A large Ferris wheel has a diameter of 90​ meters and the top of the wheel is 102 meters above the ground. The Ferris wheel has 36 passenger capsules spaced evenly along the wheel. The diagram below shows 10 of the Ferris wheel capsules arranged such that the center of the wheel is at point C, the capsule at point M is at the same height as the center of the wheel, and the capsule at point T is at the very top of the wheel.

The equation r · sin θ = 10 in rectangular coordinates is equal to y = 10.

Herein we find the representation of a equation in polar coordinates, whose form in rectangular coordinates. This can be done by using the following definitions:

cos θ = x / r

sin θ = y / r

Where:

Then, the equation in polar coordinates is:

r · sin θ = 10

y = 10

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Answer:

B. Mixed numbers with unlike denominators can be subtracted from each other.

Step-by-step explanation:

Mixed numbers are numbers that have a whole part and a fractional part, such as 2 1/4 or 3 3/5. Unlike denominators are fractions that have different numbers in the bottom, such as 1/4 and 3/5. They are also called unlikeable denominators because they make math harder and more annoying. Who likes to deal with fractions anyway?

Mixed numbers with unlike denominators can be subtracted from each other, but only if you follow some tedious steps. First, you have to find a common denominator for the fractions, which is the smallest number that both denominators can divide into. This is like finding a common enemy for two rival gangs. For example, to subtract 2 1/4 from 3 3/5, we need to find a common denominator for 1/4 and 3/5. The least common denominator is 20, because both 4 and 5 can divide into it. Then, we have to multiply both fractions by the same factor to get equivalent fractions with the same denominator. This is like dressing up both gangs in the same uniform to make them look alike. For example, we multiply 1/4 by 5/5 and 3/5 by 4/4 to get:

2 1/4 = 2 5/20

3 3/5 = 3 12/20

Now we can subtract the fractions by subtracting the numerators and keeping the denominators the same. This is like taking away some members from each gang and seeing who has more left. For example, we subtract 5/20 from 12/20 and get 7/20. Then we subtract 2 from 3 and get 1. Finally, we add the whole part and the fractional part together to get the final answer. This is like adding up the remaining members of one gang and giving them a name. For example, we get:

3 12/20 - 2 5/20 = (3 - 2) + (12/20 - 5/20) = 1 + 7/20 = 1 7/20

Therefore, the correct answer is B. Mixed numbers with unlike denominators can be subtracted from each other. But why would you want to do that? It's much easier to use decimals or percentages instead. Fractions are so last century.

Answer: x= 7191.509 ft

Step-by-step explanation:

Sin9/1 = 1125/x

X/1 = 1125/sin9

The height of the candle change over time as a linear function

The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.

We can write the equation for the height of the candle as:

h(t) = 12 - 2t

where h is the height of the candle in inches and t is the time in hours.

If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:

h(2) = 12 - 2(2) = 8

So the height of the candle after 2 hours of burning is 8 inches.

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The Surface area of the triangular prism is 26.88 cm².

The Volume of the triangular prism is 7.68 cm³.

The formulas we would used are:

Surface area of triangular prism = (S1 + S2 + S3)(L) + bh

Volume of triangular prism = 1/2 * base * height * length of prism

Perimeter of the triangular face = (S1 + S2 + S3) = 4.0 + 3.2 + 2.4 = 9.6 cm

Length of prism = 2.0 cm

base of triangular face (b) = 3.2 cm

height of triangular face (h) = 2.4 cm

Plug in the values:

Surface area of triangular prism = (9.6)(2.0) + (3.2)(2.4) = 26.88 cm²

Volume of triangular prism = 1/2 * 3.2 * 2.4 * 2.0 = 7.68 cm³

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The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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Answer:

To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:

Change in wages = $105.50 - $25.50 = $80

Change in hours = 6 - 2 = 4

Rate of pay per hour = Change in wages / Change in hours

= $80 / 4

= $20

Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:

y = $20x

Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.

Step-by-step explanation:

Answer:

The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius. The value of π is 3.14 or 22/7.

Answer: The way you can find the area of this shape is by splitting the shape into a triangle and a square find the areas of each shape and then add the values.

Step-by-step explanation:

The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made

To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:

1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.

2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).

81 reservations x 0.96 (96% as a decimal) = 77.76

Since the number of diners must be a whole number, you can round the result to the nearest whole number.

In this case, 77.76 can be rounded down to 77.

Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.

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The measure of the third angle in the triangle is 80 degrees.

The sum of the angles in a triangle is always 180 degrees.

Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,

We can subtract the sum of these two angles from 180°:

180° - (40° + 60°) = 180° - 100° = 80°

Therefore, the measure of the third angle in the triangle is 80 degrees.

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The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.

To calculate the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet, we need to use the formula:

Work = Force x Distance

In this case, the force is the weight of the crate, which is 30 pounds. The distance is the height the crate is lifted, which is 3 feet.

So, Work = 30 pounds x 3 feet

We can simplify this by converting pounds to foot-pounds, which is the unit used to measure work. To convert pounds to foot-pounds, we need to multiply the weight by the distance. So:

Work = 30 pounds x 3 feet = 90 foot-pounds

Therefore, the amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is 90 foot-pounds.

To calculate the amount of work done, in foot-pounds, for lifting a crate weighing 30 pounds a total of 3 feet, you can follow these steps:

Step 1: Identify the weight of the crate (30 pounds) and the distance it is lifted (3 feet).
Step 2: Multiply the weight of the crate by the distance lifted.

Work (in foot-pounds) = Weight (in pounds) × Distance (in feet)

In this case:

Work = 30 pounds × 3 feet
Work = 90 foot-pounds

So, the amount of work done is 90 foot-pounds.

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The work done to lift a crate weighing 30 pounds a total of 3 feet is:

Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds

So the amount of work done to lift the crate is 90 foot-pounds.

The amount of work done, in foot-pounds, to lift a crate weighing 30 pounds a total of 3 feet is given by the formula:

Work = Force x Distance x cos(theta)

where Force is the weight of the crate, Distance is the vertical distance lifted, and theta is the angle between the direction of the force and the direction of motion (which is 0 degrees in this case since the force is acting vertically upwards).

Therefore, the work done to lift a crate weighing 30 pounds a total of 3 feet is:

Work = 30 pounds x 3 feet x cos(0 degrees) = 90 foot-pounds

So the amount of work done to lift the crate is 90 foot-pounds.

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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The unit digit of 725 unit digit of (325)​ is given as 5

Unveiling the unit digit of a number raised to an exact power can be done by analyzing the pattern of the unit digits of said power sequence.

For instance, given the task of ascertaining the unit digit of 325^725, let us observe the recurrent pattern concerning 5's power line:

[tex]5^1 = 5\\5^2 = 25\\5^3 = 125\\5^4 = 625\\5^5 = 3125[/tex]

It is readily evident that the final digit of 5 raised to any affirmative integer power shall invariably remain as 5. Correlatively, the end figure for 325^725 is also 5.

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The probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 8 + 7 + 6 = 21

probability of picking a blue ball = 7/21

probability of picking a green ball = 6/21

probability of picking a blue or green ball = 7/21 + 6/21

probability of picking a blue or green ball = (7 + 6)/21

probability of picking a blue or green ball = 13/21

probability of picking a blue or green ball = 0.6190

Therefore, the probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

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The volume of the cylinder is 3532.5 metres cube.

The figure above is a cylinder. The volume of the cylinder can be found as follows:

volume of a cylinder = πr²h

where

Therefore, let's find the height using Pythagoras's theorem.

25² - 15² = h²

h² = 625 - 225

h = √400

h = 20 metres

Hence,

volume of a cylinder = 3.14 × 7.5² × 20

volume of a cylinder = 3532.5 metres cube

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The surface area of the right prism is 192.9 m².

A prism is a solid shape that is bound on all its sides by plane faces.

To calculate the surface area of the prism, we use the formula below

Formula:

Where:

From  the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the surface area is  192.9 m².

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The equation will be w = 40b

To find the total weight (w) of the soil in pounds when Yuki stacks b bags, you can use a simple linear equation. Each bag weighs 40 pounds, so the equation will be: w = 40b

This equation shows that the total weight (w) of the soil in pounds is equal to the number of bags (b) multiplied by the weight of each bag (40 pounds).

The above answer is based on the information below as seen in the picture;

Yuki works at a garden store. She is stacking 40 pounds bags of soil.

write an equation that gives the total weight, w, of the soil in pounds when Yuki stacks b bags.

+ - . =         b, w, 40

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The graph of the data from the table is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Jerome is a photographer. He earns $125 per hour

This means that the equation of the function is

f(x) = 125x

Where x is the number of hours he works

Using the above as a guide, we have the following table of values

x    f(x)

1     125

2    250

3    375

4    500

5    625

6     750

Next, we plot the graph from the table of values and the function f(x) = 125x

The graph of the function is added as an attachment

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The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.

To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.

The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:

H0: μ = $9820

The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:

Ha: μ > $9820

The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.

To calculate the test statistic, we can use the formula:

t = (X - μ) / (s / √n)

Where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:

s = θ / √n = $1580 / √50 = $223.61

Now we can calculate the test statistic:

t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45

Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.

Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.

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--The given question is incomplete, the complete question is given

"  a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.

A. state the null and alternate hypothesis.

B. Compute the   or t va;ue of the sample test statistic.

C. Find the critical value(s).

D. based on the answers to a-c, what is your conclusion?"--

Answer:

1. is (18,4)

2. is (8,10)

3. (-9,-8)

4. (9,-8)

Step-by-step explanation:

i promise its right please give brainliest

The measure of variability that the charity should use to accurately represent the data is B. The IQR of 13 is the most accurate to use, since the data is skewed.

The charity should use the Interquartile Range (IQR) as the measure of variability since the data is skewed. The IQR measures the range of the middle 50% of the data, which is less affected by outliers or skewed data.

Q1 is the median of the first half of the data: 5, 5, 6, 8, 10, 15 (Q1 = 7)

Q3 is the median of the second half of the data: 15, 18, 20, 20, 20, 20, 20 (Q3 = 20)

Now, we can calculate the IQR:

IQR = Q3 - Q1

IQR = 20 - 7

IQR = 13

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The factored form of the expression x² + 5x+6 is (x + 3)(x + 2)

To factorize the quadratic equation, we need to take the following steps;

Multiply the coefficient of the x squared by the constant value, we have;

6

Now, find the pair factors of the product that would add up to give 5, we have;

2 + 3

Substitute the values into the expression, we have;

x² + 2x + 3x + 6

Now, group the expression in pairs, we have;

(x² + 2x) + (3x + 6)

Factorize the expressions

x(x + 2) + 3(x + 2)

Then, we have;

x + 3

x + 2

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Answer:

24 meters

Step-by-step explanation:

We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.

Using Pythagoras' theorem, we can write:

w^2 + 77^2 = 85^2

Simplifying this equation gives:

w^2 = 85^2 - 77^2

w^2 = 576

Taking the square root of both sides gives:

w = sqrt(576)

w = 24

Therefore, the width of the field is 24 meters 1.

I hope this helps!

A graph which is that of the inequality shown include the following: D. Graph D.

In order to to graph the solution to the given linear inequality on a coordinate plane, we would use an online graphing calculator to plot the given linear inequality and then take note of the points that lie on its line;

y ≥ -3x + 1

Next, we would use an online graphing calculator to plot the given linear inequality as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (0, 1) and (1, -2), with a solid line that is shaded above to indicate the solution, and this must be represented with the greater than or equal to (>) inequality symbol.

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Assume that A and B are independent events. it means that the occurrence of event A does not affect the probability of event B and vice versa.

b. Assume that A and B are independent events. My response is Yes, P(A and B) can be defined as P(B) • P(A|B).

In the event that A and B are independent events, at that point the probability of A happening is one that is influenced by the event of B and vice versa. Hence, P(B) is comparable to P(B|A), showing that the probability of occasion B happening remains unaltered in any case of event A's event. Within the same vein, the likelihood of event A happening remains consistent whether event B has stay put or not, indicated as P(A) = P(A|B).

Therefore in response to question 2, The reason why independent events are not affected  by one another is that the likelihood of one event happening has no effect on the probability of the other event occurring.

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If a pizza with an 18-inch diameter is divided into 10 equal pieces, then each slice will have a surface area of roughly 25.45 square inches.

Diameter is defined as a straight line across the middle of a body or figure, particularly a circle or sphere. Pizza diameter is the length of a straight line that touches two locations on the edge of a pizza pie and passes through its center.

Each sector of the pizza, which is divided into 12 equal sections, has an arc measurement of 360/10= 36 degrees.

As = (360÷Ф) ×X r² where x is the measure of the intercepted wave, yields the area of a sector.

We know that x=36 and

d=18→r=9 in. Thus, r is the radius and A is the area of each intersecting arc of a sector.

A=1/10×81π

then each slice will have a surface area of roughly 25.45 square inches.

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The value of x is 3 unit.

The correct option is B.

We have,

P = 3√2/2

Angle= 45

Using Trigonometry

cos 45 = B /H

1/√2 = ( 3√2/2)/ x

x= 3√2/2 . √2

x = 6/2

x= 3 unit

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