A right triangle has one leg with length 7 and
another leg with length 8. What is the length of
the hypotenuse of the triangle?

a. 15
b. 113
c. 4 7
d. 7 8

Answer:A

Step-by-step explanation: 14% of the mothers work part-time in families where the father works part-time while 7% of the mothers work part-time in families where the father is not working.

Probabilities are used to determine how likely or unlikely an event is. From the 2-column table, it is twice as likely to get a family where the father and the mother work part-time than a family where the father doesn't work, and the mother works part-time.

We use the following representation:

[tex]FF \to[/tex] Father works full-time

[tex]FP \to[/tex] Father works part-time

[tex]FW \to[/tex] Father not working

[tex]MF \to[/tex] Mother works full-time

[tex]MP \to[/tex] Mother works part-time

[tex]MW \to[/tex] Mother not working

Next, we test each of the 4 options, till one of the options is true (see attachment)

Choice A:

The claim in choice A is that:

[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]

From the given table, we have:

[tex]P(FP\ and\ MP) = 0.14[/tex] ---- father works part-time and mother works part-time

[tex]P(FW\ and\ MP) =0.07[/tex] ---- father not working and mother works part-time

Put the above values in the following equation

[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]

[tex]0.14 = 2 \times 0.07[/tex]

[tex]0.14 = 0.14[/tex]

The above equation is true.

Hence, choice (A) is true

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Answer:

Step-by-step explanation:

both the length and the width of a square is the same measurement.

so if both measured to "x" then that means one side increase +7.

so one side is x + 7

and the other side decreased -4

so the other side is x - 4

area of square = length x width or just one of the sides to the power of 2

so (x+7) * (x-4) = Area

x^2 + 3x - 21 = area

Answer:

x^2-11x+24

Step-by-step explanation:

The area of a quad is lw

So, the formula would be (x-7)(x-4)

When you multiply it, it turns to be x^2 - 11x + 24

I think thats the answer

there are no choices so the answer might be in the wrong form

Answer:

In 4 years = $1,893.72

In 16 years = $3,810.53

years to contain $2,000 = 4.9371454128

years to contain $2,500 = 8.766692911

Step-by-step explanation:

In 4 years

A = 1,500 (1 + 0.06)^4

  = $1,893.72

In 16 years

A = 1,500 (1 + 0.06)^16

   = $3, 810.53

to find number of years

t = ln (A/P) / ln (1+r)

when A = 2,000

t = ln(2,000/1,500) / ln(1+0.06)

 = 4.9371454128 years

when A = 2,500

t = ln(2,500/1,500) / ln(1+0.06)

 = 8.766692911 years

PS: You can also use log in place of ln

The number of years it will take for the account to contain $2000 is 4.94 years while it will take 8.77 years to contain $2500.

Let:

PV = Present value = $1,500

r = Interest rate = 6%, or 0.06

n = number of years

FVn = Future value after a certain number of years

Therefore, we have:

The amount that will be in the account in four years can be calculated using the future value (FV) formula as follows:

FV4 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^4 = $1,893.72

Therefore, the amount that will be in the account in four years is $1,893.72.

The amount that will be in the account after 16 years can also be calculated using the future value (FV) formula as follows:

FV16 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^16 = $3,810.53

Therefore, the amount that will be in the account after 16 years is $3,810.53.

The number of years will it take for the account to contain $2000 can be calculated using the following formula:

n = (log(FV/PV)) / (log(1+r)) = (log($2,000/$1,500)) / (log(1+0.06)) = 0.1249387366083 / 0.0253058652647703 = 4.94 years

Therefore, the number of years it will take for the account to contain $2000 is 4.94 years.

The number of years it will take for the account to contain $2500 can be calculated using the following formula:

n = (log(FV/PV)) / (log(1+r)) = (log($2,500/$1,500)) / (log(1+0.06)) = 0.221848749616356 / 0.0253058652647703 = 8.77 years

Therefore, the number of years it will take for the account to contain $2000 is 8.77 years.

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Answer:

16 cups of sugar

Step-by-step explanation:

27 x 2 2/3 = 72  So 2 2/3 x 6 = 16  

If 6 cups of sugar is used to make 27 cookies. Then 16 cups of sugar is used to make 72 cookies.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

Savannah is baking cookies with a recipe that calls for 6 cups of sugar to make 27 cookies.

We need to find how much sugar she has to add to make 72 cookies.

To find this we have to form an equation.

Let x be number of cups of sugar to make 72 cookies

6/27=x/72

Apply cross multiplication

72×6=27x

432=27x

Divide both sides by 27

x=16

Hence, 16 cups of sugar is required to make 72 cookies.

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Answer:

The area is [tex]88cm^2[/tex]

Step-by-step explanation:

The formula for the area of a triangle is : [tex]\frac{base*height}{2}[/tex]

To work this out you would first need to work out the area of the square. You can do this by multiplying the length of 8 by the width of 8, this gives you 64. This is because the formula for working out the area is length multiplied by the width.

The next step is to work out the area of a triangle. You can do this by first multiplying the base of 6 by the height of 8, this gives you 48.

The next step is to divide 48 by 2, this gives you 24. this is because the formula is the same for a square, and that a triangle is half of a square with the same dimensions.

The final step is to Add the area of the square which is 64 by the area of the triangle which is 24, this gives you [tex]88cm^2[/tex].

1) Multiply 8 by 8.

[tex]8*8=64cm^2[/tex]

2) Multiply 6 by 8.

[tex]6*8=48cm[/tex]

3) Divide 48 by 2.

[tex]48/2=24cm^2[/tex]

4) Add 64 and 24.

[tex]64+24=88cm^2[/tex]

Answer:

Total paper required to wrap the gift without any overlaps: [tex]2700\ cm^{2}[/tex]

Step-by-step explanation:

Here, we need to find the total paper required without any sides overlapping to wrap the gift.

The gift is of cuboid type.

Given the following:

Length = 15 cm

Width = 30 cm

Height = 20 cm

Please refer to the attached figure.

We can infer that to find the paper required, we actually need to the find the total surface area of the cuboid.

Because the gift wrap will be done on the faces of gift (which is of cuboid shape).

Formula for Surface Area of Cuboid:

[tex]\text {Area = } 2 \times (\text{Length}\times \text{Width} + \text{Width}\times \text{Height} + \text{Length}\times \text{Height} )\\\\\Rightarrow 2 \times (15 \times 30 + 30 \times 20 + 15 \times 20)\\\Rightarrow 2 \times (450 + 600 + 300)\\\Rightarrow 2 \times (1350)\\\Rightarrow 2700 cm^{2}[/tex]

Hence, total paper required to wrap the gift without any overlaps: [tex]2700 cm^{2}[/tex]

Answer:

162

Step-by-step explanation:

1.8x10= 18

18x9=162

Answer: The Median because the distribution is skewed to the right

Step-by-step explanation:

Answer:

Option (2).It has a vertical translation by 2 units in the positive direction.

Step-by-step explanation:

Given question is not complete: find the  complete question with attachment

Errol's bike ride can be modeled by the equation,

[tex]d(t)=-\frac{1}{4}t+2[/tex]

Slope of the given equation = [tex]-\frac{1}{4}[/tex] which shows the rate of change of distance from Errol's house

Y-intercept = 2, shows the distance of the school from Errol's house

Let the equation that represents the distance of Daniel's home from the school is,

y = mt + b

Since speed of Daniel is equal to the speed of Errol, slopes of both the equations will be same.

Since y-intercept 'b' represents the distance from his home, b = 4

Now the equation will be,

[tex]d(t)=-\frac{1}{4}t+4[/tex]

Therefore, the graph representing the Daniel's equation will have a vertical translation by 2 units in the positive direction.

Answer:

72 and dignity is not important

Step-by-step explanation:

I think

Answer:

Vince began practicing piano at 11:15 P.M

He stopped at 11:35 P.M

=> He practiced in 35 - 15 = 20 mins = 1/3 hour.

=> 1/3 hour means 1/3 circle, the number of degrees the minute hand turned:

N = (1/3) x 360 = 120 deg (1 circle = 360 deg)

Hope this helps!

:)

Answer:

center: (0,0)

radius: 4 units

Step-by-step explanation:

the circle goes through points (0,4), (0,-4), (4,0), and -4,0).

if you notice, all four points are 4 away from the origin, (0,0). this means that there center is (0,0).

if you start at one of the points and go to the origin, it will be 4 units. that will be your radius

Answer: 0.71

Step-by-step explanation:

we have that cos(A) = 12/13

then:

A = Acos(12/13) = 22.62°

But A is in the fourth quadrant, so A is actually 22.62° + 180° = 202.62°

Then Sin(2A) = sin(2*202.62°) = 0.71

Answer:

±16

The principle value is 16

Step-by-step explanation:

sqrt(8) * sqrt(32)

We know that sqrt(a) sqrt(b) = sqrt(ab)

sqrt(8*32)

sqrt(256)

sqrt(16*16)

±16

The principle value is 16

Answer: 16

Step-by-step explanation:

[tex]\sqrt{8} *\sqrt{32}[/tex]

Combine

[tex]\sqrt{256}[/tex]

Simplify by finding the greatest perfect square

[tex]\sqrt{4*64}[/tex]

[tex]16[/tex]

Hope this makes sense

Answer:

Slope: 2

Y-intercept: (0,-7)

Step-by-step explanation:

2(x-3)=y+1

distribute the 2 through the parentheses

2x-6=y+1

2x+6=0+1

(change the y to 0)

2x-6=1

add 6 to both sides(+6 cancels out -6)

2x=1+6

divide both sides by 2

x=7/2 or x=3.5

hope this helps!

Answer:

2/15

Step-by-step explanation:

1/3 × 2/5 = 2/15

Answer:

60 pages

Step-by-step explanation:

1)100%-40%=60%(left to read)

2)So, 60%-36p.

         40%-(x)p.

3)60x=40*36

  60x=1440

       x=24(pages he has already read)

4)24+36=60 pages in total

Answer:

33.5 weeks

Step-by-step explanation:

Answer:

-220

Step-by-step explanation:

Answer:

784

Step-by-step explanation:

Answer:

784

Step-by-step explanation:

34+22=56

28÷2=14

56×14=784

Answer:

x = -1/24 = -0.042

Step-by-step explanation:

Step  1  :   Simplify  3/8

Step  2 :

Rewriting the whole as an Equivalent Fraction

Step  3  :

Calculating the Least Common Multiple

Equation at the end of step  3  :

 24x + 1

 ———————  = 0  

    8  

Last step:

Solving a Single Variable Equation :

5.2      Solve  :    24x+1 = 0  

Subtract  1  from both sides of the equation :  

                     24x = -1

Divide both sides of the equation by 24:

                    x = -1/24 = -0.042

Hope this helps.

Answer:

3x + 7y = −17

4x − 7y = 10

Add up both sides of 2 equations, then

7x = -7

=> x = 1

=> y =(3 x 1 - 17)/7 = -14/7 = -2

Hope this helps!

:)

the answer is V≈254.47

Answer:

529 units squared

Step-by-step explanation:

Answer:

Let's denote:

P(discount on 15 holidays) = P(A) = 0.87

P(discount on 100 weekends) = P(B) = 0.38

P(discount on 250 weekdays) = P(C) = 0.17

=> The probability of a discount of more than 10% for the randomly chosen day: P = P(A) x 15/360 + P(B) x 100/360 + P(C) x 250/360

          = 0.87 x 15/360 + 0.38 x 100/360 + 0.17 x 250/360

          = 0.26

Given she bought a machine with a discount of more than 10%, the probability that it was a weekend would be:

P  = 100/(100 + 250 + 15) = 0.27

Hope this helps!

:)

Answer:

1. 0.256

2. 0.406

Step-by-step explanation:

Total days:

15 + 100 + 250 = 365

P(more than 10% discount)

= (0.87×15/365) + (0.38×100/365) +(0.18×250/365)

= 1871/7300

0.2563013699

P(weekend/more than 10% discount)

= (0.38×100/365) ÷ (1871/7300)

= 760/1871

0.4061998931

Answer:

Yes because 3x5 is 15

Step-by-step explanation:

Answer:

The percentage of the heights that lie within one standard deviation of the mean height is 68%.

Step-by-step explanation:

Here it is given that the heights of adult males of a population are distributed normally.

The Empirical Rule states that in a normal distribution with mean µ and standard deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be divided into three parts:

        That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.

        That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.

        That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

So, the percentage of the heights that lie within one standard deviation of the mean height is 68%.

Answer:

128 tons can be processed in 8 hours.

Step-by-step explanation:

48 divided by 3 = 16 (to see how much tons are produced in 1 hr.)

16 x 8

  =128

Answer:

128 tons in 8 hours

Step-by-step explanation:

do 48 divided by 3 = 16      

to see how much tons get produced in an hr.

then when you do 16x8 which is 128

Answer:

5.18x10-5 is the correct answer

Step-by-step explanation:

Scientific notations are used to represent relatively large and small numbers.

The population per capita is (d) [tex]5.18 \times 10^{-5}[/tex]

The populations are given as:

[tex]Starbucks = 2010[/tex]

[tex]People = 38.8\ million[/tex]

The population of Starbucks per capita is calculated by dividing the population of Starbucks by the population of the people.

So, we have:

[tex]Per\ Capita = \frac{Starbucks}{People}[/tex]

Substitute known values

[tex]Per\ Capita = \frac{2010}{38.8\ million}[/tex]

Divide

[tex]Per\ Capita = 0.00005180412[/tex]

Approximate

[tex]Per\ Capita = 0.0000518[/tex]

Express as scientific notation

[tex]Per\ Capita = 5.18 \times 10^{-5}[/tex]

Hence, the population per capita is (d) [tex]5.18 \times 10^{-5}[/tex]

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Answer:

C  F

Step-by-step explanation:

Answer:

2/10 is equivalent to 1:5

6:30 is equivalent to 1:5

8 to 40 is equivalent to 1:5

Step-by-step explanation: