Consider the following frequency table representing the scores on a test.
Scores on a TestClass Frequency
30–46
10
47–63
3
64–80
13
81–97
12
98–114
12

Step 3 of 5 :

Determine the class width of each class.

Using the disk method, it can be concluded that the volume of the solid is 125π /3 cubic units.

Disk Method is a method used to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]. The volume of the solid is the integral of the area of the base times dx.

V = π ∫ Ax dx

From the question, we know that the base of the figure is a triangular region and the coordinates are (0,0), (5,0), and (0,5).

The square is perpendicular to the x-axis. Thus, we can find the side of the square, that is the straight line passing through (5,0) and (0,5) which meet the y = mx + b equation.

First, we determine the slope of the line (m).

m = (y₂ - y₁) / (x₂ - x₁)

   = ( 5 - 0 ) / ( 0 - 5 )    

   = 5 / -5

   = -1

To find b, we input the value of m into the equation for point (5,0):

y = mx + b

0 = -1*5 + b

0 = -5 + b

b = 5

So we got the side of the square:

y = mx + b

y = -x + 5

y = 5 - x

Thus the area of the square is:

A = side²

  = (5 - x)²

  = 25 + x² - 10x

The volume of the solid can be calculated as follows:

   V = π ∫ Ax dx

      = π ∫₀² (25 + x² - 10x) dx

      = π (25x + 1/3x³ - 5x² |₀⁵)

      = π (25*5 + 1/3*5³ - 5*5² - 0)

      = π (125 + 125/3 - 125 - 0)

      = 125π /3 cubic units

Thus, the volume of the solid is 125π /3 cubic units

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The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial,

P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).

To find the degree:

(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.

The polynomial has a degree of 99.

If we think about it intuitively,

Therefore, if we were to multiply it all out,

the leading word would be x⁹⁹.

The term's first derivative is 99x⁹⁸,

followed by 99(98)x⁹⁷,

and 99(98)(97)x⁹⁶.

And finally,

the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)

=99!

So, the 100th derivative will be zero.

Therefore, by the 100th derivative, all terms will cancel out.

100th derivative will be zero.

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Option C. They will walk 9 laps and run 15 laps for a total of 24 miles.

The table is given as Walk (laps) 3 B 15

Run (laps) 5 10 D

Total (laps) A C 40

The total for walk and run is 3 + 5 = 8

Walk is 3

Run is 5

We are to find the laps of both categories with respect to the total distance of 24 miles

for walk = 3/8 * 24

= 9

For run we would have 5 / 8 * 24 = 15

Hence They will walk 9 laps and run 15 laps for a total of 24 miles.

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Answer:

Look below

Step-by-step explanation:

Sale prince is $300

the commission is 3/4%

Commission amount is $2.25

Price + commission $302.25

Price - commission $297.95

I hope this gives you the answer you where looking for

The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)

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

The graph

The function of the graph is a combined function (c . d)(x)

To calculate (c . d)(4), we trace the point x = 4 to the curve

So, we have

(c . d)(4) = -12

See attachment for the graph

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Answer: x = 13

Step-by-step explanation:

First you have to move 15+ to the other side to 28.Then when 15+ moves to the other side it will be 15-. After that you subtract 28 with 15 that will make 13. So x is equal to 13.

By numbers:

15+x=28

x=28-15

x=13

Answer: To find the area of a rectangle, you can use the formula:

Area = Length x Height

In this case, the length is given in cm and the height is given in mm. Therefore, you need to convert the length to mm before you can calculate the area.

1cm = 10mm.

So, 8.2 cm = 8.2 x 10 = 82mm

Now you can find the area of the rectangle:

Area = Length x Height = 82mm x 42mm = 3,444 mm^2

So, the area of the rectangle is 3,444 mm^2

Step-by-step explanation:

Answer:

the equivalent algebraic expression is -2x -8 after applying the distributive property.

Step-by-step explanation:

The distributive property states that for any real numbers a, b, and c, a(b+c) = ab + ac.

To apply the distributive property to the expression -2(x-4), we can distribute the -2 across the parenthesis, like this:

-2(x-4) = -2x + (-2)(-4)

Simplifying the last part of the expression:

-2(x-4) = -2x -8

So, the equivalent algebraic expression is -2x -8 after applying the distributive property.

Answer:

All you have to do is divide by -2 on both sides. You're trying to get x by itself, so divide by a number by cancels itself out. Don't forget the negative sign as well, or else you'll be left with -x instead of just x. A positive number divided by a negative number will become negative.

-2x=8

x=-4

The length of the perimeter will be 121/7 cm.

Given is that a soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. The label touches end to end with no overlap.

The length of the label will be its perimeter. We can write -

P = 2πr

P = 2 x 22/7 x 11/4

P = 2 x 22/7 x 11/4

P = 22/7 x 11/2

P = 11 x 11/7

P = 121/7

Therefore, the length of the perimeter will be 121/7 cm.

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The door frame is not rectangular.

If the door frame is rectangular, the sum of the square of the height and the width would be equal to the square of the diagonal.

Height² + width = diagonal²

213² + 92²

45,369 + 8,463 = 53,833

231² = 53,361

53,833 ≠ 53,361

The door frame is not rectangular because the sum of the height and the width is not equal to the diagonal.

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By constructing 95% confidence intervals for each simulation, we can be 95% confident that the true proportion of wins lies within the range of each interval.

A confidence interval is a set of values that, given a specific level of certainty, are likely to include a population parameter like a mean or proportion.

The interval is derived using data drawn from a sample of the population and is frequently presented as a range of values with a 95% confidence level.

The probability that the range of values contains the genuine population parameter is quantified by the confidence level.

In the case of a 95% confidence interval, for instance, it means that 95% of the intervals would contain the real population parameter if we sampled the same population more than once and calculated a confidence interval each time.

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Answer:

Step-by-step explanation:

the fourth one

Answer:

first three answers.

Step-by-step explanation:

each bottle is 1/4d. so all three are 3*1/4d

The angle θ measures 53.13⁰ with the east direction.

The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.

let the angle made be θ degree to the north of east from the post office to the grocery shop

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.

What does a tangent to any angle mean?

The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.

Let the angle formed between the post office and the grocery store be degrees to the north of east.

so tan θ = p/b

where p is perpendicular , b is base of the triangle

so tan θ = 3/4

=> θ = 53.13 degree

so the angle θ measures 53.13⁰ with the east direction.

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Complete question :

What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.

In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The first comparison is in terms of rato.

The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.

The second comparison in terms of percentage,

The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.

The third comparison is in terms of fractions.

The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.

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Answer:

A is ST, PR, and UV

B is rays SQ and QT

C is point Q

D is Points S, Q, and T

A solution to the given system of equations include the following:

x = -2.

y = -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

y = 2x + 3      .......equation 1.

y = 3x + 5      .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

2x + 3 = 3x + 5

By re-arranging and collecting like terms, we have the following:

3x - 2x = 3 - 5

x = -2.

For the value of y, we have the following:

y = 2x + 3

y = 2(-2) + 3

y = -4 + 3

y = -1.

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The two lines are perpendicular because the product of their slopes is equal to 1

The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line

Given here: The two lines  x-3y =15 and y = -3y + 4

Rewriting the given expressions in slop-intercept form we get

y=x/3-5

y = -3y + 4

The respective slopes are given as 1/3 and -3

Thus the product of the two slopes is 1/3×-3=-1

Hence, The given lines are perpendicular.

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An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).

The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.

The distributive property helps to solve mathematical expressions written in the form of a(b + c).

The amount Jessica makes per hour babysitting = $10

The number of hours of babysitting on Friday = 4 hours

The number of hours of babysitting on Saturday = 7 hours

According to the distributive property, the results from 'a' and 'b' below are the same.

a) 10(4 + 7) = 40 + 70 = 110

b) 10(4 + 7) = 10 x 11 = 110

Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.

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The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

What is mean ?

Mean can be defined as the ratio sum of the observations and total number of observations.

Given

set of data,

11, 8, 5, 11, 25

we have to find the range and standard deviation,

We know that,

range = max - min

here max = 25

min = 5

range = 25-5

range = 20

Standard deviation ,

= √( ( Σx^2 - (Σx)^2 / n ) / (n-1)  )

= √( ( Σ11^2+8^2+5^2+11^2+25^2 - (Σ60)^2 / 5 ) / (5-1)  )

= √( ( 956 - (3600)^2 / 5 ) / (5-1)  )

= √( ( 956 - 720) / 4  )

= √( 59 )

=  7.68

Hence, The Range  and standard deviation of the set of data 11, 8, 5, 11, 25 is 20 and 7.68 respectively.

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5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

2x² - 10x + 15 = x

2x² - 11x + 15 = 0

2x² -6x -5x + 15 = 0

2x(x-3)-5(x-3)=0

x=5/2, 3

The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.

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The system of inequalities is:

x + y ≥ 16

x*0.75 + y*2 ≤ 20

And its graph can be seen below, there we can see that one possible solution is (14, 2)

Let's define the variables:

x = number of apples.

y = number of mangos.

Kayden needs to buy not less than 16 items, so the first inequality is:

x + y ≥ 16

And he can spend at most $20, then:

x*0.75 + y*2 ≤ 20

The system of inequalities is then:

x + y ≥ 16

x*0.75 + y*2 ≤ 20

To graph it just graph the two lines and shade the region correspondent, for the first inequality shade the region above the line, for the second one shade the region below the line.

You should get.

The solution set is the region where both shaded areas intercept. Then a possible solution is:

x = 14

y = 2

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The function represented in Cartesian plane have the following features: Domain of function: - 4 ≤ x ≤ 2, Range of function: - 4 ≤ y ≤ 4. (Right choice: B)

In this question we find the representation of a function on Cartesian plane. There are two important hints to answer this question:

Then, by direct inspection we find the following results: Domain: - 4 ≤ x ≤ 2, Range: - 4 ≤ y ≤ 4.

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A compound event is a combination of multiple simple events that can occur simultaneously or independently. When talking about coin flipping, the sample space is the set of all possible outcomes of the experiment, which in this case is flipping a coin 3 times. In this case, the sample space is {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

Option A, You get exactly 2 tails, is a compound event because it consists of three simple events, THT, HTH, and TTH. These events can happen independently of one another and therefore, it is a compound event.

Option B, You get exactly 3 tails, is not a compound event because it only consists of one simple event, TTT. This event is not a combination of other simple events and is, therefore, not a compound event.

Option C, This is not an event, is not a valid option as it is not a possible outcome.

Option D, You get exactly 3 heads, is also a compound event because it consists of one simple event, HHH. This event can happen independently of other simple events and it is, therefore, a compound event.

Hence, options A and D are compound events as they are a combination of multiple simple events that can happen independently or simultaneously.

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The upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles is 72.2 gallons.

R(t) gallons per hour of water leak from a tank. The values of the rate at two-hour intervals are shown in the table below. As time went on, the rate decreased. A Riemann sum is used to determine the overall volume of water that has leaked out.

An integral representation of the rate function would be the amount of water. Estimation with the Riemann sum and left endpoints:

F(x) ≅ ∑f(xi-1)Δx where Δx=10/5 = 2 for this case and i = 1 to 5

W = (10.7 + 8.6 + 6.6 + 5.2 + 5.0)2

= 36.1•2

= 72.2 gallons

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

As it is a triangle , so we know that sum of all angles of a triangle = 180°

=> 44 + 53 + x = 180

=> 97 + x = 180

=> x = 180 - 97

=> x = 83°

Given expression ?/(2/5)=4 where ?=x gives x=8/5.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression ? ÷ 2/5 = 4

let x=?

Therefore,

              x=4*2/5

             x=8/5

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Answer:

no clue sorry I was not able to help

The mixture is 78.25% copper for the given alloy.

The percentage is defined as a ratio expressed as a fraction of 100.

To solve the given situation, we utilize material balancing before and after mixing.

Let the total amount of material after mixing is 320.

Let x be the percent copper of the mixture and applying copper balance,

⇒ (0.42)(120 g) + (1)(200) = 320x

Solving the above equation, we get the value as

⇒ x = 0.7825

Thus, the mixture is 78.25% copper.

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