A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.​

This is about absolute value inequalities.

The set of possible values of x that make the statement true are; x = {-2, -1, 0, 1}

We are told that when it is multiplied by 3 and 1 added to it, it is between - 8 and 7. This means it is greater than -8 but less than 7.

Thus;

3x + 1 > -8  - - - (eq 1)

3x + 1 < 7  - - - (eq 2)

3x + 1 > -8

Subtract 1 from both sides to get;

3x > -9

x > -9/3

x > -3

3x + 1 < 7

Subtract 1 from both sides to get;

3x < 7 - 1

3x < 6

x < 6/3

x < 2

Thus, we can write that;

-3 < x < 2

Thus, the set of possible values of x are; x = {-2, -1, 0, 1}

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Answer:

Actual growth of population - Birth - Death + In migration - Out Migration. ...

Explanation

Mackenzie has 1 dollar, 2 dimes, and 3 pennies.

Recall

Therefore, the total sum that Mackenzie has becomes;

Let d represent dimes and p represent pennies. Therefore, the total dimes and pennies Jorge could have becomes

Since both individuals have the same amount of money

Hence the equation is model as;

ANSWER:

Answer:

5/14

Step-by-step explanation:

convert mixed number to improper fraction:

1 1/4 = 5/4

3 1/2 = 7/2

5/4÷7/2

multiply first number by reciprocal of second number. To get the reciprocal, switch the numerator and denominator.

5/4*2/7

=10/28

simplify

= 5/14

Answer:

5/14

Step-by-step explanation:

Remember: Keep, change, flip

Keep: 1 1/4 = 5/4

Change: ÷ -> ×

Flip: 3 1/2 = 7/2 = 2/7 flipped

Original: 5/4 ÷ 7/2 = x

Keep change flip method: 5/4 × 2/7 = x

x = 10/28 which simplifies to 5/14

x = 5/14

Answer:

64

Step-by-step explanation:

A negative exponent means we first calculate the exponent, then we take the reciprocal.

The first step is to calculate \((\frac{1}{4})^3\). This is equal to \(\frac{1*1*1}{4*4*4}=\frac{1}{64}\). Then, we take the reciprocal. The answer is 64.

Answer:

64

Step-by-step explanation:

Use the definition of a negative exponent.

\( a^{-n} = \dfrac{1}{a^n} \)

A non-zero number, a, raised to the exponent -n equals the reciprocal of the number, 1/a, raised to the exponent n.

Here, a = 1/4. The reciprocal of 1/4 is 4.

Therefore, the number 1/4 raised to -3 is the same as 4 raised to 3.

\( (\dfrac{1}{4})^{-3} = 4^3 = 64 \)

The algebraic rule describes the translation of quadrilateral HIJK to quadrilateral H'I'J'K' is (x, y) => (x+1, y-8)

Translation is defined as the movement on a straight line

Given: quadrilateral HIJK to that translated H'I'J'K'

To determine the algebraic rule, we need to get the coordinates of  HIJK and H'I'J'K' and then subtract them to get the translation:

H => (x, y) = (4, 6)  |  H' => (x, y) = (5, -2)

I =>  (x, y) = (6, 4)   |  I' =>  (x, y) = (7, -4)

J => (x, y) = (4, 2)   |  J' => (x, y) = (5, -6)

K => (x, y) = (4, 2)  |   K' => (x, y) = (3, -6)

Using points H and H' (you can use any point):

The difference in x is 5-4 = +1 => x+1

The difference in y is -2-6 = -8 => y-8

Therefore, the algebraic rule describes the translation is (x, y) => (x+1, y-8). Option C is the answer

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Answer:

(x, y) => (x+1, y-8)

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

1/4

I hope this helps!

Answer:

Last option, D

Step-by-step explanation:

Its right. trust me

Answer:

0.0003125%

Step-by-step explanation:

Answer:

(16y)^2

16y^2

--> 256y

Step-by-step explanation:

Hello!

We have the expression:

Let's solve it as an addition:

8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 64

Solving it, we obtain 64.

Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

27 "

Explanation

Step 1

graph

to find the total height of teh staircase we need to add all teh rises, ( in other words we can multiply the length of a rise by the number of steps)

then ; let

number of steps=4

rise=.75

therefore, the answer is

27 "

I hope this helps you

x

Answer:

2 and angle that is left of 5

Step-by-step explanation:

Angle 2 is vertical from 110, and vertical angles are congruent. From this, we can figure out that 2 and 3 (they're supplementary) are 70. Angles 5 and 3 are Alternate Interior Angles, and therefore must be congruent. The one to the left of 5 is supplementary to it, and therefore must be 110. Your answers are angle 2 and the angle that is left of 5.

Answer:

5555555555555555555225313

Step-by-step explanation:

3

6

554

Answer:

$20.00

Step-by-step explanation:

24.00/6=4 so 24-4=20.00

Answer:

28

Step-by-step explanation:

let's assumed that

x = Jerry's age

y = Carrie's age

if Jerry 4 years older that Carrie

x = y + 4

x + y = 52

(y + 4) + y = 52

2y + 4 = 52

2y = 48

y = 24

x = y + 4

x = 24 + 4

x = 28

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

An array is a set of objects or values that are organized in a specific order. It is used in programming, mathematics, and other fields to make data manipulation and analysis easier.

When it comes to arrays in mathematics, it usually involves objects or numbers that are arranged in rows and columns.In order for a set of squares to be considered an array, it must meet certain requirements. These requirements are:All rows must have the same number of squares. All columns must have the same number of squares. Squares must be organized in an orderly manner. A set of squares that does not meet these requirements is not an array.

For example, if a set of squares is arranged in a random or disorganized manner, it cannot be considered an array because it does not meet the orderly requirement. Additionally, if the number of squares in each row or column is different, it cannot be considered an array because it does not meet the uniformity requirement.

Overall, it is important to remember that an array is a specific type of organization and cannot be applied to any random set of objects or values.

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The surface area is about 157.08 square feet. use formula for the surface area of a right cylinder  to get answer .

what is surface area ?

Surface area is the measure of the total area that the surface of a three-dimensional object occupies. In other words, it is the sum of the areas of all the faces or surfaces of the object. Surface area is usually measured in square units

In the given question,

The formula for the surface area of a right cylinder is:

S = 2πr² + 2πrh

where r is the radius of the cylinder, h is its height, and π is a mathematical constant approximately equal to 3.14159.

Substituting the given values, we get:

S = 2π(2.5)² + 2π(2.5)(7.5)

S ≈ 2π(6.25) + 2π(18.75)

S ≈ 39.27 + 117.81

S ≈ 157.08

Rounding this to the nearest hundredth, we get:

The surface area is about 157.08 square feet.

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Answer:

4E

Step-by-step explanation:

Answer:

Length= 37 and Width=25

Step-by-step explanation:

2(x+6)+2(2x-1)=124

2x+12+4x-2=124

6x+10=124

6x=114

x=19

(19)+6=25

2(19)-1=37

Answer:

x =19

25m by 37 meters

Step-by-step explanation:

The perimeter of a rectangle is given by

P =2(l+w)

P = 2( x+6  + 2x-1)

Combine like terms

P = 2( 3x+5)

Distribute

P = 6x+10

We know the perimeter is  124

124 = 6x+10

Subtract 10 from each side

124-10 = 6x+10 -10

114 = 6x

Divide by 6

114/6 = 6x/6

19 =x

One dimension is x+6 = 19+6 = 25 meters

The other dimension is 2x-1 = 2*19 -1 = 38-1 = 37 meters

12. Then X is 2. a continuous variable, 13. A subset of a population is 4) a sample, 14. The median is a better measure of central tendency than the mean if 2) the distribution is skewed.

Data gathering, organization, analysis, interpretation, and presentation are all topics covered in the field of statistics. It is hence customary to start with a statistical population or a model to be studied when using stats to solve a scientific, industrial, or social problem.

There are as of now two main types of statistical analysis: descriptive stats explains and visualizes the data you have, while inferential stats extrapolates the data you have to a larger population.

Statistical analysis has a number of advantages for businesses, including cost-cutting and increased productivity. The central tendency measure and the dispersion measure are fundamental concepts in stats.

Mean, median, and mode are the three primary central tendencies, and variance and standard deviation are the main central dispersions. The observational average is referred to as mean. When observations are arranged in order, the median represents the central value.

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Answer:

A. $154.00

Step-by-Step Explanation:

Okay so, the first step is to get 12% and move the decimal to the left twice like this:

.12

Then, multiply 175 by .12 like this:

175 * .12 = 21

Lastly, subtract 21 from 175 like this:

175 - 21 = $154

Answer:

147.4 or 6338/43=147.395348837

Answer:

142 meters.

Step-by-step explanation:

Area can be found by multiplying length*width.  This means that if you have an area, but no width, you can divide the area by the length, or vice versa.  To get the answer, you divide 852/6 to get 142.

Answer:

graph A.

Step-by-step explanation:

Answer:

row 3

row 2

6 and 10

Answer:

The answers are 1( row 3 ) 2( row 2 ) 3( 6 and 10 )

Step-by-step explanation:

I got it right on edge and also the person above me is correct have a wonderful day. (✿◠‿◠)

The probability that the husband has more than $150,000 of insurance is 1.4577

Looking at the row where the husband's insurance is between $50,000 and $100,000, we can see that there are a total of 329 policies.

Out of these policies, the number of policies where the husband has more than $150,000 of insurance is 249+30+25+176 = 480.

Therefore, the probability that the husband has more than $150,000 of insurance given that his insurance is between $50,000 and $100,000 is:

480/329 ≈ 1.4577

Rounded to four decimal places, the probability is 1.4577.

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Answer:

The answer is -14

Step-by-step explanation:

P.S Can I have brainliest?