8. What number should come in the box to make the following statement true?
34 + 32 = 9 × ___

Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

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Answer and Explanation:

We can find the slope of each line by dividing the change in y by the change in x between two points on the line. In other words:

slope = rise / run

1. 2/5

2. 1/4

3. -1/3

4. -5/2

5. 6/7

6. -6/2 = -3

7. 0/0 = 0

8. -2/6 = -1/3

Answer:

78/5

Step-by-step explanation:

(15 x 5 + 3)/5

78/5

The Volume of the given solid using polar coordinate is:\(\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta\)

V= \(\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta\)

To find the volume in polar coordinates bounded above by a surface z=f(r,θ) over a region on the xy-plane, use a double integral in polar coordinates.

Consider the cylinder,\(x^{2}+y^{2} =1\) and the ellipsoid, \(4x^{2}+ 4y^{2} + z^{2} =64\)

In polar coordinates, we know that

\(x^{2}+y^{2} =r^{2}\)

So, the ellipsoid gives

\(4{(x^{2}+ y^{2)} + z^{2} =64\)

4(\(r^{2}\)) + \(z^{2}\) = 64

\(z^{2}\) = 64- 4(\(r^{2}\))

z=± \(\sqrt{64-4r^{2} }\)

So, the volume of the solid is given by:

V= \(\int\limits^{2\pi}_ 0 \int\limits^1_0{} \, [\sqrt{64-4r^{2} }- (-\sqrt{64-4r^{2} })] r dr d\theta\)

= \(2\int\limits^{2\pi}_ 0 \int\limits^1_0 \, r\sqrt{64-4r^{2} } r dr d\theta\)

To solve the integral take, \(64-4r^{2}\) = t

dt= -8rdr

rdr = \(\frac{-1}{8} dt\)

So, the integral  \(\int\ r\sqrt{64-4r^{2} } rdr\) become

=\(\int\ \sqrt{t } \frac{-1}{8} dt\)

= \(\frac{-1}{12} t^{3/2}\)

=\(\frac{-1}{12} (64-4r^{2}) ^{3/2}\)

so on applying the limit, the volume becomes

V= \(2\int\limits^{2\pi}_ {0} \int\limits^1_0{} \, \frac{-1}{12} (64-4r^{2}) ^{3/2} d\theta\)

=\(\frac{-1}{6} \int\limits^{2\pi}_ {0} [(64-4(1)^{2}) ^{3/2} \; -(64-4(2)^{0}) ^{3/2} ] d\theta\)

V = \(\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta\)

Since, further the integral isn't having any term of \(\theta\).

we will end here.

The Volume of the given solid using polar coordinate is:\(\frac{-1}{6} \int\limits^{2\pi}_ {0} [(60) ^{3/2} \; -(64) ^{3/2} ] d\theta\)

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Answer:

1 and 1.50 or 1 and 2, but most likely the first one.

Step-by-step explanation:

Step-by-step explanation:

it seems we are dealing with multiplication, as the distances between the numbers get bigger and bigger.

and then I see

7 × 2 = 14

14 × 2 = 28

28 × 2 = 56

ok, so the sequence is created by always multiplying by 2.

a1 = 7

a2 = a1 × 2 = 7 × 2 = 14

a3 = a2 × 2 = a1 × 2 × 2 = 7 × 2 × 2 = 28

an = an-1 × 2 = a1 × 2^(n-1) = 7 × 2^(n-1)

a14 = 7 × 2¹³ = 7 × 8192 = 57,344

The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)

Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc

From the information given, we have that;

x -2/x + 3 + 10x/x² - 9

Find the lowest common denominator and simplify

(x-2)(x² - 9) + (x-3)(10x)  /(x²- 9)(x+ 3)

Now, expand the bracket, we get;

x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)

collect the like terms of the denominator and that of the numerator, we get;

11x³ - 39x -2x²/(x²- 9)(x+ 3)

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The inverse of the function f(x) = 6x^5 - 7 is g(x) = ((x + 7) / 6)^(1/5), which allows us to undo the effects of the original function.

To find the inverse of the function f(x) = 6x^5 - 7, we follow a step-by-step process:

Step 1: Replace f(x) with y.

y = 6x^5 - 7.

Step 2: Swap x and y.

x = 6y^5 - 7.

Step 3: Solve for y.

We need to isolate y in the equation. Add 7 to both sides:

x + 7 = 6y^5.

Step 4: Divide both sides by 6.

Divide both sides of the equation by 6 to solve for y:

(x + 7) / 6 = y^5.

Step 5: Take the fifth root of both sides.

To eliminate the fifth power, we take the fifth root of both sides:

((x + 7) / 6)^(1/5) = y.

Thus, the inverse function of f(x) is g(x) = ((x + 7) / 6)^(1/5). The inverse function takes an input x and returns the corresponding value y. When this y value is plugged back into the original function f(x), it will yield the original input x. The inverse function allows us to "undo" the effects of the original function and retrieve the original input from the output.

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Answer:

1:4

Step-by-step explanation:

Thats it

Answer:1/4

Step-by-step explanation:

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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Answer:

The answer is 18 pounds per bucket.

In this question, we are given the expression that relates the pounds of lobster to the number of buckets:

\(\displaystyle \frac{\text{450 pounds}}{\text{25 buckets}}\)

This fraction is presented to give a proportion of pounds of lobster to the number of buckets these lobsters inhabit.

To solve this problem, we need to know exactly how this rate will work.

A rate is the same thing as a fraction, percentage, or decimal. All of these forms are convertible between one another.

For instance, if we took 25%, we know that by dividing this by 100, we receive a decimal form (0.25) or a fractional form (1/4).

We can apply the same principle here.

Part I - Set up the Rate

To solve, set up the rate:

\(\displaystyle \frac{450 \ \text{pounds}}{25 \ \text{buckets}}\)

Part II - Find the GCF

Then, find the Greatest Common Factor (GCF) of the two digits:

Check for common factors between the two trees:

Since 25 is the greatest of the three factors, it is the GCF.

Part III - Apply the GCF

Divide both the numerator and the denominator by 25:

\(\displaystyle \frac{450}{25} = 18\)

\(\displaystyle \frac{25}{25} = 1\)

Part IV - Simplify

Set up the new fraction:

\(\displaystyle \frac{18}{1}\)

Anything divided by 1 does not change:

\(\displaystyle \frac{18}{1} = 18\)

Since we got 18 an answer, this means that there are 18 pounds of lobster per bucket.

1) 2x + 7 2) 10x + 1 3) (x-4)² 4) 2x/5

5) 2x + 10 = 36 6) 3(x-7) = 18 7) 4x/8 = 3

Explanation:

1) let the number = x

twice the number = 2x

The sum of twice a number and 7 = 2x + 7

2) let the number = x

product = multiplication

the product of a number and 10 = x * 10 = 10x

The product of a number and 10, increased by 1 = 10x + 1

3) let the number = x

four less than a number = x -4

four less than a number squared: (x-4)²

4) let the number = x

twice the number = 2x

twice a number divided by 5 = 2x/5

5) let the number = x

twice the number = 2x

the sum of twice a number and 10 = 2x+ 10

the sum of twice a number and 10 is 36:

2x + 10 = 36

6) let the number = x

the difference of a number and 7 = x -7

three times the difference of a number and 7 = 3(x - 7)

three times the difference of a number and 7 is 18:

3(x-7) = 18

7) let the number = x

four times a number = 4x

four times a number divided by 8 is 3:

4x/8 = 3

Answer:

\((\frac{6}{1})(\frac{11}{4} )\)

\((-\frac{10}{3})(-\frac{17}{5})\)

\((-\frac{9}{2} )(\frac{26}{3} )\)

\((\frac{11}{6})(-\frac{9}{1} )\)

Step-by-step explanation:

I hope this help you

The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)

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Answer:

-14w+12

Step-by-step explanation:

10 - 7w - 13 - 7w + 15

Combine like terms

- 7w  - 7w + 10-13+15

-14w+12

The appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

To find the appropriate test statistic for a 2-sample z-test for two proportions, we need to calculate the standard error and then use it to compute the z-score. The formula for the standard error is:

SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]

Where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.

In this case, we have the following values:

X1 = 24 (number of successes in sample 1)

n1 = 200 (sample size 1)

X2 = 17 (number of successes in sample 2)

n2 = 150 (sample size 2)

To calculate the sample proportions, we divide the number of successes by the respective sample sizes:

p1 = X1 / n1 = 24 / 200 = 0.12

p2 = X2 / n2 = 17 / 150 = 0.1133

Now, we can plug these values into the formula to calculate the standard error:

SE = sqrt[(0.12 * (1 - 0.12) / 200) + (0.1133 * (1 - 0.1133) / 150)]

SE ≈ 0.0319

Finally, the test statistic (z-score) is calculated by subtracting the two sample proportions and dividing by the standard error:

Z = (p1 - p2) / SE

Z = (0.12 - 0.1133) / 0.0319

Z ≈ 0.2103

Therefore, the appropriate test statistic for this test is approximately 0.2103 (rounded to 4 decimal places).

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We need to calculate the power of the heater to warm up the given air to a specified temperature and relative humidity.

The process of heating air involves three essential steps. These are preheating, humidifying, and heating.

Firstly, we need to preheat the air to increase the temperature of the air. After that, the air is humidified to the desired relative humidity, and finally, the air is heated to the required temperature.
The air we want to warm up has the following parameters:
Volume flow rate of air = 5000 cubic meters per hour
Initial temperature of air = 5 deg C
Relative humidity = 40%
Final temperature of air = 30 deg C
Step 1: Preheating the air
The specific heat of air is approximately 1 kJ/kgK. To preheat the air, we need to calculate the amount of heat required to raise the temperature of the air from 5 deg C to 30 deg C.
The density of air is approximately 1.2 kg/cubic meter, and hence, the mass of air flowing per hour is given by:
Mass of air = Volume flow rate × Density = 5000 × 1.2 = 6000 kg/hour
The amount of heat required to raise the temperature of the air from 5 deg C to 30 deg C is given by:
Q = Mass × Specific heat × Temperature rise
 = 6000 × 1 × (30 - 5)
 = 150000 kJ/hour
Step 2: Humidifying the air
The air has a relative humidity of 40%, and we want to increase it to the desired relative humidity. We can use a steam humidifier to add water vapor to the air to increase its relative humidity. The amount of heat required to humidify the air is given by:
Q = Mass of water vapor × Latent heat of vaporization
The mass of water vapor required to increase the relative humidity from 40% to the desired value can be calculated using psychrometric charts. For the given parameters, the mass of water vapor required is approximately 0.012 kg/kg of dry air.
The latent heat of vaporization of water is approximately 2260 kJ/kg. Hence, the amount of heat required to humidify the air is given by:
Q = 6000 × 0.012 × 2260 = 162720 kJ/hour
Step 3: Heating the air

Finally, we need to heat the air from 5 deg C and relative humidity of 40% to 30 deg C. The amount of heat required to raise the temperature of the air is given by:
Q = Mass × Specific heat × Temperature rise
 = 6000 × 1 × (30 - 5)
 = 150000 kJ/hour
The total heat required to warm up the air is the sum of the heat required in the three steps, i.e.,
Total Q = 150000 + 162720 + 150000
         = 462720 kJ/hour
The power of the heater required to supply this amount of heat can be calculated using the following formula:
Power = Total Q / (Efficiency × Time)
     = 462720 / (0.8 × 3600)
     ≈ 160.77 kW

The power of the heater required to warm up five thousand cubic meter per hours of air + 5 deg C and relative humidity 40% to temperature + 30 deg C is approximately 160.77 kW.

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Answer:

Gabriel needs to have $3.75 for sales tax.

Step-by-step explanation:

A sales tax rate of 6.25% means that 6.25 cents is going to be charged for tax for each dollar you spend. (Because 6.25% of $1.00 is 6.25 cents.)

If he was spending $10, the sales tax would be 62.5 cents (6.25 cents per dollar x 10 dollars). Since he is spending $60 on this item, the equation would be (6.25 cents per dollar x 60 dollars) (6.25 cents x 60 = 375 cents).

And 375 cents equals $3.75.

Answer:

\(A=254.46\ cm^2\)

Step-by-step explanation:

Given that,

The diameter of the pizza, d = 18 cm

We need to find the square cm of cheese layer does she need to put on the pizza.

We know that the area of the circle is given by :

\(A=\pi r^2\)

Where

r is the radius of the circle

Here, r = 9 cm

So,

\(A=\pi (9)^2\\\\A=254.46\ cm^2\)

So, the area of the pizza is \(254.46\ cm^2\).

Answer:

Yes, negative 2 is bigger than negative six.

Answer:

(-2 is greater than -6 )it is the lower the it is such as -2 the way you know which is greater is by whatever negative is closer to 0 or to the positive numbers.

Step-by-step explanation:

Hope this heped!

1 2 7 1 7

7 8 9 0 1 9

- 7

1 9

- 1 4

5 0

- 4 9

1 1

-  7

4 9

- 4 9

0

Your answer is 12,717 with a remainder of 0.

Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

To determine the magnification if lens #2 were absent (i.e., the magnification of lens #1), we need to consider the properties of the lenses in combination.

Given the options for the magnification of lens #1, we can eliminate some options based on the properties of the final image:

real, enlarged and inverted

virtual, enlarged and upright

virtual, reduced and inverted

virtual, enlarged and inverted

real, reduced and upright

real, enlarged and upright

real, reduced and inverted

virtual, reduced and upright

Lens #2, being absent, does not contribute to the overall magnification of the system. Therefore, the magnification of the entire system is determined solely by lens #1.

From the given options, we can see that the only possible choice for the magnification of lens #1 that matches the properties of the final image is:

M1 = 1 (real, enlarged, and upright)

As for the properties of the final image for the present two-lens problem, we can conclude:

real, enlarged, and upright

Therefore, the correct answers are:

Magnification if lens #2 were absent: M1 = 1

Properties of the final image: real, enlarged, and upright.

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Answer:

I only / 1 only

Step-by-step explanation:

Function rules: no same x-values and must pass vertical line test

1: all different x-values

2: has two of the same x-values

3: doesn't pass vertical line test

Hopefully this helps!

Brainliest please?

Answer:

1 only (I hope im right)

Step-by-step explanation:

Hope this helps:)

Answer:

4^6 / 5^6

Step-by-step explanation:

We know that (a/b) ^c = a^c / b^c

(4/5) ^6 = 4^6 / 5^6

=======================================================

Explanation:

The rule is

\(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\)

Basically we raise each part of the fraction to the outer exponent. In this case, a = 4, b = 5 and c = 6.

---------------------------------

The outer exponent c = 6 tells us how many copies of (a/b) we are multiplying together. So we are multiplying 6 copies of (4/5) together like so

\(\left(\frac{4}{5}\right)^6 = \left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)\\\\\left(\frac{4}{5}\right)^6 = \frac{4*4*4*4*4*4}{5*5*5*5*5}\\\\\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\\\)

For larger values of c, it's easiest to use the formula directly instead of expand things out like what is shown above. I recommend trying out small values of c such as c = 2 or c = 3.

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

\(2^{5}\)

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

Answer:

True

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

when the x and y axis intersect, their point is always to be considered (0,0) which is also called the origin

:3))

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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To simplify the expression f(x) - g(x) where f(x) = x + 4 and g(x) = x^2 + 3x - 2, we substitute the given functions into the expression and simplify it. The simplified form will be in terms of x and will represent the difference between the two functions.

To simplify f(x) - g(x), we substitute the given functions:

f(x) - g(x) = (x + 4) - (x^2 + 3x - 2)

Expanding the expression, we get:

f(x) - g(x) = x + 4 - x^2 - 3x + 2

Combining like terms, we have:

f(x) - g(x) = -x^2 - 2x + 6

Therefore, the simplified form of f(x) - g(x) is -x^2 - 2x + 6. This expression represents the difference between the functions f(x) and g(x) in its simplest form.

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