a car company uses the table below to show customers the appropriate amount of gas used when a car has been driven a certain number of miles.


if the car always uses the same amount of gas each time, how many gallons of gas would be needed to travel 480 miles?

A. 20

B. 24

C. 33

D. 39

​

Answer:

The null hypothesis will be rejected

Step-by-step explanation:

The null hypothesis is that people who favour ban on stem cell research is less than or equal to 0.61

The alternate hypothesis is that people who favour ban on stem cell research is greater than 0.61

Proportion of population = 0.61

Total events = 360

Sample size = 554

Sample proportion = 360/554 = 0.649

As per test statistics –  

Z = (p-p0)/sqrt {(p0 (1-p0))/n} = (0.649 -0.61)/ {(0.61 (1-0.61))/554}

= 0.039/0.021

= 1.857

P (Z<1.857) = 1- P (Z<1.857) = 1-0.9664 = 0.0336

So alpha value is 0.064.  

Thus, we will reject the null hypothesis  

Answer:

I'm pretty sure it's either 3.1 or 4.1

Step-by-step explanation:

Answer:

x = (571 ± √186217) / 18

x ≈ 7.74840677368558702303.. or 55.69603767075885742140..

x ≈ 7.75 or 55.70

Step-by-step explanation:

y = -9x² + 571x – 3884.

x = (-b ± √b² – 4ac) / 2a

x =

(-(571) ± √((571)² – 4((-9) × (-3884))) / 2(-9)) →

(-571 ± √(326041 – 4(34956))) / -18) →

(-571 ± √(326041 – 139824)) / -18) →

(-571 ± √(186217)) / -18 →

(571 ± √186217) / 18 →

Answer:

1/3

Step-by-step explanation:

P(5) Represents the probability that the spinner will land on 5 after being spun once. Since 5 is one of three options on the wheel, the probability is 1/3

Answer:

[tex]Area = 90.03cm^2[/tex]

Step-by-step explanation:

Given

[tex]s_1 = 14.9[/tex]

[tex]s_2 = 14.7[/tex]

[tex]\theta = 124[/tex] --- angle in between

Required

The area of the plate

Since [tex]\theta = 124[/tex] is between [tex]s_1[/tex] and [tex]s_2[/tex]

The area is:

[tex]Area = \frac{1}{2} * s_1 * s_2 * \sin(\theta)[/tex]

[tex]Area = \frac{1}{2} * 14.9 * 14.7 * \sin(124.7)[/tex]

[tex]Area = \frac{1}{2} * 14.9 * 14.7 * 0.8221[/tex]

[tex]Area = 90.03cm^2[/tex]

For the given condition the age of the son will be 69 years.

A mathematical equation asserts the equality of two expressions, which may or may not contain variables or integers. Equations are fundamental concerns, and efforts to rationally address them have served as the primary driving forces behind the creation of mathematics.

Suppose the two-digit number is x,

The father's and son's ages are 10x+y and 10y+x respectively.According to the given condition,

(10x+y) -(10y+x)=27

9x-9y=27

x-y=27/9

x-y=3

The value of x and y will be 4 and 1.

At x=9 and y=6, the age of the son is obtained as,

=10×6+9

=69 years

Thus, the age of the son will be 69 years.

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Answer:

53.8%

Step-by-step explanation:

Answer:

u already got ur awnser so hi

Step-by-step explanation:

ui

Answer:

[tex]36\:\mathrm{in^3}[/tex]

Step-by-step explanation:

The area of a prism is given by the product of the base and the height. In this triangular prism, the area of the either base is:

[tex]A=\frac{1}{2}\cdot 3\cdot 4=6\:\mathrm{in^2}[/tex]

The height is marked as [tex]6[/tex] inches. Thus, the volume of the prism is:

[tex]\frac{1}{2}\cdot 3\cdot 4\cdot 6=\boxed{36\:\mathrm{in^3}}[/tex]

Answer:

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

Answer:

speak english plz

Step-by-step explanation:

Answer:

Rent

Step-by-step explanation:

I think

The surface area of the given composite figure will be 384 square cm.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

In the given image we have a composite figure one is a rectangular cuboid and the other is a triangular prism. The surface area will be equal to the sum of all the outer sides of the figure.

The surface area of the triangular shape will be calculated as:-

SA = 2( Area of triangle ) + Area of rectangular surfaces

SA = 2 ( (1/2) B x H )  + (5 x 6 ) + ( 6 x 3  )

SA = ( 3 x 4 ) + (  30 ) + ( 18 )

SA = 12 + 30 + 18

SA = 60 square cm

The surface area of the rectangular cuboid will be calculated as:-

SA = ( 4 x 6 ) + 2 ( 158 x 4 ) + 2 ( 15 X 6 )

SA = 24 + 120 + 180

SA  = 324 square cm

Total surface area will be = 324 + 60 = 384 square cm.

Therefore the surface area of the given composite figure will be 384 square cm.

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Answer:

YES

Step-by-step explanation:

Any straight line can be represented by an equation of the form

Y = mX + b

where m is the slope and b is the Y intercept, so these two equations are lines. The only solution is where the two lines cross, so must satisfy both equations. Plugging in 3 for X and -2 for Y we get

Y = -3X + 7

-2 = -3(3) + 7

-2 = -9 + 7

-2 = -2 True

AND,

Y = 2X - 8

-2 = 2(3) - 8

-2 = 6 - 8

-2 = -2 True

So since both are true, yes (3, -2)  is the solution.

Answer:

The signs will be + and -

Step-by-step explanation:

Required

The signs in the parenthesis of difference of two squares

Let the expression be:

[tex](x^2 - a^2)[/tex]

Expand

[tex]x^2 - a^2 = x^2 -ax + ax - a^2[/tex]

Factorize

[tex]x^2 - a^2 = x(x -a) + a(x - a)[/tex]

Factor out x - a

[tex]x^2 - a^2 = (x +a)(x - a)[/tex]

See that the sign in front of a is + and - in the parentheses

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  10, (x+4), (x -1)

Step-by-step explanation:

The given volume expression can be factored as ...

  V = 10x² +30x -40

  = 10(x² +3x -4)

  = 10(x +4)(x -1)

The expressions representing length, width, and height might be ...

  10, (x+4), (x -1)

Answer:

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Step-by-step explanation:

Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.

At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So

[tex]H_0: \mu = 350[/tex]

At the alternate hypothesis, we test if this mean increased, that is:

[tex]H_1: \mu > 350[/tex]

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

350 is tested at the null hypothesis:

This means that [tex]\mu = 350[/tex]

After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.

This means that [tex]n = 35, X = 405, s = 25[/tex].

Test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]

[tex]t = 13.02[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.

Using a t-distribution calculator, this probability is of 0.

The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.

Answer:

$150

Step-by-step explanation:

I = prt

I = 5000(.06)(.5)

I = 150

Answer: C D E

Step-by-step explanation:

Answer: it is C

Step-by-step explanation:

Translation: (4,2) -> (3,1)

Dilation: (3,1) -> (6,2)

The solution is,  the coordinates of point R' are (7, 3) and the correct option is B.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Given:

The coordinate of point R in quadrilateral RUST are (4,2).

R is dilated by a scale factor of 2, centered at the origin, followed by the translation (x, y) + (x - 1, y - 1).

To find:

The coordinates of R' after dilation and translation.

Solution:

If a figure is dilated by a scale factor of 2, centered at the origin, then

(x, y) ⇒ ( 2x, 2y )

We value R(4,2).

R(4,2) ⇒ R_1( 8,4)

The rule of translation is:

(x, y) + (x - 1, y - 1).

Using this rule, we get

R_1( 8,4) ⇒ R' ( 7,3)

Therefore, the coordinates of point R' are (7, 3) and the correct option is B.

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Answer:

[tex]C.[/tex] 5/7 × 2/3

Step-by-step explanation:

Answer:

look at the picture i have sent

Answer:

(-[tex]\frac{\sqrt{3}}{2}[/tex],-[tex]\frac{1}{2}[/tex])

Step-by-step explanation:

The corresponding point on the unit circle is ( -√3/2 , -1/2).

A unit circle is just a circle that has a radius of 1 unit. A unit circle can be used to define right triangle relationships known as sine, cosine and tangent. These relationships describe how angles and sides of a right triangle relate to one another.

For the given situation,

The radian measure is θ = 7pi/6

In unit circle, the radian θ = [tex]\frac{7\pi }{6}[/tex] lies in the third quadrant and it's equal degree measure is [tex]210[/tex]°.

The corresponding point for this radian measure is

( [tex]\frac{-\sqrt{3} }{2} ,\frac{-1}{2}[/tex] )

Hence we can conclude that the corresponding point on the unit circle is ( -√3/2 , -1/2).

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Answer:

d.

Step-by-step explanation:

The gradient is -5 meaning that it's going downwards as x increases

The y-intercept is 3

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9514 1404 393

Answer:

  5 and 8

Step-by-step explanation:

Factor pairs that make 40 are ...

  40 = 1×40 = 2×20 = 4×10 = 5×8

The pair that has a sum of 13 is 5 and 8.

Answer:

1) [tex]2^{\frac{5}{3} }[/tex] = [tex]2^{\frac{5}{3} (3) }[/tex] = [tex]2^{5}[/tex]

2) [tex]2^{\frac{5}{3} }[/tex] = [tex]\sqrt[3]{2^{5} }[/tex] = [tex]\sqrt[3]{32 }[/tex]

3) [tex]2^{\frac{5}{3} }[/tex] = 3.17...

1^2 = 1

2^2 = 4

[tex]2^{\frac{5}{3} }[/tex]  is between 1 and 2 to the power of 2

Answer:

A

Step-by-step explanation:

The pattern is blue red blue red

+

The pattern is vertical horizontal vertical horizontal

Answer:

A.

The second figure adds another red horizontal line to the first. The third adds a vertical blue line to the second. The fourth must add a red horizontal line to the third.

Answer:

D. 0

Step-by-step explanation:

I calculated logically