Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

±7 sqrt(2) = x

Step-by-step explanation:

98 - x^2 = 0

Add x^2 to each side

98 =x^2

Take the square root of each side

±sqrt(98) = sqrt(x^2)

±sqrt(49*2) = x

±7 sqrt(2) = x

Answer:

[tex]\huge \boxed{{x = \pm 7\sqrt{2} }}[/tex]

Step-by-step explanation:

[tex]98-x^2 =0[/tex]

[tex]\sf Add \ x^2 \ to \ both \ sides.[/tex]

[tex]98=x^2[/tex]

[tex]\sf Take \ the \ square \ root \ of \ both \ sides.[/tex]

[tex]\pm \sqrt{98} =x[/tex]

[tex]\sf Simplify \ radical.[/tex]

[tex]\pm \sqrt{49} \sqrt{2} =x[/tex]

[tex]\pm 7\sqrt{2} =x[/tex]

[tex]\sf Switch \ sides.[/tex]

[tex]x= \pm 7\sqrt{2}[/tex]

Answer:

work pictured and shown

Answer:

Last one

Step-by-step explanation:

● [ ( 3^2 × 5^0) / 4 ]^2

5^0 is 1 since any number that has a null power is equal to 1.

●[ (3^2 ×1 ) / 4 ]^2

● (9/4)^2

● 81 / 16

Step-by-step explanation:

utilise the formula a+(n-1)d

a is the first number while d is common difference

Answer:

22

Step-by-step explanation:

Using the formular, Un = a + (n - 1)d

Where n = 10; a = -23; d = 5

U10 = -23 + (9)* 5

U10 = -23 + 45 = 22

Answer:

1/8

Step-by-step explanation:

3/8-1/8-1/8=1/8

Answer:

The first picture's answer would be (6, 21)

Step-by-step explanation:

You have to find the points on the 8th and the 9th day, and then you would add them together, and then divide by two finding the average, which would be 24 and 18, so when added, you get 42, divided by 2 you get 21. You look on the graph for the point with 21, and you find it is on 6.

Answer:

1.16

Step-by-step explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0)  =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) =  0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the  left until the first column is reached, we see that the value was 1.1.  similarly, we did the same in the  upward direction until the top row is reached, the value was 0.06.  The intersection of the row and column values gives the area to the two tail of z.   (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877

Step-by-step explanation:

Using Sine Rule

[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]

[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]

[tex]a = 4.6[/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]

[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]

[tex]b = 7.4[/tex]

Answer:

144 ways

Step-by-step explanation:

Number of paintings = 7

Renaissance = 4

Baroque = 3

We are hanging from left to right and we will first hang Renaissance painting before baroque painting.

For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24

For baroque we have 3! Ways of doing so. 3x2x1 = 6

We have 4!ways x 3!ways

= (4x3x2x1) * (3x2x1) ways

= 144 ways

Therefore we have 144 ways to hang the painting.

Answer:

The Width = 28 inches

The Height = 21 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3

Using Pythagoras Theorem

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 35²

We are given ratio: 4:3 as aspect ratio

Width = 4x

Height = 3x

(4x)² +(3x)² = 35²

= 16x² + 9x² = 35²

25x² = 1225

x² = 1225/25

x² = 49

x = √49

x = 7

Hence, for the 35 inch tv set

The Width = 4x

= 4 × 7

= 28 inches.

The Height = 3x

= 3 × 7

= 21 inches

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          Hi my lil bunny!

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When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.

A. remainder

B. dividend

C. quotient

D. divisor

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

a. remainder

Step-by-step explanation:

took the test

dont leave your house without a vest

or you will get hit in the vital organs in your chest

Answer:

z = 83/( -c+6-t)

Step-by-step explanation:

-cz + 6z = tz + 83

Subtract tz from each side

-cz + 6z -tz= tz-tz + 83

-cz + 6z - tz = 83

Factor out z

z( -c+6-t) = 83

Divide each side by ( -c+6-t)

z( -c+6-t)/( -c+6-t)  = 83/( -c+6-t)

z = 83/( -c+6-t)

Answer:

[tex]\Large \boxed{\sf True}[/tex]

Step-by-step explanation:

[tex]\sf A \ diameter \ that \ is \ perpendicular \ to \ a \ chord \ bisects \ the \ chord.[/tex]

Answer:

True!!

I just did the assignment and got it right

Answer:

mean=87

median=87

Step-by-step explanation:

mean=sum of test score/number of subject

mean=79+91+93+85+86+88/6

mean=522/6

mean=87

Literal meaning of median is medium.

To find the number which lies in the medium, we must rearrange the number in ascending.

79, 91, 93, 85, 86, 88

79, 85, 86, 88, 91, 93

86+88/2=87

Hope this helps ;) ❤❤❤

Let me know if there is an error in my answer.

Answer:

Stratified Random sampling.

Step-by-step explanation:

As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.

Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.

Hence, according to the given situation, the correct answer is a random stratified sampling.

Answer:

Step-by-step explanation:

x² - 5x - 36

To factor the expression rewrite -5x as a difference

That's

x² + 4x - 9x - 36

Factor out x from the expression

x( x + 4) - 9x - 36

Factor out -9 from the expression

x( x + 4) - 9( x+ 4)

Factor out x + 4 from the expression

The final answer is

Hope this helps you

Answer:

[tex] \boxed{(x - 9) \: (x + 4) }[/tex]

Option A is the correct option.-

Step-by-step explanation:

( See the attached picture )

Hope I helped!

Best regards!

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

A: 19

Step-by-step explanation:

For this, we can complete the square. We first look at the first 2 terms,

t^2 and -6t.

We know that [tex](t-3)^2[/tex] will include terms.

[tex](t-3)^2 = t^2 - 6t + 9[/tex]

But [tex](t-3)^2[/tex] will also add 9, so we can subtract 9. Putting this into the equation, we get:

[tex]m(t) = (t-3)^2 - 9 +28[/tex]

[tex]m(t) = (t-3)^2 +19[/tex]

Using the trivial inequality, which states that a square of a real number must be positive, we can say that in order to have the minimum number of members, we need to make (t-3) = 0. Luckily, 3 months is in our domain, which means that the minimum amount of members is 19.

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Answer:

5 5/12

Step-by-step explanation:

31/6 feet + 1/4 foot

= 31/6 + 1/4

= [(31 * 4) / 6 * 4] + [(1 * 6) / 4 * 6]

=  [ 124/24 ] + [ 6/24 ]

= (124 + 6) / 24

= 130 / 24

= 5 10/24

= 5 5/12

Hope this helps!  Tell me if I'm wrong!

Answer:

[tex]\large \boxed{\sf \bf \ \ k=320 \ \ }[/tex]

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

[tex]64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The equation is always false

Step-by-step explanation:

arctan1/4+arctan2/7=1/2arccos3/5

0.24497866+0.27829965=1/2(0.92729521)

0.52327832                 =0.46364760

not equivalent and will never be.

Assuming the cube is closed, you can use the divergence theorem:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm dS=\iiint_T\mathrm{div}\vec F\,\mathrm dV[/tex]

where [tex]S[/tex] is the surface of the cube and [tex]T[/tex] is the region bounded by [tex]S[/tex].

We have

[tex]\mathrm{div}\vec F=\dfrac{\partial(y+z)}{\partial x}+\dfrac{\partial(x+z)}{\partial y}+\dfrac{\partial(x+y)}{\partial z}=0[/tex]

so the flux is 0.

volume of a cone

.

.

.

volume of sphere

.

.

number of spheres that can be made......

.

.

hence a hemisphere can be formed

Answer:

Step-by-step explanation:

[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]

Answer:

The legs are 12 cm each, so the hypotenuse is

√(144+144)=12√2

Step-by-step explanation:

Applying the Pythagorean Theorem, the length of the hypotenuse is:  12√2 cm.

Given the two legs of the right triangle to be 12 cm

c² = 12² + 12².

c² = 288

c = √288

c = 12√2 cm

Therefore, applying the Pythagorean Theorem, the length of the hypotenuse is:  12√2 cm.

Learn more about, the Pythagorean Theorem on:

https://brainly.com/question/654982

Answer:

A) C1 = 0.00187 m = 0.187 cm,  C2 = 0.0062 m = 0.62 cm

B)  A sample of how the graph looks like is attached below ( periodic sine wave )

C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum

Step-by-step explanation:

Given data :

mass = 5kg

length of spring = 10 cm = 0.1 m

f(t) = 10sin(t) N

viscous force = 2 N

speed of mass = 4 cm/s = 0.04 m/s

initial velocity = 3 cm/s = 0.03 m/s

Formulating initial value problem

y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m

spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m

f(t) = 10sin(t/2) N

using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion

the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)

A) finding the solution of the initial value

attached below is the solution and

B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like

C attached below

No, that is not a function.

To be a function, each different input (x) needs a different output (y)

In the given function there are two -3’s as inputs and they have different y values, so it can’t be a function.

Answer: no

Step-by-step explanation: To determine if a relation is a function, take a look at the x–coordinate of each ordered pair. If the x–coordinate is different in each ordered pair, then the relation is a function.

Note that the only exception to this would be that if the x-coordinate pairs up with the same y-coordinate in a relation more than once, it's still classified ad a function.

Ask yourself, do any of the ordered pairs

in this relation have the same x-coordinate?

Well by looking at this relation, we can see that two

of the ordered pairs have the same x-coordinate.

In this case, the x-coordinate of 3 appears twice.

So no, this relation is not a function.

Answer:

[tex]y = 4x + 14[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation we must first find the slope of the line

Slope of the line using points (−2, 6) and (2, 14) is

[tex]m = \frac{14 - 6}{2 + 2} = \frac{8}{2} = 4[/tex]

Now we use the slope and any of the points to find the equation of the line.

Equation of the line using point ( - 2, 6) and slope 4 is

[tex]y - 6 = 4(x + 2) \\ y - 6 = 4x + 8 \\ y = 4x + 8 + 6[/tex]

We have the final answer as

[tex]y = 4x + 14[/tex]

Hope this helps you