2. In a books sale, 1461 books were sold on Friday.
On Saturday 2396 books were sold.
a. How many books were sold on both days?
b. How many more books were sold on Saturday than on
Friday?

Answer:

To graph the inequality y ≤ x - 2 on the axes, you would:

Plot the line y = x - 2 on the graph. The line will be a straight line passing through the point (-2,0) and has a slope of 1.

Determine the direction of the inequality symbol. Since it is a less-than-or-equal-to symbol, we will shade the region that is less than or equal to the line.

Shade the region that is less than or equal to the line in the graph. In this case, the region above the line y = x - 2.

The line is solid, it's not dotted.

Note: The graph will be a straight line that is tilted towards the top right of the coordinate axes, the region above the line will be shaded.

Step-by-step explanation:

The student's final moment of inertia is 18.18 kgm².

The moment of inertia of an objecr is the property of an object which shows its ability to rotate.

Since a student is standing with her arms outstretched, on a platform that is rotating at 1.6 rev/s. She pulls her arms in and the platform now rotates at 2.2 rev/s. Her original moment of inertia (I0) is 25 kgm². To find the r final moment of inertia, we use the law of conservation of angular momentum.

The law of conservation of angular momentum states that for any rotation, angular momnetum is constant.

So, Iω = constant where

So, Iω = I'ω' where

Making I' subject of the formula, we have that

I' = Iω/ω'

So, substituting the values of the variables into the equation, we have that

I' = Iω/ω'

I' = 25 kgm² × 1.6 rev/s ÷ 2.2 rev/s

= 40 kgm²rev/s ÷ 2.2 rev/s

= 18.18 kgm²

So, the final moment of inertia is 18.18 kgm².

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An algebraic equation which represents this word description "Seven more than the quotient of a number b and 45 is greater than 5" is b > -90.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.

In order to translate this word problem into algebraic equation, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let the variable b represent the unknown number.

Translating the word problem into an algebraic equation, we have the following;

7 + b/45 > 5

By collecting like terms, we have the following:

b/45 > 5 - 7

b/45 > -2

By cross-multiplying, we have the following:

b > -2 × 45

b > -90

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The median of the trapezoids is given by QR = 23.5 and VW = 15.2

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the first trapezoid be represented as A

Let the second trapezoid be represented as B

Now , the median of the trapezoid M = ( 1/2 ) ( sum of longer base and shorter base )

Substituting the values in the equation , we get

a)

The length of longer base = 35.6

The length of shorter base = 11.4

So , the median of A is QR = ( 1/2 ) ( 35.6 + 11.4 )

On simplifying the equation , we get

The median of trapezoid QR = ( 1/2 ) 47

The median of trapezoid QR = 23.5

b)

The length of longer base = 19.1

The length of shorter base = 11.3

So , the median of B is VW = ( 1/2 ) ( 19.1 + 11.3 )

On simplifying the equation , we get

The median of trapezoid VW = ( 1/2 ) 30.4

The median of trapezoid VW = 15.2

Hence , the median of trapezoid is solved

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A conversion of this equation in standard form to slope-intercept is y = 4x/5 - 3.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

8x + 10y = -30

Making y the subject of formula in the above equation, we have the following:

10y = 8x - 30

y = 8x/10 - 30/10

y = 4x/5 - 3

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Using the created proportion for each set of similar triangles, the missing side lengths are 3√29 units and 24 units respectively

Similar triangles are triangles that have the same shape, but not necessarily the same size. Two triangles are similar if and only if they have the same shape, meaning they have the same angle measures.

For the 1st triangles, we can write the proportion as follows:

proportion = (√29)/5

(√29)/5 = x/15

x = 15 × (√29)/5

x = 3√29 units

Thus, the missing side length is 3√29 units

For the 2nd triangles, we can write the proportion as follows:

proportion = 12/13

12/13 = x/26

x = 26 × (12/13)

x = 24 units

Thus, the missing side length is 24units

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Answer:

$8

Step-by-step explanation:

Answer:

28.26 [tex]in^{2}[/tex]

Step-by-step explanation:

a = [tex]\pi r^{2}[/tex]

a = 3.14([tex]3^{2}[/tex])

a = 3.14(9)

a = 28.26

Answer:

12/5 = 2.4 miles

2.4 x (15/16) = 2.25 miles.

2.25, or 9/4 miles

Answer:

Step-by-step explanation:

D

It should be emphasized that this suggests that we are 90% certain that the mean GPA for all students at the institution is between 3.14 and 3.52

Sampling

If the confidence level were raised to 99%, something would happen to the interval's length, increasing it.

The difference between a 90% confidence interval based on a 200-person sample and the original 90% interval is that the latter is narrower.

Last but not least, having the students say their grades aloud could have introduced bias into Ellery's study, which is not taken into account by the margin of error. Some of them with lesser grades will start to lie as a result.

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Absolute value function f(x) = | x + 3 | written in piece wise function includes the piece  given by option B . x + 3, x > -3.

Function f(x) is represented as absolute value function:

f(x) = | x + 3 |

Absolute function is always positive when the included variable is greater than zero.

| x + 3 |  > 0

⇒ ( x + 3 ) > 0

Subtract three from both the sides we get,

⇒ x + 3 - 3 > 0 - 3

⇒ x > -3

Here piecewise function incudes the piece :

x + 3,  x > -3.

Therefore, the absolute function f(x) = | x + 3 | includes the piece after written in piecewise function form is equal to option B. x + 3,  x > -3.

The above question is incomplete , the complete question is:

Select the correct answer.

Consider this absolute value function.

f(x) = | x + 3 |

If function f is written as a piecewise function, which piece will it include?

A. x + 3, x > 3

B. x + 3, x > -3

C. -x + 3, x < -3

D. -x - 3, x < 3

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Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.

Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.

This is represented as follows:

t = k(l/p)

Where, k is the proportionality constant.

Given that, it takes 10 hours to paint 400 feet of fence with six workers.

Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:

10 = k (400 / 6)

10 = k (66.66)

k = 10 / 66.66

k = 0.15

Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:

t = (0.15) (1000 / 10

t = (0.15) (100)

t = 15

Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

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Answer:

HI = 9

Step-by-step explanation:

      HJ = HI + IJ

2x + 10 = x + 9 + 1

 2x - x = 10 - 10

      ∴ x = 0

∴ HI = x + 9

       = 0 + 9

       = 9

Statistical risk refers to the likelihood of an adverse event occurring, as determined through statistical analysis. This can include events such as financial loss, injury, or death. It is typically measured using probability, which is a value between 0 and 1 that represents the likelihood of an event occurring.

For example, in finance, the risk of an investment is often measured by the standard deviation of the returns over time. In healthcare, the risk of a particular treatment or procedure is often measured by the rate of complications or adverse events.

The board game you described, where the goal is to conquer the world, does not involve statistical risk. It is a game of strategy, and the outcome is determined by the players' decisions and actions, rather than by chance.

The long-run probability of making a particular kind of mistake is an example of statistical risk. For example, if a pilot has a history of making landing errors, we can use statistical analysis to determine the probability that they will make a similar mistake in the future.

The probability that a single flip of a coin will come up 'tails' is also an example of statistical risk. In this case, the probability of the coin landing tails is 0.5 or 50%.

In summary, Statistical risk is the likelihood of an adverse event occurring, as determined through statistical analysis. It is measured using probability, and it is used to understand and manage the risk in various fields such as finance, healthcare, and engineering.

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The number of people that attended the school play is given as follows:

The situation is modeled by a system of equations, for which the variables are given as follows:

There was a total of 937 people, hence:

a + s = 937.

s = 937 - a.

The total sales were of $1,109, hence:

2a + 0.75s = 1109.

Replacing s = 937 - a in the second equation, the number of adults is obtained as follows:

2a + 0.75(937 - a) = 1109

1.25a = 406.25

a = 406.25/1.25

a = 325.

Then the number of students is obtained as follows:

s = 937 - a

s = 937 - 325

s = 612.

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The area of an isosceles trapezoid is 45 square ft.

We have to evaluate the area of trapezoid.

The perimeter of an isosceles trapezoid is 40 ft.

The bases of the trapezoid are 11 ft and 19 ft.

The perimeter of an isosceles trapezoid = a + b + c + d

a, b, c and d all are sides of an isosceles trapezoid.

a + b + c + d = 40

According to question, c = d

11 + 19 + c + c = 40

30 + 2c = 40

Subtract 30 on both side, we get

2c = 10

Divide by 2 on both side, we get

c = 5 = d

The formula of area of an isosceles trapezoid is

A = [tex]\frac{1}{2}[/tex](a+b)h, where a and b are bases and h is the height.

We can see on the diagram that we can use Pythagorean theorem to find the height.

According to theorem;

[tex]c^2=a^2+b^2[/tex]

[tex](5)^2 = h^2+(4)^2[/tex]

25 = [tex]h^2[/tex] + 16

Subtract 16 on both side, we get

[tex]h^2[/tex] = 9

Taking square root on both side, we get

h = 3

The height of an isosceles trapezoid is 3 ft.

Now, the area of an isosceles trapezoid is

A = [tex]\frac{1}{2}[/tex](11+19)×3

A = [tex]\frac{1}{2}[/tex] × 30 × 3

A = 15 × 3

A = 45 square ft

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The negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

We need to find the solutions for the inequality k≤12

k lesser than or equal to twelve.

Which means the solution of the inequality are the values which are lesser than or equal to 12.

The solution of the inequality k≤12 is (-∞, 12]

All the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

Hence,  the negative values, zero and the positive numbers lesser than 12 and equal to twelve are solutions of inequality.

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Answer: No Solution is the answer

Step-by-step explanation:

Have a photo attached with the work

Step-by-step explanation:

Σ^n=1 -144 (1/2)n-1

This is a finite geometric series with n

=4, a₁-144, and r = 2.

S = a₁ (1-r") / (1 − r)

S-144 (1 - (1/2)) / (1 - 1/2)

S=-270

If you wanted to find the infinite sum (n

= ∞0)

:S = a₁ / (1 − r)

S-144/(1-1/2)

S=-288

After reflection over the x-axis the ordered pair is at (-4, 7).

When two different media come together at an interface, a wavefront might change direction so that it returns to the first medium, which is known as reflection.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

Here,

The reflection of point (-4, 7) across the x-axis is (-4, -7).

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Answer: It's the third down. (-1/-2) - PLEASE TAKE THIS WITH A GRAIN OF SALT. I'm not very good at this type of math.

Step-by-step explanation:

Answer:

X = 4

Step-by-step explanation:

We have to add like variables, so all the x variables will be added together. We get this:
-x + 35 = 31

Get x by itself.
-x = -4

Get rid of the negatives since what you do on one side you do to both sides.

x = 4

I hope this was able to help you out :D

16 (-x +x ) +19 + x = 31

16+19+x = 31

35+x = 31

x= -4

hey buddy i hope uh got an answer

If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet  .

le the side length of the big square board be = "x" ft ;

the side length of smaller square is = 17 ft ;

So , the area of the smaller square is = (side length) × (side length)

= 17 × 17

= 289 ft² .

and , the area of the larger square is = (x) × (x) ;

= x²  .

So , the approximate area of the remaining board is calculated as :

= x² - 289  ;

Therefore , area of remaining board is "x² - 289" .

The given question is incomplete , the complete question is

A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?

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The answer to each question are:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.

a). The probability that an insect of this type survives its first day is 1 - 0.2 = 0.8.

b). The probability that an insect of this type survives it's first three days is 0.8 * 0.8 * 0.8 = 0.512.

c). The probability that an insect of this type dies on its fourth day is 0.2.

d). The expected number of days that an insect of this type would survive is not determinable with the information given.

e). If 200 insects of this type are being studied in a laboratory, you would expect approximately 200 * 0.512 = 102.24 to be alive after the third day. Round down to 102 insects.

Hence, The answer to each question is:

a). probability of an insect of this type surviving its first day is 0.8

b). probability of an insect of this type surviving it's first three days is 0.512.

c). probability of an insect of this type dying on its fourth day is 0.2.

d). If 200 insects of this type are being studied in a laboratory, 102 to be alive after the third day.

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The probability that at least one of the next five dogs he sees is a German shepherd is 0.75.

We have from the question.

0,1, and 2: retrievers

3 and 4: terriers

5 and 6: German shepherds

7,8 and 9: other dogs

In these results, 5 and 6 represent a german shepherd "at least one of the next five dogs he sees is a German shepherd." this means that at least one of the five numbers is 5 or 6.

There are a total of 20 results among them; 12 results include at least one 5 or 6.

∴P = 12/20 = 0.75

Hence, the correct option is B.

--The given question is incomplete; the complete question is

"Ian often takes his dog to the park. He estimates that 30% of the other dogs he sees are retrievers, 20% are terriers, and 20% are German shepherds. He designs a simulation.  Let 0,1 and 2 represent retrievers. Let 3 and 4 represent terriers. Let 5 and 6 represent German shepherds. Let 7,8, and 9 represent other dogs. The table shows the simulation results. According to this simulation, what is the probability that at least one of the next five dogs he sees is a German shepherd?

A. 0.70

B. 0.75

C. 0.65

D. 0.60"--

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The perimeter of a rectangle measuring 4.1263cm long and 2.8315cm is 13.9 cm

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

Length = 4.1263 cm

Width = 2.8315 cm

The perimeter of a rectangle can be calculated using tge following equation

Perimeter = 2 x (Length + Width)

substitute the known values in the above equation, so, we have the following representation

Perimeter = 2 x (4.1263 + 2.8315)

Evaluate

Perimeter = 13.9156

Approximate

Perimeter = 13.9 to 3 significant figures

Perimeter = 13.916 to 3 decimal places

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The given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

If an inequality matching y > -ax + b is solved, area A will be shaded above a dashed line with a negative slope.

Such inequality exists between Options A and C.

The solution of an inequality that fits y ax + b will be below a solid line with a positive slope where region B is shaded (for some positive a).

The only option with the correct inequality symbol is Choice C.

We discover that choice C matches the graph when we closely examine it.

Region A matches y > -x+3 because the line with a negative slope has a slope of -1 and a y-intercept of 3.

Region B corresponds to y 2x -2 because the line with a positive slope has a slope of +2 and a y-intercept of -2.

Therefore, the given graph is represented by the following inequalities (C) y ≤ 2x − 2, y > −x + 3.

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Correct question:

In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

Graph of two intersecting lines. The line g of x is solid, and goes through the points 0, negative 2 and 1, 0 and is shaded in below the line. The other line f of x is dashed, and goes through the points 0, 3, 3, 0 and is shaded in above the line.

The graph represents which system of inequalities?

Group of answer choices

a. y > 2x − 3

y > −x − 3

b. y < 2x − 2

y < −x + 3

c. y ≤ 2x − 2

y > −x + 3

d. None of the above