Find the value of y. Round to
the nearest tenth.
y
42°
859 31
y=[?]
Law of Sines: sin A
a
=
sin B
b
=
sin C
C

Answer:

726.65 cubic inches

Step-by-step explanation:

We are going to assume that the head, middle and bottom are spheres.

The formula to get the volume of a sphere is

\(V= \frac{4}{3}\pi r^{2}\) where r is the radius of the sphere.

Now, let's proceed to apply this formula to the 3 spheres of the snowman:

The head is 12 inches wide (diameter), thus, the radius would be 6 inches:

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 6^{2}\\V= \frac{4}{3}\pi 36\\V=\frac{144\pi }{3} \\V=38\pi\) cubic inches

The middle is 16 inches wide (diameter), thus, the radius would be 8 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 8^{2}\\V= \frac{4}{3}\pi 64\\V=\frac{256\pi }{3} \\V=85.3\pi\)  cubic inches

The bottom is 18 inches wide (diameter), thus the radius would be 9 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 9^{2}\\V= \frac{4}{3}\pi 81\\V=\frac{324\pi }{3} \\V=108\pi\) cubic inches.

Now, to get the total volume of the snowman we're going to sum up the volume of all three spheres:

Total volume = \(38\pi +85.3\pi +108\pi =231.3\pi\) cubic inches.

If we take pi = 3.1416,

Total volume = \(231.3(3.1416)=726.65\) cubic inches.

Answer:

Let m be the number of muffins.

a) 4m <= 30

b) m <= 7.5, so the maximum number of muffins to buy is 7.

c) $4 × 7 = $28, so $2 will be left over.

Answer: \(a=110^{\circ}\)

Step-by-step explanation:

By the exterior angle theorem,

\(a+15^{\circ}=125^{\circ}\\\\a=110^{\circ}\)

Answer:

0.33

Step-by-step explanation:

The specific number (females prefer cycling = 0.15) and the fitting total. There are 2 possibilities for that total :

all females

all people preferring cycling

the way it was phrased I would say the reference is all females.

the conditional relative frequency is then

0.15 / 0.46 = 0.326=0.33(rounded)

Hence the conditional relative frequency that a female prefers running is 0.33

Answer:m=4

Step-by-step explanation:Use the slope formula. The set up would be -4-4/-2-0. This gives us -8/-2 which you can simplify to 4.

Answer:

126 square inches of wrapping paper

Step-by-step explanation:

To compute for the minimum amount of wrapping paper Dylan will need to completely cover the box, you have to compute the surface area of the box. The formula in getting the surface area of a rectangle is:

A = 2WL + 2LH + 2HW

Substituting the given measurements to the formula:

A = 2(5)(6) + 2(6)(3) + 2(3)(5)

A = 60 + 36 + 30

A = 126 square inches

Therefore, Dylan needs to purchase at least 126 square inches of wrapping paper to completely cover the box.

Answer:

Step-by-step explanation:

The equation of the line of best fit is given as follows:

y = -1.25x + 8.3.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given as follows:

(2, 5.8), (3, 4.55), (5, 2.05), (7, -0.45), (11, -5.45), (16, -11.7), (24, -21.7).

Inserting these points into a calculator, the equation is given as follows:

y = -1.25x + 8.3.

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3n yo _2222224455555

Step-by-step explanation

Answer: 9=n-7

Step-by-step explanation:

Answer:

y=60°

x=12°

Step-by-step explanation:

because the propertiy of parallelogram is the opposite side have equal measurement.

that is why y=60°

x+3=15 the paralla side are equal

x=15°-3°

x=12°

proof》》》》x+3=

12°+3°=15°

15°=15°

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

22/85

Step-by-step explanation:

Answer:

18 and 21

Step-by-step explanation:

Answer: $20.70

Step-by-step explanation: He pays $20.70, follow these steps:

The formula for finding the percentage:

Whole number * part percent / 100

Plug in the numbers:

23 x 10 / 100

23 x 10 = 230

230 / 100 = $2.30

That's not all, we need to subtract $2.30 from the original amount. So:

23 - 2.30 = $20.70

After the rebate, Deon pays $20.70

He saves $2.30

I hope this helps!

Answer

APY = 4.39 %

Step-by-step explanation

Compound interest formula

where

• A: final amount (value of the account after t years)

• P: principal (amount of money invested)

• r: interest rate (APR), as a decimal

• n: number of times interest applied per year

• t: time in years

Substituting, P = $1400, r = 0.043 (= 4.3/100), n = 365 (compounded daily means 365 times per year), we get:

APY formula

Substituting with the before mentioned values, we get:

3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

3⁴ / 3³ = (3 × 3 × 3 × 3) / (3 × 3 × 3) = 3

This means that 3⁴ is 3 times larger than 3³.

5³ is 5 times larger than 5².

5³ / 5² = (5 × 5 × 5) / (5× 5) = 5

7¹⁰ is 49 times larger than 7⁸.

7¹⁰/ 7⁸ = 7² =49

17⁶ is 289 times larger than 17⁴.

17⁶ /17⁴ = 289

Hence, 3⁴ is 3 times larger than 3³, 5³ is 5 times larger than 5², 7¹⁰ is 49 times larger than 7⁸ and 17⁶ is 289 times larger than 17⁴.

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The ways in which a kindergarten teacher distributes the books are (a) 20 ways (b) 100 ways (c) 3,628,800 ways.

(a) There are 20 ways for her to distribute the books if they are all the same and no child gets more than one. Each of the 20 children can receive one of the five books.

(b) There are 100 ways for her to distribute the books if they are different and no child gets more than one. Each of the 20 children can receive one of the five different books, so there are 5x4x3x2x1 = 100 possible ways for her to distribute the books.

(c) There are 3,628,800 ways for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child. This is because each child can receive any number of books from 0 to 5. Therefore, there are 6x6x6x6x6 = 6^5 = 3,628,800 possible ways for her to distribute the books.

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The complete question is:

A kindergarten teacher has five books to distribute to 20 children in her class.

(a) How many ways are there for her to distribute the books if they are all the same and no child gets more than one?

(b) How many ways are there for her to distribute the books if they are different and no child gets more than one? If Charlie gets Green Eggs and Ham and Amanda gets The Cat in the Hat, that is a different distribution from the one in which Amanda gets Green Eggs and Ham and Charlie gets The Cat in the Hat.

(c) How many ways are there for her to distribute the books if they are all the same and there is no restriction on the number of books that can be given to any child?

Answer:

0.85 kg is 850 grams

Step-by-step explanation:

Since the prefix kilo means  \(10^3\), we can write,

0.85 kg as,

(using 10^3 for kilo,)

\((0.85)*(10^3) g\\=850g\)

So, 0.85 kg is 850 grams

Answer:850 grams

Step-by-step explanation:To calculate a kilogram value to the corresponding value in gram, just multiply the quantity in kg by 1000.

Here is the formula,

Value in grams = value in kg× 1000

Here we need to convert 0.85kg into grams. Using the conversion formula above,

value in gram=0.85×1000=850 grams.

Answer:

Answer is yes

Step-by-step explanation:

yess it's yes

Answer:

Yes

Step-by-step explanation:

The ratio between x and y is equivalent, one variable is always a constant value times the other.

The probability that Juan loses his next tennis match is 48%

From the question, we have the following parameters

The proportion of tennis matches won

p = 52%

This proportion implies that the probability that the player will win his next tennis match

So, we have the following representations

Probability of winning, p = 52%

Express the percentage as decimal

So, we have the following representations

Probability of winning, p = 0.52

The probability of losing the next match is the complement of the probability of winning

This is represented as

Probability of losing = 1 - Probability of winning,

Substitute the known values in the above equation

So, we have the following equation

Probability of losing = 1 - 0.52

Evaluate

Probability of losing = 0.48

Hence, the probability is 0.48 or 48%

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Answer:

1/2x-2

Step-by-step explanation:

sise over run and then graph on desmos

Answer:

y = \(\frac{1}{2}\) x - 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 1 ) and (x₂, y₂ ) = (- 6, - 5 )

m = \(\frac{-5-1}{-6-6}\) = \(\frac{-6}{-12}\) = \(\frac{1}{2}\) , then

y = \(\frac{1}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (6, 1 )

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = \(\frac{1}{2}\) x - 2 ← equation of line

Answer:

23,000

Step-by-step explanation:

Multiply 60 with $392

60x392=23,520

Plan A makes you pay a total of $23,520 over the next 60 months (5 years).

Hope this helps! :)

The grocer should use x pounds of the $0.90 candy and y pounds of the $2.10 candy in the new mix.

To determine the quantities of each candy to use, we can set up a system of equations based on the given information. Let's denote x as the number of pounds of the $0.90 candy and y as the number of pounds of the $2.10 candy.

The total weight of the mix is 23 pounds, so we have the equation:

x + y = 23 (Equation 1)

The desired selling price of the mix is $1.90 per pound. Since the $0.90 candy and $2.10 candy are being mixed, we can calculate the average price per pound as follows:

(0.90x + 2.10y) / 23 = 1.90 (Equation 2)

We now have a system of two equations (Equations 1 and 2) that we can solve simultaneously to find the values of x and y.

To solve the system, we can start by multiplying Equation 1 by 0.90 to eliminate x's coefficient:

0.90x + 0.90y = 20.7 (Equation 3)

Next, we can subtract Equation 3 from Equation 2 to eliminate x:

(0.90x + 2.10y) / 23 - (0.90x + 0.90y) = 1.90 - 20.7

Simplifying this equation gives:

1.20y = 1.90 * 23 - 20.7

Solving for y, we find:

y = (1.90 * 23 - 20.7) / 1.20

y ≈ 11.5

Now that we have the value of y, we can substitute it back into Equation 1 to solve for x:

x + 11.5 = 23

x = 23 - 11.5

x ≈ 11.5

Therefore, the grocer should use approximately 11.5 pounds of the $0.90 candy and 11.5 pounds of the $2.10 candy in the new mix.

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The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

To find the range, we need to subtract the smallest number from the largest number in the sample. So, the range is:

94 - 15 = 79

To find the sample variance and standard deviation, we first need to find the mean of the sample. We can do this by adding up all the numbers and dividing by the total number of players:

(33 + 74 + 70 + 65 + 56 + 47 + 39 + 72 + 57 + 94 + 15) / 11 = 54.18

Next, we need to find the difference between each number and the mean, square them, and add them up. This gives us the sum of squares:

[(33 - 54.18)^2 + (74 - 54.18)^2 + (70 - 54.18)^2 + (65 - 54.18)^2 + (56 - 54.18)^2 + (47 - 54.18)^2 + (39 - 54.18)^2 + (72 - 54.18)^2 + (57 - 54.18)^2 + (94 - 54.18)^2 + (15 - 54.18)^2] = 15864.4

The sample variance is then calculated by dividing the sum of squares by the total number of players minus one:

15864.4 / 10 = 1586.44

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

√1586.44 ≈ 39.83

The results tell us that jersey numbers on a football team vary much more than expected, as evidenced by the large range and standard deviation. The sample variance is also relatively high, indicating that there is a fair amount of variability among the jersey numbers in the sample. These statistics are meaningful and can provide insight into the distribution of jersey numbers on the team.

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In order to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population, a large sample size is required.

We are given that the sample proportion must be within 0.02 of the true fraction of the voting population, and we are required to be 96% confident. This can be represented as follows:

p ± 0.02

Where p is the true population proportion. This implies that the margin of error is 0.02. We need to find the sample size, which is usually denoted by n.To find the sample size n, we use the formula:

n = (z/ε)² * p(1 - p)

where z is the critical value, ε is the margin of error, and p is the proportion of the population that is being sampled.In this case, z is the z-score that corresponds to a 96% confidence interval, which can be found using the z-table or a calculator.

The z-score is 1.75068607 (rounded to 1.751).

Also, we are given that the margin of error (ε) is 0.02. Finally, we do not have any information about the true population proportion (p), so we will use 0.5 as a conservative estimate.

Substituting these values into the formula, we have:

n = (1.751/0.02)² * 0.5(1 - 0.5)n = 1764.44 (rounded up to 1765)

Therefore, a sample size of at least 1765 is required to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population.

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The equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±11) is (x²/121) - (y²/81) = 1.

To find the equation of the hyperbola, we need to determine the values of a and b in the standard form equation (x²/a²) - (y²/b²) = 1, where a is the distance from the center to the vertices and b is the distance from the center to the co-vertices.
In this case, a = 9 (distance from center to vertices) and c = 11 (distance from center to foci). We can use the relationship c² = a² + b² to find b. Solving for b, we get:
c² - a² = b²
11² - 9² = b²
121 - 81 = b²40 = b²

So, b = √40.
Now, we can plug the values of a² and b² into the standard form equation:

(x²/121) - (y²/40) = 1

The equation in standard form for the given hyperbola is (x²/121) - (y²/40) = 1.

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Answer:

Step-by-step explanation:

Given angles of elevation of 10° and 50° measured 10 seconds apart from an observation point 1.5 miles away, you want to know the vertical change in distance, and the average speed of the shuttle between the two observations.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Then the height of the shuttle at the observed angles was ...

  Opposite = Tan · Adjacent

  h1 = tan(10°)·(1.5 mi) ≈ 0.264490 mi

  h2 = tan(50°)·(1.5 mi) ≈ 1.787630 mi

The amount of vertical travel in the 10-second interval was ...

  1.787630 mi -0.264490 mi = 1.523240 mi

The space shuttle traveled about 1.523 miles vertically in the 10-second interval.

In miles per second, the average speed during that time was about ...

  (1.523 mi)/(10 s) = 0.1523 mi/s

In miles per hour, that's about ...

  (0.1523 mi/s)(3600 s/h) ≈ 548 mi/h

The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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