6 of 8
Work out the mean for the data set
below:
5, 4, 6, 6, 5, 5, 4,3
Give your answer as a fraction in its
simplest form.

Answer:

7000

Step-by-step explanation:

Given the equation :

L=-250t+7000

L = amount owed after t months of repayment.

From the equation given, we could deduce that it is a linear equation of the form :

y = bx + c

Where, b = - 250 is the slope = fixed amount paid per month and it's negative because the amount owed will reduce with each payment made.

c = intercept, which is the value of L when t = 0

This will give amount borrowed :

L=-250t+7000

At t = 0

L = - 250(0) + 7000

L = 7000

Answer:

144 feet

5 seconds

Step-by-step explanation:

a.

we want the maximum (or the vertex)

-64/-32= 2

-16*2²+64*2+80=144

b.

Here we want the point in which the y=0

In other words, we want the x-intercept

-16x²+64x+80= -16(x-5)(x+1)

so we have

(5,0) and (-1,0)

reject the negative answer to get 5 seconds

A) the maximum height of the apple is 144 feet. B) it will take 1 second for the apple to reach the ground.

How to determine How many seconds will it take for the apple to reach the ground

a. To find the maximum height of the apple, we need to determine the vertex of the parabolic equation. The vertex represents the maximum point of the parabola.

The equation for the height of the apple is given as h = -16t^2 + 64t + 80.

To find the t-value at the vertex, we can use the formula t = -b / (2a), where a, b, and c are the coefficients in the equation.

In this case, a = -16 and b = 64. Substituting these values into the formula:

t = -64 / (2 * -16)

t = -64 / -32

t = 2

So, the apple reaches its maximum height at t = 2 seconds.

To find the maximum height (h), we substitute the value of t = 2 into the equation:

h = -16(2)^2 + 64(2) + 80

h = -64 + 128 + 80

h = 144

Therefore, the maximum height of the apple is 144 feet.

b. To find the time it takes for the apple to reach the ground, we set h = 0 in the equation and solve for t:

0 = -16t^2 + 64t + 80

We can factor this equation or use the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 64, and c = 80. Substituting these values:

t = (-64 ± √(64^2 - 4(-16)(80))) / (2(-16))

t = (-64 ± √(4096 + 5120)) / (-32)

t = (-64 ± √9216) / (-32)

t = (-64 ± 96) / (-32)

We have two possible solutions:

t1 = (-64 + 96) / (-32) = 1

t2 = (-64 - 96) / (-32) = 5

Since the apple was launched upward, we consider the positive solution t1 = 1.

Therefore, it will take 1 second for the apple to reach the ground.

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Answer:

The rate of simple interest is 0.125, or 12.5%.

Step-by-step explanation:

If the man must repay $750 after 4 years on a $500 loan, the simple interest would be ($750-$500), or $250.

The simple interest formula is i = p*r*t.  Solving this for the interest rate, r, yields

        i

r = ----------

       p*t

and so, with i = $250, p = $500 and t = 4 yr, we find r as follows:

         $250

r = ----------------- = 0.125

         $500*4

The rate of simple interest is 0.125, or 12.5%.

Answer:

The statue is 10cm tall in Kia's drawing.

Step-by-step explanation:

We know the statue is 80ft tall, as Bob's drawing was 1cm to 5ft and his drawing was 16cm tall. 16 x 5 = 80ft.

Because the new scale is 1cm to 8ft, you divide the 80ft tall statue with 8, and that leaves you with a 10cm tall replica statue.

Answer:

10 cm

Step-by-step explanation:

Answer:

3=1+2 because An exterior angle of a triangle is equal to the sum of the opposite interior angles

when 2=1

we can also write it as

3=1+1

3=21(this means twice of angle 1)

Answer:

3486784401 / 9^-6

Step-by-step explanation:

Hi!

(9^2)/(9^-8)

= 81/(9^-8)

= 81/1/43046721

Or

9^-6

Try both to see if they work. if they don't, hit me up in the comments

Answer:

3 5 dollar bills, 6 1 dollar bills, and 8 20 dollar bills

Step-by-step explanation:

Answer:

Step-by-step explanation:

By the Isosceles Triangle Theorem, angle O and angle M are congruent because the sides across from each of these angles are congruent. therefore, O = M = 4y - 15. Since, by the Triangle Angle-Sum Theorem all the angles of a triangle have to add up to equal 180 AND angle O and angle M are the same:

7y + 4y - 15 + 4y - 15 = 180 and

15y - 30 = 180 and

15y = 210 so

y = 14. Plug 14 in for y in 7y and get that

∠N = 98°

Answer:

pls provide diagram

it will hep

Answer:

$32.96

Step-by-step explanation:

38.50 (20%) + 7.70

38.50 - 7.70 = 30.80

:Before tax:

$30.80

30.80(7%) = $2.16

30.80 + 2.16 = 32.96

:Total after tax:

$32.96

Answer:

189 and 202

Step-by-step explanation:

An outlier is a value that will have an effect on the mean of a set of values. It has an obvious difference compared to other values. They can be easily determined in a set of given data by mere observation.

From the given data in the question, it would be observed that the chronological difference among set of the data is either 1, 2, 3 or 4. But the two numbers that could be referred to as outliers are 189 and 202. This is because the have a wider range than others.

Answer:

Here are the answer choices you forgot:  

There are no outliers.

153

202

192, 202

-----------

C & D are incorrect.

I think it is A : no outliers.

Answer:

a + b = 54

a + 9 = 54

Use inverse operations to solve

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

a p e x

Answer:

(1,2)

Step-by-step explanation:

y = 2x. y = -x+3

Set the two equations equal

2x = -x+3

Add x to each side

2x+x = -x+x+3

3x = 3

Divide by 3

3x/3 = 3/3

x = 1

Now find y

y =2x = 2(1) = 2

(1,2)

Solve like how you solve the system of equations. System of Equations are to find the intercept of both graphs or to find which coordinate points are solution to both equations.

We are given the equations below:

[tex] \large{ \begin{cases} y = 2x \\ y = - x + 3 \end{cases}}[/tex]

Since both equations are y-isolated and we want to find the coordinate point that both equations have or the coordinate point that is a part of two equations.

[tex] \large{2 x = - x + 3}[/tex]

Isolate the x-term by adding both sides by x.

[tex] \large{2x + x = - x + 3 + x} \\ \large{3x = 3}[/tex]

Divide both sides by 3 so we can finally get the x-isolated equation.

[tex] \large{ \frac{3x}{3} = \frac{3}{3} \longrightarrow x = 1 }[/tex]

Next step is to find the value of y. x-term and y-term both have relations. That means when substituting x-term, we get y-term. Therefore, substitute x = 1 in any given equations. It is not necessary to substitute both, only one is fine. I will choose the first equation to solve for y-value.

[tex] \large{y = 2x}[/tex]

Substitute x = 1:

[tex] \large{y = 2(1) \longrightarrow y = 2}[/tex]

The value of y is 2 when x is 1. Since we want the answer to be in coordinate form or ordered pair. From (x,y) - we get (1,2).

Answer

I hope this helps! Let me know if you have any questions or doubts. Do not hestitate to ask if you've got a question. Good luck on your assignment and have a great day!

Answer:

Solution given:

length of arc LM={angle}/360*2*π*r

=here π=180 for angle and π for length

=(3π/4)/360*2*π *6

=(3*180/4)/360*2*π*6

=9/2π

option C

9/2π is a required answer.

Answer:

x = 134 degrees

Step-by-step explanation:

The two angles are alternate interior angles, therefore they equal.

I hope this helped!

It can definitely be a bit tricky to remember all of the different types of angles! But let's see what we've got here.

Our given measures/variables, 134 and x, are both on the inside of the parallel lines (clue: INTERIOR). Then, we can see that they are on opposite sides (clue: ALTERNATE). Therefore, these are alternate interior angles.

Alternate interior angles are congruent, which means that x = 134 degrees.

Hope this helps!! :)

Answer:

Step-by-step explanation:

Answer:

[tex](5m - 2n)(25 {m}^{2} + 10mn + 4 {n}^{2}) [/tex]

[tex]5m(2 {m}^{2} + 10mn + 4 {n}^{2} ) - 2n(25 {m}^{2} + 10mn + 4 {n}^{2} )[/tex]

[tex]10 {m}^{3} + 50 {m}^{2}n + 20m {n}^{2} - \\ 50 {m}^{2} n - 20m {n}^{2} - 8 {n}^{3} [/tex]

[tex]10 {m}^{3} - 8 {n}^{3} (ans)[/tex]

Answer:

B

Step-by-step explanation:

A)  -4

B)  results in a non-terminating, non-repeating decimal, which is irrational

C)  2

D)  4

Surface area of cone2 is equals to 96π.

"Surface area is defined as the sum of the area of all the faces of given three dimensional shape."

Formula used

Surface area of the cone = πr² + πr l

According to the question,

Given,

'r' represents the radius of the cone

'h' represents the height of the cone

'l' represents the slant height of the cone

Cone1 and Cone2 are congruent cones.

⇒Radius of cone1 = Radius of cone2

  Slant height of cone1 = Slant height of cone2

As per the given dimensions we get,

Radius of both the cones 'r' = 6units

Slant height of both the cones 'l' = 10units

Substitute the values in the formula we get,

Surface area of the cone2 = π (6)² + π (6) (10)

                                            = 36π +60π

                                            = 96π square units

Hence, surface area of cone2 is equals to 96π.

Learn more about surface area here

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Answer:

7 1/3

Step-by-step explanation:

Step-by-step explanation:

According to the question,

~The product of 10 and a number is 3 less than the number.

Let us suppose the number as n. Writing it in the form of an equation,

→ 10 × Number = Number - 3

→ 10n = n - 3

Option B ✓

[tex] \rule{200}2 [/tex]

I want to help you but ... What's the question?

Answer:

x = 3.5

Step-by-step explanation:

2x + 5 = 12

2x = 7

x = 3.5

Hope that helped!

[tex]\sf\purple{The\:value\:of\:x\:is\:3.5.}[/tex] ✅

Step-by-step explanation:

[tex]2x + 5 = 12 \\ ⇢ 2x = 12 - 5 \\ ⇢ 2x = 7 \\ ⇢ x = \frac{7}{2} \\ ⇢ x = 3.5[/tex]

[tex]\boxed{The\:value\:of\:x\:is\:3.5.}[/tex]

[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]

[tex]2x + 5 = 12 \\ ⇝2 \times 3.5 + 5 = 12 \\ ⇝7 + 5 = 12 \\ ⇝12 = 12 \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

overdraft fees is your answer

Step-by-step explanation:

Answer:

30 m

Step-by-step explanation:

Midsegment of a Trapezoid

[tex]\frac{(Base_{1}) +( Base_{2}) }{2}[/tex]

[tex]\frac{12 + 38}{2}[/tex]

[tex]\frac{60}{2}[/tex]

30

Average of the top and bottom = the middle