Karl set out to Alaska on his truck. The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is graphed.

What distance did Karl travel by the time he had 200 liters of fuel?

_____ kilometers​

Answer:

the input x is 3

Step-by-step explanation:

2x+5=11

   2x=6

     x=3

Sample variance = 228.408

Standard deviation = 15.113

The well formatted frequency table has been attached to this response.

To calculate the sample variance and standard deviation of the given grouped data, follow these steps:

i. Find the midpoint (m) of the class interval.

This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e

For class 0 - 9, we have

m = (0 + 9) / 2 = 4.5

For class 10 - 19, we have

m = (10 + 19) / 2 = 14.5

For class 20 - 29, we have

m = (20 + 29) / 2 = 24.5

For class 30 - 39, we have

m = (30 + 39) / 2 = 34.5

For class 40 - 49, we have

m = (40 + 49) / 2 = 44.5

This is shown in the third column of the attached table.

ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e

For class 0 - 9, we have

frequency (f) = 13

midpoint (m) = 4.5

=> f x m = 13 x 4.5 = 58.5

For class 10 - 19, we have

frequency (f) = 7

midpoint (m) = 14.5

=> f x m = 7 x 14.5 = 101.5

For class 20 - 29, we have

frequency (f) = 10

midpoint (m) = 24.5

=> f x m = 10 x 24.5 = 245

For class 30 - 39, we have

frequency (f) = 9

midpoint (m) = 34.5

=> f x m = 9 x 34.5 = 310.5

For class 40 - 49, we have

frequency (f) = 11

midpoint (m) = 44.5

=> f x m = 11 x 44.5 = 489.5

This is shown in the fourth column of the attached table.

iii. Calculate the mean (x) of the distribution i.e

This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e

x = ∑(f x m) ÷ ∑f

Where;

∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205

∑f = 13 + 7 + 10 + 9 + 11 = 50

=> x = 1205 ÷ 50

=> x = 24.1

Therefore, the mean is 24.1

This is shown on the fifth column of the attached table.

iv. Calculate the deviation of the midpoints from the mean.

This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint

For class 0 - 9, we have

midpoint (m) = 4.5

=> m - x = 4.5 - 24.1 = -19.6

For class 10 - 19, we have

midpoint (m) = 14.5

=> m - x = 14.5 - 24.1 = -9.6

For class 20 - 29, we have

midpoint (m) = 24.5

=> m - x = 24.5 - 24.1 = 0.4

For class 30 - 39, we have

midpoint (m) = 34.5

=> m - x = 34.5 - 24.1 = 10.4

For class 40 - 49, we have

midpoint (m) = 44.5

=> m - x = 44.5 - 24.1 = 20.4

This is shown on the sixth column of the attached table.

v. Find the square of each of the results in (iv) above.

This is done by finding (m-x)²

For class 0 - 9, we have

=> (m - x)² = (-19.6)² = 384.16

For class 10 - 19, we have

=> (m - x)² = (-9.6)² = 92.16

For class 20 - 29, we have

=> (m - x)² = (0.4)² = 0.16

For class 30 - 39, we have

=> (m - x)² = (10.4)² = 108.16

For class 40 - 49, we have

=> (m - x)² = (20.4)² = 416.16

This is shown on the seventh column of the attached table.

vi. Multiply each of the results in (v) above by their corresponding frequencies.

This is done by finding f(m-x)²

For class 0 - 9, we have

=> f(m - x)² = 13 x 384.16 =  4994.08

For class 10 - 19, we have

=> f(m - x)² = 7 x 92.16 = 645.12

For class 20 - 29, we have

=> f(m - x)² = 10 x 0.16 = 1.6

For class 30 - 39, we have

=> f(m - x)² = 9 x 108.16 = 973.44

For class 40 - 49, we have

=> f(m - x)² = 11 x 416.16 = 4577.76

This is shown on the eighth column of the attached table.

vi. Calculate the sample variance.

Variance σ², is calculated by using the following relation;

σ² = ∑f(m-x)² ÷ (∑f - 1)

This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.

∑f(m-x)² = sum of the results in (vi)

∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192

∑f - 1 = 50 - 1 = 49         {Remember that ∑f was calculated in (iii) above}

∴ σ² = 11192 ÷ 49 = 228.408

Therefore, the variance is 228.408

vii. Calculate the standard deviation

Standard deviation σ, is calculated by using the following relation;

σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]

This is done by taking the square root of the variance calculated above.

σ = [tex]\sqrt{228.408}[/tex]

σ = 15.113

Therefore, the standard deviation is 15.113

Answer:

379

Step-by-step explanation:

a23 = 27 + (23-1)(16)

= 27 + (22)(16)

= 27 + 352

= 379

Answer:

x= 83

first take vertical opposite angle then take corresponding angles then you're done

Answer:

x value is 83 degree

because they both are alternate exterior angle

Answer:

168cm^3

Step-by-step explanation:

Q to P is going to be 3cm. it is identical to the length T to U.

R to T , W to Q, S to U is going to be identical to P to V. P to V has been identified as 12 cm.

in the middle of the shape, there are 4 identical triangles. the height time length will give us the area of that one shape:

e.g for shape P to V to W to Q and back to P is one rectangle. the length is 12 cm and the width is 3 cm.

12 x 3= 36

36cm^3 is one rectangles surface area, we have 4 identical triangles that means we need to times 36 by 4.

so 36x4=144.

now on the left and right side, we have two squares. on the right, we have T to U to V to W back to T this has the height of 3 width of 4 then we do 3 X 4 which is 12, we times it by 2 because we have two identical squares.

12 X 2=24

finally we add 24 and 144 = 168cm^3.

hope this helps :)

Answer:

,here is the answer

Step-by-step explanation:

here is your answer

Answer:

O  0.5 units

Step-by-step explanation:

so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6

Since WX has an initial measure of 3 units, therefore the measure of W'X' is:

W'X' = 3 units *(1/6) = 0.5 units

Answer:

A  =  P  ( 1  + r / n)  ^( t * n)

where

A  =  the amt  owed

P  = amt borrowed

r  = the  interest  rate  as a decimal

n =  the  number of compoundings  per year

t  = the  number of years

A  =    10000  (  1  + .10  / 2)^(2 *1)    =   10000  ( 1.05)^2    =  $11025

Step-by-step explanation:

Answer:

osjdiajsjoasnndosnsnd

Answer: 15268.1403 unit^3 (unit: cm,m,mm)

Step-by-step explanation:

volume of a cone= 1/2*pi*r^2*h

r= radius (unit: cm,m,mm)

h= perpendicular height (unit: cm,m,mm)

volume= 1/2*pi* (9)^2* 120 = 15268.1403 unit^3

Answer:

1060

Step-by-step explanation:

Answer:

the answer is 2

Step-by-step explanation: because 250 -22 is i dont even know

Answer:

55

Step-by-step explanation:

Answer:

[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]

Answer: [tex]14\ ft[/tex]

Step-by-step explanation:

Given

Length of rectangle is [tex]6\ ft[/tex]

Perimeter must be greater than 40 ft

Suppose l and w be the length and width of the rectangle

[tex]\Rightarrow \text{Perimeter P=}2(l+w)\\\Rightarrow P\geq 40\\\Rightarrow 2(l+w)\geq40\\\Rightarrow l+w\geq20\\\Rightarrow w\geq20-6\\\Rightarrow w\geq14\ ft[/tex]

So, the smallest width can be [tex]14\ ft[/tex]

Answer:

I thimk it is B

Step-by-step explanation:

Answer:  r = 5

Step-by-step explanation:

Answer:

7=x

Step-by-step explanation:

6(x-3)=8(x-4)

Distribute

6x -18 = 8x-32

Subtract 6x from each side

6x-18 -6x = 8x-32-8x

-18 = 2x-32

Add 32 to each side

-18+32 = 2x-32+32

14 = 2x

Divide by 2

14/2 =2x/2

7=x

[tex]\sf\purple{x= 7}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex]➺\:6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6x - 18 = 8x - 32[/tex]

[tex]➺ \: 6x - 8x = - 32 + 18[/tex]

[tex]➺ \: - 2x = - 14[/tex]

[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]

[tex]➺ \: x = 7[/tex]

Therefore, the value of [tex]x[/tex] is 7.

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]

[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]

[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]

[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]

[tex]➺ \: 24 = 24[/tex]

➺ L. H. S. = R. H. S.

Hence verified.

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]

Answer:

x = 2.8

Step-by-step explanation:

sin = opp/hyp

hyp = opp/sin

x = 2.4/sin60

x = 2.771281292110204

rounded

x = 2.8

Answer:

5

Step-by-step explanation:

WHen we raise a power to a power, we multiply them, in this case 5 is the base so we can just ignore it for now and replace it with x.

(X^1/3)^3

Multiply 1/3 by 3 and we get 1

So:

X^1

Which does nothing, so we can simplify to just:\

X

Remember x is 5 so the answer is:

5

A

A

B

C

A

D

B

C

May choices po yan saamen

Step-by-step explanation:

Love you

Answer:

She has 90.96 miles of the trail to hike.

Step-by-step explanation:

Length of the trail:

The length of the trail is of 113.7 miles.

On the first day she hiked of 1/10 the distance of the trail.

Thus:

[tex]\frac{1}{10(113.7) = 11.37[/tex]

On the first day she hiked 11.37 miles.

On the second day she hiked the same distance as the first day.

Also 11.37 miles on the second day, and thus, 2*11.37 = 22.74 miles on the first two days.

How much of the trail does she have left to hike?

113.7 - 22.74 = 90.96

She has 90.96 miles of the trail to hike.

[tex]\huge\bold{Given:}[/tex]

Length of the perpendicular = 7

Length of the base = 10

[tex]\huge\bold{To\:find:}[/tex]

The length of the missing side (hypotenuse).

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\longrightarrow{\purple{x\:=\: 12.21}}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Let the length of the missing side be [tex]x[/tex].

Using Pythagoras theorem, we have

(Hypotenuse)² = (Perpendicular)² + (Base)²

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = (7)² + (10)²

[tex]\longrightarrow{\blue{}}[/tex] [tex]{x}^{2}[/tex] = 49 + 100

[tex]\longrightarrow{\blue{}}[/tex]  [tex]{x}^{2}[/tex] = 149

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = [tex]\sqrt{149}[/tex]

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = 12.206

[tex]\longrightarrow{\blue{}}[/tex]  [tex]x[/tex] = 12.21.

Therefore, the length of the missing side [tex]x[/tex] is [tex]12.21[/tex].

[tex]\huge\bold{To\:verify :}[/tex]

[tex]\longrightarrow{\green{}}[/tex] (12.21)² = (7)² + (10)²

[tex]\longrightarrow{\green{}}[/tex] 149 = 49 + 100

[tex]\longrightarrow{\green{}}[/tex] 149 = 149

[tex]\longrightarrow{\green{}}[/tex] L.H.S. = R. H. S.

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]

Answer:

H0 : μ ≥ 350

H1 : μ < 350

Step-by-step explanation:

It is claimed that the mean is atleast 350 psi ;

10 such pipes were experimentally sampled ;

Here, the null hypothesis is the claim ; this means that the alternative hypothesis will be the opposite of the claim.

The hypothesis

H0 : μ ≥ 350

H1 : μ < 350

Answer:

[tex]radius=6.68cm[/tex]

Step-by-step explanation:

Formula to find radius:

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

[tex]r=42/2\pi[/tex]

[tex]r=42/2(3.14)[/tex]

[tex]r=6.68cm[/tex]

hope this helps......

Answer:

The correct answer is - 178.

Step-by-step explanation:

The standard deviation is a measure of the amount of dispersion in a set of values.

Given:

Mean of a normal distribution (m) = 154

Standard deviation (s) = 15

z-score = 1.6

Solution:

To find: value (x) that has a z-score of 1.6

z-score is given by = x-u/15

1.6*15 = x-154

=> 154+24 = x

x = 178

Answer:

$34

Step-by-step explanation:

price of the product = $40

coupon = 15% off

discount price = 15% of price of a product

=15/100 * $40

=$600/100

=$6

New price of the product = original price - discount

=$40 - $6

=$34