solve 14A and 14B please

Kylar is a lifeguard at a swimming pool, The total number of hours in a single shift done by Kylar is 3 hours.

Let the total number of hours in a single shift be = A

Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts

The total length of equal shifts Skylar worked last week = 15 / 4 shifts

The total number of hours Skylar worked in the week = 11 1/4 hours

The total number of hours Skylar worked in the week = 45 / 4

Now , the equation will be

Total length of equal shifts Skylar worked last week is equal to total number of hours Skylar worked in the week.

So ,

Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week

On substituting the values in the equation , we get

Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )

On simplifying the equation , we get

A = ( 45/4 ) / ( 15/4 )

A = 45 / 15

A = 3 hours

Therefore, The total number of hours in a single shift done by Kylar is 3 hours.

Complete question: Skylar is a lifeguard at a swimming pool. Last week, they worked 3(3)/(4) equal -length shifts, because rain closed the pool early one day. Those shifts totaled 11(1)/(4) hours of work. How long is a single shift?

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Average rate of change for the given function is 2.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that the graph is a line. So the function is linear.

Average rate of change of a linear function is equal to the slope of the given function, and it will be a constant at any two points on the line.

We have two points from the line (-2, -3) and (1, 3).

Slope of a line with two points (x, y) and (x', y') is,

slope = (y' - y) / (x' - x)

Slope of the given function with two points (-2, -3) and (1, 3) is,

Slope = (3 - -3) / (1 - -2) = 6/3 = 2

Average rate is same value from x = 1 to x = 2.

Hence the average rate of change is 2 for the given function.

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If f′ is growing, the f graph is concave up on the interval. In the event that f′ is decreasing, the f graph is concave down on the interval. This has been obtained by using the concept of derivatives.

What are derivatives?

In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

Assume that f is differentiable on interval I.

If f′ is increasing, the f graph is concave up on I. In the event that f′ is decreasing, the f graph is concave downward on I. The graph of f is considered to have no concavity if f′ is constant.

Hence, concave up is when f' is increasing and when it is decreasing, it is concave down.

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Filling in the chart below with the interest and maturity future value is as follows:

Purpose               Principal  Interest Term (Days)  a) Interest  b) Maturity

Wedding Dress  $250.00      6%       75 days           $3.10          $253.10

College Books   $360.50     3.5%    180 days          $6.28         $366.78

The future value represents the compounded present value.

Compounding involves the interest of subsequent months computed on the accumulated interest.

The future value can be computed using an online finance calculator.

N (# of periods) = 75 days

I/Y (Interest per year) = 6%

PV (Present Value) = $250

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $253.10

Total Interest = $3.10

N (# of periods) = 180 days

I/Y (Interest per year) = 3.5%

PV (Present Value) = $360.50

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $366.78

Total Interest = $6.28

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Answer:

The answer is c. 30 cm, 40 cm, 50 cm. This set of measures could not be the side lengths of a right triangle, as it does not satisfy the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the square of the hypotenuse (50 cm) is not equal to the sum of the squares of the other two sides (30 cm and 40 cm).

Step-by-step explanation:

The number that is 1.5 standard deviations below the mean is 1.55 (rounded to three decimal places).

To find :  The number that is 1.5 standard deviations below the mean

We need to first calculate the mean and standard deviation of the random variable X.

First, let's find the mean. The mean, also known as the expected value, is calculated as follows:

[tex]Mean = (1 * 15 + 2 * 30 + 3 * 28 + 4 * 10) / 100 = 2.8[/tex]

Next, let's find the variance, which is calculated as:

[tex]Variance = ( ( (1 - 2.8)^2 * 15) + ( (2 - 2.8)^2 * 30) + ( (3 - 2.8)^2 * 28) + ( (4 - 2.8)^2 * 10) ) / 100 = 0.72[/tex]

Finally, the standard deviation is calculated as the square root of the variance:

[tex]SD = \sqrt{0.72} = 0.85[/tex]

Now that we have the mean and standard deviation, we can calculate the number that is 1.5 standard deviations below the mean:

[tex]Number = Mean - 1.5 * SD = 2.8 - 1.5 * 0.85 = 1.55[/tex]

So, the number that is 1.5 standard deviations below the mean is 1.55 (rounded to three decimal places).

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The complete question is :

A sample of 100 clients of an exercise facility was selected. Let X = the number of days per week that a randomly selected client uses the exercise facility.

X Frequency

0 2

1 13

2 31

3 29

4 11

5 7

6 7

Find the number that is 1.5 standard deviations BELOW the mean. (I also have to round the answer to three decimal places.)

∠DEF ≅ ∠FHG as, The other two corresponding angles are equal.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, Are two triangles DEF and FGH.

DE || FG so the m∠D = m∠F.

Therefore, The sides opposite to ∠D and ∠F are equal and they are

EF and GF.

Given, m∠E = m∠G>

Therefore, The measure of angle D is equal to the measure of angle F.

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The p-value in this example would be 1 - 0.99865 = 0.00135.

A p-value is a measure of how likely it is to observe a result from a statistical test, given that the null hypothesis is true. It is calculated by taking the probability of the observed result under the assumption of the null hypothesis, then subtracting this probability from 1.

Formula:

P-value = 1 - Probability(observed result | null hypothesis)

For example, if the observed result is that the mean of a sample is 5 and the null hypothesis states that the mean is 3, the p-value is calculated by taking the probability of observing a mean of 5 or greater under the assumption that the mean is 3. This probability can be calculated from a standard normal distribution table by looking up the z-score corresponding to the mean of 5 and subtracting it from the total area under the curve (which is equal to 1).

Therefore, the p-value in this example would be 1 - 0.99865 = 0.00135.

By interpreting the p-value, we can determine the likelihood that the observed result would occur given that the null hypothesis is true. In this example, the p-value of 0.00135 indicates that it is very unlikely that the mean of the sample would be 5 or greater if the true mean is 3. Therefore, we can reject the null hypothesis and conclude that the true mean is not 3.

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Step-by-step explanation:

I cannot see the diagram at the bottom, so I cannot tell you a correct answer

There are 200 teachers in a school.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100, also defines a fraction or a ratio in which the value of the whole is always 100

Given information is

25 % of the teachers teach basic math, there are 50 basic math teachers

To calculate how many teachers are there in the school.

Let the total number of teachers =c

Number of basic maths teacher=50

Percentage of teachers of basic math = 25

According to question

25% of x=50

0.25*x=50

x=200

Hence the total number of teachers is 200

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The required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The sample size is given as,
n = p × q × (Z/E)²

Assume the estimate for population proportion,
p = 0.5

Now,
q = 1 - p
q = 1 - 0.5
q = 0.5

Confidence level = 99%

Z value = 2.58
The margin of error,
E = 0.02

The sample size is given as,
Substitute the value in equation 1.
n = 0.5×0.5×(2.58/0.02)²

n = 4160

Thus, the required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

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He must anticipate drawing a red tile. 30 times minimum.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given this, Alex placed 8 blue tiles and 12 red tiles in a container. He plans to draw a tile, record its color, and replace it in the container before drawing another.

Let X be the number of times a red tile is drawn from the container

Number of red tiles = 12

Total tiles = 12 + 8 = 20

p = P(randomly drawing a red tile) = 12/20 = 0.6

n = 50 number of draws or trials

Since Alex replaces the tile before he draws the next tile, we can model

the distribution of X according to Binomial Distribution

Thus, X ~ Binomial with n = 50 and p = 0.6

The Expected value of a binomial variable is E(X) = np

E(X) = n * p

= 50 * 0.6

= 30

therefore,  he should expect to draw a red tile At least 30 times.

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The value of fraction in simplest form is, 1/1296.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

⇒ 1/6 with an exponent of 4.

Now, We can simplify as;

⇒ (1/6)⁴

⇒ 1 / 6⁴

⇒ 1/ 6×6×6×6

⇒ 1 / 1296

Thus, The value of fraction in simplest form is, 1/1296.

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Answer: $50

Step-by-step explanation:

F(x, y, y', y",..., y(n-1)) is the expression for the function f.

1. Rewrite the given differential equation as y (n) = f (x, y, y', y",..., y (n 1)).

2. Identify y as the dependent variable, y', y",..., y(n-1), as the derivatives of y up to order n-1. X is the independent variable.

3. The right-hand side of the equation, f(x,y,y',y",...,y(n-1)), provides the expression for the function f.f(x,y,y',y",...,y(n-1)) is the expression for the function f, where x is an independent variable, y is the dependent variable, and y', y",...,y(n-1) are y's derivatives up to order n-1. The right-hand side of the equation provides the expression for the function f when the differential equation is written as y (n) = f (x, y, y', y",..., y (n 1)). Consequently, f is a function of x, y, y', y",..., and y. (n-1). The differential equation is resolved using this expression for f.

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well, 100% - 20% = 80%, so the discounted price is really 80% of the original 20 bucks, what's 80% of 20?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 20}}{\left( \cfrac{80}{100} \right)20}\implies \text{\LARGE 16}[/tex]

To do this you would do

$20 times (20/100) to get $20*(.20) = $4 which is the discounted price.

%(Percent) means "a specified amount in or for every hundred." In this case 20 for every 100.

The equation of the line passing through the points (1, -9), and (-3, -9) is y = -9.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Points are (1,3) and (3,2)

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

m = 2 - 3 / 3 - 1

m = -1/2

The equation of the line is given as

y - y₁ = m (x - x₁)

y - 3 = -1/2(x - 1)
y = -1/2x + 1/2 + 3
y = -1/2x + 7/2

As point (0, a) lies on the line, so
a = -1/2(0) + 7/2
a = 7/2

Thus, the required value of a is given as 7/2 and the equaiton of the line is y = -1/2x + 7/2.

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If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , then the value of xy is (a) 1  .

The values of x and y are solutions to two equations:

⇒ y = x²   ....equation(1)

⇒ 2y + 6 = 2(x + 3)    ....equation(2)

To find the value of xy, we first need to find the values of x and y which satisfy both equations.

We can put value of y from the equation(1) into the equation(2) :

⇒ 2y + 6 = 2(x + 3)

⇒ 2x² + 6 = 2(x + 3)

⇒ 2x² + 6 = 2x + 6

⇒ 2x² - 2x = 0

⇒ 2x(x - 1) = 0

that means either "2x=0"   or "x-1=0" ;

⇒   x = 0  or x = 1 .

when x = 1  , we have y = (1)² = 1 .

So , the product is = 1 × 1 = 1 .

Therefore , the value of xy is (a) 1  .

The given question is incomplete , the complete question is

If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , what is the value of  xy ?

(a) 1

(b) 2

(c) 3

(d) 9

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On, solving the provided question, we can say that from the provided number line, the value of b is = 1

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

from the provided number line,

the value of b = 13/8 - 5/8 =

1.625 - 0.625 = 1

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c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

A quantity known as length has the ability to calculate approximate distance between two areas. In addition to height the breadth, it creates an object's length. Children will learn about length in math lessons to help them solve practical challenges both inside and outside of the classroom. the length or width that is possible to measured; a thing's greatest or longest dimension. 10 feet in length. Table of Metric units, Metric System Table: The length characteristic. The quantity or measurement between two points is the definition of length. In other words, a geometric arrangement or object's largest two or highest three dimensions.

given

Start by calculating the length of the base's diagonal using the Pythagorean theorem:

a² + b² = c²

Fill in the equation with the length and width:

8² + 3² = c²

64 + 9 = c²

73 = c²

c ≈ 8.54 cm

Using our estimated diagonals for the base and the height, we can now determine the prism's diagonal's length. Apply the same formula:

(8.54)² + 7² = c²

73 + 49 = c²

122 = c²

√122 = c

c = 11.05 ≈ 11 cm. When the diagonal length for the rectangular prism is given is to the nearest whole unit, the correct answer is B.

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Answer:

Step-by-step explanation:

solve what's in the parenthesis.

1,204-299=905

so....

905/1

answer is: 905.

if you would like, use a website called Desmos graphing calculator.

its a calculator of all subjects, and it graphs.

Answer:

4.5

Step-by-step explanation:

2 time 4.5 is 9

Answer: x=4.5

Step-by-step explanation:

2x=9

2*x=9, now flip the 2, and make it division.

x=9/2

x=4.5

She used 7.90 paint with white paint on her bedroom walls.

To solve such problems we must know about fractions and subtraction.

Fraction

A fraction is a way to describe a part of a whole, the amount of white paint Jane used is 7.4 pints.

Given to us,

Total paint used my Jane = 8.3 pints = 83/10 pints,

the amount of blue paint = 2/5 pints,

Amount of white paint

amount of white paint = Total paint used - the amount of blue paint

=83/10-2/5

=83/10-2*2/5*2

=83/10-4/10

=79/10

=7.9pints

Hence, the amount of white paint Jane used is 7.9pints.

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The solution to the inequality 5/w > 4/45 is given as follows:

w < 56.25.

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable. The difference is that the solution is composed by infinity values in a range of values, instead of a finite number of values.

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2 is the fifth root of 32.

Using the problem as a starting point, we may write the equation as x5=32 x 5 = 32. This equation has to have a solution. The log function can be used to both sides of the equation. Therefore, the right response is 2.

A. In mathematics, the term "root" refers to a number that, when multiplied by itself, equals the original number.. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.

[tex]\sqrt[5]{32}[/tex]

[tex]\sqrt[5]{2*2*2*2*2}[/tex]

= 2

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Answer:

Step-by-step explanation:

400x2% of that amont would equal 800

The characteristics of the absolute value functions in this problem are given as follows:

The absolute value function is defined by the following rule:

f(x) = |x - h| + k.

For which:

For item a, we have that h = -3, meaning that the function was shifted 3 units left, and then:

The vertex is at (h,0), as h = -3, while there was no change to k.

The domain is all real values, as is the standard for the absolute value function.

The range is [0, ∞), as there was no vertical shift.

For item b, we have that k = 2, meaning that the function was shifted 2 units up, and then:

The vertex is at (0,2), as k = -2, while there was no change to h.

The domain is all real values, as is standard.

The range is [2, ∞), due to the vertical shift of k = 2 moving the graph 2 units up.

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Answer:

D

Books Cost

10

$122.50

11

$134.75

12

$147

Step-by-step explanation:

The table format is all messed up but I was able to figure out the numbers.

Since 10 books cost $122.50, each book must cost $122.50/10 = $12.25

For 1 book => 10 x $12.25 = $122.50

For 11 books => 11 x $12.25 = $134.75

For 12 books => 12 x $12.25 = $147

Answer choice is D which perfectly fits the numbers