A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1825 miles, for a total gas consumption of 75 gallons. How many gallons were consumed by each of the two cars that week?

Answer:

3 ( a ) : x = 3.6,

3 ( b ) : x = 5

Step-by-step explanation:

For 3a, we can calculate the value of x through Pythagorean Theorem, which seemingly was your approach. However, the right triangle with x present as the leg, did not have respective lengths 9.6 and 12. The right angle divides 9.6 into two congruent parts, making one of the legs of this right triangle 9.6 / 2 = 4.8. The hypotenuse will be 12 / 2 as well - as this hypotenuse is the radius, half of the diameter. Note that 12 / 2 = 6.

( 4.8 )² + x² = ( 6 )²,

23.04 + x² = 36,

x² = 36 - 23.04 = 12.96,

x = √12.96, x = 3.6

Now as you can see for part b, x is present as the radius. Length 3 forms a right angle with length 8, dividing 8 into two congruent parts, each of length 4. We can form a right triangle with the legs being 4 and 3, the hypotenuse the radius. Remember that all radii are congruent, and therefore x will be the value of this hypotenuse / radius.

( 4 )² + ( 3 )² = ( x )²,

16 + 9 = x² = 25,

x = √25, x = 5

Answer:

Step-by-step explanation:

from the question,

the mean 14

the standard deviation is 3

and sample size is 10.

since the n which is the sample size is 10, then the distribution is mound shaped.

why?

this is due to the fact that the random variable from which we took the sample is mound shaped.

The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.

the standard deviation of the mean is

3/√10

= 0.948

Answer:

A is the appropriate option.

Step-by-step explanation:

The question given is a conditional statement.

With the condition that all master photographers are artist. This implies that any person who is a master photographer is automatically an artist.

A. Comparing the statement here, since Ansel Adam's is a master photographer, he is an artist.

B. Ansel Adams is an artist, but it is possible that not all artists are master photographer.

A is the correct option.

1. All master photographers are artists.

2. Ansel Adams is a master photographer.

Therefore, Ansel Adams is an artist.

Answer:

The correct answer is A.

Step-by-step explanation:

9514 1404 393

Answer:

  π = 2A/r²

Step-by-step explanation:

Multiply by the inverse of the coefficient of π.

  A = π(r²/2)

  π = 2A/r²

the answer is: combation

Answer:

9e -3

Step-by-step explanation:

Perform the indicated multiplication:

6 e + 3 (e-1) = 6e + 3e - 3

This, in turn, simplifies to

9e -3, or 3(3e - 1).

Answer:

ANSWER: 9e-3

Step-by-step explanation:

6e+3(e−1)

As we need to simplify the above expression:

First we open the brackets :

3(e-1)=3e-33(e−1)=3e−3

Now, add it to 6e.

So, it becomes,

$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$

Hence, equivalent expression would be 9e-3.

Answer:

Your question lacks some parts attached below is the complete question

Answer : 2.66

Step-by-step explanation:

The expected number ( E ) can be calculated using the formula below

[tex]E = \frac{row total * column total }{gross total}[/tex]

since we are computing the number of subjects that would prefer Linux operating system and are also rated as exceptional

The row total to be used = 53 ( row total of exceptional )

The column total to be used  = 13 ( column total of Linux )

The gross total to be used = summation of row total of both exceptional and no-exceptional = 259

BACK TO THE EQUATION

E = [tex]\frac{53*13}{259}[/tex]  = 689 / 259

E = 2.6602 ≈ 2.66

Answer:

[tex]a = \frac{3}{4}[/tex]

Step-by-step explanation:

Let's convert everything to sixths to make it easier to work with.

[tex]\frac{4}{6}a - \frac{1}{6} = \frac{2}{6}[/tex]

Add 1/6 to both sides:

[tex]\frac{4}{6}a = \frac{3}{6}[/tex].

Dividing both sides by 4/6:

[tex]a = \frac{3}{6} \div \frac{4}{6}\\\\a = \frac{3}{6} \cdot \frac{6}{4}\\\\a = \frac{18}{24}\\\\a = \frac{3}{4}[/tex]

Hope this helped!

Answer:

-1

Step-by-step explanation:

Hello, please consider the following.

[tex](-i)^6=(-1)^6\cdot(i^2)^3=1\cdot (-1)^3=\boxed{-1}\\[/tex]

Thank you

Answer:

Hello,

60L

Step-by-step explanation:

Quantity of water /Quantity of milk =2/1

Quantity of mixture= Quantity of water +Quantity of milk =60L

Quantity of milk =40 L

Quantity of water =20 L

Let say x the quantity of water to be added

New ratio =1/2=40/(20+x)

20+x=80 (cross products)

x=60 (L)

Answer:

Student is ready for college level mathematics.

The null hypothesis will be H0 = 25

The alternative hypothesis is Ha > 25

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to  test a hypothesis.

Your question is not complete but I guess you want to know the total price to be paid. This will be:

= $145 + (5.5% × $145)

= $145 + (0.055 × $145)

= $145 + $7.975

= $152.975

Answer:

145

Step-by-step explanation:

Angles in a straight line = 180

So,

Let unkown angle be x,

x+35=180

x=180-35

x=145

Answer:

[tex]\text{n}(A \bigcup B)[/tex] = 6.

Step-by-step explanation:

We are given that n(A) = 4, n(B) = 5, and [tex]\text{n}(A \bigcap B)[/tex] = 3.

And we have to find the value of [tex]\text{n}(A \bigcup B)[/tex].

As we know that the union formula is given by;

[tex]\text{n}(A \bigcup B) = \text{n}(A) + \text{n}(B) - \text{n}(A \bigcap B)[/tex]

Now, substituting the values given in the question in the above formula, we get;

[tex]\text{n}(A \bigcup B) = 4+5-3[/tex]

[tex]\text{n}(A \bigcup B) = 9-3[/tex]

[tex]\text{n}(A \bigcup B) = 6[/tex]

Hence, the value of [tex]\text{n}(A \bigcup B)[/tex] = 6.

Answer:

first term = -1/5

I cant see part b (sorry its too blurry)

thirteenth term = -0.2

part d: -19a/95a -0.2a

Step-by-step explanation:

socratic

Rewrite f in terms of the unit step function:

[tex]f(t)=\begin{cases}5&\text{for }0\le t<7\\-3&\text{for }t\ge7\end{cases}[/tex]

[tex]\implies f(t)=5(u(t)-u(t-7))-3u(t-7)=5u(t)-8u(t-7)[/tex]

where

[tex]u(t)=\begin{cases}1&\text{for }t\ge0\\0&\text{for }t<0\end{cases}[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]=e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\dfrac ks[/tex]

So we have

[tex]L[f(t)]=L[5u(t)-8u(t-7)]=5L[1]-8e^{-7s}L[1]=\boxed{\dfrac{5-8e^{-7s}}s}[/tex]

In this exercise you have to find the laplace transform:

[tex]L[f(t)]=\frac{5-8e^{-7s}}{s}[/tex]

Rewrite f in terms of the unit step function:

[tex]f(t)=\left \{ {{5, for 0\leq t\leq 7} \atop {-3, for t\geq 7}} \right. \\f(t)= 5(u(t)-u(t-7)-3u(t-7)=5u(t)-8u(t-7)[/tex]

Where:

[tex]u(t)= \left \{ {{1, t\geq 0} \atop {0, t<0}} \right.[/tex]

Recall the time-shifting property of the Laplace transform:

[tex]L[u(t-c)f(t-c)]= e^{-cs}L[f(t)][/tex]

and the Laplace transform of a constant function,

[tex]L[k]=\frac{k}{s}[/tex]

So we have:

[tex]L[f(t)]= L[5u(t)-8u(t-7)]= 5L[1]-8e^{-7s}L[1]= \frac{5-8e^{-7s}}{s}[/tex]

See more about Laplace transform at : brainly.com/question/2088771

Answer:

396 in^2

Step-by-step explanation:

The perimeter of a triangle is given by the formula:

● P = 2w+2L

L is the length and w is the width

■■■■■■■■■■■■■■■■■■■■■■■■■■

The width hereis 18 inches and the perimeter is 80 inches.

Replace w by 18 and P by 80 to find L.

● P= 2L+2w

● 80 = 2L + 2×18

● 80 = 2L + 36

Substrat 36 from both sides

● 80-36 = 2L+36-36

●44 = 2L

Divide both sides by 2

● 44/2 = 2L/2

● 22 = L

So the length is 22 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area of a rectangle is given by the formula:

● A= L×w

● A = 22×18

● A = 396 in^2

Answer:

Step-by-step explanation:

y varies with the square of x:

y = kx²

y equals 24 when x equals 10

24 = k·10²

constant of proportionality k = 0.24

when x = 20, y = 0.24·20² = 96

"select two answers"  —where are the choices?

Answer:

Hello,

I have reply too quick in comments (sorry)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}log_x (27)+log_y (4)=5\\log_x (27)-log_y (4)=1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2*log_x (27)=6\\2*log_y (4)=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}log_x (27)=3\\log_y (4)=2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x^{log_x (27)}=x^3\\y^{log_y (4)}=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}27=x^3\\4=y^2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x=3\\y=2\\\end{array}\right.\\\\[/tex]

Answer:

0.9719

Step-by-step explanation:

Find the mean and standard deviation of the sampling distribution.

μ = 5.1

σ = 1.1 / √49 = 0.157

Find the z score.

z = (x − μ) / σ

z = (4.8 − 5.1) / 0.157

z = -1.909

Use a calculator to find the probability.

P(Z > -1.909)

= 1 − P(Z < -1.909)

= 1 − 0.0281

= 0.9719

The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

Given,

Mean = 5.1 inches

Standard deviation = 1.1 inches

Sample size = 49

New mean = 4.8

Z score = Difference in mean /(standard deviation / [tex]\sqrt{sample size}[/tex])

Z score = [tex]\frac{4.8-5.1}{1.1/\sqrt{49} }=-1.909[/tex]

Z score = -1.909

Then the probability

P(Z>-1.909)

=1-P(Z>-1.909)

=1-0.0281

=0.9719

Hence, The probability of the randomly used item mean length is greater than 4.8 inches is 0.9719

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Answer:

450 runners

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

[tex] \sqrt[4] {27} \cdot \sqrt[4] {3} = [/tex]

[tex] = \sqrt[4] {27 \cdot 3} [/tex]

[tex] = \sqrt[4] {3^3 \cdot 3^1} [/tex]

[tex] = \sqrt[4] {3^4} [/tex]

[tex] = 3 [/tex]

Question:

A research center poll showed that 78% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.)

Answer:

[tex]q = 0.22[/tex]

Step-by-step explanation:

Given

Let p represent the given proportion

p = 78%

Required

Determine the probability that someone holds a contrary belief

Start by converting the given proportion to decimal

[tex]p = 78\%[/tex]

[tex]p = \frac{78}{100}[/tex]

[tex]p = 0.78[/tex]

In probability, the sum of opposite probability is equal to 1

Represent the probability that someone holds a contrary belief with q

So;

[tex]p + q = 1[/tex]

Make q the subject of formula

[tex]q = 1 - p[/tex]

Substitute 0.78 for p

[tex]q = 1 - 0.78[/tex]

[tex]q = 0.22[/tex]

Hence, the probability that someone does not believe is 0.22

Answer:

See the explanation for the answer.

Step-by-step explanation:

Given function:

[tex]f(x) = x^{1/4}[/tex]

The n-th order Taylor polynomial for function f with its center at a is:

[tex]p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}[/tex]

As n = 3  So,

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}[/tex]

[tex]p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}[/tex]

[tex]p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} } (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} + (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}[/tex]

[tex]p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} } (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} + (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}[/tex]

[tex]p_{3} (x)[/tex] = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6  

                                                                                  (0.0000018522752) (x-81)³

[tex]p_{3} (x)[/tex]  =  0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254

                                                                                                       (x-81)³ + 2.25

Hence approximation at given quantity i.e.

x = 94

Putting x = 94

[tex]p_{3} (94)[/tex]  =  0.0092592593 (94) - 0.000042866941 (94 - 81)² +          

                                                                 0.00000030871254 (94-81)³ + 2.25

         = 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +    

                                                                                                                       2.25

         = 0.87037 03742 - 0.000042866941 (169) +  

                                                                      0.00000030871254(2197) + 2.25

         = 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25

[tex]p_{3} (94)[/tex]  = 3.113804102621

Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Compute [tex]\sqrt[4]{94}[/tex] as [tex]94^{1/4}[/tex] using calculator

Exact value:

[tex]E_{a}[/tex](94) = 3.113737258478

Compute absolute error:

Err = | 3.113804102621 - 3.113737258478 |

Err (94)  = 0.000066844143

If you round off the values then you get error as:

|3.11380 - 3.113737| = 0.000063

Err (94)  = 0.000063

If you round off the values up to 4 decimal places then you get error as:

|3.1138 - 3.1137| = 0.0001

Err (94)  = 0.0001

Answer:

i. Colonel is about 201 feet away from the fire.

ii. Sarge is about 125 feet away from the fire.

Step-by-step explanation:

Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.

The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]

                                           = [tex]93^{0}[/tex]

Thus,

<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]

<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]

Sine rule states;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;

[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

b = [tex]\frac{0.8290*242}{0.9986}[/tex]

  = 200.8993

Colonel is about 201 feet away from the fire.

ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;

[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]

[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]

cross multiply,

a = [tex]\frac{0.5150*242}{0.9986}[/tex]

  = 124.8073

Sarge is about 125 feet away from the fire.

Answer:

BELOW

Step-by-step explanation:

242: multiply it by 2 to get 484 and its square root is 22

1280: multiply it by 5  to get 6400 and its square root is 80.

245: multiply it by 5 to get 1225  and its square root is 35.

968: multiply it by 2 to get 1936 and its square root is 44.

1728: multiply it by 3 to get 5184 and its square root is 72

4851: multiply it by 11 to get 53361 and its square root is 231.

HOPE THIS HELPED

Answer:

Hello,

Answer A

Step-by-step explanation:

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

The equation of the sinusoid will be y=Sin(2x)

It is defined as the relation between two variables, for a sinusoidal wave the equation will be in the form of Sin or Cos.

if x=0 then sin(2*0)=sin(0)=0

if x= π/4 then sin(π/2)=1

if x= π/2 then sin(π)=0

Hence the equation of the sinusoid will be y=Sin(2x)

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Answer:

392

Step-by-step explanation:

1.49×10⁸/3.8×10⁵ = 392

Answer:

  1/8, 3/8

Step-by-step explanation:

Let x and y represent the two fractions. Then we are given ...

  x + y = 1/2

  x + 5y = 2

Subtracting the first equation from the second, we get ...

  (x +5y) -(x +y) = (2) -(1/2)

  4y = 3/2 . . . . . simplify

  y = 3/8 . . . . . . divide by 4

  x = 1/2 -3/8 = 1/8

The two numbers are 1/8 and 3/8.

Answer:

C, y=-2/3x+1

Step-by-step explanation:

using points (0, 1) and (3, -1) obtained from the graph:

slope = -1-1/3-0 = -2/3

use one of the points above lets take (1, 0) and another point (x,y)

slope = y-0/x-1 = -2/3

y=-2/3x+1