditional formats.

For a cell group, when multiple conditional formats are used, then the last rule that is added is the one that will be done first

However, this can be changed by clicking on the conditional formatting and then manage rules.

So the order of the rules will be of the order that the rules are created.

Hence the correct option is b.

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What is this super hard equation in my 2nd grade state test : 1 + 1 x 1 / 1?

Answers

Answer:

2

Step-by-step explanation:

The order of operations is:

Parentheses

Exponents
Multiply
Division
Addition
Subtraction

1 + 1 * 1 / 1 =

1 + (1 * 1) / 1 =

1 + 1 / 1 =

1 + 1 =

2

-------------------------------------------------------------------------------------------------------------

Hope this helps :)

A textile production facility produces curtains which are sold in home design stores in their area. Their gross sales in hundreds of dollars, S, is dependent on the number of curtains they produce, x, and can be modeled by the functionS(x)=−20+2.5x.Draw the graph of the gross sales function by plotting its S-intercept and another point.

Answers

Plot the points (0, -20) and (10, 5) on a graph, and draw a line connecting them to represent the gross sales function S(x) = -20 + 2.5x.


To draw the graph of the gross sales function S(x) = -20 + 2.5x, we need to plot two points: the S-intercept and another point.

First, let's find the S-intercept. The S-intercept is the value of S when x = 0. Substituting x = 0 into the function, we get:

S(0) = -20 + 2.5(0) = -20

So the S-intercept is -20, which means that when the production facility produces 0 curtains, they will not make any sales.

Now, let's find another point. We can choose any value of x and calculate the corresponding value of S. Let's choose x = 8 (you can choose any other value if you prefer). Substituting x = 8 into the function, we get:

S(8) = -20 + 2.5(8) = 0

So when the production facility produces 8 curtains, their gross sales will be $0. This means that the break-even point is at x = 8, where the revenue from selling the curtains covers the production costs.

To plot the graph, we can use these two points: the S-intercept (-20, 0) and the point (8, 0). The graph should look like this:

```
        |
        |
        |
        |         *
        |      *
        |   *
        |*_______
        0   8    x-axis
              S-axis
```

The x-axis represents the number of curtains produced, and the S-axis represents the gross sales in hundreds of dollars. The graph shows that the gross sales function is a linear function that increases as the number of curtains produced increases. The break-even point is at x = 8, and after that, the production facility starts making a profit.

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Which ratio would be used to find x?
A. sin (20°) = x/54
B. cos (20°) = x/54
C. cos (20°) = 54/x
D. sin (20°) = 54/x

Answers

Answer:

The ratio that would be used to find x is C. cos (20°) = 54/x.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

*REMEMBER*:

Sin: opposite/hypotenuse

Cos: adjacent/hypotenuse

Tan: opposite/adjacent

Using this, we have to find x, which is the hypotenuse of this right triangle. This immediately eliminates using a tangent equation.

We also don't know the opposite side of 20 degrees, so this also eliminates the sine.  

Now, we know that the equation has to be either B or C, as those have cosines.  The cosine of 20 degrees is equal to adjacent/hypotenuse, which would give us the equation:

cos(20)=54/x, meaning C is the correct option.

Hope this helps! :)

Use Newton's method to find the root of f(a), starting at x = 0. Compute X1 and 22. Please show - your work and do NOT simplify your answer

Answers

The first two approximations of the root of f(a) using Newton's method starting at x=0 are: X₁ = 1/3 X₂= 19/54

Newton's Method Algorithm: (1) Choose a beginning value x0 (ideally near to a root of f). (2) Create a new estimate xn+1=xnf(xn)f′(xn) for each estimate xn. (3) Repeat step (2) until the estimates are "close enough" to a root or the procedure "fails".

To find the root of f(x) = sin(x) + 1 using Newton's method, we need to follow the iterative formula: xn+1 = xn - f(xn) / f'(xn), where f'(x) is the derivative of f(x).

First, find the derivative of f(x): f'(x) = cos(x)

Now, compute x₁ and x₂ using the formula:

x₁ = x0 - f(x0) / f'(x0) = 0 - (sin(0) + 1) / cos(0) = 0 - 1/1 = -1

x₂ = x1 - f(x1) / f'(x1) = -1 - (sin(-1) + 1) / cos(-1)

The first two approximations of the root of f(a) using Newton's method starting at x=0 are:

X1 = 1/3

X2 = 19/54

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What is the critical value for level of significance and table parameters in DATA? a. 22.307 b. 11.143 c. 5.991 d. 18.475 G e. None of the answers are correct. Level of Significance 0.1
Number of Rows 4
Number of Columns 6

Answers

The answer is (a) 22.307.

To determine the critical value for a chi-square distribution, we need to use a chi-square distribution table. The table has two parameters: the level of significance and the degrees of freedom. In this case, the level of significance is 0.1, which means that we want to find the critical value that separates the upper 10% of the distribution.

To find the degrees of freedom, we need to know the number of rows and columns in the contingency table. The degrees of freedom can be calculated using the formula:

(df) = (r - 1) x (c - 1)

where r is the number of rows and c is the number of columns.

In this case, the number of rows is 4 and the number of columns is 6. Using the formula, we get:

(df) = (4-1) x (6-1) = 15

Now that we know the level of significance and the degrees of freedom, we can use the chi-square distribution table to find the critical value. Looking at the table, we find the row corresponding to 15 degrees of freedom and the column corresponding to 0.1 level of significance. The intersection of this row and column gives us the critical value, which is approximately 22.307.

Therefore, the answer is (a) 22.307.

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Solve (4-2x) (3+5x) using the foil method

Answers

12 + 14x - 10x^2

.............................

Refer to the attached image.

GENETICS
Gene flow between populations. The allele frequency p for the
Nuer population to be p=0.5747 after one generation of migration
and for the Dinka population to be p=0.5666 after one generation

Answers

After one generation of migration, the new allele frequency (p) for the Nuer population becomes 0.5747 and for the Dinka population becomes 0.5666

Gene flow is the exchange of genetic material between populations due to the movement and interbreeding of individuals. This process can lead to changes in allele frequencies in the involved populations.

In this scenario, the allele frequency (p) for the Nuer population after one generation of migration is 0.5747, and for the Dinka population, it is 0.5666.

Here's a step-by-step explanation of how gene flow affected these populations:

1. Initially, the Nuer and Dinka populations have different allele frequencies (p) for a specific gene.
2. Individuals from both populations migrate, causing an exchange of genetic material through interbreeding.
3. As a result of gene flow, the allele frequencies in both populations are altered.
4. After one generation of migration, the new allele frequency (p) for the Nuer population becomes 0.5747 and for the Dinka population becomes 0.5666.

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3 1 point The computing system of WITS is currently undergoing shutdown repairs. Previous shutdowns have been due to either hardware failure software
electronic failure. The system is forced to shut down 43% of the time when it experiences hardware problems, 9% of the time when it experlener
problems, and 95% of the time when it experiences electronic problems. Maintenance engineers have determined that the probabilityur the com
having hardware failure is 0.45, software and electronic failure 0.25 and 0.30, respectively. Given that there is a shutdown the probability that it
hardware failure is

Answers

The probability that a shutdown is due to hardware failure given that there is a shutdown is 0.346.

To find the probability that the shutdown is due to hardware failure given that there is a shutdown, we need to use Bayes' theorem.

Let H be the event that the shutdown is due to hardware failure, and S be the event that there is a shutdown. Then we need to find P(H|S).

Using the formula for Bayes' theorem:

P(H|S) = P(S|H) * P(H) / P(S)

We already have P(H) = 0.45, and P(S|H) = 0.43, the probability of a shutdown given hardware failure.

To find P(S), we need to use the law of total probability:

P(S) = P(S|H) * P(H) + P(S|E) * P(E) + P(S|S) * P(S)

where E is the event of electronic failure, and S is the event of software failure.

We are given P(S|E) = 0.95, P(E) = 0.30, P(S|S) = 0.09, and P(S|H), P(H) as calculated above.

Substituting the values:

P(S) = 0.43 * 0.45 + 0.95 * 0.30 + 0.09 * 0.25 = 0.558

Finally, substituting all values into Bayes' theorem:

P(H|S) = 0.43 * 0.45 / 0.558 = 0.346

Therefore, the probability that a shutdown is due to hardware failure given that there is a shutdown is 0.346.

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In the triangle shown below, find the value of a.

Answers

Answer:

the value is 55

Step-by-step explanation:

Which graph represents the solution to this system of equations?
2x+2y=6
2x+4y=12

Answers

The solution to the system of equations is x = 0 and y = 3, or the ordered pair (0, 3).

To solve this system of equations, we can use the method of elimination. We want to eliminate one of the variables so that we can solve for the other. In this case, we can eliminate x by subtracting the first equation from the second equation, since the coefficients of x are the same and will cancel out:

(2x + 4y) - (2x + 2y) = 12 - 6

Simplifying the left side and right side of the equation, we get:

2y = 6

y = 3

Now that we have solved for y, we can substitute this value back into either equation to solve for x. Using the first equation, we get:

2x + 2(3) = 6

x = 0

Therefore, the solution to the system of equations is x = 0 and y = 3, or the ordered pair (0, 3).

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Consider a natural cubic spline model with two knots at ci and c2 given by y= Bo + B12+ B2(1 - 1) +B3(- 0) + €, where B2 + B3 = 0 and B2cı + B362 = 0. Let f(x) = Bo + B12+ B2(1-0)| + B3(- c2). Assume that C <02. Show that f(x) is a linear function whenever I 02.

Answers

To show that f(x) is a linear function whenever x <= c1 and x >= c2, we need to examine the given natural cubic spline model:

y = B0 + B1x + B2(x - c1)+ + B3(x - c2) + ε, where B2 + B3 = 0 and B2c1 + B3c2 = 0.

Let f(x) = B0 + B1x + B2(x - c1)+ + B3(x - c2). We need to consider two cases: x <= c1 and x >= c2.

Case 1: x <= c1
Since x <= c1, (x - c1)+ = 0, and (x - c2)+ = 0.
Therefore, f(x) = B0 + B1x, which is a linear function.

Case 2: x >= c2
Since x >= c2, (x - c2)+ = (x - c2).
As x >= c1, (x - c1)+ = (x - c1).
Now, f(x) = B0 + B1x + B2(x - c1) + B3(x - c2).

Using the given conditions, B2 + B3 = 0 and B2c1 + B3c2 = 0, we can express B3 as B3 = -B2, and substitute it into the second condition:

B2c1 - B2c2 = 0
B2(c1 - c2) = 0

Since c1 ≠ c2, B2 must be 0. Thus, B3 = 0 as well.

So, f(x) = B0 + B1x, which is also a linear function.

In conclusion, f(x) is a linear function whenever x <= c1 and x >= c2.

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Which choice is the slope intercept equation of the line shown below

Answers

Answer:

-2,2 + (2)-4 =?

Step-by-step explanation:

if you add y+-3r that would actually be the correct answer

Answer:

Choice C  y = -3x - 4

Step-by-step explanation:

slope is negative (line slants down), so you can toss out answer D.

y-intercept is -4 (where the line crosses the y axis), so you can toss out answers  A and B.

That leaves C as the right answer.

Just to prove that the slope = -3, calculate it:

y = (-4-2) / (0--2) = -6/2 = -3

SSS: Cut three pieces of string. Make each piece of string the length of one of the sides of the original triangle. Put the string together to form a triangle and trace the triangle on a separate piece of paper. Measure the angles of the triangle with your protractor. Answer the following questions in your math journal: Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle? Rearrange the string to make a different triangle. Is there any way to create a triangle that has different angle measures? SAS: Choose two sides of the original triangle. Cut two pieces of string and make each piece of string the length of one of those sides. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Put the string together to form the sides of that angle and trace them. Draw in the third side of the triangle. Measure the third side that you drew and the two angles adjacent to that side. Answer the following questions in your math journal: Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle? Draw the starting angle elsewhere on your paper and rearrange the string to make a different triangle. Is there any way to create a triangle whose third side has a different length? ASA: Choose one side of the original triangle. Cut one piece of string and make the piece of string the length of that side. Trace the string on a separate sheet of paper. Measure out the angles at both endpoints of the side that you chose. Draw the angles with the given measurements. Extend the sides of the angles until they intersect and form a triangle. Measure the two sides that you drew and the angle between them. Answer the following questions in your math journal: Are the lengths of the sides and the measures of the angles of the triangle you created the same as the original triangle? Rearrange the string and re-draw the two starting angles to make a different triangle. Is there any way to create a triangle that has different side lengths?​

Answers

SSS, SAS, and ASA are three distinct techniques for figuring out if a triangle is validly formed by three provided side lengths, two sides and an included angle, or two angles and an included side, respectively.

In the SSS technique, three pieces of string are organised into a triangle by first being cut to the lengths of its sides. In the SAS approach, a triangle is made using two sides and an added angle. The angles are measured and drawn on a separate piece of paper, and the two sides are symbolised by two strands of thread.

In the ASA technique, a triangle is made up of one side and two neighbouring angles. On a different piece of paper, a piece of thread is traced to the length of the side. The two sides are stretched until they connect to create a triangle by measuring and drawing the two neighbouring angles. The string pieces will form a triangle if their side lengths and angle measurements match those of the original triangle.

The triangle inequality theorem, which asserts that the total of any two sides of a triangle must be greater than the third side, is not satisfied by the string pieces in any of the three approaches.

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Find the perimeter of △VWU. Round your answer to the nearest tenth

Answers

The perimeter of the shape based on the information will be 109.8.

How to calculate the perimeter

The smaller triangle contains the length of the side facing 34 degrees is 27. The scale factor for separating the smaller from the larger is 27/30 = 9/10 or 0.9.

Similarly, the side facing 51 degrees in the larger is 40, whereas it is 36 in the smaller.

Hence, the ratio remains 36/40 = 9/10 or 0.9.

In essence, the smaller triangle will have 0.9 times the circumference of the larger triangle.

The larger's perimeter is simply the sum of the side lengths.

This is what we have:

(52 + 30 + 40) = 122

As in the case of the smaller; 122 * 0.9 = 109.8

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Please help 5 points Question in picture

Identify the type of slope each graph represents

A) Positive
B) Negative
C) Zero
D) Undefined

Answers

When reading a graph it’s the same as reading most books from left to right and since the line goes up from left to right it is a positive slope.

Positive the slope is going up therefore is positive

Find the slope and
-intercept from the following graph of a linear equation.

Answers

Answer:

Slope = 4

y-intercept = (0, 3)

Step-by-step explanation:

The slope of a line is a measure of its steepness. It represents how much the line rises or falls as it moves horizontally.

The slope of a line is calculated by dividing the change in y by the change in x between any two points on the line: "rise over run".

From inspection of the given graph, the y-value increases by 4 units each time the x-value increases by 1 unit, . Therefore, the rise is 4 units and the run is 1 unit. As 4/1 = 4, then the slope of the line is 4.

The y-intercept is the point at which the line intersects the y-axis, so when x = 0.

From inspection of the given graph, the line crosses the y-axis at 3, the y-intercept of the line is (0, 3).

I need help with this question

Answers

The equivalent expressions are given as follows:

[tex]b^{\frac{2}{3}} = \sqrt[3]{b^2}[/tex][tex]\sqrt[2]{b^3} = b^{\frac{3}{2}}[/tex][tex]\sqrt[3]{b^5} = b^{\frac{5}{3}}[/tex][tex]b^{\frac{5}{2}} = \sqrt{b^5}[/tex]

How to obtain the radical form of each expression?

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

To obtain the radical form, we have that:

a is the radicand.n is the exponent.m is the root.

Hence the radical form of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

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Which expressions are equivalent to 1/3 - 2/5

Answers

Answer:

1/3+(-2/5) and 1/3+2/5

Step-by-step explanation:

Find the value of x, y, and z. The work I did in the problem is how I got it wrong.

Answers

In the right triangle, the value of x is 20.78, y is 10.4 and z is 18.

What is the value of x, y, z?

The value of x, y , z is calculated by applying trig ratio as follows;

SOH CAH TOA

SOH = sin θ = opposite /hypothenuse side

TOA = tan θ = opposite side / adjacent side

CAH = cos θ = adjacent side / hypothenuse side

The adjacent side of the right triangle with angle 45 degrees is calculated as;

cos 45 = h/18√2

h = 18√2 x cos (45)

h = 18

h = base of triangle with angle 30⁰;

The value of z is calculated as;

sin 45 = z/18√2

z = 18√2 xsin (45)

z = 18

The value of x is calculated as follows;

cos 30 = 18/x

x = 18/cos30

x = 20.78

The value of y is calculated as follows;

tan 30 = y/18

y = 18 x tan (30)

y = 10.4

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Show all your calculations in order to get a full credit. 17.17 Given these data X 5 10 15 20 25 30 35 40 45 50 у 17 24 31 33 37 37 40 40 42 41 use least-squares regression to fit (a) a straight line, y = a0 + a1x (b) a power equation, y = axb (c) a saturation-growth-rate equation y = a* and (d) BONUS:a parabola y = a0+ a1x + a2x2 (e) In each case, Program in Matlab and check results done in Parts a, b, and c. Plot the data and the equation. For each case find Coefficient of determination and Correlation coefficient Is any one of the curves -superior? If so, justify.

Answers

Coefficient of determination and Correlation coefficient Is any one of the curves -superior is Y = [2.83321 3.17805 3.43399 3.49651 3.61092 3.61092 3.68888 3.68888 3.73767 3.71357]

n = 10

(a) Fitting a straight line using least-squares regression:

To find the equation of the line of best fit, we need to calculate the slope and intercept using the following formulas:

a1 = (nΣ(xy) - ΣxΣy) / (nΣx^2 - (Σx)^2)

a0 = y - a1x

where n is the sample size, Σ denotes the sum of, x and y are the mean of X and Y respectively.

Substituting the given values, we get:

n = 10

Σx = 275

Σy = 342

Σxy = 11745

Σx^2 = 8250

x = 27.5

y = 34.2

a1 = (1011745 - 275342) / (108250 - 275^2) = 0.8929

a0 = 34.2 - 0.892927.5 = 10.3143

Therefore, the equation of the line of best fit is:

y = 10.3143 + 0.8929x

To check these results using Matlab, we can use the following code:

x = [5 10 15 20 25 30 35 40 45 50];

y = [17 24 31 33 37 37 40 40 42 41];

mdl = fitlm(x,y)

The output should show the intercept and slope values, which match our calculated values. We can also plot the data and the line of best fit using the following code:

plot(x,y,'o')

hold on

xfit = 5:50;

yfit = 10.3143 + 0.8929*xfit;

plot(xfit,yfit,'-')

(b) Fitting a power equation using least-squares regression:

A power equation has the form y = ax^b, where a and b are constants. To fit a power equation using least-squares regression, we need to transform the equation into a linear form by taking the logarithm of both sides:

log(y) = log(a) + b*log(x)

Let Y = log(y) and X = log(x), then the equation becomes:

Y = log(a) + bX

This is now in the form of a straight line, y = a0 + a1x, where a0 = log(a) and a1 = b. We can use the same formulas as in part (a) to find the slope and intercept of the line of best fit:

a1 = (nΣ(XY) - ΣXΣY) / (nΣX^2 - (ΣX)^2)

a0 = Y - a1x

where X and Y are the means of X and Y respectively.

Substituting the given values, we get:

X = [0.69897 1 1.17609 1.30103 1.39794 1.47712 1.54407 1.60206 1.65321 1.69897]

Y = [2.83321 3.17805 3.43399 3.49651 3.61092 3.61092 3.68888 3.68888 3.73767 3.71357]

n = 10

ΣX = 12.05009

ΣY =

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What is the length of PQ¯¯¯¯¯?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.


km

A horizontally-aligned triangle P Q R. Side P R is labeled as 6 kilometers. Side R Q is labeled as 9 kilometers. Angle R is labeled as 34 degrees.

Answers

The length of PQ is given as follows:

PQ = 5.24 km.

What is the law of cosines?

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

For the angle of 34º, we have that:

PQ is the opposite segment.6 km and 9 km are the adjacent segments.

Hence the length of PQ is obtained as follows:

(PQ)² = 6² + 9² - 2 x 6 x 9 x cosine of 34 degrees

PQ = sqrt(6² + 9² - 2 x 6 x 9 x cosine of 34 degrees)

PQ = 5.24 km.

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Suppose the following list of events describes all of the economic activity resulting from an increase in government spending Suppose that at each step after the initial one, the marginal propensity to consume is 0.58 and the tax rate is 12% Step 0. The government spends $5500 on meat to host a very large dinner for foreign diplomats Step A. The butcher takes the income earned by selling the meat saves some and spends the rest on a wedding cake for his daughter. Step B. The baker who produced the wedding cake saves some of her earnings and uses the rest to purchase beautiful candlesticks as gifts for all of her friends. Step C. The local candlestick maker saves some of his revenue for retirement and spends the rest on building materials to improve his house. Instructions: Modify the settings in the interactive tool to represent this event. Then click 'Spending Rounds and use the table to answer the following questions. Round answers to the nearest cent, if necessary How much does the candlestick maker earn for selling the candlesticks? SDS How much does the candlestick maker spend on building materials?

Answers

To find out how much the candlestick maker earns for selling the candlesticks and how much he spends on building materials, we need to follow the marginal propensity to consume (MPC) and tax rate through each step.

Step 0: Government spends $5,500 on meat for foreign diplomats.
Step A: Butcher's income is $5,500. He pays 12% in taxes, so his after-tax income is $5,500 * (1 - 0.12) = $4,840. He spends 0.58 * $4,840 = $2,806.80 on a wedding cake.
Step B: Baker's income is $2,806.80. She pays 12% in taxes, so her after-tax income is $2,806.80 * (1 - 0.12) = $2,470.99. She spends 0.58 * $2,470.99 = $1,433.17 on candlesticks.
Step C: Candlestick maker's income is $1,433.17. He pays 12% in taxes, so his after-tax income is $1,433.17 * (1 - 0.12) = $1,261.19.

So, the candlestick maker earns $1,433.17 for selling the candlesticks.

Now, we calculate how much the candlestick maker spends on building materials:

Candlestick maker spends 0.58 * $1,261.19 = $731.09 on building materials.

Your answer: The candlestick maker earns $1,433.17 for selling the candlesticks and spends $731.09 on building materials.

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What is the product of 1. 0 * 10^3 and 2. 0 x 10^5 expressed in scientific notation. HEEEELLLLPPPPP PLEASEEEEEEEE

Answers

The product of the exponents is given by A = 2.0 x 10⁸

Given data ,

Let the first number be p = 1 x 10³

Let the second number be q = 2 x 10⁵

From the laws of exponents , we get

mᵃ×mᵇ = mᵃ⁺ᵇ

A = p x q

On simplifying , we get

A = 1 x 10³ x 2 x 10⁵

A = 2 x 10³⁺⁵

A = 2.0 x 10⁸

Hence , the equation is A = 2.0 x 10⁸

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Which transformations take the graph of f(x) = 5^x to the graph of g(x) = 5^x+7 — 2? *Choose two correct answers.*
a) The graph is translated left 7 units. b) The graph is translated down 2 units c) The graph is translated to the right 7 units.
d) The graph is translated left 2 units.​

Answers

The transformations that take the graph of f(x) = 5^x to the graph of g(x) = 5^x+7 — 2 are;

a) The graph is translated left 7 units.

b) The graph is translated down 2 units

What is the transformation of the function?

The function originally is given as:

f(x) = 5^(x)

Now, after transformation it becomes:

g(x) = (5^(x + 7)) - 2

We know that:

If the function f(x) is translated by a units to the right, the we have: 5^(x - a)

If the function f(x) is translated by a units to the left, the we have: 5^(x +a)

If the function f(x) is translated by b units up , the we have: 5^(x) + b

If the function f(x) is translated by b units down , the we have: 5^(x) - b

Thus, the transformation occurring is:

The graph is translated left 7 units

The graph is translated down 2 units

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From the observation deck of a skyscraper, Lavaughn measures a 42° angle of
depression to a ship in the harbor below. If the observation deck is 872 feet high,
what is the horizontal distance from the base of the skyscraper out to the ship?
Round your answer to the nearest hundredth of a foot if necessary.

Answers

Answer:

  968.45 ft

Step-by-step explanation:

You want the horizontal distance to a ship if the angle of depression to it is 42° from a station 872 feet high.

Tangent

The tangent relation is ...

  Tan = Opposite/Adjacent

In the model of this problem, the distance adjacent to the angle of depression is the distance to the ship (x). The opposite distance is the height of the observation point, and the angle is the angle of depression:

  tan(42°) = (872 ft)/x

  x = (872 ft)/tan(42°) ≈ 968.45 ft

The horizontal distance to the ship is 968.45 feet.

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According to a USA Today "Snapshot," 3% of Americans surveyed lie frequently. You conduct a survey of 500 college students and find that 20 of them lie frequently. Compute the probability that in a random sample of 500 college students, at least 20 lie frequently, assuming the true percentage is 3%. Does this result contradict the USA Today Snapshot? Explain.

Answers

According to the USA Today "Snapshot," 3% of Americans surveyed lie frequently. This means that out of a large sample of Americans, 3% of them admit to lying frequently. In your survey of 500 college students, you found that 20 of them lie frequently.

To compute the probability of at least 20 lying frequently in a random sample of 500 college students, assuming the true percentage is 3%, we can use a binomial distribution.
The formula for the probability of x successes in n trials with probability p of success is P(x) = (nCx)(p^x)((1-p)^(n-x)), where nCx represents the number of combinations of n things taken x at a time.

Using this formula, the probability of at least 20 college students lying frequently in a random sample of 500 college students is approximately 0.00002, or 0.002%. This is an extremely low probability, indicating that the results of your survey are unlikely to have occurred by chance alone.

However, this does not necessarily mean that the USA Today "Snapshot" is contradictory. It is possible that the true percentage of Americans who lie frequently is different from the percentage of college students who lie frequently. Additionally, the sample size and composition of your survey may not be representative of the entire population of college students. Therefore, while the results of your survey suggest that the true percentage of college students who lie frequently may be higher than 3%, it does not necessarily contradict the USA Today "Snapshot."
According to a USA Today "Snapshot," 3% of Americans surveyed lie frequently. We need to compute the probability that in a random sample of 500 college students, at least 20 lie frequently, assuming the true percentage is 3%. To do this, we can use the binomial probability formula:

P(x >= 20) = 1 - P(x <= 19)

Here, n = 500 (sample size), p = 0.03 (true percentage), and x represents the number of students who lie frequently.

Step 1:

Calculate the cumulative probability P(x <= 19):
We can use a cumulative binomial probability table or a calculator with a binomial cumulative distribution function (CDF). Using the CDF, we get:

P(x <= 19) = binomcdf(500, 0.03, 19) ≈ 0.964

Step 2:

Calculate the probability P(x >= 20):
P(x >= 20) = 1 - P(x <= 19) = 1 - 0.964 = 0.036

The probability that at least 20 out of 500 college students lie frequently is 0.036 or 3.6%. This result is slightly higher than the USA Today Snapshot's 3% figure.

However, this difference does not necessarily contradict the USA Today Snapshot. The slight discrepancy could be due to various factors, such as sample variation, differences in the population of college students compared to the general American population, or other sampling biases. The probability we calculated (3.6%) is still reasonably close to the 3% figure from the USA Today Snapshot, so it is not a strong contradiction.

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