The following data points represent the volume
of gas in each race car driver's tank (in liters).
4,5, 13, ?
If the mean of the data set is 7 L, find the
missing volume of gas.

Answer:

x = 6±sqrt( 31)

Step-by-step explanation:

x^2 -12x +5 =0

Subtract 5 from each side

x^2 -12x +5-5=0-5

x^2 -12x = -5

Take the coefficient of x

-12

Divide by 2

-12/2 =-6

Square it

(-6 )^2 = 36

Add this to each side

x^2 -12x +36= -5+36

(x-6)^2 = 31

Take the square root of each side

sqrt((x-6)^2) =±sqrt( 31)

x-6 =±sqrt( 31)

Add 6 to each side

x-6+6 =6±sqrt( 31)

x = 6±sqrt( 31)

Answer:

66 ft^2

Step-by-step explanation:

the formula for the area of a triangle is b x h over 2. the base is 22 and the height is 6. 22 x 6=132. 132/2=66

Answer:

equal to ab

Step-by-step explanation:

The area of a parallelogram is Area =  ab

therefore, the area is ab

Answer:

Less than ab

Step-by-step explanation:

Answer:

Where (h,k) is the center and r is the radius

Step-by-step explanation:

[tex]r^2 = (x-h)^2+ (y-k)^2[/tex]

Answer:

Step-by-step explanation:

Area of a parallelogram = base × height

From the question

base = 14 cm

height = 5 cm

Substituting the values into the above formula we have

Area = 14 cm × 5 cm

Hope this helps you

Answer:

1,750

Step-by-step explanation:

Answer:

Step-by-step explanation:

Tan θ = [tex]\sqrt{13} \div \sqrt{2}[/tex] = 2.5495

Therefore θ = [tex]Tan^{-1}[/tex] (2.5495) =68.5832°

Answer:

Tan θ =  2.5495097...

​

Answer:

A) Quadrilaterals

Step-by-step explanation:

All squares, rectangles, and rhombuses are parallelograms because their sides are parallel. However, quadrilaterals have four sides, but not all will be parallel.

Answer:

x = 70

Step-by-step explanation:

[tex] \sqrt{x - 6} = 8 \\ squaring \: both \: sides \\ {( \sqrt{x - 6)} }^{2} = {8}^{2} \\ x - 6 = 64 \\ x = 64 + 6 \\ \huge \red{ \boxed{ x = 70 }}\\ [/tex]

Answer:

Step-by-step explanation:

[tex]\sqrt{x-6}=8[/tex]

Take square,

[tex](\sqrt{x-6})^{2}=8^{2}\\\\x-6=64\\\\[/tex]

Add 6 to both sides,

x - 6 + 6 = 64+6

x = 70

Answer:

True

Step-by-step explanation:

Let A denotes the point (1,7)

Let B denotes the point (5,5)

We are supposed to find The length of the line segment containing the points

Formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(1,7)\\(x_2,y_2)=(5,5)\\ d = \sqrt{(5-1)^2+(5-7)^2}\\ d = \sqrt{4^2+(-2)^2}\\ d = \sqrt{4^2+(-2)^2}\\d=4.47[/tex]

So,The length of the line segment containing the points (1,7) and (5,5)  is 4.47 units is true.

Hence Option A is true

Answer:

A) 348m^2

Step-by-step explanation:

you just find the area of each individual shape then and all the sides together

Answer:

You find the base and height then divide by 2

Step-by-step explanation:

Answer:

height x 2 divided by 1/2  

Step-by-step explanation:

Answer:

1. 158

2. 120.125

3. 148.6

4. 158.6

Step-by-step explanation:

You divide the number inside by the number outside

Answer:

12.9 [tex]in^{2}[/tex]

Step-by-step explanation:

So to find the area of this triangle, you will need to use the equation

Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)

Here, we have ∠A, ∠C, and side c

We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.

First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,

∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°

Now that we have all three angles, we can solve for the sides

Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.

Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b

Now we can solve for the remaining side, a, using the same method.

Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a

Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒

Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]

Answer:

angle of depression = -12 degrees

Step-by-step explanation:

Sin = opposite/hypotenuse

sin = -208/1000

inv sin 0.208 = -12

To solve this problem, we just need to use trigonometric ratio and use the ratio that best fits this problem. The angle of depression is equal to 76.23 degrees.

Using SOHCAHTOA, we can easily solve this problem, but we need to first know which ratio to use

Data;

since we have the value of opposite and adjacent, we can solve this using the tangent of the angle

[tex]tan\theta = \frac{opposite}{adjacent} \\tan \theta = \frac{1000}{208} \\tan\theta = 4.807\\\theta = sin^-^1 (4.0807)\\\theta = 76.23^0[/tex]

From the calculation above, the angle of depression is equal to 76.23 degrees.

Learn more on angle of depression here;

https://brainly.com/question/15580615

#SPJ2

Answer:

Is there anything else to this question cause it's confusing and I would help you but if there is more information

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

2(n - 1) + 4n = 2 ( 3n - 1 )

2n - 2 + 4n = 6n - 2

6n - 2 = 6n - 2

6n - 6n = -2 + 2

0 = 0

Answer: C

Step-by-step explanation:

[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]

Find the least common denominator of 4, 3, and 12.

4-3-12 | 3

4-1-4   | 4

1-1-1    |-------- 12

The first fractions needs to be multiplied by 3, and the second fraction, by 4

[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]

Solve;

[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]

Add the fractions with positive signs and subtract the one with negative sign.

[tex]\frac{(9a+8a)-a}{12}[/tex]

Solve;

[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]

Simplify by 4;

16/4=4

12/4=3

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

Answer:

(4a)/3

Step-by-step explanation:

3a/4+2a/3-a/12

find L.C.M

9a+8a-1a/12=16a/12

16a/12=(4a)/3

Answer:

5.3

Step-by-step explanation:

Answer:

The answer is 5.3

Step-by-step explanation:

5.3x3-2= 13.9 but when you round its 14

Answer:

Your answer is 67.47$

Step-by-step explanation:

Hope this helped stay safe bye!

Answer:

-8

Step-by-step explanation:

-8

Answer:

6.

Step-by-step explanation:

Difference between -1 and -7.

-1-(-7) = -1 + 7 = 6

two negative signs makes it a positive sign

Answer:

That's my best answer.

Step-by-step explanation:

So for number 1 it says the total amount of wrapping paper. You should just find the surface area. I'll send a screenshot.

Answer:

It would be B.

Step-by-step explanation:

Hope it helpssss

Answer:

The z score of the 65-mph speed limit is -0.75

Step-by-step explanation:

The z score is given by the relation;

[tex]z = \frac{x- \mu}{\sigma}[/tex]

Where:

Z = Normal (Standard) or z score

x = Observed speed  score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

[tex]z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}[/tex]

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.

Answer:

The answer should be 4800

I Think There is ALLWAYZ a 50-50 CHANCE

Answer:

pretty sure it is 45mins

Step-by-step explanation:

U add 4+5=9 so that is one lap

then take 9*5=45 and that would be 5 laps

Answer:

45

Step-by-step explanation: first we want to find out the time it takes to do one full lap of skiing. in order to do this you have to add 4 to 5. we do this because if we start at the bottom of the hill we have to ride 4 min up to the top then 5 min to get back to the bottom. so in all it will 9 min to do one full lap. because we want to find out how long it will take to do 5 laps we do 9x5=45

Answer:

the formulae for the volume of a cylinder= πr²h

so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14

Answer:

7/100

Step-by-step explanation:

7 yellow, 6 blue, 9 red, and 3 green ribbons in a drawer

Total ribbons = 25 ribbons

P( yellow) = yellow / total = 7/25

Then not replaced

6 yellow, 6 blue, 9 red, and 3 green ribbons in a drawer

Total ribbons = 24 ribbons

P( blue) = blue / total = 6/24 = 1/4

P(a yellow ribbon and then a blue ribbon) = 7/25 * 1/4 =7/100

Answer:

A: [tex]\frac{7}{100}[/tex]

Step-by-step explanation:

There are 25 ribbons total. The probability would be out of the 25 ribbons.

(1):

Yellow: [tex]\frac{7}{25}[/tex]

Blue:[tex]\frac{6}{25}[/tex]

Red:[tex]\frac{9}{25\\}[/tex]

Green:[tex]\frac{3}{25}[/tex]

When removing a ribbon that can't be replace, it'll leave you with a total of 24 ribbons.

(2):

Yellow: [tex]\frac{6}{24}=\frac{1}{4}[/tex]

Blue: [tex]\frac{5}{24}[/tex]

Red:[tex]\frac{8}{24}=\frac{1}{3}[/tex]

Green:[tex]\frac{2}{24}=\frac{1}{12}[/tex]

Multiply {(1) × (2)}:

Yellow:[tex]\frac{7}{25}[/tex] ×[tex]\frac{6}{24}[/tex] = [tex]\frac{7}{100}[/tex]

Blue:[tex]\frac{6}{25}[/tex] × [tex]\frac{5}{24}[/tex] = [tex]\frac{1}{20}[/tex]

Answer:

I can find that the measure of RS

Step-by-step explanation:

The measure of RS can be discovered as both have corresponding sides. Therefore, both are the same

Answer:

Step-by-step explanation:

(-9+2)/2= -7/2= -3.5

(8 + (-1))/2 = 7/2= 3.5

(-3.5, 3.5) is the solution

Answer:

No there is no correlation between the hours spent on homework and the test scores.

Hope this helps!!!