Which of the following is a composite number? A. 23 B. 11 C. 25 D. 19

Answer:

The way that you would be able to show -63 is 126/-2

The decimal 2.63 is not recurring. However, 2.63 can be expressed as the fraction 263/100 but it cannot be simplified further.

To express the repeating decimal number 2.63 as a quotient of two integers, we can use a straightforward method. First, let's identify the repeating part, which is the "63" after the decimal point. This part repeats infinitely. To convert this into a fraction, we need to set up an equation where x is the repeating decimal:

x = 2.63

Now, we'll subtract the non-repeating part to isolate the repeating part:

100x = 263 (multiplied both sides by 100 to eliminate the decimal)

Now, we'll subtract x from 100x:

100x - x = 263 - 2.63

99x = 260.37

To isolate x, we divide both sides by 99:

x = 260.37 / 99

Now, we can simplify the fraction:

x = 26037 / 9900

To express 2.63 as a quotient of two integers, it is equal to 26037/9900. This fraction can be simplified further if needed, but it is already in the form of two integers.

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Answer:

Jason's collection: 21 books.

Nathan's collection 24 books.

Step-by-step explanation:

Let number of books owned by Jason be j books and that for Nathan be n books.

So we have the system:

6j + 1/3 n = 134.........(1)

1/3j + n = 31................(2)

Multiply the first equation by -3. We get:

-18j - n = -402............(3)

Adding (2) + (3):

-53/3 j = -371

j = -371 * 3 / -53

j =  21.

Now substitute j = 21 in equation (2):

1/3(21) + n = 31

n = 31 - 7 = 24

n = 24.

We can use the law of cosines as follows:

[tex]7^2 = 8^2+10^2-2\cdot 8 \cdot 10 \cdot \cos(\theta)[/tex]

We can rewrite this equation as

[tex]49 = 164-160 \cdot \cos(\theta) \iff 160 \cdot \cos(\theta) = 115 \iff \cos(\theta)=\dfrac{115}{160}\approx 0.72[/tex]

For this case we have by definition of the Cosines Law that:

[tex]7 ^ 2 = 10 ^ 2 + 8 ^ 2-2 (10) (8) [/tex]* cosΘ

[tex]49 = 100 + 64-160[/tex]cosΘ

[tex]49 = 164-160[/tex]cosΘ

[tex]49-164 = -160[/tex]cosΘ

[tex]-115 = -160[/tex]cosΘ

[tex]115 = 160[/tex]cosΘ

cosΘ= [tex]\frac {115} {160} = 0.71875[/tex]

Rounding off we have, 0.72

ANswer:

Option C

Answer:

25.8

Step-by-step explanation:

114 ft ---> 31 inches

114 ft = 1368 inches

31/1368=0.02266081871 inch scale model

95 feet = 1140 inches, so 1140 * the scale factor of 0.02266081871= 25.83333..

This means, to the nearest tenth inch, the wingspan of the scale model is 25.8

The wingspan of the scale model is approximately 25.8 inches when calculated using the scale factor based on the model's length and the actual length of the plane, both in inches.

To find the wingspan of the scale model, we need to set up a proportion based on the scale between the actual size and the model size of the plane. First, we will find the scale factor by comparing the actual length of the plane to the length of the model in the same units:

Actual length of plane: 114 ft

Model length of plane: 31 inches

We must convert the actual length into inches because the model is measured in inches (1 foot = 12 inches) 114 feet × 12 inches/foot = 1368 inches

The scale factor is the ratio of the model length to the actual length.

Scale Factor = Model Length / Actual Length in inches = 31 inches / 1368 inches

Now, to find the wing span of the model, we use the same scale factor:

Actual wingspan of plane: 95 ft

95 ft × 12 inches/ft = 1140 inches (Actual wingspan in inches)

Model Wingspan = Actual Wingspan in inches × Scale Factor

= 1140 inches × (31 inches / 1368 inches)

We calculate this to get the model's wingspan in inches and round it to the nearest tenth of an inch:

Model Wingspan = (1140 × 31) / 1368 ≈ 25.8 inches

Therefore, the wingspan of the scale model is approximately 25.8 inches when rounded to the nearest tenth.

the answer would be D

The number of ways to choose 2 pairs of jeans from 5 is calculated using combinations, resulting in 10 different ways, corresponding to option A.

To determine the number of ways to choose 2 pairs of jeans from 5, we need to use the combination formula, which is defined as C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number of items to choose from, 'k' is the number of items to choose, and '!' denotes factorial.

In this case, n = 5 and k = 2. Therefore, the calculation becomes:

C(5, 2) = 5! / (2! * (5 - 2)!)
= (5 * 4 * 3 * 2 * 1) / ((2 * 1) * (3 * 2 * 1))
= (5 * 4) / (2 * 1)
= 20 / 2
= 10 ways.

So, there are 10 ways to choose 2 pairs of jeans from 5 pairs, which corresponds to option A.

You are right, it is in fact 8(15-m)

:D

Answer:

8(15 - m)

Step-by-step explanation:

The answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

[tex]x_{FirstCar}=x_o+v*t[/tex]

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

[tex]x_{SecondCar}=x_o+(v+14mph)*t[/tex]

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

[tex]RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph[/tex]

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

[tex]2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours[/tex]

Writing the equation:

[tex]264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph[/tex]

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

[tex]SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph[/tex]

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

[tex]FirstCarSpeed=41mph\\SecondCarSpeed=55mph[/tex]

Have a nice day!

Step-by-step explanation:

It is solved above

no of children and adult are let as x and y respectively

Galen sold 195 adult tickets and 645 children's tickets at the church carnival.

Let's assume that the number of adult tickets sold is x.

The number of children's tickets sold is 30 more than 3 times the number of adult tickets sold. So, the number of children's tickets sold would be 3x + 30.

The total amount earned from selling adult tickets would be 5x, and the total amount earned from selling children's tickets would be 3(3x + 30) = 9x + 90.

Since the total amount earned from selling all the tickets is $2820, we can set up the equation:

5x + 9x + 90 = 2820

Simplifying the equation,

14x + 90 = 2820

Subtracting 90 from both sides,

14x = 2730

Dividing both sides by 14,

x = 195

Therefore, Galen sold 195 adult tickets. And the number of children's tickets sold would be 3(195) + 30 = 615 + 30 = 645.

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Answer:

(x, y ) → (x - 8, y + 11)

Step-by-step explanation:

L(7, - 3) and L'(- 1, 8)

The x-coordinate 7 → - 1 , that is a shift of - 8

The y- coordinate - 3 → 8, that is a shift of + 11

The rule to translate LMN → L'M'N' is

(x, y ) → (x - 8, y + 11 )

Answer:

Room and board

30%

Step-by-step explanation:

If you look at the numbers in the table, you can easily see Room and board is the largest expense, with $127.50, three times more than the second place.

Now, to find the percent of that expense vs her income we just have to divide this big expense ($127.50) by the total income she has ($425).

% = $127.50 / $425 = 30%

So, that expense is 30% of her income, that's a big chunk, but it's normal for lodging expenses.

Answer:

42 1/2>42.500

Step-by-step explanation:

The expression (5y+4)*(-2y+6) simplifies to -10y² + 22y + 24 when multiplied out using the distribution method. Note, it's very important to use the correct syntax when writing mathematical expressions, clarity helps avoid mistakes.

Your question appears to be asking for the result of multiplying two polynomial expressions. However, your question contains a syntax error. It should properly be written as '(5y+4)*(-2y+6)'.

To find the result, you can use the distribution method also known as the FOIL method(First, Outer, Inner, Last). Let's walk through this step by step.

First: Multiply the first terms in each binomial: 5y*-2y=-10y²

Outer: Multiply the outer terms: 5y*6=30y

Inner: Multiply the inner terms: 4*-2y=-8y

Last: Multiply the last terms: 4*6=24

So we have -10y² + 30y - 8y + 24. Combine like terms to get the final answer: -10y² + 22y + 24.

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Answer:

the cost increased the most in 2006 - 2012

The cost increase at the greatest average rate in the time interval from 2006 to 2012 will be 1.833.

The average rapid change describes how quickly one quantity changes in comparison to another.

The table is shown.

It is clear that in six years, the rate of the cost of mailing a postcard will be 11. Then the average rate will be

Average rate = 11/ 6

Average rate = 1.833

Thus, the cost increase at the greatest average rate in the time interval from 2006 to 2012 will be 1.833.

More about the average rate link is given below.

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Use the slope-intercept form y = mx + b to find the slope m and y intercept 'b'

Y - Intercept: 5

(Slope:) -3/4

To find the y intercept you must make x zero and solve for y:

3(0) + 4y = 20

0 + 4y = 20

4y/4 = 20/4

y = 5

This means that the y intercept is:

(0, 5)

Hope this helped!

Answer:

The total liters of oil in the first container originally was 32 liters

total liters of oil in the second container originally was 64 liters

Step-by-step explanation:

Let

x----> total liters of oil in the first container originally

y----> total liters of oil in the second container originally

we know that

y=2x ----> equation A

(y-7)=3(x-13) ----> equation B

substitute equation A in equation B

(2x-7)=3(x-13)

2x-7=3x-39

3x-2x=39-7

x=32 liters

Find the value of y

y=2(32)=64 liters

B is your answer hope it helps

Answer:

x = 6

Step-by-step explanation:

Equation: x² - 12x + 36 = 0

Quadratic formula: ax² + bx + c = 0 --> x = (-b ± √(b² - 4ac))/2a

Substitute: x = (12 ± √(12² - 4 * 36))/2

Multiply: x = (12 ± √(144 - 144))/2

Subtract: x = (12 ± 0)/2

Solve: x = 6

Answer:

The value of x = 6

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

It is given that,

x² -12x + 36 = 0

To find the solution of given equation

Here a = 1, b = -12 and c = 36

x = [-b ± √(b² - 4ac)]/2a

 =  [--12 ± √((-12)² - 4*1*36)]/2*1

 = [12 ± √(144 - 144)]/2

 = 12/2 = 6

The value of x = 6

Answer:

(17 × 2) ÷ ( 5x × y )

Step-by-step explanation:

Difference = Division

The English phrase 'the difference of 17x2 and 5xy' translates to 17x2 - 5xy in algebraic expression.

The phrase 'the difference of 17x2 and 5xy' can be translated into an algebraic expression by replacing the words with their corresponding algebraic symbols. 'Difference' in mathematics means subtraction, '17x2' is a multiplicative expression and '5xy' is as well. So, the phrase can be translated to 17x2 - 5xy.

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Answer:

i would say b

Step-by-step explanation:

Answer:

b: cylinder

Step-by-step explanation:

because it's shaped like one

Your Answer is top right (:

Answer:

B

Step-by-step explanation:

The volume of a rectangular prism is the length times width times height.

V = LWH

V = (4√3)(3√6)W

V = 12√18 W

V = 36√2 W

If the volume is irrational, then W cannot have a radical that is half of a perfect square, because when multiplied by √2, that would yield a rational volume.  For example, √18 × √2 = √36 = 6.

Therefore, the answer must be B, because 12 is not half of a perfect square.

V = 36√2 (4√12)

V = 144√24

V = 288√6

Answer:

[tex]-5m^2+7m+8[/tex]

Step-by-step explanation:

We are given the equations

[tex](-m^2+6)+(-4m^2+7+2)[/tex]

We need to combine like terms. As there are no exponents or numbers outside the parenthesis, we can just drop them and add all like terms

[tex]-m^2+6-4m^2+7m+2\\\\-5m^2+7m+8[/tex]

Answer:

choice A is correct

Step-by-step explanation:

For a fair coin, the theoretical probability of obtaining heads or tails is 50%

Increasing the number of trials has the effect of making the experimental probability and theoretical probability equal

Answer:

It's the first option.

Step-by-step explanation:

Assuming it is a fair coin you would expect the experimental probability to get closer to 50%.  

50% is the theoretical probability  for a fair coin because there are 2 equally possible outcomes ,heads or tails.

Answer:

both sets have the same number of points

Answer:

It is d.

Step-by-step explanation:

They have different medians and modes.  The 7th grade results , as you would expect, show better results than the 5th grade data.

The trim is the frame minus the glass.

[tex]A = (5x+3)(x+6) - (4x^2 + 26x + 15)[/tex]

[tex] = 5x^2+33x+18 - 4x^2 -26x - 15[/tex]

[tex] =x^2+7x+3[/tex]

Answer: Choice A

Answer with Step-by-step explanation:

A window frame has a length of (5x + 3) inches and a width of (x + 6) inches.

Area of window frame=(5x+3)(x+6)

                                    = 5x(x+6)+3(x+6)

                                    = 5x²+30x+3x+18

                                   = (5x²+33x+18) square inches

area of the glass in the window is (4x² + 26x + 15) square inches.

Area of trim around the glass=Area of window frame-Area of glass

                                                = 5x²+33x+18-(4x²+26x+15)

                                                =5x²-4x²+33x-26x+18-15

                                                =(x²+7x+3) square inches

Hence, Correct option is:

A. (x² + 7x + 3) square inches

Answer:

10.8 miles

Step-by-step explanation:

You need to multiply 7.2 by .5 to get half of 7.2.

You now add this answer (which is 3.6) to 7.2 and the sum is 10.8.

This means your answer is 10.8 miles

The total cost y varies directly with the number of hours x needed to complete a job, with a direct variation coefficient of 100.

When analyzing the variation between two variables, specifically how y varies with x, we consider whether the relationship is direct or inverse. In the scenario provided, where it takes 10 workers 24 hours to do a job, if we let x represent the number of hours it takes to get the job done and y represent the total cost to the customer, we can establish that as the number of hours increases, the total cost also increases, assuming workers are paid by the hour. This suggests a direct variation.

Given that widget workers receive $10 per hour, the cost y to the customer for x hours of work would be 10 workers × $10 per hour × x hours. So, y = 10 × 10 × x = 100x. Hence, the relationship between y and x is directly proportional with a coefficient of variation of 100.

20/25 x 100 —> 2000/25 = 80%

Answer:

80%

Step-by-step explanation:

The portion of the trip through the mountains was 112.5 miles.

To find this, first, let's denote the time spent in the plains as [tex]\( t_1 \)[/tex] and the time spent in the mountains as [tex]\( t_2 \)[/tex]. Since the total trip took 3 hours and 48 minutes (which is[tex]\( \frac{3}{4} \) hours[/tex]), we have:

[tex]\[ t_1 + t_2 = 3.75 \][/tex]

The distance traveled in the plains is [tex]\( d_1 = 90t_1 \)[/tex] and in the mountains is[tex]\( d_2 = 37.5t_2 \)[/tex]. The total distance traveled is 300 miles, so:

[tex]\[ d_1 + d_2 = 300 \][/tex]

Substituting the expressions for [tex]\( d_1 \)[/tex] and [tex]\( d_2 \):[/tex]

[tex]\[ 90t_1 + 37.5t_2 = 300 \][/tex]

We can rearrange the first equation to express [tex]\( t_1 \)[/tex] in terms of [tex]\( t_2 \)[/tex]:

[tex]\[ t_1 = 3.75 - t_2 \][/tex]

Substituting this into the second equation:

[tex]\[ 90(3.75 - t_2) + 37.5t_2 = 300 \][/tex]

[tex]\[ 337.5 - 90t_2 + 37.5t_2 = 300 \][/tex]

[tex]\[ 337.5 - 52.5t_2 = 300 \][/tex]

[tex]\[ 52.5t_2 = 37.5 \][/tex]

[tex]\[ t_2 = \frac{37.5}{52.5} \][/tex]

[tex]\[ t_2 = \frac{5}{7} \] hours[/tex]

Now, to find the distance traveled in the mountains:

[tex]\[ d_2 = 37.5 \times \frac{5}{7} \][/tex]

[tex]\[ d_2 = 112.5 \] miles[/tex]

So, the portion of the trip through the mountains was 112.5 miles.

Complete question

A train averages a speed of 90 miles per hour across the plains and 37.5 miles per hour through the mountains. If a trip of 300 miles took 3 hour and 48 minutes, how much of it was through the mountains?

There is 336 ways the runners can finish first, second, and third.