The Flat Rock auto assembly plant in Detroit, Michigan, produces three different makes of automobiles. In two years, the plant constructed a total of 390,000 cars. If 90,000 more cars were made in the first year than in the second year, how many cars were made in each year?


a. first year: 90,000
second year: 180,000

b. first year: 300,000
second year: 90,000


c. first year: 240,000
second year: 150,000


d. first year: 180,000
second year: 90,000

For this case we have that the figure shown is composed of a cylinder and a cone.

We have that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \pi * (5) ^ 2 * 10\\V = \pi * 25 * 10\\V = 250 \pi \ m ^ 3[/tex]

On the other hand, the volume of a cone is given by:

[tex]V = \frac {\pi * r ^ 2 * h} {3}[/tex]

Where:

A: It's the radio

h: It's the height

Substituting the values:

[tex]V = \frac {\pi * (5) ^ 2 * 4} {3}\\V = \frac {\pi * 25 * 4} {3}\\V = \frac {100 \pi} {3} \ m ^ 3[/tex]

Then, the total volume is:

[tex]V_ {t} = 250 \pi \ m ^ 3 + \frac {100 \pi} {3} \ m ^ 3[/tex]

Taking [tex]\pi = 3.14[/tex], we have to:

[tex]V_ {t} = 889.67 \ m ^ 3[/tex]

Answer:

Option D

Answer:

A) - 39,991

Step-by-step explanation:

Sum of geometric sequence formula is

[tex]S = a(\frac{1 -r^n}{1-r} )\\a=-1, r=6/(-1)=-6, n=7\\\\S = -1(\frac{1 -(-6)^7}{1-(-6)} )= -\frac{279937}{7} = -39991[/tex]

Answer:

The correct answer option is A) -39,991.

Step-by-step explanation:

We know that the sum of the geometric sequence is given by the formula:

[tex] S _ n = \frac { a _ 1 ( 1 - r ^ n ) } { 1 - r } [/tex]

where [tex]a_1[/tex] is the first term, [tex]r[/tex] is the common ratio and [tex]n[/tex] is the number of terms.

Here,

[tex]a_1 = -1[/tex]

[tex]r = -6[/tex]

[tex]n=7[/tex]

Substituting these values in the above formula to get:

[tex] S _ 7 = \frac { -1 ( 1 - (-6) ^ 7 ) } { 1 - (-6) } [/tex]

S_n = -39,991

Answer:

x must be 5

Step-by-step explanation:

Recall that the area formula for a trapezoid is

A = (average of base lengths)(width)

Here we have

                                                                   17 cm + x

      (average of base lengths) = 11 cm = ----------------

                                                                           2

So 2(11 cm) = 17 cm + x, or

      22 cm = 17 cm + x

Then x must be 5.

To find the length of the other base of the trapezoid with a midsegment of 11 cm and one base of 17 cm, use the average property of the midsegment. The calculation reveals the other base is 5 cm in length.

The question is about finding the length of the other base of a trapezoid when the length of the midsegment and one of the bases is known. The midsegment of a trapezoid is parallel and equal to the average of the two bases. Therefore, if the midsegment is 11 cm and one base is 17 cm, the other base can be found by setting up the equation:

Midsegment = (Base1 + Base2) / 2

Substitute the known values:

11 = (17 + Base2) / 2

Multiplying both sides by 2 gives:

22 = 17 + Base2

Subtracting 17 from both sides gives:

Base2 = 22 - 17

Base2 = 5

Thus, the length of the other base of the trapezoid is 5 cm.

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Answer:

D. [tex]y=\frac{7}{x}[/tex]

Step-by-step explanation:

Let y varies inversely with x.

Then we can write the variation equation:

[tex]y\propto \frac{1}{x}[/tex]

We introduce the constant of proportionality, k and obtain the inverse variation equation:

[tex]y=\frac{k}{x}[/tex]

From the given options, the only equation in this form is

[tex]y=\frac{7}{x}[/tex]

In this case, k=7 is the constant of proportionality or constant of variation.

Answer:

31.4cm

Step-by-step explanation:

C = 2*pi*r

2r = d

2r=10

r=5

C = 2*5*pi

C = 10*3.14

C = 31.4cm

Answer:

Blank 1. Professional engineer

Blank 2. ABET( Accreditation Board for Engineering and Technology)

It takes 5 meters per second.

If you divide 250 by 50 you would get his average speed

The average speed of Ahmed is 5 meters per second.

Important information:

We need to find the average speed of Ahmed.

Formula for average speed is:

[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Using this formula, the average speed of Ahmed is:

[tex]\text{Average Speed}=\dfrac{250}{50}[/tex]

[tex]\text{Average Speed}=5[/tex]

Thus, the average speed of Ahmed is 5 meters per second.

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Answer:

It would be 139$

Step-by-step explanation:

In order to find a percent of a value you first move the decimal place over 2 to the left or divide by 100(percentage is no longer there). In this case it would be .20. You multiply that with the total number(695) and the product is your answer.

ABC is a right triangle, so AC has length given by

[tex]AC^2=(6\,\mathrm m)^2+(8\,\mathrm m)^2\implies AC=\sqrt{100\,\mathrm m^2}=10\,\mathrm m[/tex]

Then the circumference of circle M is [tex]10\pi\,\mathrm m[/tex].

Answer: A: there is not enough evidence to support a relationship between lunch preference and role at school

The relationship between poll result and the student preference is: option A, not enough evidence

This due to the fact that the statistics in the question is incomplete. W do not have sufficient data that would be used for hypothesis testing.

Due to the fact above, we conclude that there is insufficient evidence to get the relationship between variables.

In conclusion, there is not enough evidence to support a relationship between lunch preference and role at school

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To find (ƒ + g)(x) for the given functions ƒ(x) = 5x² + 4 and g(x) = 6x² - x, we add the like terms to get

(ƒ + g)(x) = 11x² - x + 4.

To find (ƒ + g)(x) where ƒ(x) = 5x²  + 4, and g(x) = 6x²  – x, we simply add the two functions together. We combine like terms to calculate the sum.

By adding the corresponding terms:

Combining these, we get

(ƒ + g)(x) = f(x) + g(x)

(f + g)(x) = 11x² - x + 4.

Answer:

x = 1+12z, y = -1+10z, and z = z

Step-by-step explanation:

Step 1: Convert the system into the augmented matrix form:

• 3 -4 4 | 7  

• 1 -1 -2 | 2

• 2 -3 6 | 5

Step 2: Multiply row 2 with -2 and add it into row 3:

• 3 -4 4 | 7  

• 1 -1 -2 | 2

• 0 -1 10 | 1

Step 3: Multiply row 2 with -3 and add it into row 1:

• 0 -1 10 | 1  

• 1 -1 -2 | 2

• 0 -1 10 | 1

Step 4: Replace row 1 with row 2 and multiply the updated row 2 with -1 and add it into row 3:

• 1 -1 -2 | 2

• 0 -1 10 | 1  

• 0 0 0 | 0

Step 5: Multiply row 2 with -1 and add it in row 1:

0 1 -10 -1

• 1 0 -12 | 1

• 0 -1  10 | 1  

• 0 0  0 | 0

Step 6: It can be seen that there are infinite solutions of this system since the last row is all zeroes. It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:

• x - 12z = 1

• -y + 10z = 1

Step 7: Make x and y the subject of their respective equations:

• x = 1 + 12z

• y = -1 + 10z

So final answer is x = 1+12z, y = -1+10z, and z = z!!!

Answer:

A = 48x + 24 (square units)

Step-by-step explanation:

L = 6x + 3

W = 8

A = L * W

A = 8(6x + 3)

A = 48x + 24

Answer:

e = 8x + 0.1y

Step-by-step explanation:

If Gustavo makes no sales at all, he still gets $8 per hour worked (x).  We can model this part with this equation:

e = 8x

But then, if he sells something, he makes extra money.. He makes 10% (0.1) of every sale (y).  So the equation becomes:

e = 8x + 0.1y

or you can express it this way:

e = 8x + y/10

which is the same thing just written differently.

Answer:

Quadrant II

Step-by-step explanation:

I attached an image of the quadrants system.

You'll see that the scenario where we have a point with a negative X value and a positive Y value, it belongs to Quadrant II.

Quadrant I

Degrees: 0-90

X values: positive (+)

Y values: positive (+)

Quadrant II

Degrees: 90-180

X values: negative (-)

Y values: positive (+)

Quadrant III

Degrees: 180-270

X values: negative (-)

Y values: negative (-)

Quadrant IV

Degrees: 270-360

X values: positive (+)

Y values: negative (-)

Answer:

[tex]\boxed{\text{b. \$1845 a month}}[/tex]

Step-by-step explanation:

   Amount if retired at 66 = $2460/mo

Less 25 % = 0.25 × 2460 =    -615

   Amount if retired at 62 = $1845/mo

John would receive [tex]\boxed{\text{\$1845/mo}}[/tex] if he retired at 62.

Answer:

  62 Sunday papers were sold

Step-by-step explanation:

Let x represent the number of Sunday papers sold. Then half that many, or x/2, is the number of Friday papers sold. The total revenue from the sales is the sum of products of quantity and price:

  1.50 · x + 0.75 · (x/2) = 116.25

Multiplying by 2, this becomes ...

  3.00x +0.75x = 232.50

  3.75x = 232.50

Dividing by the coefficient of x gives ...

  232.50/3.75 = x = 62

The number of Sunday newspapers sold is 62.

Answer:

The only possible groups that could be made if each group have the same number of people is 2 groups of 14 or 4 groups of 7. Since each group cannot have more than 10 people, the only group left is 4 groups of 7.

Answer:

"the addition of a negative constant"

Step-by-step explanation:

Please note the following points of functions regarding transformations:

1. If there is a change in amplitude, the function will be compressed/stretched vertically, keeping other variables constant

2. If there is a phase shift, the function would be horizontally transformed

3. If there is a period change, the function would be horizontally compressed/stretched

4. If there is addition of positive/negative constant, the function would shift vertically upward/downwards, respectively.

We can clearly see from the graph that the new function is a vertical downward shift from the original. Hence, looking at the above points, point #4, addition of a negative constant, is correct.

Answer:

Final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Step-by-step explanation:

using given information from the attached picture, we need to find the value of cos(H) so let's apply the formula of cosine.

[tex]\cos\left(\theta\right)=\frac{adjacent}{hypotenuse}[/tex]

[tex]\cos\left(H\right)=\frac{GH}{FH}[/tex]

[tex]\cos\left(H\right)=\frac{36}{85}[/tex]

[tex]\cos\left(H\right)=0.423529411765[/tex]

Hence final answer is approx [tex]\cos\left(H\right)=0.4235[/tex].

Using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

Cosine ratio is expressed as, cos ∅ = adjacent/hypotenuse of a right triangle.

Given:

Therefore:

Cos H = 36/85

Cos H = 0.4235

Therefore, using the cosine ratio, the value of cos H to 4 decimal places is: A. 0.4235.

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Answer:

x= 0 and x=-3/4

Step-by-step explanation:

[tex]4x^2 + 3x =0[/tex]

We need to solve this equation using quadratic formula.

The quadratic formula is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

for the type of equation

[tex]ax^2 +bx+c=0[/tex]

So, for our given equation:

a= 4

b= 3

c=0

putting values in the formula

[tex]x=\frac{-3\pm\sqrt{9-0}}{8}\\x=\frac{-3\pm3}{8}\\x=\frac{-3+3}{8}\,and\, x=\frac{-3-3}{8}\\x=\frac{0}{8}\,and\, x=\frac{-6}{8}\\x=0\,and\, x=\frac{-3}{4}[/tex][/tex]

so, x= 0 and x=-3/4.

Answer:

A

Step-by-step explanation:

Taking the square root of both sides, you get

[tex]\sqrt{x^2} = \pm\sqrt{180}[/tex]

which simplifies to

[tex]x = \pm\sqrt{180}[/tex]

The square root of 180 is approximately 13.42 and since it is the plus or minus square root, the answer is A, -13.42, 13.42.

Final answer:

The equation x²=180 is solved by taking the square root of both sides, yielding two solutions: x = 13.42 and x = -13.42. Thus, option A is corect.

Explanation:

To solve the equation x² = 180 algebraically, we need to take the square root of both sides of the equation. This gives us two solutions, since both a positive and negative number squared will yield 180. The square root of 180 once calculated is approximately 13.42. Therefore, the two solutions are x = 13.42 and x = -13.42.

Final answer:

After removing one bulb of each type, the probability of the next customer getting an amaryllins bulb is 5/16, which is 31.25%. Thus, the closest answer provided is 31%, option B.

Explanation:

The question asks for the probability of the next customer getting an amaryllins bulb after four bulbs of different types have been removed from a basket containing miscellaneous flower bulbs. Initially, there were 6 amaryllins, 7 daffodils, 4 lilies, and 3 tulips. Since one bulb of each type was bought by the previous customer, we now have 5 amaryllins, 6 daffodils, 3 lilies, and 2 tulips remaining.

To find the probability of selecting an amaryllins bulb, we divide the number of amaryllins bulbs left by the total number of bulbs remaining:

Probability of selecting an amaryllins = Number of amaryllins bulbs remaining / Total number of bulbs remaining

Probability = 5 / (5 + 6 + 3 + 2) = 5 / 16

To convert this to a percentage, we multiply it by 100: (5 / 16) * 100 = 31.25%

Therefore, the probability is closest to 31%, which corresponds to option B.

There was 23.29 inches used on a headband for each player.

And 8.54 inches used on a wristband for each player.

To find out how much fabric for headbands and would beused for each player/person you would do

[tex]total \: fabric \: used \: \div \: total \: amount \: of \: people[/tex]

So, if you substitute the values in it is

[tex]791.86÷34=23.29 \: inches \: for \: 1 \: headband. \: [/tex]

And finally, to find how much fabric is used on a wristband for each player/person you would use the same formula.

[tex]273.28 \: \div 32 = 8.54 \: inches[/tex]

Answer:

Use the square root function on your calculator

Step-by-step explanation:

Look at the third line down, where is says that 936 = AD^2.  If you hit the 2nd button on your calculator then the x^2 button, you will get the square root function.  After you hit those buttons in that order, you'll get the opportunity to find the square root of 936 by entering it in and hitting "enter" on your calculator.  The square root of 936 is 30.59417

Answer:

Option D. [tex]x=10[/tex]

Step-by-step explanation:

step 1

Find the midpoint of the given line segment

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

[tex]A(5,10),B(15,10)[/tex]

substitute the values

[tex]M=(\frac{5+15}{2},\frac{10+10}{2})[/tex]

[tex]M=(10,10)[/tex]

step 2

Find the equation of the perpendicular bisector

we know that

The equation of a perpendicular bisector is equal to the x-coordinate of the midpoint, because is a vertical line (parallel to the y-axis)

therefore

the equation is equal to

[tex]x=10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

A=BH/2

A=9x12/2

A=54

Answer: 54

Step-by-step explanation:

A = base * height ÷ 2

A = 12 * 9 ÷ 2

A = 108 ÷ 2

A = 54

Answer:

7

Step-by-step explanation:

In similar triangles, corresponding elements are proportional. Then we get,

(2x + 1)/(x-1) = 10/4

4(2x +1)       = 10(x-1)

8x + 4         = 10x - 10

8x               = 10x - 14

2x               = 14

x                 = 7

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Answer:

7

both sides are corresponding so triangleABC AB=AC.

Answer:

28

Step-by-step explanation:

7*4

Answer:

28

Step-by-step explanation:

7*4