This answer was confusing for sure

Answer:

To maximize the monthly rental profit, 90 units should be rented out.

The maximum monthly profit realizable is $38,200.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

In this question:

Quadratic equation with [tex]a = -12, b = 2160, c = -59000[/tex]

To maximize the monthly rental profit, how many units should be rented out?

This is the x-value of the vertex, so:

[tex]x_{v} = -\frac{b}{2a} = -\frac{2160}{2(-12)} = \frac{2160}{24} = 90[/tex]

To maximize the monthly rental profit, 90 units should be rented out.

What is the maximum monthly profit realizable?

This is p(90). So

[tex]p(90) = -12(90)^2 + 2160(90) - 59000 = 38200[/tex]

The maximum monthly profit realizable is $38,200.

Answer:

A

Step-by-step explanation:

The first term of the sequence is 4, the common difference is 3. So the equation of this sequence is 4+(n-1)*3 or 1+3*n. Plug in n=100

Step-by-step explanation:

Ratio of height (large to small) = ratio of radii (large to small).

(h / 14) = (8 / 2)

h / 14 = 4

h = 56

The height of the larger cylinder is 56m.

Volume of cylinder is

V = πr2h

V = π(8)2(56)

V = 3584π

x=3

Step-by-step explanation:

x+2=5

x=5-2

x=3

[tex]\\ \sf\longmapsto 0.0000000015[/tex]

[tex]\\ \sf\longmapsto 0.0015\times 10^{-6}s[/tex]

[tex]\\ \sf\longmapsto 0.015\times 10^{-7}s[/tex]

[tex]\\ \sf\longmapsto 0.15\times 10^{-8}s[/tex]

[tex]\\ \sf\longmapsto 1.5\times 10^{-9}s[/tex]

Answer: 0.0000000015 = 1.5 × 10⁻⁹

Concept:

When converting an integer to scientific notation:

- If the number is ≥1, then count the moves of the decimal point to the right until the number is 0<number<10. The number of moves will be the exponent that is positive.

- For example: If converting 300, since there are two moves until it is left with 0<3<10. Thus, the scientific notation will be 3 × 10²

- If the number is <1, then count the moves of the decimal point to the left until the number is 0<number<10. The number of moves will be the exponent that is negative.

- For example: If converting 0.004, since there are three moves until it is left with 0<4<10. Thus, the scientific notation will be 4 × 10⁻³

Solve:

0.0000000015

The decimal point needs to move 9 times to the left to get a number that is between 0 and 10. The number is 1.5.

Thus, the scientific notion of 0.0000000015 will be 1.5 × 10⁻⁹

Hope this helps!! :)

Please let me know if you have any questions

We have to find LCM

3 | 45,75,63

3 | 15,25,21

5 | 5,25,7

5 | 1,5,7

7 | 1,1,7

LCM=3×3×5×5×7=1575

The least common denominator for the group of denominators using the method of prime numbers is 1575.

LCM stands for Least Common Multiple. It is a method to find the smallest common multiple between any two or more numbers.  A factor is one of the numbers that multiplies by a whole number to get that number.

For the given situation,

The numbers are 45, 75, 63​

Prime factors of 45 = [tex]3,3,5[/tex]

Prime factors of 75 = [tex]3,5,5[/tex]

Prime factors of 63 = [tex]3,3,7[/tex]

Then the LCM can be found by, first take the common factors then multiple the remaining factors as,

⇒ [tex](3)(3)(5)(5)(7)[/tex]

⇒ [tex]1575[/tex]

Hence we can conclude that the least common denominator for the group of denominators using the method of prime numbers is 1575.

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Answer:

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

Pvalue < α ;

There is sufficient evidence

r = 0.945 ;

Pvalue = 0.01524

Step-by-step explanation:

Given the data :

Lemon_Imports_(x) Crash_Fatality_Rate_(y)

230 15.8

264 15.6

359 15.5

482 15.3

531 14.9

Using technology :

The regression equation obtained is :

y = 16.3363-0.002455X

Where, slope = - 0.002455 ; Intercept = 16.3363

The Correlation Coefficient, r = 0.945

H0 : correlation is equal to 0

H1 : correlation is not equal to 0 ;

The test statistic, T:

T = r / √(1 - r²) / (n - 2)

n = 5 ;

T = 0.945 / √(1 - 0.945²) / (5 - 2)

T = 0.945 / 0.1888341

T = 5.00439

The Pvalue = 0.01524

Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.

Answer:

Step-by-step explanation:

3*(2k + 3) - 8k + 5 + 5           Remove the brackets on the left

6k + 9 - 8k + 5 + 5                Combine like terms

6k-8k+9 + 5 + 5

-2k + 19

Answer:

1130

Step-by-step explanation:

1109+7 = 1116

1116+7 = 1123

Adding 7 each time

1123+7 = 1130

Answer:

Step-by-step explanation:

triangol BCD = triangle BDA

so

3x - 1 = 34 - 2x

5x = 35

x = 35 : 5

Answer:

x = 7

Step-by-step explanation:

BD is an angle bisector , so

∠ ABD = ∠ DBC , that is

3x - 1 = 34 - 2x ( add 2x to both sides )

5x - 1 = 34 ( add 1 to both sides )

5x = 35 ( divide both sides by 5 )

x = 7

Answer:

probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)

=194/285 or 0.6807.

Step-by-step explanation:

The sample space of all possible choices of three integers from the set {1,2,…..,20} has C(20,3) = (20×19×18)/3! elements.

The complement of the event space E consists of all possible choices of three integers from the complement of the set of all the multiples of 3 in the above set because the product of the chosen integers is a multiple of 3 if and only if at least one of them is a multiple of 3. Hence we have to choose three elements from the set {1,2,4,5,7,8,10,11,13,14,16,17,19,20} which has 14 elements.

Hence

|E'| = C(14,3)

= 14×13×12/3!.

Therefore probability P(E')

= |E'|/|S|

= (14×13×12)/(20×19×18)

= (14×13×2)/(20×19×3)

=(7×13)/(5×19×3)

= 91/285.

Therefore the required probability of the product of the chosen integers being a multiple of 3 is P(E)= 1 - (91/285)=194/285 or 0.6807.

Step-by-step explanation:

X= -4,-2,2,4 (respectively)

Y=4,-4 (respectively)

hope it helps

Answer:

slope is undefined

Step-by-step explanation:

(9, 1 ) and (9, - 4 )

Since the x- coordinates of the 2 points are 9, then the line is vertical and parallel to the y- axis with slope being undefined.

Slope is the change in y over the change in x.

Slope = (-4 - 1) / (9 -9) = -5/0 you cannot divide by 0,so the slope is undefined. This means it is a vertical line

Answer:

[tex]y = 7 - 7x \\ y + 7x = 7 \\ 7x + y = 7[/tex]

Answer:

7x + y = 7

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 7 - 7x ( add 7x to both sides )

7x + y = 7 ← in standard form

Step-by-step explanation:

[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]

Step-by-step explanation:

hope it helps youu.........

Answer:

good morning

Step-by-step explanation:

hope u have a nice day

volume= a^2 * h

area= a^2+4ah

take the second equation, solve for h

4ah=1100-a^2

h=1100/4a -1/4 a now put that expression in volume equation for h.

YOu now have a volume expression as function of a.

take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.

Cited from jiskha

9514 1404 393

Answer:

  perimeter ≈ 12.4 units

Step-by-step explanation:

The side adjacent to the angle is given. The relationships useful for the other two sides are ...

  Tan = Opposite/Adjacent

  Cos = Adjacent/Hypotenuse

From these, we have ...

  opposite = 5·tan(22°) ≈ 2.02

  hypotenuse = 5/cos(22°) ≈ 5.39

Then the perimeter is ...

  P = a + b + c = 2.02 + 5 + 5.39 = 12.41

The perimeter of ∆ABC is about 12.4 units.

Answer:

d) you can reach a large audience with one communication

Step-by-step explanation:

common sense

Answer:

Swimming pool

Step-by-step explanation:

Let's say that we invite x people. The cost of the bowling alley will be $15 for the room, and we add $5 dollars for each person. Therefore, we can represent the cost of the bowling alley as

5 * x + 15

Similarly, the cost of the swimming pool is

4 * x + 12

To find the maximum of the function, one thing we can do is set the expressions of the cost equal to 40. This will give us the amount of people we can invite for exactly 40 dollars. Because cost increases with amount of people, this will give us the maximum number of people we can invite with $40.

We thus have

5 * x+ 15  = 40

subtract 15 from both sides to isolate the x and its coefficient

25 = 5 * x

divide both sides by 5 to isolate x

25/5 = x = 5

We can therefore invite 5 people to the bowling alley

4 * x+ 12  = 40

subtract both sides by 12 to isolate the x and its coefficient

28 = 4 * x

divide both sides by 4 to isolate x

x = 7

Therefore, we can invite 7 people to the swimming pool. As 7 > 5, we can invite more people to the swimming pool.

A quicker way to solve this could be by looking at the cost of each location. Because the bowling alley costs more both per person and for the room, and there is no way to decrease the cost except by decreasing the amount of people, there is no way that the bowling alley could get as many people as the swimming pool with the same amount of money

Answer in picture

….

9514 1404 393

Answer:

  400 mL/h

Step-by-step explanation:

The required rate is ...

  (100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h

Answer:

2.5+2.5+45+45

=95.0m

therefore area of the square= 95.0m

45m×0.5=45.5÷95=

Step-by-step explanation:

2.5m

2.5 m tiles are required

[tex]area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles[/tex]

Answer:

False

True

True

Step-by-step explanation:

Angle 1 cannot be equal to angle 4. Even by just viewing one can see that they can't be equal.

Angle 1 and 2 when combined give a 90 degree angle going from a to c.

Angle 3 and 4 form a 180 degree angle.

HOPE THIS HELPED

Answer:

First, let's find how far away the pier is.

Using the distance formula, we can see that the pier is [tex]\sqrt{58}[/tex] units away.

So, the radius is sqrt 58.

Area = pi (r)^2

So,  the area is 182.82 square units.

Let me know if this helps!

We have that The area that the light covers is  is mathematically given as

[tex]A=\pi x^2[/tex]

From the Question we are told that

Revolving beam of light as far as the pier

Let distance to pier be x

Generally the revolving beam turns a complete angle of 360

Therefore

Its goes in a circle

The area that the light covers is  is mathematically given as

[tex]A=\pi r^2[/tex]

[tex]A=\pi x^2[/tex]

In conclusion

The area that the light covers is  is mathematically given as

[tex]A=\pi x^2[/tex]

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The estimated slope is approximately 2.344

The given table is presented as follows;

[tex]\begin{array}{ccc}Number \ of Bids &&Price \ in \ Dollars\\1&&23\\2&&34\\4&&44\\9&&46\\10&&50\end{array}[/tex]

The regression line formula to be considered = [tex]\bar u = b_0 + b\cdot \bar x[/tex]

The required parameter is;

The estimated slope

The method to find the estimate slope;

The least squares regression formula (method) is presented as follows;

[tex]\bar u = b_0 + b\cdot \bar x[/tex]

Where;

b₀ = The y-intercept

[tex]\mathbf{ b = \dfrac{\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right) }{\sum \left(x_i - \bar x\right )^2 } = The \ estimated \ slope}[/tex]

From MS Excel, we have;

[tex]\bar x[/tex] = 5.2, [tex]\bar u[/tex] = 39.4

[tex]\sum \left(x_i - \bar x\right) \times \left(u_i - \bar u\right)[/tex] = 156.6

[tex]{\sum \left(x_i - \bar x\right )^2 }[/tex] = 66.8

Therefore;

The estimated slope, b = 156.6/66.8 ≈ 2.344 (by rounding the answer to three decimal places)

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