A sports ball has a diameter of 23 cm. Find the volume of the ball. Round your answer to 2 decimal places, and use 3.14 as an approximation of n cm³,​

The linear function is given as follows:

\(y = \sqrt{x} + 4\)

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The y-intercept is of 4, hence the parameter b is given as follows:

b = 4.

The line is inclined to 60° with the positive direction of X-axis, hence the slope m is given as follows:

m = tan(60º)

\(m = \sqrt{3}\)

Thus the function is given as follows:

\(y = \sqrt{x} + 4\)

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The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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The statement that best describes the type of triangle is;

The triangle is a scalene triangle and also an acute triangle.

Triangles could be classified based on their interior angles or even the number of equal sides of the triangle. Thus;

A triangle is called an acute triangle if all three angles are less than 90°

A triangle is called a right triangle if one angle is 90°

A triangle is called an obtuse triangle if one angle is greater than 90°

A triangle is called an Equilateral triangle if all three sides are the same length

A triangle is called an Isosceles triangle if two sides are the same length

A triangle is called a Scalene triangle if all three sides are of different lengths.

We are given the three angles of the triangle as; 40 °, 60°, and 80°.

Likewise we are given the length of the three sides as 8 cm, 10 cm, and 20 cm.

Since none of the angles nor sides are equal nor 90 degrees, then we can call this a scalene triangle. It can also be classified as an acute angle as all three angles are less than 90 degrees.

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The entry that it will pass on the accounting book based on the information about Galaxy Star Corporation is the credit sales.

It should be noted that credit sales are the sales where the amount that is owed will be paid at alter date.

From the information given, we were informed that the payment will be made after 20 days. Therefore, the appropriate entry will be in town credit sales.

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Answer:

13

Step-by-step explanation:

The midpoint is 1/2 way between points A and B

(A+B)/2 = (0+26)/2 = 26/2 = 13

Answer:

y = -6, x =2

Step-by-step explanation:

To solve by elimination, you have to line both equations up together. Then, you multiply both equations until one variable is removed.

2x+y = -2

5x + 3y = - 8

There are many different ways to solve an elimination problem, but generally you should look for the simplest route. Here, I would multiply the top equation by -3.

-6x -3y = 6

5x +3y = -8

Imagine you are adding the two equations together. You end up with

-x = -2

Then solve for x. In this situation, it is fairly simple. Take out a factor of -1.

x = 2

Finally, choose one of your beginning equations and plug your new-found x value back into the equation.

2(2) +y = -2

4 + y = -2

y = -6

Answer:

3x + 2y ≤ 30

0.5x + y ≤ 9

Step-by-step explanation:

Number of deluxe model = x

Number of economy models = y

Assembly hours :

Maximum hours = 30

Deluxe model = 3 hours

Economy model = 2 hours

3x + 2y ≤ 30

Painting :

Maximum hours = 9

Deluxe model = 1/2 = 0.5 hours

Economy model = 1 hours

0.5x + y ≤ 9

Therefore the inequality constraints are:

3x + 2y ≤ 30

0.5x + y ≤ 9

The composite function is positive at the interval (-7, ∝)

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

The table of values of the function f(x)

Also, we have

The table of values of the function g(x)

The composite function (f - g)(x) is calculated as

(f - g)(x) = f(x) - g(x)

From the table of values, we have the following values

(f - g)(-10) = f(-10) - g(-10) = -3 - 9 = -12 --- negative

(f - g)(-7) = f(-7) - g(-7) = 6 - 6 = 0 --- zero

Also, we have

(f - g)(-4) = f(-4) - g(-4) = 15 - 3 = 12 --- positive

This means that the interval is (-7, ∝)

Hence, the composite function (f - g)(x) is positive at the interval (-7, ∝)

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Answer:

the fully built T-Rex skeleton display cannot fit inside the large case

Step-by-step explanation:

compare the dimensions of the skeleton to the dimensions of the case.

Given:

T-Rex skeleton dimensions:

Height = 12 ft.

Width = 6 ft.

Length = 40 ft.

Case dimensions:

Height = 5 yards

Width = 3 yards

Length = 13 yards

To compare the dimensions, we need to convert the case dimensions from yards to feet, as the T-Rex skeleton dimensions are given in feet.

1 yard = 3 feet

Case dimensions in feet:

Height = 5 yards * 3 feet/yard = 15 feet

Width = 3 yards * 3 feet/yard = 9 feet

Length = 13 yards * 3 feet/yard = 39 feet

Now we can compare the dimensions of the T-Rex skeleton and the case:

T-Rex skeleton:

Height = 12 ft.

Width = 6 ft.

Length = 40 ft.

Case:

Height = 15 ft.

Width = 9 ft.

Length = 39 ft.

Based on the dimensions, we can see that the height of the T-Rex skeleton (12 ft.) is smaller than the height of the case (15 ft.). Similarly, the width of the T-Rex skeleton (6 ft.) is smaller than the width of the case (9 ft.). However, the length of the T-Rex skeleton (40 ft.) is larger than the length of the case (39 ft.).

Therefore, the fully built T-Rex skeleton display cannot fit inside the large case because the length of the skeleton exceeds the length of the case.

The equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

According to the question,

We have the following information:

y = 3x-1 and the point through which line is passing is (3,2)

We know that the slope of the given line (denoted by m) is 3.

Now, the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

In this case, we have x' = 3 and y' = 2.

y-2 = 3(x-3)

y-2 = 3x-9

Moving 2 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

y = 3x-9+2

y = 3x-7

Hence, the equation of the line passing through y = 3x-1 and (3,2) is y = 3x-7.

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The inequality is p < 15.

To solve this inequality, you can start by dividing both sides by -4. However, since you are dividing by a negative number, you need to flip the inequality sign.

So, you get:

p < 15

This means that any value of p that is less than 15 would satisfy the inequality. For example, if you plug in p = 10, you get:

-4(10) > -60

-40 > -60

which is true, so p = 10 is a valid solution to the inequality.

Answer

p < 15

In-depth explanation

To solve the inequality, we need to divide each side by -4 :

-4p > -60

p < 15 *

*I reversed the sign of the inequality, because I have divided both sides by a negative number. In inequalities, whenever each side is multiplied or divided by a negative, the inequality sign needs to be reversed.

Therefore, p < 15

Answer:

your answer is √7/3

Step-by-step explanation:

your answer is √7/3

Hi, there!

 ______

\(\begin{tabular}{c|1} \boldsymbol{Things \ to \ Consider} \\\cline{1-3} \end{tabular}\)

(1)

 - The slopes of parallel lines are identical.

{The line \(\sf{y=7x-1}\) has a slope of 7}

Thus,

{The slope of the line that is parallel to the aforementioned line (whatever its equation happens to be) is \(\sf{7}\).}

(2)

 - The slopes of perpendicular lines are negative inverses of each other.

The negative inverse of 7 is

\(-\dfrac{1}{7}\).

Therefore,

\(\textsc{Answers:\begin{cases} \bf{7} \\ \bf{-\dfrac{1}{7}} \end{cases}}\)

Hope the answer - and explanation - made sense,

happy studying!!                                                                 \(\tiny\boldsymbol{Frozen \ melody}\)

The solution to interval notation or inequality "Nineteen less than p is no less than 47" is p ≥ 66.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The interval notation is - Nineteen less than p is no less than 47.

The inequality expression is -

p - 19 ≥ 47

Solve the inequality -

p - 19 ≥ 47

p ≥ 47 + 19

p ≥ 66

Therefore, the solution to inequality is p ≥ 66.

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Answer:

Step-by-step explanation:

1/5³ = 1/125

The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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Answer:

LCM stands for Least Common Multiple

To calculate LCM you need to divide the no.s given by smallest divisor going to the greatest until the no.s can be divided no more

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

m = 4

Step-by-step explanation:

We know that,

( 15 , -3 ) ⇒ ( x₁ , y₁ )

( 17 , 5 ) ⇒  ( x₂ , y₂ )

You have to use y = m x + c to find the equation of the line.

Here,

m = slope

c = y - intercept

Let find the slope now.

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

\(m=\frac{-3-5}{15-17}\)

\(m=\frac{-8}{-2}\)

\(m=4\)

Slope = 4

Hope this helps you.

Let me know if you have any other questions :-)

The intervals are denoted as:

Closed intervals = [a, b]

This interval includes a and b.

Open intervals = (a, b)

This interval does not include a and b.

The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].

What are intervals?

The intervals are numbers or values between two given point

The intervals are denoted as:

Closed intervals = [a, b]

This interval includes a and b.

Open intervals = (a, b)

This interval does not include a and b.

We have

A number line.

The set of values that is in the blue line is from -4 to 3.

This means that the blue line includes values from -4 to 3.

There are infinite numbers between -4 to 3.

The blue line denoted that the values -4 and 3 are also included.

The interval that denotes the values between -4 and 3 is:

= [-4, 3]

Thus,

The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].

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Answer:

no because it fails the vertical line test

Answer:

-234

Step-by-step explanation:

Subtracting 275 from 41 would equal -234.

The difference between 41 and 275 is -234.

To find the difference between 41 and 275, we perform subtraction.

Subtraction is the process of finding the difference between two numbers. In this case, we are subtracting 275 from 41, which means we want to find how much smaller 275 is compared to 41.

Let's set up the subtraction:

    41

 - 275

Starting from the rightmost column, we subtract 5 from 1. Since 5 is greater than 1, we borrow 1 from the tens column, making the ones column 11 - 5 = 6. Then, we move to the tens column and subtract 7 from 4, which is not possible without borrowing from the hundreds column. So, we borrow 1 from the hundreds column, making it 3 - 1 = 2. Now, we can subtract 7 from 12 in the tens column, which gives us 5. Finally, we subtract the 2 in the hundreds column from 2, resulting in 0.

The final result is 234, indicating that 275 is 234 units larger than 41. In other words, the difference between 41 and 275 is 234.

Subtraction is an essential arithmetic operation used in various real-life situations, such as calculating changes in quantities, measuring distances, determining differences between values, and more. Understanding subtraction helps us comprehend the relationships between numbers and enables us to solve a wide range of mathematical and practical problems.

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The equation of the perpendicular line in slope-intercept form is y = 4x + 25

The equation of line p given as

y = –4x + 1

Also, from the question

The point on line q is given as

Point = (-6, 1)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope of y = –4x + 1 is -4

So, we have

m = 4

The slopes of perpendicular lines are opposite reciprocals

This means that the slope of the line q is 1/4

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = 4

(x₁, y₁) = (-6, 1)

Substitute the known values in the above equation

So, we have the following equation

y = 4(x + 6) + 1

Evaluate

y = 4x + 24 + 1

Evaluate the sum

y = 4x + 25

Hence, the perpendicular line has an equation of y = 4x + 25

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Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Answer:

15/32

Step-by-step explanation:

5/8 divided by 1 1/3

5/8 divided by 4/3

5/8 x 3/4

= 15/32

Answer:

\(\frac{15}{32\\}\)

Step-by-step explanation:

\(\frac{5}{8}\) ÷ \(\frac{4}{3}=\)

\(\frac{5}{8}*\frac{3}{4}=\)

\(=\frac{15}{32}\)

Hope this helps

The amount more in income tax that Cho pays than Helen each month would be £56.

First, find Helen's yearly salary :

= 1, 720 x  12

= £ 20, 640

Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.

Cho 's monthly tax would be:

= (( 24, 000 - 12, 570 ) x 20 % ) / 12

= £ 190. 50

Helen's monthly tax :

= (( 20, 640 - 12, 570 ) x 20 % ) / 12

= £ 134.50

The difference is therefore :

= 190. 50 - 134.50

= £56

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Answer:

\(8.5x+4y=99.5,\ x+y=17\)

Step-by-step explanation:

\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)