If 70% of a class is girls, and there are 30 students in the class; how many boys are in the class?

Answer:

10) Exact Answer: 36

Estimate: 36

11) Exact Answer: 2001

Estimate: 1900

Step-by-step explanation:

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. We know that any "hundred" number is easily divisible by 5. Therefore, 900/5 = 36.

It is possible for the estimate to be the same as the exact answer.

10a) To find the exact answer, simply divide the given numbers.

10b) To find the estimated answer, use compatible numbers. There is no pattern we can look for, so round to the nearest whole number.

We know that if we rounded .38 to 0 or 1, the answer would not be nearly as close as if we rounded .38 to .4.

Therefore, 760/.4 = 1900

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[tex]\bf \stackrel{mixed}{-3\frac{3}{8}}\implies -\cfrac{3\cdot 8+3}{8}\implies \stackrel{improper}{-\cfrac{27}{8}}~\hfill \stackrel{mixed}{-1\frac{3}{4}}\implies -\cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{from left to right}}{-\cfrac{\stackrel{9}{~~\begin{matrix} 27 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{4}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\times -\cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\div -\cfrac{7}{4}}\implies \cfrac{9}{4}\div -\cfrac{7}{4}[/tex]

[tex]\bf \cfrac{9}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\times-\cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{7}\implies -\cfrac{9}{7}[/tex]

Answer:

420 minutes

Step-by-step explanation:

1 hour = 60 minutes

7 * 1 hour = 7 * 60 minutes

7 hours = 420 minutes

We know that 1 hour = 60 minutes

To find how many minutes is in seven hours, we can multiply 60 by 7 and we will get a product of 420.

1 hour = 60 minutes

2 hours = 120 minutes

3 hours = 180 minutes

4 hours = 240 minutes

5 hours = 300 minutes

6 hours = 360 minutes

7 hours = 420 minutes

Let r = amount customer gets back

r = 1000 - (1000)(0.03)

r = 1000 - 30

r = $970

Answer:

The answer is -3.

Step-by-step explanation:

-3(-3+2)-6

First solve the parenthesis. -3+2= -1.

-3(-1)-6

-3 times -1 is 3. Two negatives always equal a positive.

3-6 = -3.

Answer:

-2a²

Step-by-step explanation:

The question is  2a × -a

This means 2a(-a)

= -2×(a×a)

=-2(a²)

=-2a²

Answer:

A=1512

Step-by-step explanation:

The area of a rectangle with a length of 27 and a height of 56 is 1512.

Formula: A=wl

A=wl=56·27=1512

Answer: 1,512 units^2

Step-by-step explanation: To find the area of a rectangle, multiply the length by the width. 27 x 56 =1512. Since you are finding the area, the answer would be squared.

Answer:

corresponding angles

Step-by-step explanation:

Corresponding angles are in matching corners .

Both 5 and 6 are in the lower left corner

Answer:

8y³ + 6y² - 29y + 15

Step-by-step explanation:

Take each separate term in the second set of parentheses and multiply it by the terms in the first set of parentheses. Put them altogether, and you will arrive at the above answer.

I am joyous to assist you anytime.

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

The product of two numbers is the result you get when you multiply them together. So 12 is the product of 3 and 4, 20 is the product of 4 and 5, and so on.

multiplying corresponding terms,

[tex](4y-3)(2y^2+3y-5)\\8y^3+12y^2-20y-6y^2-9y+15\\8y^3+6y^2-29y+15[/tex]

Hence, the product is [tex]8y^3+6y^2-29y+15[/tex]

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Answer:

A

Step-by-step explanation:

Lets say x=1

y: 3(1)+1=4

x: 4(1)-1=3

Final answer:

The correct option is (D) (2,7). To solve the system of equations, set them equal to each other and solve for x, which is 2, and then substitute x back into either equation to find y, which is 7. Hence, the intersection point is (2, 7).

Explanation:

To find the solution to a system of equations when graphed, you look for the point where the two lines intersect. The given equations are y=3x+1 and y=4x-1.

Since both equations equal y, you can set them equal to each other to find the point of intersection:

3x + 1 = 4x - 1.

To solve for x, subtract 3x from both sides:

1 = x - 1.

Then, add 1 to both sides to isolate x:

x = 2.

To find the corresponding y value, substitute x into one of the original equations, let's use the first one:

y = 3(2) + 1,

which simplifies to y = 6 + 1 = 7.

Therefore, the solution to the system of equations and the point of intersection is (2, 7).

Answer:

25

Step-by-step explanation:

If the mean of the temperatures in the chart is 24° with standard deviation of 4º, there has been 25 years within one  standard deviation of the mean.

27° is the temperature value that is within one standard deviation of mean.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given

Mean of the temperatures in the chart [tex]\mu[/tex] [tex]\mew[/tex]= 24°

Standard deviation [tex]\sigma[/tex] = 4º

The lower and upper bound for temperature within one standard deviation of the mean is given as:

Lower bound =  [tex]\mu[/tex] -  [tex]\sigma[/tex] = 24° - 4º =  20°

Thus, the lower bound is  = 20°

Upper bound =  [tex]\mu[/tex] + [tex]\sigma[/tex] = 24° + 4º =  28°

Thus, the upper bound is  = 28°

Now, the temperature value between (Lower bound, Upper bound) that is (20°, 28°) is said to be within one standard deviation of the mean.

Hence, 27° is the temperature value that is within one standard deviation of mean.

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Answer:

4

Step-by-step explanation:

Start by multiplying both sides by 4.

[tex]\frac{1}{4} x-\frac{1}{8} =\frac{7}{8} +\frac{1}{2} x\\x-\frac{1}{2} =\frac{7}{2}+2x[/tex]

Next, combine like terms.

[tex]x-\frac{1}{2} =\frac{7}{2}+2x\\-\frac{1}{2} =\frac{7}{2} +x\\x=\frac{8}{2} \\x=4[/tex]

Answer:

Explanation:

The type of model that best fits the situation of a $500 raise in a salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case m = $500 and b is the starting salary: y = 500x + b.

Answer:

Choice 4.

Step-by-step explanation:

f(g(x))

Replace g(x) with x^2+8 since g(x)=x^2+8.

f(g(x))

f(x^2+8)

Replace old input,x, in f with new input, (x^2+8).

f(g(x))

f(x^2+8)

2(x^2+8)+5

Distribute:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

Combine like terms:

f(g(x))

f(x^2+8)

2(x^2+8)+5

2x^2+16+5

2x^2+21

Answer:

D

Step-by-step explanation:

Took the test

To solve (sin(x))^2 = 1/36, we find the arcsine of ±1/6. The solutions are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6) within the interval [0,2π].

To solve the equation (sin(x))^2 = 1/36 in the interval [0,2π], we first take the square root of both sides to get sin(x) = ±1/6. The sine function oscillates between -1 and 1 every 2π radians, which means that we are looking for angles where the sine value is ±1/6.

To find the specific angles, we use the arcsine function or inverse sine function. The principal value of sin⁻¹(1/6) gives us one of the solutions, and considering the symmetry of the sine function, the other solutions can be found in the second and fourth quadrants, where the sine function is positive and negative, respectively.

The solutions to sin(x) = 1/6 in the interval [0,2π] are x = sin⁻¹(1/6) and x = π - sin⁻¹(1/6). For sin(x) = -1/6, the solutions are x = 2π - sin⁻¹(1/6) and x = π + sin⁻¹(1/6). Thus, the solutions to the original equation (sin(x))^2 = 1/36 within [0,2π] are sin⁻¹(1/6), π - sin⁻¹(1/6), 2π - sin⁻¹(1/6), and π + sin⁻¹(1/6), all of which can be calculated to find the exact values.

Answer:

Option A is the correct answer.

Step-by-step explanation:

Period of simple pendulum is given by the expression,

            [tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]

Where l is the length of pendulum, g is acceleration due to gravity.

Here given for Venus

         Period, T = 2.11 s

        Length of pendulum, l = 1 m

     We need to find acceleration due to gravity, g

Substituting

            [tex]2.11=2\pi \sqrt{\frac{1}{g}}\\\\\sqrt{g}=\frac{2\pi}{2.11}\\\\g=8.87m/s^2[/tex]

Acceleration due to gravity of Venus = 8.9 m/s²

Option A is the correct answer.

Answer:

5.

Step-by-step explanation:

1 1/3 * 3 3/4

= 4/3 * 15/4

= 60/12

= 5.

First we simplify,

[tex]1\dfrac{1}{3}\cdot3\dfrac{3}{4}[/tex]

to

[tex]\dfrac{4}{3}\cdot\dfrac{15}{4}[/tex]

Then we continue simplifying,

[tex]

\dfrac{4\cdot15}{4\cdot3}=\dfrac{15}{3}=\boxed{5}

[/tex]

Hope this helps.

r3t40

Answer:

Option C is correct.

Step-by-step explanation:

-x+3y=2

4x-2y=22

In matrix form is represented as:

[tex]\left[\begin{array}{cc}-1&3\\4&-2\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{c}2&22\end{array}\right][/tex]

AX=B

[tex]X = A^{-1}B[/tex]

[tex]A^{-1} = |A|/Adj A[/tex]

|A| = (-1)(-2)-(3)(4)

|A| = 2-12

|A| = -10

Adj A = [tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]

A^-1 = -1/10[tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]

A^-1 = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex]

X= A^-1 B

X = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex][tex]\left[\begin{array}{c}2&22\end{array}\right][/tex]

X=1/10[tex]X=1/10\left[\begin{array}{c}2*2+3*22\\4*2+1*22\end{array}\right]\\X=1/10\left[\begin{array}{c}4+66\\8+22\end{array}\right]\\X=1/10\left[\begin{array}{c}70\\30\end{array}\right]\\X=\left[\begin{array}{c}70/10\\30/10\end{array}\right]\\X=\left[\begin{array}{c}7\\3\end{array}\right][/tex]

So, x = 7 and y =3

Hence Option C is correct.

Answer:

7

Step-by-step explanation:

right on edge

Answer:

964.62

Step-by-step explanation:

Let x = the original price

35% less than means we pay 65% of  the original price

627 = 65% x

Changing to decimal form

627 = .65x

Divide each side by .65

627/.65 = .65x/.65

964.6153846 =x

Rounding to the near cent

964.62

Answer:

[tex]\large\boxed{y>\dfrac{5}{2}x-3}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

We have dotted line (<, >) and shaded region above the line (>, ≥).

Therefore your answer is:

[tex]y>\dfrac{2}{5}x-3[/tex] or [tex]y>\dfrac{5}{2}x-3[/tex]

Calculate the slope.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Put the coordinates of the given points from the graph:

(0, -3) and (2, 2):

[tex]m=\dfrac{2-(-3)}{2-0}=\dfrac{5}{2}[/tex]

Answer:

The correct answer would be option A, 21.37

Step-by-step explanation:

In order to find out the percentage change of price of a product, either increase of decrease, that is found by finding the change in the price and then divide it by the base price and then finding the percentage of that price. The whole process is as follows:

Original price of iPod: $210.95

New Price of iPod: $165.88

Decrease in the price of iPod: 210.95-165.88= 45.07

Now dividing decreased price with the original price we get:

45.07/210.95=0.213652

Now to find the percentage, we need to multiply it with 100

0.213652*100=21.3652% which is approximately 21.37%

Answer:

C 90

Step-by-step explanation:

Answer: OPTION B.

Step-by-step explanation:

You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:

[tex]m\angle 3=70\°[/tex]

You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:

[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]

Then:

[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]

Answer:

  F ≥ 45

Step-by-step explanation:

"No less than" means "greater than or equal to", so you can write the expression as ...

  F ≥ 45 . . . . . miles per gallon

Answer:

-1½ = b

Step-by-step explanation:

Combining all like-terms on the right side of the equivalence symbol will give you this:

4b + 6 = 0

- 6 -6

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

4b = -6 [Divide by 4]

b = -1½ [OR -1,5]

I am joyous to assist you anytime.

Answer:

54

Step-by-step explanation:

Answer:

54 square units

Step-by-step explanation:

In order to calculate the surface area of the prism you have to calculate the area of each face of the prism, and you have to remember the different formulas to calculate the areas:

[tex]Rectangle=Length*Width[/tex]

[tex]Triangle=\frac{Base*Height}{2}[/tex]

So you just have to insert the values into the formulas:

[tex]Rectangle1=4*3.5[/tex]

[tex]Rectangle1=14[/tex]

[tex]Rectangle2=5*3.5[/tex]

[tex]Rectangle2=17.5[/tex]

[tex]Rectangle3=3*3.5[/tex]

[tex]Rectangle3=10.5[/tex]

[tex]Triangle1=\frac{4*3}{2}[/tex]

[tex]Triangle1=6[/tex]

[tex]Triangle2=\frac{4*3}{2}[/tex]

[tex]Triangle2=6[/tex]

If you add up all the faces, you get the surface area of the prism:

14+17.5+10.5+6+6=54

Answer:

see below

Step-by-step explanation:

41

-4 ≤2+4x<0

Subtract 2 from all sides

-4-2 ≤2-2+4x<0-2

-4 ≤2+4x<0

Divide all sides by 4

-6/4 ≤4x/4<-2/4

-3/2 ≤x <-1/2

graph is attached

45

2x-3 ≤-4  or 3x+1 ≥4

Lets solve the left side first

2x-3≤-4

Add 3 to each side

2x-3+3 ≤-4+3

2x ≤-1

Divide by 2

2x/2  ≤-1/2

x  ≤-1/2

Now solve the right inequality

3x+1 ≥4

Subtract 1 from each side

3x+1-1 ≥4-1

 3x ≥3

Divide by 3

3x/3 ≥3/3

x≥1

So we have

x  ≤-1/2 or x≥1

see attached

Notice closed circles where there is a greater than equal to  or less than equal to

For this case we have the following polynomial:

[tex]-24a ^ 6b ^ 4-40a ^ 3[/tex]

We must find the greatest common factor of the terms of the polynomial.

The GCF of the coefficients is given by:

[tex]24 = 3 * 8\\40 = 5 * 8[/tex]

Then we look for the GFC of the variables:

We have then:

[tex]a ^ 6 = a ^ 3a ^ 3\\a ^ 3 = a ^ 3[/tex]

Finally rewriting we have: [tex]-24a ^ 6b ^ 4-40a ^ 3 = -8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]

Answer:

the complete factored form of the polynomial is:

[tex]-8a ^ 3 (3a ^ 3b ^ 4 + 5)[/tex]

Answer:

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

b) Point rules:

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

        x ≥ 0 and y ≥ 0

The resulting graph is attached.

Answer:

D

Thank me later!! Just did the test on edge