What is the mean of 9, 8, -15 and -12?

The Mean is:

Answer:

1) Please find the attached drawing of the archway created with MS Excel

2) The y-intercept is (0, 24)

The x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base is 11

The height of the archway at its highest point = 30.25

Step-by-step explanation:

1) Please find the attached drawing of the archway created with MS Excel

2) The y-intercept is (0, 24)

The x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base is 11

The height of the archway at its highest point = 30.25

Step-by-step explanation:

The given function representing the archway is y = -x² + 5·x + 24

1) Please find attached the required drawing of the archway created with MS Excel

2) The y-intercept is given by the point where x = 0

Therefore, we have, the y-value at the y-intercept = -0² + 5×0 + 24 = 24

The y-intercept = (0, 24)

The x-intercept is given by the point where y = 0

Therefore, the x-values at the x-intercept are found using the following equation;

0 = -x² + 5·x + 24

x² - 5·x - 24 = 0

By inspection, we have;

x² - 8·x + 3·x - 24 = 0

x·(x - 8) + 3·(x - 8) = 0

∴ (x + 3) × (x - 8) = 0

Either (x + 3) = 0, and x = -3, or (x - 8) = 0, and x = 8

Therefore, the x-intercepts are (-3, 0), and (8, 0)

3) The width of the archway at its base = The distance between the x-values at the two x-intercepts

∴ The width of the archway at its base = 8 - (-3) = 11

The highest point of the arch is given by the vertex of the parabola, y = a·x² + b·x + c, which has the x-value of the vertex = -b/(2·a)

∴ The x-value of the vertex of the given parabola, y = -x² + 5·x + 24, is x = -5/(2×(-1)) = 2.5

Therefore;

The y-value of the vertex, is y = -(2.5)² + 5×2.5 + 24 = 30.25 = The height of the archway at its highest point

∴ The height of the archway at its highest point = 30.25

The vertex of the parabola is at (-2.5, 17.75). And the y-intercept of the parabola is at (0, 24).

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given as,

y = x² + 5x + 24

Convert the equation into a vertex form, then we have

y = x² + 5x + 25/4 - 25/4 + 24

y = (x + 5/2)² + 71/4

y = (x + 2.5)² + 17.75

The vertex of the parabola is at (-2.5, 17.75). The y-intercept of the parabola is given as,

y = (0)² + 5(0) + 24

y = 24

The y-intercept of the parabola is at (0, 24).

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

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Answer:

12

Step-by-step explanation:

You need the GCF of 48 and 60

48 = 2 x 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

Both have 2 x 2 x 3, so the answer is 12

Answer:

answer is 19............

The ratio of the height of the triangle to the side of the square (B) 1 : 2

The area of a triangle is (1/2)×base×height.

The area of a square is (side)².

Given, The area of a square is four times the area of a triangle.

∴ (side)² = 4{(1/2)×base×height}.

The base of the triangle and the side of the square are equal let this be 'a'.

∴ a² = 4(1/2)×a×height.

a = 2×height.

a = 2h.

learn more about squares here :

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(hopefully I read this right)

-5 1/4 - (-7 1/2)

-5 1/4 - -7 1/2

-5 1/4 - -7 2/4

-21/4 - -30/4

-21/4 - -30/4 = 9/4 = 2 1/4

Hopefully I am correct!

Answer:

b

Step-by-step explanation:

We want to get the expected value for the given experiment. We will see that the expected value is $2.33

For an experiment with outcomes {x₁, ..., xₙ} each one with probability {p₁, ..., pₙ} the expected value is defined as:

EV = x₁*p₁ + ... + xₙ*pₙ

Here we have 3 outcomes:

For x₁ we need to roll a 6, this is a probability of 1 out of 6, then:

p₁ = 1/6

For x₂ we need to roll a 3, 4, or 5 (3 out of 6), then:

p₂ = 3/6

For x₃ we need to roll a 1 or a 2 (2 out of 6) so the probability is:

p₃ = 2/6

Then the expected value is:

EV = $8*(1/6) + $2*(3/6) + $0*(2/6) = $2.33

If you want to learn more about expected values, you can read:

https://brainly.com/question/15858152

Answer: the x or the input of a function

Step-by-step explanation:

Answer:

y = 3x + 2

Step-by-step explanation:

3 is the slope

2 is the y-intercept

G=45.89 gallons 46 gallons.

I hope this answers your question!

:)

Step-by-step explanation:

in that case we can imagine a diagonal line DB that splits the quadrilateral into 2 right-angled triangles: ADB and CDB.

the area of the quadrilateral is then the sum of the areas of the 2 triangles.

the area of a right-angled triangle is

leg1 × leg2 / 2

with the legs being the sides that enclose the 90 degree angle.

so, for ADB we get

AD × AB / 2 = 3 × 11 / 2 = 33/2 = 16.5

for CDB we get

BC × CD / 2 = 7 × 9 / 2 = 63/2 = 31.5

so, in total for the area of the quadrilateral we get

16.5 + 31.5 = 48

Answer:

The value of k is -21

Step-by-step explanation:

ax² + bx + c = 0

Sum of the roots = -b/a

3x² + kx + 1 = 0

= sum of the roots = -k/3

-k/3 = 7

Now, Multiply both side by (-3) we get,

(-3)-k/3 = 7(-3)

k = -21

Thus, The value of k is -21

-TheUnknownScientist 72

Answer:

25

Step-by-step explanation:

Answer: The answer is 25.

Have a great Day/Night!

I had this question earlier, and if I remember correctly the answer was 56.40

Answer: graph b

Step-by-step explanation:

Vertex:  ( 3 ,0 )

Focus:  ( 3 , 1 4 )

Axis of Symmetry:  x = 3

Directrix:  y = − 1 4

So the Lincoln middle school will have +5.75 pounds or ounces of ffod

Answer:

nth term = 4 + n^2

Step-by-step explanation:

Sorry if the answer is long but I'm hoping my explanation can help.

In order to understand the issue, we should try to find the pattern between the terms given.

The terms given were 5, 8, 13, 20 and 29.

Between the first term and second term, the difference is 3.

Between the second and third term, the difference is 5.

The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is

2n - 1.

Hence, we can determine the pattern of the numbers is

nth term = (n-1) term + 2n - 1

We can use this to find term 0 (before term 1) by plugging in the values for term 1

5 = 0th term + 2 (1) - 1

5 = 0th term + 1

Hence the 0th term = 4

If we expand on the summation,

We can find the nth term

nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1

As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.

We can rewrite it as

nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n

Now, we will move 4 and n to one side.

nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n

We can factorize 2 out from every term to the right of -n. This would give out

nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)

The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.

The triangular formula is stated such that

Tn = (n*(n+1))/2

This heavily simplifies the equation into

nth term = 4 - n + 2 [(n*(n+1))/2]

This equation becomes

nth term = 4 - n + n^2 + n.

Now, we can finally simplify into the final equation

nth term = 4 + n^2

Answer:

$8.01

Step-by-step explanation:

Answer:

67

Step-by-step explanation:

Because 180-113 is 67.

Answer:

67°

Step-by-step explanation:

A line is 180° so subtract the 113°

180 - 113 = 67°

hope that helps and have a great day :D

Answer:

multiply the length and the width of a rectangle or a square

Answer:

The correlation coefficient r measures the direction and strength of a linear relationship. Calculating r is pretty complex, so we usually rely on technology for the computations. We focus on understanding what r says about a scatterplot.❤

The perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s

To find the perimeter of any figure, add all the side lengths of the figure together.

Thus, the given side lengths of the figure are:

p, p, q, q, r, r, s, s, s, and s.

To find the perimeter add them together.

Perimeter of the figure = p + p + q + q + r + r + s + s + s + s

Perimeter = 2p + 2q + 2r + 4s

Therefore, the perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s

Learn more about perimeter on:

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Answer:

x = 122

Step-by-step explanation:

Answer: (weight = w)

This is a lot to answer but. (A)  (13 x 1.2) - 14 = w

w = 1.6

Step-by-step explanation:

Answer:

19.47

Step-by-step explanation:

Use the law of sines.

sin(90)/6 = sin(x)/2

Multiply both sides by 2

2 * sin(90)/6 = sin(x)

Use a calculator

0.33333 = sin(x)

sin^-1 0.3333 = 19.47

Answer:

ok so first take a way 100 from 350

250 then divide by 20

12

Hope This Helps!!!

We know

[tex]\\ \sf\Rrightarrow Speed=Distance/Time[/tex]

[tex]\\ \sf\Rrightarrow Distance=Time\times {Speed}[/tex]

Let hours be x

[tex]\\ \sf\Rrightarrow 12x+10x=34[/tex]

[tex]\\ \sf\Rrightarrow 22x=34[/tex]

[tex]\\ \sf\Rrightarrow x=34/22[/tex]

[tex]\\ \sf\Rrightarrow x=17/11[/tex]

[tex]\\ \sf\Rrightarrow x=1.5h[/tex]

Answer:

35% of 800 = 280

...........

Answer:

(-10,8)(0,12)(4,-20)

Step-by-step explanation:

You just have to insert the points into the equation and then solve.

Ex: 2(4)-20=-12- True