There are 40 students in a class. 24 of those students are men. What percent of the class are women?

Answer:

[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

Step-by-step explanation:

Given equation:

[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]

[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]

Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:

[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]

[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]

[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]

[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]

[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]

The greatest common multiple of 60 and 72 is 6.

The given numbers are 60 and 72.

The greatest common factor (GCF) is a term used to describe the biggest number that can divide evenly into two or more numbers. Sometimes, this is also referred to as the greatest common divisor (GCD) or highest common factor (HCF). A factor is a smaller number that can divide evenly into that number.

Now, 60 = 2×2×3×5 and 72 = 2×2×2×3×3

The common factors are 2 and 3

So, the greatest common factor =2×3=6

Therefore, the greatest common multiple of 60 and 72 is 6.

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The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.

Total distance the Andersons are planning to take is 960-mile

They will travel 840 miles by car

Distance they will not travel by car = total distance - distance travelled by car

= 960 - 840 miles

=120 miles

Percentage formula = (value/ total value) x 100

percent of the distance will they not travel by car =

         (total distance - distance travelled by car) x 100/total distance

=((960 - 840)/ 960) x100

=(120/ 960) x 100

12.5

If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then ​the percentage of distance they will not travel by car is 12.5%

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Answer:

QR = 11

Step-by-step explanation:

P-Q-R-S

PQ = RS

PS = 23

PR = 17

so RS = PS - PR = 23 - 17 = 6

RS = PQ = 6

QR = PS - (RS + PQ) = 23 - (6 + 6) = 23 - 12 = 11

The percentage of observations which we expect to lie between 100 and 200 is 3.38%

Given, the mean is 150 and

standard deviation(sd) = 25

what percentage of observation lie between 100 and 200.

x + 1sd = 175

x - 1sd = 125

x + 2sd = 200

x - 2sd = 100

x + 3sd = 225

x - 3sd = 7

observation between 100 and 200 lie from x + 1sd

Therefore P(x) = (100-175)÷25

= -3

=3.38%

Hence the percentage of observations that lie between 100 and 200 is 3.38%

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Therefore the width of the rectangle is 33 yards

length of the rectangle is 196 yards.

Let the width of the rectangle be 'x'

Given the length of the rectangle = 35 yards less than 7 times the width

                                                          = 7x - 35

Given the area of rectangle = 6468 square yards

We know that area of rectangle = length * width

                                                       = (7x - 35 ) * x

By comparing both we get,

(7x - 35) * x = 6468

7x² - 35x - 6468 = 0

By dividing the equation by '7' we get

x² - 5x - 924 = 0

Factorize the above equation we get

x² - 33x + 28x - 924 = 0

x ( x - 33) +28 (x - 33 ) = 0

( x - 33 ) ( x + 28 ) = 0

∴ x = 33 , -28

Negative values are not consider

Therefore the width of the rectangle is 33 yards

length of the rectangle = 7(33) - 35

                                        = 231 - 35

                                        = 196 yards

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Using proportions, it is found that he needs 39.5 grams of protein each day.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

First we have to convert his weight to kg. Each lb has 0.453592 kg, hence his weight in kg is given by:

132 x 0.453592 = 59.87 kg.

Each day, he needs to consume 0.66 g for each kilogram in his body, hence the amount of protein that he needs to consume each day is given by:

0.66 x 59.87 = 39.5.

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Answer:

no solution

Step-by-step explanation:

Multiplying the second equation by 2 gives 2x-14y=38.

Adding this to the first equation, we get 0=9, and thus there is no solution.

Answer:

d

Step-by-step explanation:

Answer:The answer would most likely be c Read the problem carefully,find the question,understand the problem and find out what you know.

Answer: 12 electoral college votes

Step-by-step explanation:

4*100%=

4*100/100=

400/100=4

4*300%=

4*300/100=

1200/100=12 votes

Answer:

The ratio is 8:1 and it is a rectangle so x is 56

If on the similar image the sides are the same the other image will be aswell

Hope thie helps!

If you have any other question feel free to ask!

The Excel formulas to enter in cell B16 is = SUM(B12 : F12)

From the question, we can assume the following:

Using the sum function, we have:

Total = SUM(B12 : F12)

So, the formula to enter in cell B16 is:

= SUM(B12 : F12)

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2. The solution to the given system of equation is x = 1 and y = 6

3. The solution to the given system of equations is x = 1, y = 2

4. The simplified form of the expression is y²

5. The simplified form of the expression is 2

8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9. The multiplication yields x² - 4x - 96

10. The factored form of the expression is (x + 6)(x- 6)

11. The solutions to the given quadratic equation are x = 5 and x = -6

From the question, we are to solve the given system of equations

The given system of equation is

y = 10 - 4x      --------- (1)

2x + 3y = 20  --------- (2)

Substitute equation (1) into equation (2)

2x + 3y = 20

2x + 3(10 -4x) = 20

2x + 30 - 12x = 20

2x - 12x = 20 - 30

-10x = -10

x = -10/-10

x = 1

Substitute the value of x into equation (1)

y = 10 - 4x

y = 10 - 4(1)

y = 10 - 4

y = 6

Hence, the solution to the given system of equation is x = 1 and y = 6

3.

From the question, we are to solve the system of equations using the elimination method

The given system of equations is

5x + 2y = 9

-5x + 4y = 3

Add the two equations

5x + 2y = 9

-5x + 4y = 3

----------------------

0x + 6y = 12

6y = 12

y = 12/6

y = 2

Substitute the value of y into the first equation

5x + 2y = 9

5x + 2(2) = 9

5x + 4 = 9

5x = 9 - 4

5x = 5

x = 5/5

x = 1

Hence, the solution to the given system of equations is x = 1, y = 2

4. From the question, we are to simplify the expression

y⁻⁴(y³)²

First, multiply the exponents in (y³)²

(y³)² = y ³ ˣ ²

= y⁶

Thus,

The expression becomes y⁻⁴y⁶

Applying the multiplication law of indices

y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶

= y²

Hence, the simplified form of the expression is y²

5.

From the question, we are to simplify

∛8

First, express 8 in exponent form

8 = 2³

Thus,

The expression becomes

∛2³

Applying one of the laws of indices,

∛2³ = (2³)¹/³

Multiplying the exponents, we get

2¹

= 2

8.

From the question, we are to subtract the polynomial

(3x² + 5x - 8) - (2x³  - 4x + 3)

Subtracting

(3x² + 5x - 8) - (2x³  - 4x + 3)

3x² + 5x - 8 -(2x³  - 4x + 3)

Open the parentheses by distributing negative

3x² + 5x - 8 -2x³  + 4x - 3

Collect like terms

-2x³ + 3x² + 5x + 4x - 8 - 3

Simplify

-2x³ + 3x² + 9x - 11

Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11

9.

From the question we are to multiply

(x + 8)(x - 12)

Applying the distributive property

x(x -12) +8(x -12)

x² - 12x + 8x - 96

Simplifying

x² - 4x - 96

10.

From the question, we are to factor

x² - 36

This can be written as

x² - 6²

From the rule of difference of two squares, we have that

a² - b² = (a + b)(a - b)

Thus,

x² - 6² = (x + 6)(x- 6)

11.

From the question, we are to find the solutions for

x² - x - 30 = 0

Solve by factoring

x² - x - 30 = 0

x² + 6x - 5x - 30 = 0

x(x + 6) -5(x + 6) = 0

(x - 5)(x + 6)  = 0

∴ x - 5 = 0 and x + 6 = 0

x = 5 and x = -6

Hence, the solutions to the given quadratic equation are x = 5 and x = -6

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Answer: [tex]-7^2 * 5^4[/tex]

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

If x = -2, then plug -2 into the equation where the x is:

y = 3(-2) - 2

Then solve:

3 * -2 = -6

-6 - 2 = -8

So, y = -8

Answer:

A) y = 0.3x+24

B) 283.5 dollars

Step-by-step explanation:

A) To create an equation in slope-intercept form, we can start by using the numbers the problem gave us and represent them as coordinates. Generally, time is always our x-value.

(230,93)

(530,183)

Now that we have our two coordinates, we can plug them into the slope-intercept formula: y₂-y₁/x₂-x₁ to find our slope.

(183-93)/(530-230) = 0.3

Now that we have our slope, we can plug it into our equation.

y = 0.3x + b

To find our y-intercept, we can take either one of our 2 coordinates (x,y) and plug them into the equation to solve for b.

93 = 0.3(230) + b

93 = 69 + b

93 - 69 = b

b = 24

Now that we have found our y-intercept, we can plug it into b to complete the equation.

y = 0.3x +24

B) If 865 minutes are used, we can plug 865 into x in our equation to find the total cost.

0.3(865) + 24 = 283.5

The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

The given parameters can be represented using the following table of values

                              Mine 1 (x)              Mine 2 (y)   Available

Regular grade          6                            18             420

Low grade               16                             8              480

Operating cost      20500                     10200

Time                        55                              36

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 20500x + 10200y

Subject to:

6x + 18y >= 420

16x + 8y >= 540

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (26.5, 14.5)

This means that

Mine 1 hour = 26.5 hours

Mine 2 hour = 14.5 hours

Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours

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Answer:

its c

Step-by-step explanation:

Solution :-

As we know that,

Therefore ,

>> m = -2 - (-3) / -1 - (-8)

>> m = -2 + 3 / -1 + 8

>> m = 1 / 7

We have that the data are:

(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)

The slope is equal to the change in and with respect to change in X, or what rises when moving forward.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]

The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).

Introduce the values of x and y In the equation to find the slope.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]

The value of the expression when t=4 is 16

It should be noted that from the information given, it was stated that Mathes purchases 4 tickets for his family.

Therefore, the value of the expression when t=4 will be:

C = 4t

C = 4(4)

C = 4 × 4.

C = 16

Therefore, the value of the expression when t=4 is 16.

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The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .

Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.

Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.

The prime factorization of 6912 gives:

6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³

Hence the prime factors of 6912 are 2 and 3.

The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)

Therefore the cube root of 6912 is approximately 19.05 .

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Answer:

3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

when the nearest number from the right side is lower than 5 it just disappears and all of the numbers after that will disappear as well.

Answer: i think it might be 72

Answer:72

Step-by-step explanation:

The least common multiple is the smallest common(of equal value) number. we get this number by multiplying the two numbers by a number value till we get a common number between the two.

The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;

D: -4 ≤ n ≤ 5

A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.

Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;

[tex] - 4 \: \leftrightarrow \: 5[/tex]

The expression of the required set of numbers as inequalities is therefore;

The compound inequality is therefore;

D: -4 ≤ n ≤ 5

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Answer:

9

Step-by-step explanation:

Edge

Answer:20

Step-by-step explanation:

n x 40% =8

So n = 8 / 40%
n = 20

40,60,80,100,120,140,160,180,200 are the class boundaries.

The lower class boundary (LCB) is the LCL minus one-half the tolerance, and the upper class boundary (UCB) is the UCL plus one-half the tolerance. Class borders are the end points of an open interval that contains the class interval.

given that

8 classes for n = 75measurements

minimum value = 40

maximum value = 195

from the question

smallest class boundary = (maximum - minimum value) / n classes

= (195 - 40) / 75 = 19.375 = 20

round off the value means 20

using minimum value and smallest class boundary.

Hence, the 40,60,80,100,120,140,160,180,200 are the class boundaries.

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Disclaimer: the question is incomplete on portal. Here is the complete question.

Question: Use the information given to find a convenient class width. Then list the class boundaries that can be used to create a relative frequency histogram. (Round your class width up to the nearest multiple of 5. Use the minimum value as the smallest class boundary. Enter your class boundaries as a comma separated list.)

8 classes for  n = 75 measurements; minimum value = 40; maximum value = 195.

Answer:

15.6 in² (nearest tenth)

Step-by-step explanation:

Circumference of a circle

[tex]\large\boxed{C=2\pi r}[/tex]

Where r is the radius of the circle.

Given:

Substitute the given value into the equation for the circumference and solve for r:

[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]

Area of a circle

[tex]\large\boxed{A=\pi r^2}[/tex]

Where r is the radius.

Substitute the found radius into the equation for area and solve for A:

[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]

Therefore, the area of the circle with a circumference of 14 in is 15.6 in².