When Brooklyn runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 3 seconds. Using the empirical rule, what percentage of races will her finishing time be between 70 and 82 seconds?

Answer:

x = 8

Step-by-step explanation:

Given equation:

[tex]\dfrac{-2}{3} (x+12)+\dfrac{2x}{3} =\dfrac{-5x}{4} +2[/tex]

Start out by simplifying the distributive property on the left hand side.

[tex]\implies \dfrac{-2x}{3} + \dfrac{(-24)}{3} +\dfrac{2x}{3} =\dfrac{-5x}{4} +2[/tex]

Combine like terms on the left hand side.

[tex]\implies x\huge\text{(}\dfrac{-2}{3} + \dfrac{2}{3}\huge\text{)}+ \dfrac{(-24)}{3} =\dfrac{-5x}{4} +2[/tex]

Simplify the left hand side.

[tex]\implies x\huge\text{(}0\huge\text{)}+ \dfrac{(-24)}{3} =\dfrac{-5x}{4} +2[/tex]

[tex]\implies x\huge\text{(}0\huge\text{)} - 8 =\dfrac{-5x}{4} +2[/tex]

[tex]\implies0- 8 =\dfrac{-5x}{4} +2[/tex]

[tex]\implies-8 =\dfrac{-5x}{4} +2[/tex]

Subtract 2 both sides.

[tex]\implies-8 -2 =\dfrac{-5x}{4} +2 - 2[/tex]

[tex]\implies-10 =\dfrac{-5x}{4}[/tex]

Use cross multiplication.

[tex]\implies-10 \times 4 =-5x[/tex]

[tex]\implies-40 =-5x[/tex]

Divide -5 both sides.

[tex]\implies \dfrac{-40}{-5} =\dfrac{-5x}{-5}[/tex]

[tex]\implies 8=x[/tex]

Thus, the value of x is 8.

Answer:

x = 8

Step-by-step explanation:

Given equation:

[tex]-\dfrac23(x+12)+\dfrac23x=-\dfrac54x+2[/tex]

Multiply both sides by 3:

[tex]\implies -2(x+12)+2x=-\dfrac{15}{4}x+6[/tex]

Multiply both sides by 4:

[tex]\implies -8(x+12)+8x=-15x+24[/tex]

Expand brackets:

[tex]\implies -8x-96+8x=-15x+24[/tex]

Combine like terms:

[tex]\implies -96=-15x+24[/tex]

Add 15x to both sides:

[tex]\implies 15x-96=24[/tex]

Add 96 to both sides:

[tex]\implies 15x=120[/tex]

Divide both sides by 15:

[tex]\implies x=8[/tex]

Considering that the mile counter increases by 50 every hour, a linear function should be empathized.

A linear function is modeled by:

y = mx + b

In which:

In this problem, they start at mile 62, and the counter increases by 50 every hour, which is a fixed amount, hence a linear function should be used.

More can be learned about linear functions at https://brainly.com/question/24808124

Answer:

the

• the population of the first germ is represented by the function a(x) = (1. 3)+9

Answer:

  u = v = 14

Step-by-step explanation:

The ratios of side lengths in a 45-45-90 triangle are ...

  1 : 1 : √2

Here, the long side is 14√2, so is 14 times this basic ratio.

  1 : 1 : √2 = u : v : 14√2 = 14 : 14 : 14√2

This means ...

  u = v = 14

Answer:

Below in bold.

Step-by-step explanation:

The ratio of the sides in a 45-45-90 are 1:1:√2.

so V / 14√2 = 1 / √2

V = 14√2 / √2 = 14.

and U = V = 14 also.

Answer:

9.21954445729

Step-by-step explanation:

A^2 + B^2 = C^2

7^2 = 6^2 = 85

The square root of 85 is...

9.21954445729

Answer:

  200

Step-by-step explanation:

Of the apartments in the building, 20% are singles and 70% of those do not have balconies.

That is, (0.20 × 0.70) = 0.14 of the building's apartments are singles without balconies. That is 28 apartments. If A is the number of apartments in the building, this means

  0.14A = 28

  A = 200 . . . . . divide by 0.14

There are 200 apartments in the building.

Answer:

it's the last one, and the missing number is 70 (the P)

The expression that represents this scenario is 35/p = 70/100.

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

Given, Alex has 70% of her weekly paycheck automatically deposited into a savings account.

This week $35  is deposited,

∴ The expression that represents this situation is 35/p = 70/100.

learn more about numerical expressions here :

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Answer:

  c. 33.0%

  d. 14.5%

Step-by-step explanation:

For answering questions about percentages in different categories or combinations of categories, it is convenient to find the totals of rows and columns in the table. These totals are shown in the attached.

__

Students who surf total 32+65 = 97. Of those, 32 also skateboard. The requested percentage is ...

  32/97 × 100% ≈ 33.0% . . . . surfers who also skateboard

__

The total number of students is 166. Of those, the number who neither surf nor skateboard is 24. That percentage is ...

  24/166 × 100% ≈ 14.5% . . . . students who don't surf or skateboard

_____

Additional comment

a. 97/166 ≈ 58.4% surf

b. 89/166 ≈ 53.6% do not skateboard

__

This sort of table is called a "two-way table." One set of categories is represented in rows, another set is represented in columns. This table is filled with frequencies. Such tables can also display relative frequencies by dividing the entire table by the total of totals in the lower right corner.

Answer:

79-22=57.

Your answer is correct. You also have to fill in the second one (B)

Answer:

79-22=57

Step-by-step explanation:

I can explain on phone

Step-by-step explanation:

[tex]y = \frac{3}{4} x - 2[/tex]

is the required equation

I hope it helped you

Answer:

y = [tex]\frac{3}{4} x-2[/tex]

Step-by-step explanation:

y = mx + c

m = gradient= [tex]\frac{-5-(-2)}{-4-0}[/tex]= [tex]\frac{3}{4}[/tex]

c = y-intercept = -2

Answer:

B

Step-by-step explanation:

its b bc its inclusive and rhe others font make much sense

Answer:

2√13

Step-by-step explanation:

15-9 to find a^2, 4 is b^2, and then pythagorean thereoum, a^2+b^2=c^2.

Answer:

Step-by-step explanation:

The base of the triangle used to solve for x (Pythagorean Theorem) is 15 - 9 = 7

The height of the right triangle is 4 so now you have enought to solve for x

Givens

a = 7

b = 4

c = x

Equation

x^2 = b^2 + a^2

Solution

x^2 = 7^2 + 4^2

x^2 = 49 + 16

x^2 = 65               Take the square root of both sides

√x^2 = √65

Answer x = √65

The ship movement is an illustration of distance and bearing

The ship is 31.97 miles from its point of departure

The given parameters are:

See attachment for the image of the above parameters

The distance (x) from the point of departure is then calculated using the following cosine function

a^2 = b^2 + c^2 - 2bc * cos(Ф)

So, we have:

x^2 = 40^2 + 70^2 - 2 * 40 * 70 * cos(12)

Evaluate the exponent and the product

x^2 = 6500 - 5477.63

Evaluate the difference

x^2 = 1022.37

Evaluate the exponent

x = 31.97

Hence, the ship is 31.97 miles from its point of departure

Read more about distance and bearing at:

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Answer:

21

Step-by-step explanation:

You can tell that AB=2x7

BC=4x7

So, you're increasing each by multiplying each by 7.

3x7=21.

Answer:

sine

.....................

Answer:

f(-8) = 64

Step-by-step explanation:

Given conditions :

We have x = -8

⇒ It follows x < 0

Therefore, substituting x = -8 in the function :

The volume of the cylinder that has same height and radius with the given cone is: D. 5,346 cubic centimeters

Volume of a cylinder = 3(volume of a cone), given that the cylinder and the cone has the same radius and the same height.

We are told that a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder, therefore:

Volume of the cylinder = 3(1,782)

Volume of the cylinder = 5,346 cubic centimeters

Learn more about volume of cylinder on:

https://brainly.com/question/9554871

Answer:

Step-by-step explanation:

The volume of the cylinder that has same height and radius with the given cone is: D. 5,346 cubic centimeters

What is the Volume of a Cylinder?

Volume of a cylinder = 3(volume of a cone), given that the cylinder and the cone has the same radius and the same height.

We are told that a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder, therefore:

Volume of the cylinder = 3(1,782)

Volume of the cylinder = 5,346 cubic centimeters

Learn more about volume of cylinder on:

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Answer:

Step-by-step explanation:

[tex]n=\dfrac 45 (m+7)\\\\\implies 5n = 4(m+7)\\\\\implies 5n = 4m+28\\\\\implies 4m = 5n-28\\\\\implies m = \dfrac{5n-28}{4}[/tex]

Answer:

8 inches

Step-by-step explanation:

Nacho cheese

v= Pi×radius×2×height

v = 3.14×8×2×4 = 200.96

jalapeño

3.14×4×2=25.12

200.96÷25.12=8

the height is 8

to check your work you can do

(multiply by 8 and see if it equals 200.96)

3.14×4×2×8 = 200.96

since the volume is the same as the volume for nacho cheese we can say that 8 inches for height is correct

Answer:

2/81

Step-by-step explanation:

Firstly find out the common ratio.

And then the general term.

And at last you can find any term(7th term in this case).

The 7th term of the sequence will be 13122.

We have the following sequence -

18, 6, 2 ...

The nth term of the geometric sequence will be a[n] = arⁿ ⁻ ¹.

a[7] = 18 x 3⁶

a[7] = 18 x 9 x 9 x 9

a[7] = 13122

Therefore, the 7th term of the sequence will be 13122.

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Answer:

Step-by-step explanation:

Given the equation: y = 8 * 2ˣ, substitute the x-values in the table for x in your equation, to find the y-values.

For x = -1

[tex]y = 8 * 2^x\\y=8*2^{-3}\\y=8*\frac{1}{2^3} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{8}\\y=8*0.125\\y=1\\\\(-1,1)[/tex]

For -2:

[tex]y = 8 * 2^x\\y=8*2^{-2}\\y=8*\frac{1}{2^2} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{4}\\y=8*0.25\\y=2\\\\(-2,2)[/tex]

For -1:

[tex]y = 8 * 2^x\\y=8*2^{-1}\\y=8*\frac{1}{2^1} < ==negative\ exponent\ property: x^{-n}=\frac{1}{x^n}\\y=8*\frac{1}{2}\\y=8*0.5\\y=4\\\\(-1,4)[/tex]

For 0:

[tex]y = 8 * 2^x\\y=8*2^0\\y=8*\frac{1}{2^2} < ==zero\ exponent\ property: x^0=1\\y=8*1\\y=8\\\\(0,8)[/tex]

For 1:

[tex]y = 8 * 2^x\\y=8*2^1\\y=8*2\\y=16\\\\(1,16)[/tex]

For 2:

[tex]y = 8 * 2^x\\y=8*2^2\\y=8*4\\y=32\\\\(2,32)[/tex]

For 3:

[tex]y = 8 * 2^x\\y=8*2^3\\y=8*8\\y=64\\\\(3,64)[/tex]

Hope this helps!

Answer:

105 Bowls

Step-by-step explanation:

6.825 ÷ 0.065 = 105 Bowls

Answer:

The cost of one T-shirt is £4

The cost of a hat is £1

Step-by-step explanation:

Answer:

2:4 3:6 and 8:2, and 4:1 are equivalent pairs of ratios.

2 : 4 and 3 : 6 are an equivalent pair of ratios.

( to find equivalent ratios just multiply or divide both quantities by the same number. )

Answer:

Slope: 3/2

Y-Intercept: 3

Step-by-step explanation:

The y-intercept is very easy to discover as it is just the Y coordinate when X is zero or "intercepts" the x axis. So if you look directly above the origin you see that the line has the point (0, 3).

The Y Intercept is 3

The slope is found using the slope formula of y2-y1/x2-x1

Lets take two points from the line. We have the (0, 3) point that I mentioned earlier and we can get the x-intercept of (-2, 0)

Lets Solve!

3- 0 = 3

0-(-2) = 2

3/2 is the slope

So the formula is Y = 3/2 + 3

Answer:

20/2.5 =? (Answer is 8)

Step-by-step explanation:

Aaden needs 40 points.

He gets 20 at the start, just for signing up, so he needs only 20 now.

If he gets 2.5 points for each visit, after 8 days he will have been given 20 more points, allowing him to get a free movie ticket.

Brainliest please?

Answer:

#1 20

#2 17

#3 14

#4 14

#5 12

#6 14

#7 10

#8. 20

#9. 20

Step-by-step explanation:

1 12+8=20

2 10+7=17

3 8+6=14

4 8+6=14

5 10+2=12

6. 8+6=14

7 4+6=10

8. 12+8=20

9 14+6=20

Now honey I can't do all your work for you im.not trying to be mean but work some.out heres a tip use a calculator to help you when you get stuck ask me your question and then I will hold you ok