Divide 42 apples in the ratio 3:4​

Thus, the length of the missing side for the given Right triangles using  the Trigonometric Ratios is found as :x = 18.47 units.

The leg, denoted as, that is next to the 30 degree angle θ is represented by Side BC. To get the length of side BD, the hypotenuse of triangle BCD, we use the cosine ratio.

cos θ = Adjacent leg / Hypotenuse = BC/BD

cos 30° = 8√2 / BD

Now, we know.

cos 30° = √3/2

√3/2 =  8√2 / BD

BD = 8√2 / √3/2

BD = 16√2 / √3

On rationalising;

BD = 16√2*√3 / √3*√3

BD = 16√6 / 3

Sin A = Opposite leg /Hypotenuse = BD / x

Sin 45° = (16√6 / 3) / x =  16√6 / 3x

We know that:

Sin 45° = 1/√2

(1/√2) = 16√6 / 3x

(1/√2) * x = 16√6 /3

Or,

√2/2 * x = (16√6 /3) * (2/√2)

x = 32√3 / 3

x = 18.47

Thus, the length of the missing side for the given Right triangles using  the Trigonometric Ratios  is found as :x = 18.47 units.

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The correct question is-

Find the missing side length. Give the answer as radicals in simplest form.

The linear inequality in open-sentence form are

An open sentence is a mathematical statement that contains at least one blank or unknown and that becomes true or false when the blank is filled or a quantity is substituted for the unknown.

Now, since we have the expressions,

First, we note that there are 3 open sentences and only two of them are inequalities.

The 3 open sentences are

The two inequalities are

So, the linear inequality in open-sentence form are

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Penny plans to distribute a questionnaire at the entrance to the coffee shopping center in order to do market research because she would love to build a coffee shop there which are explained.

Market research is crucial for helping you understand the present status of the coffee shop business as well as for figuring out how to shape various areas of your company to draw in the suitable clients.

Penny plans to distribute a questionnaire at the entrance to the shopping center in order to do market research because she would love to build a coffee shop there.

Penny may utilize a questionnaire to collect the data she needs, which would include the following:

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The numeric value of f(x) = 3x² - 7x - 4 at x = 0 is given as follows:

f(0) = -4.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² - 7x - 4

We want to find the numeric value of the function at x = 0, hence both instances of x in the definition of the function are replaced by zero and then we add the terms, as follows:

f(0) = 3(0)² - 7(0) - 4

f(0) = -4.

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The revised questionnaire that is more suitable that includes reasons for taking a GAP year is given below:

The new questionnaire includes four questions aimed at gaining insight into the participant's motivations, goals, and timeframe for taking a gap year:

Have you considered taking a gap year before starting your next academic or professional endeavor?

What are your top 5 reasons for considering a gap year? (Please list in order of importance)

What are your goals for your gap year? (e.g., travel, volunteer work, internships, personal development, etc.)

How long do you plan to take for your gap year?

Reasons for taking a gap year may vary from person to person, but here are five common motivations for doing so:

To gain life experience and personal growth

To travel and explore new cultures

To gain work experience or internships in a desired field

To take a break from academic or professional responsibilities

To pursue passions or hobbies that may not be feasible during a regular academic or work schedule.

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Revise the suggested questionnaire so that it is more suitable. Include 5 reasons for taking a GAP YEAR. Submit a copy of a new revised questionnaire

Have you considered taking a gap year before starting your next academic or professional endeavor?

What are your reasons for considering a gap year?

What are your goals for your gap year?

How long do you plan to take for your gap year?

The domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.

Function in mathematics is a relation which assigns each element of a set (called the domain) to exactly one element of another set (called the codomain). It can also be thought of as a type of mapping from one set to another. Functions are used to model real-world problems and to simplify the expression of a certain problem. They are widely used in algebra, trigonometry and other areas of mathematics.

The domain of a function is the set of all possible inputs for the function. In other to determine the domain of a function, we must first identify the independent variable (x) and then determine which values of x can be used in the function.

In the given function, f(x)=7x+5/3x-1, the independent variable is x. To find the domain of this function, we must identify the values of x that will produce results that are real numbers. To do this, we must set the denominator (3x-1) equal to zero and solve for x.

We can solve this equation by factoring and setting each factor equal to zero:

3x - 1 = 0

3x = 1

x = 1/3

Therefore, the domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.

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Answer: Jill earns the most money.

Step-by-step explanation:

Bridgette:1230

Jill: 1340

Barb:300

The firm's profit in this case is = $360.

What is the total cost?

The total economic cost of production is made up of two types of costs: the variable cost, which changes depending on how much of a good is produced and includes inputs like labour and raw materials, and the fixed cost, which is unaffected by how much of a good is produced and includes inputs like buildings and machinery that cannot be changed in the short term, possibly including sunk costs.

In economics, the whole cost of each unit of production, whether fixed or variable, includes the total opportunity cost (benefits from the next-best alternative).

Example:

Q        Fixed       Variable    Total    Marginal    Aver.     Aver.     Aver.

       Costs        Costs         Cost    Cost           FC         VC         TC      

0          100             0              100         -               -             -             -

1           100           50               150       150           100         50         150

2          100           70               170         20            50         35          85

3          100           90               190        20           33.33      30        63.33

4          100          140               240       50            25          35          60

5          100         200               300       60            20          40          60

6          100         360              460      160           16.67       60        76.67

The firm's profit in this case is = $360.

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The value of the 5 measurements according to the given function is 66.

When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is specified can all be added together, in addition to integers. The position of the items in a sequence is frequently used to characterise them through a regular pattern. Long sequences can be summarised for basic patterns by replacing most summands with ellipses.

The function is given as:

[tex]\sum_{i = 1}^5 (x_i^2)\\\\\sum_{i = 1}^5 = x_1 + x_2 + x_3 +x_4 + x_5\\\\\sum_{i = 1}^5 (x_i^2) = 12 + 14 + 16 + 7 + 17 = 66[/tex]

Hence, the value of the 5 measurements according to the given function is 66.

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The actual difference between the twο temperatures is: 94 degrees F

Temperature is measure οf  degree οf hοtness οr cοldness οf  οbject οr substance. It is  physical quantity that describes average kinetic energy οf  particles that make up οbject οr substance.

Temperature is a usually measured using thermοmeter, which cοnsists οf  narrοw, unifοrm tube filled with  liquid, like mercury οr alcοhοl

Nο, Martin's calculatiοn is nοt cοrrect. The difference between twο temperatures cannοt be greater than the sum οf the twο temperatures. In this case, the difference Martin calculated is 94 degrees F, which is greater than the sum οf the twο temperatures (-12 degrees F + 82 degrees F = 70 degrees F). Therefοre, Martin must have made an errοr in his calculatiοn οr recοrded the temperatures incοrrectly.

The actual difference between the twο temperatures is:

82 degrees F - (-12 degrees F) = 94 degrees F

This cοnfirms that Martin must have recοrded οne οf the temperatures incοrrectly οr made a mistake in his calculatiοn.

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Answer:

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.

Step-by-step explanation:

If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.

The factors of the polynomial are then:

(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))

Simplifying the factors, we get:

x(x^2+49)(x^2-4x+5)

Expanding the last factor, we get:

x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x

Finally, we have the 5th degree polynomial:

f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x

Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.

The solution is, f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x, is  a 5th degree polynomial with real coefficients that has zeros 0, -7i, and 2-i.

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

here, we have,

If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.

The factors of the polynomial are then:

(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))

Simplifying the factors, we get:

x(x^2+49)(x^2-4x+5)

Expanding the last factor, we get:

x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x

Finally, we have the 5th degree polynomial:

f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x

Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.

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Answer:

Step-by-step explanation:

SEE THE GRAPH

Answer:

30.4 meters

Step-by-step explanation:

Just plug in the given values of
V = 24.4 and

g = 9.8

in the given equation and you can solve for H

[tex]H = \dfrac{V^2}{2g}\\\\= \dfrac{(24.4)^2}{2\times 9.8}\\\\= 30.37551 \dots\\\\= 30.4\\\\[/tex]correct to 3 significant figures

The dimensions of the square-ended rectangular package of greatest volume that meets the airline's requirement are x = y = 90 cm and z = 90 cm.

Dimensions refer to measurements or quantities that describe the size, shape, or extent of an object or space, often expressed in length, width, and height.

Let x, y, and z represent the dimensions of the rectangular package. Since the package has square ends, we know that x = y.

We want to maximize the volume of the package, which is given by V = x² × z.

The airline requires that the sum of the three dimensions is at most 270 centimeters, so we have the constraint x + y + z ≤ 270.

Substituting x = y, we get 2x + z ≤ 270.

We can solve for z in terms of x: z ≤ 270 - 2x.

Substituting this inequality into the expression for V, we get V = x^2 * (270 - 2x) = 270x² - 2x³.

To maximize V, we take the derivative of V with respect to x, set it equal to zero, and solve for x:

dV/dx = 540x - 6x² = 0

6x(90 - x) = 0

x = 0 or x = 90

Since x represents a length, it must be positive, so x = 90.

Since x = y, y = 90 as well.

Substituting x = y = 90 into the inequality z ≤ 270 - 2x, we get z ≤ 270 - 2(90) = 90.

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Answer:

The number of hamburgers is 136.

Step-by-step explanation:

What we know:

We got cheeseburgers and hamburgers

The total: 408

The number of cheese burgers was 2 times the number of hamburgers

This is pretty much all the info we need to know.

Lets define our variables:

x = hamburgers

y = cheeseburgers

Now, we need our two equations to make a system.

[tex]x+y=408[/tex]

[tex]y=2x[/tex]

To find hamburgers, x, we plug the value of y into our first equation.

[tex]x+2x=408[/tex]

Add like terms

[tex]3x=408[/tex]

Divide by 3

[tex]x=136[/tex]

The number of hamburgers is 136.

Just to check our work, lets find the cheeseburgers.

[tex]y=2(136)[/tex]

[tex]y=272[/tex]

[tex]272+136=408[/tex]

Answer:

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a Vertical Shrink.

To see this, note that the 2 in f(x) causes a vertical stretch of the absolute value graph. Removing the 2 in g(x) results in a Vertical Shrink of the absolute value graph. The +4 and +2 only cause a vertical shift of the graph.

Answer: Vertical Shrink

Step-by-step explanation:

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a vertical shrink.

To see why, let's examine each function separately:

Therefore, the transformation from f(x) to g(x) involves removing the vertical stretch by dividing the absolute value term by 2. This results in a smaller "V" shape for the graph of g(x), or a vertical shrink.

The answer is:

[tex]$\boxed{\text{Vertical Shrink}}$[/tex]

Two points on the graph of the parabola h(x) = (x-4)^2 - 1 other than the vertex and x-intercepts are (1, 8) and (6, 3).

To find two points on the graph of the parabola other than the vertex and x-intercepts

We can simply choose two values of x and find their corresponding y values using the function h(x).

Let's choose x = 1:

h(1) = (1-4)^2 - 1 = 9 - 1 = 8

So one point on the graph is (1, 8).

Now let's choose x = 6:

h(6) = (6-4)^2 - 1 = 4 - 1 = 3

So another point on the graph is (6, 3).

Hence, the two points are (1, 8) and (6, 3)

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The dataset is evenly distributed, so the appropriate measure of variability is the range

The dataset is evenly has no outliers, so the appropriate measure of center is the mean

Measure of variability

When the data set is evenly distributed, a measure of variability appropriate for stem and leaf plot would be the range

The range is simply the difference between the largest and smallest value in the data set.

It is a simple measure of spread that can be easily calculated from a stem and leaf plot.

Measure of center

When there are no outliers in a dataset, the appropriate measure of center to use in a stem and leaf plot is the mean

The mean, also known as the average, is calculated by summing all the values in the dataset and then dividing by the total number of values.

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Answer:  [tex]\frac{-3+\sqrt{7}}{2}, \ \frac{-3-\sqrt{7}}{2}[/tex]

========================================================

Explanation:

Let

Each derivative is,

which will be useful in the next section.

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

[tex]f(\text{x}) = \frac{4\text{x}+6}{\text{x}^2+\text{x}+1} = \frac{g(\text{x})}{h(\text{x})}\\\\f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\[/tex]

Apply the derivative with respect to x. We'll use the quotient rule.

[tex]f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\\\f'(\text{x}) = \frac{g'(\text{x})h(\text{x})-g(\text{x})h'(\text{x})}{\big[h(\text{x})\big]^2}\\\\\\f'(\text{x}) = \frac{4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1)}{(\text{x}^2+\text{x}+1)^2}\\\\[/tex]

The critical value(s) occur when either...

The first criteria will be handled in the next section.

The second criteria is handled in the section after that.

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

f ' (x) is in the format A/B. It means f ' (x) = 0 leads to A/B = 0 and A = 0.

We set the numerator equal to zero and solve for x.

[tex]4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1) = 0\\\\4(\text{x}^2+\text{x}+1)-(8\text{x}^2+16\text{x}+6) = 0\\\\4\text{x}^2+4\text{x}+4-8\text{x}^2-16\text{x}-6 = 0\\\\-4\text{x}^2-12\text{x}-2 = 0\\\\-2(2\text{x}^2+6\text{x}+1) = 0\\\\2\text{x}^2+6\text{x}+1 = 0\\\\[/tex]

From here we use the quadratic formula.

Plug in a = 2, b = 6, c = 1.

[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(2)(1)}}{2(2)}\\\\\text{x} = \frac{-6\pm\sqrt{28}}{4}\\\\\text{x} = \frac{-6\pm2\sqrt{7}}{4}\\\\\text{x} = \frac{2(-3\pm\sqrt{7})}{4}\\\\\text{x} = \frac{-3\pm\sqrt{7}}{2}\\\\\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}\\\\[/tex]

If x is equal to either of those values, then f ' (x) = 0 would be the case. Therefore, these are the critical points of f(x).

There may be other critical values. We'll still need to check the second criteria.

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

f ' (x) doesn't exist when we divide by zero.

Set the denominator equal to 0 and solve for x.

[tex](\text{x}^2+\text{x}+1)^2 = 0\\\\\text{x}^2+\text{x}+1 = 0\\\\[/tex]

Plug a = 1, b = 1, c = 1 into the quadratic formula.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-1\pm\sqrt{(1)^2-4(1)(1)}}{2(1)}\\\\x = \frac{-1\pm\sqrt{-3}}{2}\\\\[/tex]

We have a negative number as the discriminant, which leads to complex number solutions in the form a+bi where [tex]i = \sqrt{-1}[/tex]

Therefore, there aren't any real number values for x that lead [tex](\text{x}^2+\text{x}+1)^2[/tex] to be zero.

No matter what we pick for x, the expression [tex](\text{x}^2+\text{x}+1)^2[/tex] will never be zero.

In short, the second criteria yields no real value critical points (assuming your teacher is only focused on real-valued functions and not complex-valued functions).

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

Summary:

Therefore, the only critical values are [tex]\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}[/tex]

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

Extra info:

A critical value is where a local/absolute min, a local/absolute max, or a saddle point would be at this x value. The 1st derivative test or 2nd derivative test would be used to determine the nature of each critical value.

A real world application of a critical value would be to determine the max revenue. Another example is to minimize the surface area while holding the volume constant. Linear regression relies on a similar concept.

To check the answer, you can type in "critical points of (4x+6)/(x^2+x+1)" without quotes into WolframAlpha.

Answer:BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB TRUST ME

Step-by-step explanation:

The prοbabiIity that exactIy οne οf the six chοsen femaIe cats weighs mοre than 4.5 kg is apprοximateIy 0.2834 οr 28.34%.

The binοmiaI distributiοn fοrmuIa:    

The binοmiaI distributiοn fοrmuIa gives the prοbabiIity οf οbtaining exactIy k successes in n independent BernοuIIi triaIs, where each triaI has a prοbabiIity οf success p.

The formuIa is:

[tex]P(X = k) = ^{n}C_{k} P^{k} \times(1-P)^{n-k}[/tex]

Here we have

Weights οf female cats οf a certain breed are nοrmally distributed with a mean οf 4.1 kg and a standard deviatiοn οf 0.6 kg.

The prοbability that οne chοsen at randοm will weigh mοre than 4.5 kg is 0.2514.

Tο find the prοbability that exactly οne οf the six chοsen female cats weighs mοre than 4.5 kg, we can use the binοmial distributiοn with parameters

Using the binοmial distributiοn fοrmula  

[tex]P(X = k) = ^{n}C_{k} P^{k} \times(1-P)^{n-k}[/tex]

where:

n = 6 and p = 0.2514,  

The probabiity of exacty one success in six trias can be cacuated as

P(X = 1) = (6 choose 1) × 0.2514¹ × (1 - 0.2514)⁵

P(X = 1) = 6 × 0.2514 ×  0.7486⁵

P(X = 1) = 0.2834

Therefore,  The probabIIty that exacty one of the sIx chosen femae cats weIghs more than 4.5 kg Is approxImatey 0.2834 or 28.34%.

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Answer:

To find the numbers between which the square root of 72 lies, we need to determine the perfect squares that are closest to 72.

The perfect squares closest to 72 are 64 (8^2) and 81 (9^2). Since 72 is closer to 81 than to 64, we know that the square root of 72 is closer to 9 than to 8.

Therefore, the square root of 72 lies between the numbers 8 and 9. We can write this as:

8 < √72 < 9y-step explanation:

Answer:71

Step-by-step explanation:

-3-(-10)-(-64)=-3+10+64=71

Answer:

$630.00

Step-by-step explanation:

IF THIS IS WRONG I AM SORRY BUT I KNOW THIS IS RIGHT AND IF YOU NEED MORE ANSWERS I AM ALWAYS OPEN!

Answer: 5x10^4, 8x10^4, 10^-5, 10^4

Step-by-step explanation: calculator

The equation of the line passing through the points (0, 7) and (2, -5) is y = -6x + 7

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The standard form of a linear equation is:

y = mx + b

where m is the slope(rate of change) and b is the y intercept

As shown in the graph, the line passes through the points (0, 7) and (2, -5). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-7=\frac{-5-7}{2-0} (x-0)\\\\y=-6x+7[/tex]

The equation of the line is y = -6x + 7

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Answer:

x = log(3) (8)

or log 8 base 3

Step-by-step explanation:

some number^x = another number

some number = base (the lower case number)

another number = the big number next to it.

put log infront in these situations.