The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.

Which equation should she use?

k = 2Px2
k = k equals StartFraction one-half EndFraction P x squared.Px2
k = k equals StartFraction 2 P Over x squared EndFraction.
k = k equals StartFraction P Over 2 x squared EndFraction.

Answer:

To estimate the total weight of the pet food Adam buys, we can use benchmark fractions to compare the weight of the dog food (7/8 pound) and the weight of the cat food (1 3/4 pounds) to a benchmark fraction that we are familiar with.

We know that 1 whole pound is equal to 16 ounces. So, we can use this as a benchmark to estimate the weight of the dog food and cat food.

First, we'll convert 7/8 pound to ounces. 7/8 pound is equal to 7/8 * 16 = 14 ounces

Next, we'll convert 1 3/4 pound to ounces. 1 3/4 pound is equal to 1 * 16 + 3/4 * 16 = 16 + 12 = 28 ounces.

Now we can add the weight of the dog food and the cat food to get the total weight of the pet food Adam buys.

14 ounces + 28 ounces = 42 ounces

So, the total weight of the pet food Adam buys is approximately 42 ounces, which is roughly 2.6 pounds.

The estimate was made with benchmark fractions, which allows us to make a rough estimation of the weight of the pet food, but it's not as precise as the exact weight in pound or ounces.

The length of the longest side is solved to be 3.76 cm

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

The perimeter o the quadrilateral have a formula that add all the sides together, assuming the factor of the original length is x, the perimeter is solved by

9.6 = 3x + 5x + 6x + 9x

9.6 = 23x

x = 9.6 / 23

x = 0.4174

The length of the longest side

= 9x

= 9 * 0.4174

= 3.76 cm

3.76 cm is the length of the longest side

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Approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.

Given that:

Mean u = 74.04

Standard deviation S.D. = 9.75

Distribution of ages is mound-shaped and symmetric.

We have to find percentage of the respondent between 64.29 and 93.54 years old.

For 93.54

z-score = [tex]\frac{x-u}{S.D}[/tex]

Z score = (93.54 – 74.04)/9.75 = 19.5/9.75 = 2

For 64.29

Z score = (64.29 – 74.04)/9.75 = -9.75/9.75 = -1

Now p-value from z-table:

P(x<93.54) = p(z<2) = 0.97725

P(x>64.29) = p(z>-1) = 0.15866

Probability between 64.29 and 93.54 year old = .97725 – 0.15865

= 0.8186

Percentage of the respondent = 0.8186 * 100 = 81.8%

Therefore, approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.

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The length of the room are y2 – 5y = 750 , y(y – 5) + 750 = 0 and (y + 25)(y – 30) = 0

it is important to note that the formula for calculating the area of a rectangle is expressed as;

A = lw

Such that;

From the information given, we have that;

Length = y

Width = y - 5

Area = 750 square feet

Substitute the values into the formula

750 =y(y - 5)

expand the bracket

750 = y² - 5y

y² - 5y- 750 = 0

This is factorized to give;

(y + 250 (y - 30)

Hence, the expression is y² - 5y- 750 = 0

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Answer:

Step-by-step explanation:

let the number be x and y

x + y = 30 -----(1)

x = y + 15 -----(2)

y + y + 15 = 30

2y = 15

y = 7.5

x = 7.5 + 15 = 22.5

x= 22.5 , y = 7.5

The total wage can only be an integer multiple of the wage per person.

The number of people working in the factory on a particular day can be calculated by dividing the total wage by the wage per person. This can be expressed mathematically as:

Number of People = Total Wage ÷ Wage per Person

For the given scenario, the number of people working on the day when the factory paid 9225 can be calculated as:

Number of People = 9225 ÷ 7175

Number of People = 1.287

Since the number of people has to be a whole number, this means that there were 1 people working in the factory on the day when the factory paid 9225. This is because when the wage per person is the same for everyone, the total wage can only be an integer multiple of the wage per person.

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the measure of ∠ABE is 47°.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

ΔABE and ΔCEB both are congrurent trinalge.

∠ABE =∠ CEB

The ∠ CEB+ ∠CBE = 90

∠ CEB = 90-43 = 47

As ∠ABE =∠ CEB  =47°

So the measure of ∠ABE is 47°.

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Linear function would better model the data because as x increases, the y values change additively. The common difference of this function is approximately 159.

A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

For this problem, the function is classified as linear, as the difference between consecutive terms is of approximately 159, while the ratios are different.

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After 45 seconds they blink together again.

Least Common Multiple is a mathematical term. The smallest number that is a multiple of both of two numbers is called the least common multiple.

For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20.

Given:

One sign blinks every 9 seconds. The other sign blinks every 15 seconds.

Now, to find they blink together again we have to find the LCM of 9 and 15.

For 9 the lights will blink at seconds: 0, 9, 18, 27, 36, 45, 54, 63,

and, For 15 the lights will blink at seconds: 0, 15, 30, 45, 60, 75

Hence, they blink together at 45 seconds.

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Answer: 4 in

Step-by-step explanation:

Answer:

X= 7 1/6

Step-by-step explanation:

-3/4x-5=3/8

-Add 5 on both sides

-3/4x=43/8

-Divide 3/4 on both sides

-X= 7 1/6 (there is no way for this not to be a fraction or decimal.)

Answer:

780

Step-by-step explanation: The answer is 780!

If Neely has $1.73 in coins and he gives his friend 1 quarter and 3 nickel , then the value of coins he has left is $1.65   .

the value of number of coins Neely has is = $1.73  ;

he gives his friend "1 quarter" , and the value of 1 quarter in dollar is = $0.25

the amount left with Neely is = $1.73 - $0.25 = $1.48 ;

next he gave his friend "3 nickels" , and value of 3 nickels in dollars in $0.15 ;

So , the amount left with Neely is - $1.48 - $0.15 = $1.65  .

Therefore , the Neely is left with $1.65 value of coins .

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Answer:

58

Step-by-step explanation:

error: 64+2p = 180.  he missed 1 p.

so 2p =180-64

p = 58

The number of cups of soda Sidney will use for 15 cups of ice cream is 45 cups of soda.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

3.5 cups of ice cream = 10.5 cups of soda.

This means,

1 cup of ice cream = 3 cups of soda.

Multiply 15 on both sides.

15 cups of ice cream = 45 cups of soda.

Thus,

45 cups of soda are used.  

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For the table of values gives, the equation of line is obtained as y = 1/3x.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The coordinate points for cups of flour, x and loaves of bread y is given in the table.

The slope-intercept form of an equation is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

(3 - 2)/(9 - 6)

1/3

So, the slope point is obtained as m = 1/3.

The equation becomes - y =1/3 x + b

To find the value of b substitute the values of x and y in the equation -

2 = 1/3(6) + b

2 = 2 + b

b = 2 - 2

b = 0

So, the value for b is 0.

Now, the equation becomes -

y = 1/3x + 0

y = 1/3x

The graph is plotted for the equation.

Therefore, the equation is y = 1/3x.

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the values of m in the equation m^2 = 36 , is m= ±6.

A square root of a number is a value that, when multiplied by itself, gives the number. In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square is x.

here, we  have,

given that,

the equation m^2 = 36.

taking root on both side, we get,

m= ±6.

Hence, the values of m in the equation m^2 = 36 , is m= ±6.

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Using the arithmetic operations the balance amount for 28/03/20 and incoming amount for 29/03/20 is obtained as £ 747 and £ 210 respectively.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The statement of bank account is given.

On 25/03/20 the balance amount left in bank was £ 1200.

On 28/03/20 the outgoing amount from the bank was £ 453.

To find the balance amount for 28/03/20, use the arithmetic operation of subtraction -

Balance amount = Previous Balance - Outgoing Amount

Substitute the values in the equation -

Balance amount = 1200 - 453

Balance amount = 747

Therefore, the balance amount for 28/03/20 was £ 747.

Now, On 29/03/20 the balance amount left in bank was £ 957.

To find the incoming amount for 29/03/20, use the arithmetic operation of subtraction -

Incoming Amount = New Balance - Previous Balance

Incoming Amount = 957 - 747

Incoming Amount = 210

Therefore, the incoming amount for 29/03/20 was £ 210.

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The Area of the base of the basket is 10 ft².

Given,

Volume of basket = 15 cubic feet

h = 1.5 ft

V = πr²h

15 = πr² (1.5)

πr² = 15/1.5

πr² = 10 ft²

Area of base of the basket = 10 ft²

(or)

15 = πr² (1.5)

r = √15/π(1.5)

Simplifying the values, we can get radius of basket = 1.78

Then, area of base of basket = πr²

Substituting the values of π = 3.14 and r = 1.78 in above formula, we get,

Area of base of the basket ≈ 9.95 ft²

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A cylinder can be measured in two separate ways: volume and area. As area gauges an object's two-dimensional surface, volume gauges how much space an object takes up.

If the cylinder's height and base area are known, the cylinder's volume may be determined by multiplying the base area by the cylinder's height. By dividing the base's circumference by its height, one may get the cylinder's area.

Given,

Volume of basket = 15 cubic feet

h = 1.5 ft

V = πr²h

15 = πr² (1.5)

πr² = 15/1.5

πr² = 10 ft²

Area of base of the basket = 10 ft²

(or)

15 = πr² (1.5)

r = √15/π(1.5)

We may obtain radius of basket = 1.78 by simplifying the numbers.

Then, area of base of basket = πr²

By replacing the values of 3.14 and 1.78 in the formula above, we obtain,

Area of base of the basket ≈ 9.95 ft²

Therefore, The Area of the base of the basket is 10 ft².

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Equation with inversely proportional relation gives answer of the following questions :

1.  a.  w = k₁ / f                                b. f =60 ⇒ w = 8

2. a. B = k₂/ y                                  b. y = 5 ⇒ B = 2.08

1. Representation of the formula connecting :

w is inversely proportional to the variable f

a . w ∝ ( 1 / f )

⇒ w = k₁ / f  

where k₁ is the constant of proportionality.

When w = 40 , f = 12

40 = k₁ / 12

⇒ k₁ = (40)(12)

⇒ k₁ = 480

b . f = 60

Value of 'w' is equal to :

⇒ w= 480 / 60

⇒ w = 8

2. B is inversely proportional to the variable y

a . B ∝ ( 1 / y )

⇒B = k₂ / y

where k₂ is the constant of proportionality.

When B = 0.8 , y = 13

0.8 = k₂ / 13

⇒ k₂ = (0.8)(13)

⇒ k₂ = 10.4

b . y = 5

⇒ B= 10.4 / 5

⇒ B = 2.08

Therefore, the required values and formula to represents the inversely proportional relation are:

The above question is incomplete, the complete question is :

1. W is inversely proportional to f , When f = 12, w = 40

(a) Find a formula connecting w and f .

(b) Find the value of w when f = 60.

2. B is inversely proportional to y , When B = 0. 8, y = 13

(a) Find an equation for B in terms of y.

(b) Work out the value of B when y = 5

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The test-statistic (z-score) is 1.19984.

To find the test statistic (z-score) using the p-value, you will need to use the inverse of the standard normal cumulative distribution function (CDF), also known as the inverse normal function or the "normal inverse function." This function can be found using a calculator or a spreadsheet program with built-in functions, or you can use a table of standard normal probabilities to find the corresponding z-score for a given p-value.

For example, if the p-value is 0.05, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.645. This means that the test statistic (z-score) for a p-value of 0.05 is 1.645.

It's important to note that this method only works for a one-tailed test, for a two-tailed test you need to divide your p-value by 2 and then use the inverse normal function.

so, the p-value is 0.1151, you would look up the corresponding z-score in a table of standard normal probabilities and find that it is approximately 1.19984.

Therefore, the test-statistic (z-score) is 1.19984.

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The average speed of the ball which travelled 24 meters in 8 seconds is 3m/s.

Speed is simply referred to as distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Given the data in the question;

To determine the average speed of the ball, plug the given values into the above equation and simplify.

Speed = Distance / time

Speed = 24 meters / 8 seconds

Speed = 3m/s

Therefore, the speed is 3 meters per seconds.

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The probability that the mean loss from f-i-re is larger than $300 for an S-R-S of 1000 home owners is 0.3085.

This problem can be solved using the Central Limit Theorem, which states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough (typically if n > 30).

Since the population is strongly right-skewed and the sample size is large (n = 1000), we can assume that the sampling distribution of the mean loss from fi-re will be approximately normal.

The mean of the sampling distribution is equal to the population mean, and a standard deviation equal to the population standard deviation divided by the square root of the sample size. In this case, we have:

Populatio mean (μ) = $250

Population standard deviation (σ) = $5000

Sample size (n) = 1000

Sample mean = $300

Probability of sample mean > $300 = ?

Now, standard deviation of sample mean = σ / sqrt(n) = $5000 / sqrt(1000) = $158.11

Now, we need to standardize the sample mean using the z-score formula:

z = (sample mean- population mean) / (σ / sqrt(n)) = (300 - 250) / 158.11 = 0.316

Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than 0.316 to be approximately 0.3765 or about 37.65%.

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The expression -3(-3v^3+3-4w^2) after using the distributive property is  9v³ - 9 + 12w²

The distributive property of multiplication over addition is a mathematical method of expanding bracket mostly applied when you need to multiply a value by a sum.

This property of multiplication explains how to solve expressions that are in the form of a(b + c).

From the information given, we have the expression;

-3(-3v^3+3-4w^2)

To carry out the distributive multiplication , we need to remove the parentheses of the expression by taking the following steps, we have;

expand the bracket and take note of the mathematical signs, we get

-3(-3v³ + 3 - 4w²)

9v³ - 9 + 12w²

Note that we can no longer add the terms because they are not like terms.

Hence, the expression is 9v³ - 9 + 12w²

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The Probability that the next pair Michael takes out is black = 8 / 19

What is Probability?

Probability is deals with "occurrence of Random event. The value is expressed from 0 to 1".

According to the question,

Total number of pairs of socks = 8 + 12 =20

Probability of taking pairs of black socks,  P(B )= 8 / 20

Probability of taking pairs of white socks,  P(W) = 12 / 20

But after taking Black pair socks the total number socks = 19.

Hence, the Probability of taking Black pair socks from drawer is 8 / 19 .

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The value of w in the rhombus is 19 degrees

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

Angle CFD = 2w

Angle FED = 52 degrees

The figure is a rhombus

using the above as a guide, we have the following:

2w + 52 = 90

This is so because the angles in the base of the individual triangle are equal

Evaluate the like terms

2w = 38

Divide by 2

w = 19

hence, the solution is w = 19

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The number line which best conveys Gregg's situation is B.

line B is the answer and the image is attached,

Since Greg has calculated that his least or minimum speed should be 50 miles per hour ,

Then the line starts at 50 with the starting point shaded due to the at least notation.

Then at least means that,

Gregg may need to travel at a higher speed than 50, so the direction of the arrow moves to the right of the number line depicting a possible increase in Gregg's speed.

Therefore, the number line which best conveys Gregg's situation is B.

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