4. The wheels of a bicycle have a
diameter of 22 inches. How many
full revolutions will the wheels need
to make to travel 300 feet? Use 3.14
for .
A 105 revolutions
B 10 revolutions
C164 revolutions
D 53 revolutions
no

The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

Given Sample size (n) is 120 workers

Proportion of workers who are college graduates (p): 34% or 0.34

a) Mean and Standard Deviation:

The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).

Substituting the values:

μ = 120 ×0.34 = 40.8

σ = √120 × 0.34 × (1 - 0.34)) = 5.37

To find the probability that the number of workers with a college degree is at least 35

we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.

Using a binomial probability calculator or a statistical software, we can find this probability.

Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:

P(X ≥ 35) = 1 - P(X < 35)

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

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Answer:

Step-by-step explanation:

The factored expressions of 9x⁴ - 225y⁸ is (3x² + 15y⁴)(3x² - 15y⁴)

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

9x⁴ - 225y⁸

²⁴

For the expression, we can apply the difference of two squares

Where

9x⁴ = (3x²)²

225y⁸ = (15y⁴)²

Using the above as a guide, we have the following:

9x⁴ - 225y⁸ = (3x²)² - (15y⁴)²

So, we have

9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)

Hence, the factored expressions is 9x⁴ - 225y⁸ = (3x² + 15y⁴)(3x² - 15y⁴)

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Answer:

∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.

It is shown below that the partition of G into left cosets of H is different from its partition into right cosets when n ≥ 3.

Let us first find the left cosets of H in G:

H = {1, s₀}

s₁H = {s₁, s₁s₀}

s₂H = {s₂, s₂s₀}

s₃H = {s₃, s₃s₀, s₂s₁, s₂s₁s₀}...

Now, find the right cosets of H in G:

H = {1, s₀}

Hs₁ = {s₁, s₀s₁}

Hs₂ = {s₂, s₀s₂}

Hs₃ = {s₃, s₀s₃, s₁s₂, s₀s₁s₂}...

Observe that the left cosets of H in G and the right cosets of H in G are not the same when n≥3. This is because s₁s₀ is not in H, but s₀s₁ is in H.

Therefore, the left coset s₁H is not the same as the right coset Hs₁. Similarly, s₂s₁s₀ is not in H, but s₀s₁s₂ is in H, so the left coset s₃H is not the same as the right coset Hs₃.

Thus, it is shown that the partition of G into left cosets of H is different from its partition into right cosets when n≥3.

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Answer:

[tex]3 {cos}^{2} x - {sin}^{2} x = 0[/tex]

[tex]3 - 3 {sin}^{2} x - {sin}^{2} x = 0[/tex]

[tex]3 - 4 {sin}^{2} x = 0[/tex]

[tex]4 {sin}^{2} x = 3[/tex]

[tex] {sin}^{2} x = \frac{3}{4} [/tex]

sin(x) = +(1/2)√3

x = π/3 + 2kπ or x = 2π/3 + 2kπ

x = -π/3 + 2kπ or x = -2π/3 + 2kπ

(k is an integer)

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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The equation of the line is: x = 1 + 3t,, y = 10, z = 3 + 3t.

To determine the equation of the line passing through points M(1, 10, 3), N(4, 10, 6), and P(7, 10, 9), we need to find the direction vector of the line.

Let's denote the direction vector as D = (a, b, c). The line can be represented by the parametric equations:

x = 1 + at,

y = 10 + bt,

z = 3 + ct,

To find the direction vector, we can use two points on the line, for example, M and N. The direction vector can be obtained by subtracting the coordinates of M from the coordinates of N:

D = N - M = (4 - 1, 10 - 10, 6 - 3) = (3, 0, 3).

So, the equation of the line passing through M(1, 10, 3) and having the direction vector D = (3, 0, 3) is:

x = 1 + 3t,

y = 10 + 0t = 10,

z = 3 + 3t.

Therefore, the equation of the line is:

x = 1 + 3t,

y = 10,

z = 3 + 3t.

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a) The state sales tax on a $2,800 used car in Washington is given as follows: $257.6.

b) The total cost of the car, including tax, is given as follows: $3,057.6.

The sales tax and the total cost of the car are obtained applying the proportions in the context of the problem.

The sales tax rate is given as follows:

9.2%.

Hence, for a car of $2,800, the sales tax is given as follows:

0.092 x 2800 = $257.6.

The total cost is then obtained adding the base cost to the sales tax, as follows:

2800 + 257.6 = $3,057.6.

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Answer:

weight = gxg = 12kg to g = 0.12 and then using formula we get 0.12x0.12 = 1.44 is the weight

Step-by-step explanation:

Answer:

Therefore, the weight of the object is approximately 117.72 Newtons.

Step-by-step explanation:

The weight of an object is given by the formula:

weight = mass x acceleration due to gravity

The acceleration due to gravity on Earth is approximately 9.81 m/s².

So, the weight of an object with a mass of 12 kg is:

weight = 12 kg x 9.81 m/s² = 117.72 N

Therefore, the weight of the object is approximately 117.72 Newtons.

Answer:

450°

Step-by-step explanation:

Answer:

[tex] \sin(x) + \sin(2x) = 0[/tex]

[tex] \sin(x) + 2 \sin(x) \cos(x) = 0[/tex]

[tex]( \sin(x) )(1 + 2 \cos(x) ) = 0[/tex]

sin(x) = 0 or 1 + 2cos(x) = 0

2cos(x) = -1

cos(x) = -1/2

x = kπ or x = 2π/3 + 2kπ or

x = 4π/3 + 2kπ

(k is an integer)

Sue's total pay for the year based on the values will be £38110

Sue's total pay of year will have three parts

Fixed Salary for 12 months

 one month salary = £1410

 so 12 month salary = £1410 x 12 = £16920

26% of total profit

  Total cost to the company- £473,500

  Total income for the company - £549,000

  Profit =  Total income for the company - Total cost to the company

            =  £549,000 - £473,500 = £75500

   Sues income from profit = 26% of £75500 = (26 × 75500)/100 = £19630

Bonus if Sue sells at least 16 cars

  Given number of months when sue solds atleast 16 cars = 4

  So bonus income = 4 × 390 = £1560

Adding the three above parts

Sue's total pay for the year = £16920 + £19630 + £1560 = £38110

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Complete question

Ace autos sell cars and pay sue each month as follows

-salary of £1410

-26% of the total profit the company makes from her sales

- a £390 bonus if she sells at least 16 cars

The table shows information about the cars she sold last year

Total cost to the company- £473,500

Total income for the company - £549,000

Number of months when she sold at least 16 cars - 4

work out sues total pay for the year

Answer:

Step-by-step explanation:

Let's factor the expression w^2(w+8)-5(w+8):

First, we can see that (w+8) is a common factor in both terms of the expression.

So, we can factor out (w+8) from both terms:

(w+8)(w^2 - 5)

Now, the expression is factored as (w+8)(w^2 - 5).

The pattern in the table should be completed as follows;

Number of                      1          3        9       27        81

students with pets

Total number                  3         9        27     81        243

of students

A ratio that compares the number of blue squares to the total number of squares is 3 : 4.

In Mathematics and Geometry, a proportional relationship can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would find the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1 = 9/3

Constant of proportionality, k = 3.

y = 3x

81 = 3x

x = 27

x = 9/3

x = 3

y = 3(81)

y = 243

For the ratio of blue squares to total squares, we have:

18/24 = 3/4 = 3 : 4

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The required rates are: Unit rate of graph K = 3, Unit rate of graph P = 0.5, and Unit rate of graph F = 1. The order from lower to greater is Graph P, graph F, graph K

Step 1: As we know that Unit Rate

Step 2: Notice that the in graph K line passes through the point (1,3)

Step 3: (1,3)

It means the value of function is 3 when x= 1

Step 4: So the unit rate of graph K is, 3/1

Step 5: Simplify the expression.

3/1 = 3

Step 6: Similarly we can see that the graph P have the point (2, 1)

Step 7: So the unit rate of graph P will be 1/2

Step 8: Simplify the expression.

1/2 = 0.5

Step 9: The graph F have point (1, 1) so it have unit rate of 1/1

Step 10: Simplify the expression.

1/1 = 1

Step 11: So we have unit rate of graph K = 3, F= 1 and graph P = 0.5

Step 12: Putting them in least to greater order as,

0.5, 1, 3

It follows that;

graph P, graph F, graph K

Therefore, the required answer is,

Unit rate of graph K = 3

Unit rate of graph P = 0.5

Unit rate of graph F = 1

And the order from lower to greater is, Graph P, graph F, graph K

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Answer:

V = 381.7 or 121π

Step-by-step explanation:

V=4/3πr³

Radius is half the diameter so, 9/2 = 4.5

r=4.5

V = 4/3π(4.5)³

V=4/3π(91.125)

V = 381.7 or 121π

The measure of <MNL is (71 - 3x²)/2.

We have,

Far Arc = 59 - 2x²

Near Arc = 12 - x²

Angle = 180- 2x²

Using the Formula

Angle= Average of vertical chords

180 - 2x² = (59 - 2x² + 12 - x²)/2

360 - 4x² = 71 - 3x²

289 = x²

x= 17

So, the measure of <MNL

= (71 - 3x²)/2

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The required angles are,

∠BAC = 73 degree

∠BCA = 17 degree

∠DCF = 17 degree

∠CDF = 80 degree

∠CFD = 95 degree

Since we can see that,

In triangle ABC

The angle B is right angled

Since we know that,

Sum of interior angles of triangle = 180 degree

Therefore, in triangle ABC

⇒ (9x -8 ) + (2x-1) + 90 = 180

⇒ 11x  = 99

⇒    x  = 9

Thus,

Angle BAC =  9x - 8

                   = 9x9 - 8

                   = 73 degree

Angle BCA = 2x - 1

                   = 2x9 - 1

                    =  17 degree

Now in triangle, CDF,

Angle C is alternate angle for both the triangles,

Therefore,

Interior angle C of triangle CDF = angle DCF = 17 degree

Angle CDF = 9y  - 1

                   = 9x9 - 1

                   = 80 degree

Angle CFD = 11y + 4

                   = 11x9 - 4

                   = 95 degree

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The equations and their graphs are:

Graph 4: I(x)=P(x)−4

Graph 2: I(x)=P(x+4)

Graph 1: I(x)=P(x)+4

Graph 3: I(x)=P(x−4)

Here we have,

to match the equations and their graphs:

The parent function is given as:

P(x) = x^2

As a general rule of function transformation, we have:

Vertical translation up: I(x) = P(x) + k

Vertical translation down: I(x) = P(x) - k

Horizontal translation left: I(x) = P(x + k)

Horizontal translation right : I(x) = P(x - k)

Using the above rules and the assumption that k is 4;

We have:

Vertical translation up: I(x) = P(x) + 4

Vertical translation down: I(x) = P(x) - 4

Horizontal translation left: I(x) = P(x + 4)

Horizontal translation right : I(x) = P(x - 4)

Hence, the graphs of the equations are:

Graph 4: I(x)=P(x)−4

Graph 2: I(x)=P(x+4)

Graph 1: I(x)=P(x)+4

Graph 3: I(x)=P(x−4)

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complete question;

Consider the function P(x)=x2, which is a parabola that opens upward, with a vertex at (0,0).

It undergoes four separate transformations as indicated by the graphs that follow.

P(x) represents the preimage and is placed correctly on all images. I(x) represents the image after the transformation.

Match each transformation indicated by I(x) to the correct graph.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

I(x)=P(x)−4

I(x)=P(x+4)

I(x)=P(x)+4

I(x)=P(x−4)

The values of

1. cosθ = √3/2

2. sinθ = √3/2

3. tanθ = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

cosθ = adj/hyp

sinθ = opp/hyp

tanθ = opp/adj

sec θ = 1/cosθ

cosec θ = 1/sinθ

cot θ = 1/tanθ

We need to find the hypotenuse of the triangle

x² = 3² +3²

x = √9+9

x = √18

x = 2√3

cosθ = 3/2√3 = 6√3/12

= √3/2

2. sinθ = 3/2√3 = √3/2

3. tanθ = 3/3 = 1

4. sec θ = 2/√3

5. cosec θ = 2/√3

6. cot θ = 1

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The difference between the record high and low temperatures is 149 degrees.

A negative number is a number that is less than zero. A negative number usually has a minus sign in front of it. An example of a negative number is -35. A positive number is a number that is greater than zero. An example of a positive number is 10.

In order to find the difference between two or more numbers, subtract the numbers from each other.

Difference between the temperature = record high temperature - record low temperature

114 - -35

114 + 35 = 149 degrees

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Answer:

Step-by-step explanation:

1 = 20cm

2 = 0.56cm^2

3 = 77.5m2

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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Answer:she can make three 5 ounce candles. she had 15 ounces left over , 15/5=3 .

Step-by-step explanation: 5 of 10% of 20 ounces is 10 ounces, and both the 5 five ounce candles and the twenty five one ounce candles are each 2.5 extra ounces left. (5 for both), making a totalm of 15 ounces left to put into new candles.

To achieve a mean of 78 with four scores, the fourth score must be 90.

We need to consider the current mean, the number of tests, and the desired mean in order to find the fourth score needed to achieve a mean of 78

Let's assume the three test scores are x1, x2, and x3.

We know that the mean of these three scores is 74. So we can assume that

The sum of these numbers is 74 or

(x1 + x2 + x3)/3 = 74

Let's denote it as x4 ,to find the fourth score we will use the formula to calculate the mean:

(x1 + x2 + x3 + x4)/4 = 78

To solve for x4, we can rewrite it as:

x1 + x2 + x3 + x4 = 78 * 4

Now, we can substitute the value of the mean of the first three scores into the equation:

(x1 + x2 + x3) + x4 = 312

we know that,

(x1 + x2 + x3) = 3 * 74

or,

3 * 74 + x4 = 312

Simplifying this, we get:

222 + x4 = 312

Subtracting 222 from both sides:

x4 = 312 - 222

x4 = 90

Therefore, to achieve a mean of 78 with four scores, the fourth score must be 90.

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Answer:The correct answer is C. 3 liters.

Step-by-step explanation:

To determine the total amount of liquid in the pot, we need to add the volume of the broth and the volume of the water.

The broth has a volume of 500 milliliters, and the water has a volume of 1,500 milliliters. Adding these together, we get:

500 mL + 1,500 mL = 2,000 mL

Since there are 1,000 milliliters in a liter, we can convert the volume to liters:

2,000 mL ÷ 1,000 = 2 liters

Therefore, the total amount of liquid in the pot is 2 liters.

The coefficients used to perform the synthetic division are given by the first option in this problem.

The standard format of the polynomial in this problem is given as follows:

[tex]6x^4 - 7x^3 + x^2 + 3[/tex]

Considering that x has a coefficient of zero, the order of the coefficients of  the polynomial function is given as follows:

6, -7, 1, 0 and 3.

The divisor is of:

x + 4.

Hence the term on the left box is of:

x + 4 = 0 -> x = -4.

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Answer:

Step-by-step explanation:

The cylinder contains three areas, the top circle, the bottom circle, and the middle. The surface area of it is the sum of the three;

[tex]As = \pi r^{2} + \pi r^{2} + 2\pi r (h) \\[/tex]

or

[tex]As = 2\pi r^{2} + 2\pi r (h)[/tex]

where h is the height,

104[tex]\pi[/tex] = [tex]2 \pi (4)^{2} + 2\pi (4)(h)[/tex]

h = 9m

The difference in mean growth per week is 3.7cm/week

From the graph given :

Growth per week for Basil = 2, 6, 9, 10, 14, 16

Growth per week for Mint = 1, 2, 4, 7, 9, 12

Mean growth per week = (2+6+9+10+14+16) / 6 = 9.5 cm/week

Mean growth per week (Mint) = (1+2+4+7+9+12)/6 = 5.83 cm/week

The difference cannbe obtained by subtracting the mean Values thus ;

Difference in average growth = 9.5 - 5.83 = 3.67 cm/week

Therefore, the difference in mean growth per week is 3.7cm/week

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