4. (03.01)
Is the following relation a function? (1 point)
Yes
No

The volume in a pyramid is given by the next formula:

Where:

Ab is the area of the base

h is the heigh of the pyramid.

The area of the base is:

where l is length and w is the width

l=49cm

w=36cm

Then, the volume of the figue is:

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

Step-by-step explanation:

Given

Shape: Cube

Dimension: (x+7y), (7x-y) and (xy-5).​

Required

Determine the volume

The volume is calculated by multiplying the dimensions:

\(Volume = (x+7y) * (7x-y) * (xy-5)\)

Evaluate the first 2 brackets

\(Volume = [x(7x-y)+7y(7x-y)] * (xy-5)\)

\(Volume = [(7x^2-xy)+(49xy-7y^2)] * (xy-5)\)

\(Volume = [7x^2-xy+49xy-7y^2] * (xy-5)\)

\(Volume = [7x^2+48xy-7y^2] * (xy-5)\)

Open brackets

\(Volume = xy[7x^2+48xy-7y^2] -5[7x^2+48xy-7y^2]\)

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

Answer:

Step-by-step explanation:

Use Foil method

(2x  + 4)(x -1) = (2x*x)+ (2x *(-1)) + 4*x + 4*(-1)

                    = 2x² - 2x  + 4x - 4   {Combine like terms}

                    = 2x² + 2x - 4

Solution

For this case we can solve the problem with the following operation:

And rounded the answer we got 3.25 ft

16.24*100 = 1624

5*100 = 500

And we can do this:

1624/500 = 812/250 = 406/125

003

_____

125 / 406

-0

____

-40

-0

____

406

-375

_____

31

Answer:

15

Step-by-step explanation:

1.5*10 =15

Answer:

15.

Step-by-step explanation:

1.5 x 10 is expanded notation, so you just solve it (by multiplying) to convert it into standard notation.

A scatterplot shows the number of miles driven versus the gallons of gasoline remaining in the gas tank of a car. Which correlation best describes the relationship shown on the scatterplot?

Answer:

Negative correlation

Step-by-step explanation:

The kind of relationship which exists between two variables can be obtained whwn plotted in a graph such that we can visually access the data and note its trend. Datasets with fit lines trending downward will always have a slope value which is negative. In the scenario above, gallon of gasoline falls as the number if miles driven increases. This is a very reasonable relationship. And thus correlation between Both variables will be negative

Answer:

The answer would be 50m units squared.

The required answer is (f −1)'(-9) = -2√13/9.

To find (f −1)'(a), we first need to find the inverse function f −1(x).

Using the given function f(x) = x3 + 7x − 1, we can find the inverse function by following these steps:
1. Replace f(x) with y:
y = x3 + 7x − 1
The informal descriptions above of the real numbers are not sufficient for ensuring the correctness of proofs of theorems involving real numbers. The realization that a better definition was needed. Real numbers are completely characterized by their fundamental properties that can be summarized

2. Swap x and y:
x = y3 + 7y − 1
3. Solve for y:
0 = y3 + 7y − x + 1
We need to find the inverse function , Unfortunately, finding the inverse function for f(x) = x^3 + 7x - 1 is not possible algebraically due to the complexity of the function. A number is a mathematical entity that can be used to count, measure, or name things. The quotients or fractions of two integers are rational numbers.

Using the cubic formula, we can solve for y:
y = [(x - 4√13)/2]1/3 - [(x + 4√13)/2]1/3 - 7/3
Therefore, the inverse function is:
f −1(x) = [(x - 4√13)/2]1/3 - [(x + 4√13)/2]1/3 - 7/3
Now we can find (f −1)'(a) by plugging in a = -9:
(f −1)'(-9) = [(−9 - 4√13)/2](-2/3)(1/3) - [(−9 + 4√13)/2](-2/3)(1/3)
(f −1)'(-9) = [(−9 - 4√13)/2](-2/9) - [(−9 + 4√13)/2](-2/9)
(f −1)'(-9) = (4√13 - 9)/9 - (9 + 4√13)/9
(f −1)'(-9) = -2√13/9

Therefore, (f −1)'(-9) = -2√13/9.

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Answer:

https://socratic.org/questions/at-their-annual-car-wash-the-science-club-washes-30-cars-in-45-minutes-at-this-r

Step-by-step explanation:

answer is in here yw

Answer:

3.14 in²

Step-by-step explanation:

π= pi = 3.14

r = 2/2 = 1 inch

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

3.14 x 1² = 3.14 in²

Answer: 12.56

Step-by-step explanation: Find area with Pie:

A= Pie x radius squared so 2 x 2 = 4 with what then we multiply

3.14 x 4 = 12.56

OR

Unless the radius is not 2 and 2 is diameter than we just divided 2 by 2 and get 1 the whole then 1 squared is 1 and 3.14 x 1 = 3.14

Given:

There are given that the two points:

Explanation:

According to the question:

We need to find the equation of the line:

Then,

To find the equation of the line, first, we need to find the slope of the line.

So,

From the formula of the slope of the line:

Where,

Then,

Put all the values into the given formula:

So,

Then,

From the formula of the equation of the line:

Then,

Put the value of m into the above equation:

So,

Then,

Final answer:

Hence, the equation of line is shown below:

We have the following probabilites:

Following the definition of conditional probability:

In this case, we want to calculate the conditional probability that a person has a daughter given that he/she already has a son. Then, the probability is:

therefore, the conditional probability that a person who has a son also has a daughter is 34%

Using a system of equations, the correct statement is:

The value when n = 3 is 13.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variable is n.

The expression “two less than the quotient of a number cubed and nine, increased by twelve” is given by:

\(n = \frac{n^3}{9} + 12 - 2\)

When n = 3:

\(n = \frac{3^3}{9} + 12 - 2\)

\(n = 13\)

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Our new measures of central tendency and spread are Mean: (9+9+13+15+19)/5=13(9+9+13+15+19)/5=13.

acc to our question-

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The completed ANOVA table is

Source of variance  | SS   | df | MS   | F-ratio

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

Treatment          | 70   | 2  | 35   | -------

Error              | 30   | 22 | -----| -------

Total              | -----| ---| -----| -------

To complete the ANOVA table, we need to calculate the missing values for degrees of freedom (df), mean squares (MS), and the F-ratio.

Source of variance: Treatment

SS (Sum of Squares): 70

To calculate the degrees of freedom (df) for Treatment, we use the formula:

df = number of groups - 1

Since we are comparing 3 different vitamin supplements, the number of groups is 3.

df = 3 - 1 = 2

Now, let's calculate the mean squares (MS) for Treatment:

MS = SS / df

MS = 70 / 2 = 35

Next, we need to calculate the missing values for Error:

Given:

Source of variance: Error

SS (Sum of Squares): 30

To calculate the degrees of freedom (df) for Error, we use the formula:

df = total number of observations - number of groups

Since the total number of observations is 25 and we have 3 groups, the degrees of freedom for Error is:

df = 25 - 3 = 22

Finally, we can calculate the F-ratio:

F-ratio = MS Treatment / MS Error

F-ratio = 35 / (SS Error / df Error)

However, the value for SS Error is missing in the provided information, so we cannot calculate the F-ratio without that value.

In conclusion, the completed ANOVA table is as follows:

Source of variance  | SS   | df | MS   | F-ratio

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

Treatment          | 70   | 2  | 35   | -------

Error              | 30   | 22 | -----| -------

Total              | -----| ---| -----| -------

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The first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

Given that, a hiking trail is 24 miles from start to finish. There are two rest areas located along the trail.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other.

Given that the ratio of the distance from the start of the trail to the rest area and the distance from the rest area to the end of the trail is 2:9.

Now, 2/11 ×24=4.3636

The nearest hundredth of a mile is 4.367 miles.

Given that Anne claims that the distance she has walked and the distance she has left to walk has a ratio of 5:7.

Now, 5/12 ×24=10 miles

Anne walked 10 miles.

Therefore, the first rest area from the starting point of the trail is 4.367 miles and the distance Anne walked is 10 miles.

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We get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

Given that,

The equation is q²+ 5/6q+---

We have to find to create a flawless quarte trinomial, finish the quadrilateral.

We know that,

Take the equation

q²+ 5/6q+---

By adding some thing we get the quadratic equation.

The missing term we add is 5/2×6

We get

q²+ 5/6q+(5/6×2)²

q²+ 5/6q+(5/12)²

We can write as

(q+5/12)²

Therefore, we get the flawless quarte trinomial, finish the quadrilateral is (q+5/12)² we can say as a quadratic equation is q²+ 5/6q+---.

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Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

The solar flux density also referred to as the solar constant is the total amount of energy derived from the sun per unit area per given unit of time. It is considered to be equal to solar luminosity divided by the surface area of a given sphere that has a radius equivalent to the distance between the respective planet from the sun.

using the formula for finding the solar flux density,

solar flux density =  solar luminosity /(4 x π x distance between mercury and the sun)

solar flux density =  3.865 x \(10^{26}\) /(4 x π x ( 5.791 x \(10^{10}\)))

solar flux density = 9.12 x 10⁻³ W/m²

Therefore, the solar flux density for mercury after the calculation is 9.12 x 10⁻³ W/m².

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Answer:

100 minutes cost Todd $24. He had extra bill of 26.38 - 24 = $2.38

$2.38 = 238 cents

7 cents billed for 1 extra minute

1 cents billed for 1/7 extra minute

238 cents billed for 238/7 = 34 extra minutes

total minutes = 134 minutes

The gradient of a function points in the direction in which the function increases the fastest because it represents the direction of greatest increase of the function.

The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. This means that if we move in the direction of the gradient, the value of the function increases the fastest.

To understand why this is true, let's consider the definition of the gradient. The gradient of a function f(x) is defined as a vector of partial derivatives:

∇f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)

Each component of the gradient vector represents the rate of change of the function with respect to the corresponding variable. In other words, the gradient tells us how much the function changes as we move a small distance in each direction.

When we take the norm (or magnitude) of the gradient vector, we get the rate of change of the function in the direction of the gradient. This means that if we move in the direction of the gradient, the value of the function changes the fastest, because this is the direction in which the function is most sensitive to changes in the input variables.

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Answer:

3. 17.2°

Step-by-step explanation:

The angles for the right triangle are 90°, 72.8°, and 17.2°.

The correct answer is $4.50 option (c).

To calculate the cost of 2.6 lb of oatmeal at $1.73/lb, we simply multiply the weight of the oatmeal by the cost per pound.

2.6 lb × $1.73/lb = $4.498

Rounding to two decimal places, the cost of 2.6 lb of oatmeal is $4.50.

Therefore, the correct response is $4.50.

o find the cost of 2.6 lb of oatmeal, we can multiply the price per pound by the number of pounds. So:

Cost of oatmeal = price per pound x number of pounds

= $1.73/lb  × 2.6 lb

= $4.498

Rounding this to two decimal places gives us $4.50. Therefore, the correct answer is $4.50.

To calculate the cost of 2.6 lb of oatmeal at a price of $1.73/lb, we can use the formula:

Cost = Price per unit  × Quantity

In this case, the price per unit is $1.73/lb and the quantity is 2.6 lb. So the cost would be:

Cost = $1.73/lb  × 2.6 lb = $4.498

Rounding to the nearest cent, the cost of 2.6 lb of oatmeal would be $4.50. Therefore, the correct response is $4.50.

To calculate the cost of 2.6 lb of oatmeal at $1.73/lb, we need to multiply the weight (in pounds) by the price per pound.

So, the cost would be:

2.6 lb  × $1.73/lb = $4.498

Rounding this to two decimal places gives us $4.50, which is one of the options provided. Therefore, the correct answer is $4.50.

Complete Question:

oatmeal costs $1.73/lb. how much would 2.6 lb of oatmeal cost? responses

a. $1.50  

b. $4.48  

c. $4.50  

d. $4.58

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There are 75% of red cars and blue cars if you add them together.

Hope this helps, please give me brainliest if I'm correct. ;)

Answer:

0.00002163799

Step-by-step explanation:

Answer:

0.00002163799

Step-by-step explanation:

Answer:

155.5 square feet

Step-by-step explanation:

A = (1/2)(10)(8.6 + 6.3 + 8.6 + 7.6)

= 5(31.1)

= 155.5 square feet

Yes, the result obtained in part a is statistically significant, indicating that the population mean customers served per hour is indeed less than 120.

a. To test whether the population mean customers served per hour is less than 120, we can use a one-sample t-test. The null hypothesis (H0) is that the population mean is 120, and the alternative hypothesis (Ha) is that the population mean is less than 120. We calculate the test statistic t using the formula:

where  is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. Plugging in the values from the problem, we get:

Since the test statistic t is less than the critical value -1.645 (for a one-tailed test with a 5 significance level), we reject the null hypothesis. This means that there is sufficient evidence to conclude that the population mean customers served per hour is less than 120.

b. "Statistically significant" means that the results of a statistical test indicate a significant difference or relationship between variables, and this difference is unlikely to have occurred by chance alone.

In this context, it means that the difference between the sample mean and the hypothesized population mean (120) is not likely due to random sampling variability.

The result obtained in part a is statistically significant because we rejected the null hypothesis based on the test statistic falling in the rejection region, indicating a significant difference between the observed sample mean and the hypothesized population mean.

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Explanation: Just like any of your two-step equations,

in this inequality,  start by isolating the x term which in this

case is -3x by subtracting 5 from both sides.

That leaves you with -3x < -24.

To get x by itself, divide both sides by -3 but watch out.

When you multiply or divide both sides of an inequality by a

negative number, you must switch the direction of the inequality sign.

So we have x < 8 and put your final answer in

set notation and it look like this → {x: x < 8}.