Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?

The trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ is 11/√2 cos θ.

The write the  trigonometric expression in the required, we can start by using the second formula:

a sin Bθ + b cos Bθ = a^2 + b^2 cos(Bθ − C)

where;

Let a = 11 and b = 11/√2, and Bθ = θ − π/4.

Then C = arctan(a/b) = arctan(11/(11/√2)) = arctan(√2).

Substituting these values, we get:

11 cos (θ − π/4) = 11/√2 cos (θ − π/4 + arctan(√2))

= 11/√2 cos (θ - π/4 + π/4)

= 11/√2 cos θ

Thus, we have written the trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ as 11/√2 cos θ.

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sample=38

To calculate the size of the sample you need to take in order to estimate the proportion of center party sympathizers with a 95% confidence interval and a statistical margin of error of at most 2% points, you can use the formula n = (Zα/2/E)2 × p × (1-p), where n is the sample size, Zα/2 is the z-score of the desired confidence level (in this case, 1.96 for a 95% confidence interval), E is the margin of error (2%), and p is the population proportion (6%).

Plugging in the values from the question, we get n = (1.96/2)2 × 6% × (1 - 6%) = 38.4. Therefore, the sample size needed to estimate the proportion of center party sympathizers with a 95% confidence interval and a statistical margin of error of at most 2% points is 38.

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1. If there were two people dividing the cost of the gift, each person would spend $180. If there were three people dividing the cost, each person would spend $120. If there were five people dividing the cost, each person would spend $72. If there were ten people dividing the cost, each person would spend $36. If there were one hundred people dividing the cost, each person would spend $3.60.

2. The function that could be used to model the amount each person would spend depending on the number of people contributing to the gift is:

cost per person = total cost / number of people

3. The table will be:

Number of people Amount per person

2. $180

3 $120

5. $72

10. $36

100. $3.60

The graph of the function would be a straight line passing through the points (2, $180), (3, $120), (5, $72), (10, $36), and (100, $3.60).

4. The domain of the function is all positive integers greater than zero, since you cannot have a fractional or negative number of people contributing.

The range of the function is all positive real numbers, since the cost per person can be any positive amount.

The function is decreasing, since the cost per person decreases as the number of people contributing increases.

There is no maximum or minimum value for the cost per person, since it can be any positive amount. The function is continuous, but the number of people contributing must be a discrete value (i.e., a whole number).

As the number of people contributing approaches infinity, the cost per person approaches zero. The y-intercept of the function is the cost of the gift, and the x-intercept is not applicable in this context.

There is a horizontal asymptote at y = 0, since the cost per person approaches zero as the number of people contributing approaches infinity.

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Chile is celebrating her Quinceañera. Hannah knows the perfect gift to buy Chile, but it costs $360. Hannah can't afford to pay for this on her own so thinks about asking some friends to join in and share the cost.

1. How much would each person spend if there were two people dividing the cost of the gift? How much would each person spend if there were three people dividing the cost? Five people? Ten? One hundred?

2. Determine the function that could be used to model the amount each person would spend depending on the number of people contributing to the gift.

3. Use multiple representations to show how the amount each person would contribute to the gift would change depending on the number of people contributing. Describe the connections between the representations.

4. Describe the features of the function based on the context (domain/range, increasing/decreasing, maxima/minima, discrete/continuous, end behavior, intercepts, asymptotes).

Answer:

2.05 yards, Fredic and Fioana's answers are in the same range.

The probability is 0.05.

When using two water heaters as the inspection unit, the center line and control limits consistent with the past 22 days of inspection data are calculated as follows:

Center line (CL) = (X1 + X2)/2

Upper control limit (UCL) = CL + 3 * s/2

Lower control limit (LCL) = CL - 3 * s/2

Where X1 and X2 are the means of the two water heaters, and

s is the standard deviation of the sample data.

The probability of type I error for the control chart in part (b) is typically set at 0.05,

meaning that there is a 5% chance of rejecting the null hypothesis when it is actually true.

Complete question:

When using two water heaters as the inspection unit, (b) calculate the center line and control limits that are consistent with the past 22 days of inspection data. (c) what is the probability of type i error for the control chart in part (b)?

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Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.

Here,

The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:

=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)

Condensing each term:

=> 3x³ - 5x²- 3x - 3x² + 5x + 3

=> 3x³ - 8x²+ 2x + 3

Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

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Answer: 61 degrees

Step-by-step explanation:

just trust me

Answer:

You must know the value of x

Answer:

6

Step-by-step explanation:

y is 6..

If The total revenue earned (in dollars) from selling the books is given by the function R-34.60N. the equation relating P to N is P = 18.95N - 750.

Profit made (P) can be calculated by subtracting the total production cost (C) from the total revenue earned (R), so:

P = R - C

P = 34.60N - (18.95N + 750)

P = 34.60N - 18.95N - 750

P = 15.65N - 750

Therefore, the equation relating P to N is P = 18.95N - 750.

The equation shows that the profit made by the company is a linear function of the number of books printed. The slope of the line is the revenue per book (34.60 dollars), minus the cost per book (18.95 dollars), which is 18.95 dollars.

The intercept of the line is the fixed cost for editing (750 dollars). The equation can be used to estimate the profit for any given number of books printed, and to determine the break-even point, which is the number of books that need to be sold to cover the total production cost.

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Answer: k

Step-by-step explanation:

tddthvbkj

Answer:

and painting has 100kg or 1kg bcs thats not same

Option B, 18 million, is the answer to this question.

In September 1998, the population of West Goma in millions was modeled by the function f(x) = 17.9e0.002x, and the population of East Goma in millions was modeled by the function g(x) = 13.6e0.017x. Here, x represents the year, with x=0 corresponding to September 1998.

To find out the point of intersection where the populations are equal, we equate both formulas and solve for x:

17.9e0.002x = 13.6e0.017x

Taking the natural logarithm of both sides of the equation gives:

x ln(17.9) + 0.002x = x ln(13.6) + 0.017x

Simplifying and rearranging terms, we get:

ln(17.9) - ln(13.6) = (0.017 - 0.002)x

0.079 = 0.015x

Solving for x, we get:

x = 5.27 years

Since x is the year, when x = 5.27, it corresponds to the year 1998 + 5.27 ≈ 2003.

When the populations are equal, the population will be f(5.27) ≈ 18 million for West Goma.

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After the 15% increase in her hourly rate, Carmen's new hourly rate will be $18.40 per hour.

Carmen currently makes $480 in a month by working 30 hours. To find her hourly rate, we can divide her total earnings by the number of hours she worked:

Hourly rate = Total earnings ÷ Number of hours worked

So Carmen's current hourly rate is:

Hourly rate = $480 ÷ 30 = $16 per hour

If Carmen gets a 15% increase in her hourly rate, we can calculate her new hourly rate by multiplying her current hourly rate by 1.15 (since a 15% increase means the new rate is 115% of the current rate):

New hourly rate = Current hourly rate x 1.15

New hourly rate = $16 x 1.15

New hourly rate = $18.40 per hour

This means she will earn $2.40 more per hour than she did before the increase.

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The surface area of the cone is 1,966.896 mm²

We can see that the surface area of a cone of slant height H and radius R is:

SA = pi*R² + pi*R*H

Here we can see that R = 27mm/2 = 13.5mm

And H = 32.9 mm

And we know that pi = 3.14

So, replacing that we will get:

SA = 3.14*(13.5mm)²  + 3.14*13.5mm*32.9mm

SA = 1,966.896 mm²

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Answer:

F(x)=x^3+2x^2+15

Step-by-step explanation:

The 95% confidence interval for the proportion of nonconforming items is (0.093, 0.250). This indicates that there is a 95% chance that the true proportion of nonconforming items lies between 9.3% and 25%.

To calculate the 95% confidence interval for the proportion of nonconforming items, we first calculate the sample proportion p of nonconforming items: p = 16/300 = 0.053.

Next, we calculate the standard error of the sample proportion, which is SE = √(p(1-p)/n) = √(0.053(1-0.053)/300) = 0.01.

Finally, we calculate the lower and upper limits of the 95% confidence interval for the proportion of nonconforming items by subtracting and adding 1.96 x SE to the sample proportion, respectively. This gives us the confidence interval of (0.093, 0.250).

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Answer:

the midpoint is at -8

Step-by-step explanation:

Step-by-step explanation:

See image below

The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.

Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.

From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,

FG ⊥ HB.

Also, DE ⊥ HB, thus the segments FG ║ DE.

Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.

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Answer:

50.47°

Step-by-step explanation:

We can use the trigonometric function sine to determine the angle the ladder makes with the ground. Let's call this angle theta. We have:

sin(theta) = opposite/hypotenuse

where the opposite side is the height of the ladder on the wall (15 ft) and the hypotenuse is the length of the ladder (19 ft). Solving for theta, we get:

theta = sin^-1(15/19) ≈ 50.47°

Since this angle is less than 75°, the ladder will be safe at this height.

the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1. Multiply this answer by the common denominator (18) to get the final answer: -5/2.

To solve this fraction division problem, first convert the fractions to have a common denominator. To do this, multiply the denominator of the first fraction (-1/3) by the denominator of the second fraction (6), and the denominator of the second fraction (6) by the denominator of the first fraction (-1/3). This will change the fractions to -5/18 and 5/18, respectively.

Next, divide the numerators of the fractions. Since the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1.

Multiply this answer by the common denominator (18) to get the final answer: -5/2.

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From the given data, the probability that the sample proportion is between 0.45 and 0.51 is approximately 0.7372 and between 0.42 and 0.54 is 0.9772.

To solve this problem, we can use the central limit theorem, which states that the distribution of sample proportions will be approximately normal for large sample sizes.

Given that the population proportion is p = 0.48 and the sample size is n = 350, we can calculate the standard error of the sample proportion as:

SE = √(p × (1 - p) / n) = √(0.48 × 0.52 / 350) = 0.025

We want to find the probability that the sample proportion is within three percentage points of the population proportion, or in other words, between 0.45 and 0.51. To do this, we can standardize the sample proportion using the standard error:

z = (P - p) / SE = (0.45 - 0.48) / 0.025 = -1.2

z = (P - p) / SE = (0.51 - 0.48) / 0.025 = 1.2

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values, which represents the probability that the sample proportion is within three percentage points of the population proportion:

P(-1.2 < z < 1.2) = 0.7372

To find the probability that the sample proportion is within six percentage points of the population proportion, or between 0.42 and 0.54, we can use the same approach:

z = (P - p) / SE = (0.42 - 0.48) / 0.025 = -2.4

z = (P - p) / SE = (0.54 - 0.48) / 0.025 = 2.4

Again, using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values:

P(-2.4 < z < 2.4) = 0.9772

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The probability of awarding the scholarship to a student who is either a math major or an engineering major is 0.2787 .Option (c) is the correct answer.

In this question, we are asked to find the probability of awarding the scholarship to a student who is either a math major or an engineering major. Total students (n) = 61 Chemistry majors (C) = 23 Math majors (M) = 12 Engineering majors (E) = 9 Undecided (U) = 17Students with declared majors in Math and Engineering (M ∩ E) = 4

We have to find P(A) = P(student is either a math major or an engineering major).To solve this problem, we will use the addition rule of probability. The addition rule states that the probability of event A or B occurring equals the probability of event A plus the probability of event B minus the probability of both A and B occurring. P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)

Here, P(M) = probability that the student is a math major= number of math majors / total students = 12/61 P(E) = probability that the student is an engineering major= number of engineering majors / total students = 9/61 P(M ∩ E) = probability that the student has declared both math and engineering majors = 4/61So,P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)P(A) = 12/61 + 9/61 - 4/61= 17/61≈ 0.2787

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Answer:

-35 - 5/6x

Step-by-step explanation:

The correct answer is B Parametric equations for the path of each player is Receiver: x=5, y=50-10t Defensive: x=10-0. 9t, y=54-10. 72t

The given paths of the receiver and defensive player can be described parametrically, using the parameter t, as:

Receiver: x = 5, y = 50 - 10t

Defensive: x = 10 - 0.9t, y = 54 - 10.72t

We can use the parameter t to represent the time that has elapsed since they started moving. The parametric equations describe the x and y coordinates of each player as functions of t.

By plugging in different values of t, we can determine the positions of the players at different points in time. In this case, the receiver moves horizontally while the defensive player moves at an angle, so their equations are different.

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In conclusion, a yardstick or ruler can be a reasonable tool to use to measure the length of a canoe paddle.

Then, move the yardstick along the length of the paddle, counting the marks until you reach the other end. This will give you an estimate of the length of the paddle in terms of the number of yardstick marks.
For a more precise measurement, you can also use a ruler. Place the zero mark of the ruler at the tip of the paddle and move the ruler along the length of the paddle, counting the small marks that correspond to 1/16th of an inch. This will give you a more precise estimate of the length of the paddle.

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Answer:

We can use proportions to find out the tax on goods worth $60.00:

Let x be the tax on goods worth $60.00.

Then, we can set up the following proportion:

tax/sales = tax rate

or

2.42/44 = x/60

To solve for x, we can cross-multiply and simplify:

44x = 2.42 * 60

44x = 145.20

x = 145.20/44

x = 3.3 (rounded to the nearest cent)

Therefore, the tax on goods worth $60.00 would be $3.30.

Step-by-step explanation:

The slope of the line is 1. Two different points have the same slope.

Rise or fall is a number or ratio that determines the direction or slope of the line. The slope of a straight line is the ratio of the slope of the straight line to the course of the straight line. The point is:

-XY

twenty-five

−2 1

0 3

-7 -4

The slope of a straight line is generally calculated using the formula:

slope = [tex](y_{2} - y_{1} ) / (x_{2} - x_{1} )[/tex]

Points (2, 5) and (-2, 1) of part (A).

Slope = [tex]( 1 - 5 ) / ( -2 - 2 )[/tex]

Slope = -4 / -4 = 1

Split (B) at the points ( 0, 3 ) and ( -7, - 4 ).

Slope = [tex]( -4 - 3 ) / ( -7 - 0 )[/tex]

Slope = -7 / -7 = 1

The slope of the line at two different points is the same. 

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Complete question is: A table with certain points is shown. x 2 −2 0 −7 y 5 1 3 −4 Part A: Choose two points from the table and calculate the slope between them. Show all necessary work. (4 points) Part B: Choose two different points from the table and calculate the slope between them. Show all necessary work. (4 points) Part C: What do the slopes from parts A and B tell you about the relationship between the points? Explain.

Answer:

187

Step-by-step explanation:

We can calculate the number by doing 153/.45 to give us 340.

We can also do 34/.1 to give us 340.

Since we got 340 as our answer for the first two numbers, convert 55% to .55 and multiply by 340 to get 187.