Ward is planning to install a new countertop in his kitchen. The new countertop costs $42.50 per square foot. What will be the cost of the new countertop

Answer:

-7.25

Step-by-step explanation:

because the dolphin is going down, its negative so you add -4.5+-2.75

Answer:

The tallest player on the team was 78 inches tall

Step-by-step explanation:

Answer:

137,257

Step-by-step explanation:

Answer:

137,527

Step-by-step explanation:

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Answer:

Always

Step-by-step explanation:

Rhombi hold all the characteristics of parallelograms and have their own too added on.

Hope that helps!!

Answer:

Step-by-step explanation:So, if the graph is a straight line, it is the graph of a linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change for y with respect to x remains constant for a linear function. This rate of change is called the slope.Mar 9, 2011

Answer:

Terrell has 5 tickets left.

Step-by-step explanation:

Part (a)

\((x-1)^2=0 \implies x=\boxed{1}\)

Part (b)

\(x^3-3x^2 x+3x-1=0 \\ \\ -2x^3+3x-1=0\)

By inspection, x=1 is a root, so we can consider dividing by x-1.

\(\frac{-2x^3+3x-1}{x-1}=-2x^2-2x+1 \\ \\ \implies (x-1)(-2x^2-2x+1)=0 \\ \\ x-1=0 \implies x=\boxed{1} \\ \\ -2x^2-2x+1=0 \implies x=\frac{2 \pm \sqrt{4+8}}{-4} \\ \\ =\boxed{\frac{-1 \pm \sqrt{3}}{2}}\)

If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

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Answer:

B, 8 hundreds + 4tens+ 7 ones

Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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Answer: The answer is option C: $17,925.00.

Step-by-step explanation: Using the simple interest formula:

I = Prt

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

We can find the interest earned over the 6 years:

I = P * r * t = $15,000 * 0.0325 * 6 = $2,925

Adding the interest to the principal, we get the balance at the end of the 6 years:

Balance = Principal + Interest = $15,000 + $2,925 = $17,925

Therefore, the answer is option C: $17,925.00.

Answer:

153.94 in²

Step-by-step explanation:

The equation for Area is

Area = πr²

Plugging in the value for the radius into r, it will be

(note, r means radius)

Area = π(7)²= 49π ≈ 153.94

The units is -> in² so add that in the end

The probability of not selecting a purple marble when choosing one marble from the bag is 60%.

To determine the probability of not selecting a purple marble when choosing one marble from the bag, we need to find the number of marbles that are not purple and divide it by the total number of marbles in the bag.

The number of marbles that are not purple is the sum of red, green, and yellow marbles. Therefore, the number of marbles that are not purple is 3 + 3 + 9 = 15.

The total number of marbles in the bag is the sum of all the marbles: 3 + 3 + 9 + 10 = 25.

So, the probability of not selecting a purple marble is 15/25 = 0.6, which is equivalent to 60%.

Therefore, the probability of not selecting a purple marble when choosing one marble from the bag is 60%.

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Answer:

x = 8

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion , that is

\(\frac{JK}{AB}\) = \(\frac{KL}{BC}\) , substitute values

\(\frac{x}{4}\) = \(\frac{6}{3}\) = 2 ( multiply both sides by 4 to clear the fraction )

x = 8

The mean weight of the cats is the sum of the weights divided by the number of cats:

Use a calculator to get the mean rounded to the nearest tenth:

22 because the bottom corner is 68. 68 time 2= 138 then you do 160-138=22 meaning x=22

Answer:

a)2975

b)3450

Step-by-step explanation:

Total Total revenues will exceed = 8782.01

What is Total Revenue?

Total revenue is the overall sum of money received by a business through the sale of its products and services. Based on demand and price, it measures how successfully a company is generating revenue from its main operations.

Let x - normal (101.15 ,12.15)

where µ = 101.15

σ = 12.15

Mean for 85 customers

µ = 85 * 101.15 =8597.75

standard deviation for 85 customers

σ = \(\sqrt{85}\) * 12.15 = 112.017

P ( x >x₁ ) = 0.05

P ( x-µ/ σ > x₁-8597.75/112.017) = 0.05

P (Z >Z₁) = 0.05

Where

Z₁ = x- 8597.75/112.017

Z₁ = 1.645

Then x = 112.017 *1.645 +8597.75

x = 8782.01

Total total revenues will exceed = 8782.01

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True. For simpler amount analysis and management, data can be grouped into classes that represent related categories.

Data can be grouped into groups in order to identify patterns, trends, and similarities that can then be utilised to influence decisions. As classes may be used to organise and make data easier to interpret, this can be very helpful when working with huge datasets. Classes can also be used to find outliers and abnormalities in data, which can improve results and offer more precise insights. With classes, data can be processed and analysed more quickly and correctly, enabling more effective decision-making.For simpler analysis and management, data can be grouped into classes that represent related categories. With the process of categorising, data can be divided into smaller, easier-to-manage chunks for easier analysis.

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Using sampling concepts, it is found that the 100 students surveyed in this example would be the would be the sample.

It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.

Hence, in this problem:

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Answer:

6,720 inches or 560 feet

Step-by-step explanation:

20 x 14 x 24 = said number above.

Remember volume is just length times width times height.

Answer:

n = 4.5

Step-by-step explanation:

5.8n + 3.7 = 29.8 ( subtract 3.7 from both sides )

5.8n = 26.1 ( divide both sides by 5.8 )

n = 4.5

Answer:

so the answer to this is n= 4.5

Step-by-step explanation:

so first because you can't subtract the one with the variable you subtract 3.7 from 3.7 and 29.8 - 3.7 that cancels the 3.7 so it looks like this

5.8n + 3.7=29.8

         -3.7   -3.7

5.8n = 26.1

____   ____  n= 4.5    the lines means divide

5.8        5.8

Answer:320

Step-by-step explanation:PEMDAS. So first you would do the exponent 2^5= 32 (2x2=4 4x2=8 8x2=16 16x2=32)

Then you multiply 10x32 which equals 320

Answer:

Step-by-step explanation:

the answer would be x=0 because if this problem is proportional 5 x 4 = 20

and 0 x 4 =0

Answer:

4=x

Step-by-step explanation:

0 X

— = —

5 20

What times 5 gives you 20 ?

4 so x would be 4

Let's begin by using the formulas for the volume and surface area of a cube:

Volume = edge^3

Surface Area = 6 * edge^2

1. To find how fast the volume is shrinking when each edge is 13 cm, we need to take the derivative of the volume formula with respect to time:

dV/dt = 3(edge)^2 * (d(edge)/dt)

We know that the rate of change of the edge is -3 cm/sec (since it is shrinking), and we are given that the edge length is 13 cm. Substituting these values into the derivative formula, we get:

dV/dt = 3(13)^2 * (-3) = -1521 cm^3/sec

Therefore, the volume is shrinking at a rate of 1521 cm^3/sec when each edge is 13 cm.

2. Similarly, to find how fast the surface area is decreasing when each edge is 13 cm, we need to take the derivative of the surface area formula with respect to time:

dS/dt = 12(edge) * (d(edge)/dt)

Using the same values as before, we get:

dS/dt = 12(13) * (-3) = -468 cm^2/sec

Therefore, the surface area is decreasing at a rate of 468 cm^2/sec when each edge is 13 cm.
1. To find the rate at which the volume is shrinking, we can use the formula for the volume of a cube (V = a³) and differentiate with respect to time (t):

dV/dt = d(a³)/dt = 3a²(da/dt)

Given that the edges are shrinking at a rate of 3 cm/sec (da/dt = -3 cm/sec), and each edge is 13 cm:

dV/dt = 3(13²)(-3) = -1521 cm³/sec

The volume is shrinking at a rate of 1521 cm³/sec.

2. To find the rate at which the surface area is decreasing, we can use the formula for the surface area of a cube (S = 6a²) and differentiate with respect to time (t):

dS/dt = d(6a²)/dt = 12a(da/dt)

Given that the edges are shrinking at a rate of 3 cm/sec (da/dt = -3 cm/sec), and each edge is 13 cm:

dS/dt = 12(13)(-3) = -468 cm²/sec

The surface area is decreasing at a rate of 468 cm²/sec.

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Answer:

its positive 5 a negative divided by a negative is a positive

Step-by-step explanation:

Answer:

Positive 5

Step-by-step explanation:

a negative divided by a negative or a negative multiplied by a negative will always equal a positive. This equation is equal to 15 divided by 3 which is equal to 5.

Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.