f(x)=−x
2
+8x+14
\text{Find }f(-8)
Find f(−8)

The height of the mountain using the angles of elevation is 2.346 miles

let

x = distance from the mountain to your current position

h = height of the mountain

Therefore, using trigonometric ratios,

angle of elevation of the current position to the mountain = 8°

angle of elevation of the former position to the mountain = 4.5°

Therefore,

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

tan 8  = h / x

tan 4.5 = h / x + 13

Hence,

x tan 8 = h

(x + 13) tan 4.5 = h

using substitution,

x tan 8  = (x + 13) tan 4.5

x tan 8 = x tan 4.5 + 13 tan 4.5

0.1405408347x = 0.07870170682x + 1.02312218872

0.1405408347x - 0.07870170682x =  1.02312218872

0.0613x = 1.02312218872

x = 1.02312218872 / 0.0613

x = 16.6900489396

x = 16.690 miles

Therefore,

h = 16.6900489396 × tan 8

h = 16.6900489396 × 0.1405408347

h = 2.34561947798

h = 2.346 miles.

Therefore, the height of the mountain using the angles of elevation is 2.346 miles

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Answer:0.66

Step-by-step explanation:

hope this helps

Answer:0.66

Step-by-step explanation:33%50=0.66

Answer: y = 7x + 5 (maybe, please make sure, I'm very doubtful of myself sometimes)

Step-by-step explanation:

1. With the given numbers, m is slope, so 7 is the slope and b is y-intercept, and 5 is the y-int in this case.

2. This is hinting that the equation is in slope intercept form, which is      y = mx + b.

3. Since y = mx + b is the formula, then it means y = 7x + 5 is the likely answer

The Equation representing the following inequality will be 2x + 8 < -18

In the given question, it is stated that a number is 8 more than twice a number that is less than -18.

Let the number be x.

The twice of a number = 2x

A number eight more than twice a number = 2x +8

With the following statements,  we get the Number = (2x+8). Also, we have a condition that this new number is lesser than -18. So we get our equation,

                 =>  2x + 8 < -18

Hence, This  2x + 8 < -18 represents the inequality mentioned in the question stating that a two number is created in which it is lesser than -18.

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The population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8

For given question,

We need to find  the population variance of the following set of numbers: 3, 5, 8, 9, 10

The formula for the Population variance is,

[tex]\sigma = \frac{\sum (x-\bar x)^2}{N}[/tex]

Here,

[tex]\bar x[/tex] = sample average

x = individual values in sample

N = count of values in the sample.

For given question,

[tex]\bar x=\frac{3+ 5+ 8+ 9+ 10}{5} \\\\\bar x=7[/tex]

Using the formula for variance,

[tex]\sigma = \frac{1}{5} [(3-7)^2 + (5 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (10 - 7)^2]\\\\\sigma = \frac{1}{5} \times 34\\\\\sigma = 6.8[/tex]

Therefore, the population variance of the following set of numbers: 3, 5, 8, 9, 10 is 6.8

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Harriette has 58 songs in her playlist.

No of the songs in Lashondra's playlist = Nine times Harriette's playlist

No of the songs in Velora's playlist = Seven times Harriette's playlist

Total number of songs combined by all = 986

Let the number of songs in Harriette's playlist be x.

According to the problem,

9x + 7x + x = 986

⇒ 17x = 986

⇒ x = 58

Answer) Harriette's playlist has 58 songs.

         We have taken the number of songs in Harriette's playlist as x as the other numbers were given in relation to this playlist. Thus, the variable is used to create a generalized formula.

         Since the total number of songs is given, we can carry out simple algebraic addition and simplification to find out the answer.

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The entire question is given below:

Lashondra's playlist has 9 times as many songs as Harriette's playlist.-Velora-has 7 times as many songs on her playlist as Harriette does. If they combined their playlists, they would have 986 songs. How many questions does Harriette have in her playlist?

Answer: x = 50°

Step-by-step explanation:

As you can see in the triangle, the two sides are congruent. One of the angles next to the congruent side is 50 degrees. Therefore the other angle also has to be 50 degrees.

Answer:

X=50°

Step-by-step explanation:

This is because the triangle is an isocele triangle and as we all know an isocele triangle is a triangle with 2 sides equal.

Answer:

x = 39

Step-by-step explanation:

As we can see in the diagram, the triangle is a right-angled triangle, meaning that one of the angles inside the triangle has a measure of 90°.

Whenever we have a right-angled triangle and are given the lengths of two of its sides, and we are asked for the length of the third side, we must use the Pythagorean theorem, which states that:

[tex]\boxed{\mathrm{a^2 + b^2 = c^2}}[/tex],

where:

c = hypotenuse (longest side, opposite to 90° angle)

a, b = the two other sides of the triangle.

In this question, we are asked for the value of x, which is the hypotenuse of the given triangle, while the lengths of the other two sides are 15 and 36.

Therefore, using the Pythagorean theorem, we get:

[tex]15^2 + 36^2 = x^2[/tex]

⇒ [tex]x = \sqrt{36^2 + 15^2}[/tex]

⇒ [tex]x = \sqrt{1296 + 225}[/tex]

⇒ [tex]x = \sqrt{1521}[/tex]

⇒ [tex]x = \bf 39[/tex]

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Answer:

39

Step-by-step explanation:

This is called the Pythagorean Theorem. You are trying to find x or the hypotenuse. The a and b side are the two shorter side of the triangle(the a and b side can be interchangeable), these are the legs. The c side is the hypotenuse the long side. Plug in the numbers to the formula and get your answer.

Answer: x3+5x2+6x

Hope this helps

Answer:

There were 248 adult tickets and 248 kid tickets.

Step-by-step explanation:

a = number of adult tickets

k = number of kid tickets

a + k = 524                                 10a + 5k = 3860

Multiply the equation on the right all the way through by -5 so that we can eliminate the k's when we add the equations together.

-5(a+ K) = 524(-5)

-5a - 5k = -2620

Add the two equations together:

-5a - 5k = -2620

10a + 5K = 3860

5a           = 1240  Divide both sides by 5

a = 248  There are 248 adult tickets.  Plug in 248 for a in either of the original equations.

a + k = 524

248 + k = 524  Subtract 248 from 524 to find the number of kid tickets.

There are 276 kid tickets.

Check:

Plug in 276 for k and 248 for adult to both equations to see if they work

a + k = 524

248 + 276 = 524

524 = 524

10a + 5k = 3860

10(248) + 5(276) = 3860

2480 + 1380 = 3860

38060 = 3860

As per the question, the study investigated the link between walking and the improved health. The researchers reported that the adults walked at an average of [tex]6.4[/tex] days that means [tex]9216[/tex] minutes in the past month for the purpose of health or recreation.

Now to claim for the null hypothesis, the true average number of days as well as minutes in the past months that the adults walked for the purpose of health or recreation is lower than the [tex]6.4[/tex] days as well as [tex]9216[/tex] minutes. That means [tex]u < 9216.[/tex]

And as per the standard theory of the null hypotheses which contains equal sign. And it can be represented as:

[tex]H(0):u = 9216[/tex] but [tex]H(0):u < 9216[/tex]

What are null hypotheses and alternative hypotheses?

The two hypotheses that is null hypotheses and alternative hypotheses are used in statistical testing. The test prediction based on the null hypotheses has no effect as well as no relationships between the variables. And the alternative hypotheses has both a relationship with the variables as well as effect on the variables.

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Answer: single random sample

Step-by-step explanation:

Answer:

1 3/4

Step-by-step explanation:

so the question will be done like this

5 =3x-1/4

The (-1/4) will go to the other side where 5 is and the equation becomes

5+1/4=3x which will be

7/4=3x hence you divide both sides by 3 to get the value of x as 1 as the whole number and 3/4 as the remainder

Answer:

x = 7

Step-by-step explanation:

[tex]5=\frac{3x-1}{4}[/tex]

multiply both sides by 4 (Multiplication property of equality)

[tex]20=3x-1[/tex]

add both sides by 1 (Addition property of equality)

[tex]21=3x[/tex]

divide both sides by 3 (Division property of equality)

[tex]7 = x[/tex]

switch sides (Symmetric property of equality)

[tex]x=7[/tex]

Answer:

no

Step-by-step explanation:

it would be 87.5

The constant of proportionality is $0.50.

A mathematical constant is a significant integer whose value is determined by an explicit definition. It is frequently denoted by a symbol or by the names of mathematicians to make it easier to use in a variety of mathematical situations.

The amount paid by Rocko is $12.50 for 25 game tickets.

The amount paid by Rocko is $17.50 for 35 game tickets.

A proportional relation can be written as:

y = k × x

where k is a constant, y is the cost, and x represents the number of tickets purchased in this instance.

Substituting the values, for Rocko

$12.50 = k × 25

Therefore

k = $12.50 / 25

k = $0.50

For Louisa,

$17.50 = K × 35

K = $17.50 / 35

K = $0.50

Now, k = K

So we have the same value of the constant in both cases, which means that the constant of proportionality is k = $0.50.

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To solve the inequality, add 13 to both sides. The solution is y < 15 or (∞, 15)

Tips to solve linear inequalities:

Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis (  or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.

Example:  x ≥ 2 can be written as [2, ∞), while

                x > 0 is written as (2, ∞)

The given problem:

y-13 < 2

Add 13 to both sides. Adding a number to both sides will not change the inequality. Hence,

y -13 + 13 <  2 + 13

y < 15

Using the interval notation, the solution is (∞, 15)

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Answer:

11.5

Step-by-step explanation:

The dimension which this rug should have is 23 feet × 13 feet.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

Let x represent the width of this rug.

Also, the dimension of this rug is given by:

299 = (29 - 2x) × (19 - 2x)

299 = (29 - 2x)(19 - 2x)

Evaluating the equation, we have:

299 = 551 - 58x - 38x + 4x²

4x² - 58x - 38x + 551 - 299 = 0

4x² - 96x + 252 = 0

Dividing all through by 4, we have:

x² - 24x + 63 = 0

x² - 21x - 3x + 63 = 0

x(x - 21) - 3(x - 21) = 0

(x - 3)(x - 21) = 0

x = 3 or 21 feet.

Note: The plausible solution is x = 3.

Therefore, the width and length of this rug is given by:

Length = 29 - 2(3)

Length = 29 - 6

Length = 23 feet.

Width = 19 - 2(3)

Width = 19 - 6

Width = 13 feet.

In conclusion, the dimension of this rug is 23 feet × 13 feet.

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The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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Answer:

1 1/2

1/2

2 hours

Step-by-step explanation:

Answer: 1/2 hour and 1/2 hour and 1 hour

Step-by-step explanation:

Hope this helps you! :) Have an Amazing day! ^-^

The Volume generated when the region between the curves is rotated around the y - axis is 1216500335.46

Volume of the curves:

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫dc [f(y)]2dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Given,

y = x³

Here we have to find the volume along to the y axis.

With limit as y = 0 and y = 27.

When we apply the values it can be written as,

=>[tex]V=\pi \int\limits^0_{27} {(x^3)^2} \, dx[/tex]

[tex]\implies V=\pi \int\limits^0_{27} {(x^6)} \, dx[/tex]

Apply the limits then we get,

[tex]\implies V = \pi [0^6 - (27)^6][/tex]

=> V = π [0 - 387420489]

=> V =   π x 387420489

=> V = 1216500335.46

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Answer:

5,000

Step-by-step explanation:

Answer:

Money spent on playstation games per week: =$8169861

Money spent on other video games per week: = $5542467

Step-by-step explanation:

Hi to answer this first, we have to calculate how much Americans spend on non Playstation video games. So, we have to subtract the money spent on Sony Playstation games to the total money spent:

$1958904.00-$1167123.00= 791781 on other video games per day

Now, since each week has 7 days. We have to multiply each daily amount by 7.

Money spent on playstation games per week: $1167123.00 x 7=8169861

Money spent on other video games per week: $791781 x 7= 5542467

( - 1.5 , -5 ) is  a horizontal translation one unit right.

What is the formula for a vertical shrink?

Describe the transformation of the parent graph

f(x)=x^2 represented by g.

g(x)= -(2x+3)^2 - 5

Graph represents ( - 1.5 , -5 )

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Answer:

£23

Step-by-step explanation:

£12 + £20 = £23

or

£20 - £12 = £8 difference.

we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.

Sara has 2 items:

Weight of 1st item = 7 ounces.

Weight of second item = 6 3/5 ounces = 33 / 5 ounces.

Total Weight of items to be mailed = 7 ounces + 33 / 5 ounces

Total Weight = 35 + 33 / 5 ounces = 68 / 5 ounces.

Now, cost of mailing 1 ounce per mail = $ 0.45

Cost of mailing 68 / 5 ounce of mails = 68 / 5 × $ 0.45

Total cost = $ 6.12

Therefore, we get that the total cost that Sara has to pay to mail these two mails will be equal to 4 6.12.

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Answer:

< DGB = 101

Step-by-step explanation:

< CGB is equal to 79

< CGB is another name for < 1

We want to find < DGB which is another name for <2

< 1 and < 2 are a linear pair

<1 + <2 = 180

79 + <2 = 180

<2 = 180-79

<2 = 101

< DGB = 101

Answer:

The answer is 101

Step-by-step explanation:

Since a line has an angle of 180°

To know DGB we will just subtract 79 from 180

hence DGB=180°-79°

=101°

Answer: 980.17691.

Step-by-step explanation:

Answer:

980.5714286 ft² or 979.68 ft²

If we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.

Given,

The confidence level =97%

Critical z value of 97% confidence interval =2.170

Margin error E= 0.27

We know,

Sample size n= [tex]0.25(\frac{z}{E})^{2}[/tex]

Substitute the values in the equation

[tex]n=0.25(\frac{2.170}{0.27})^{2}\\ n=0.25( 8.03)^{2}[/tex]

n=16.12

n≈16

Hence, if we want to estimate 97% confidence interval for the true proportion of Americans who support gun control in 2019 with a 0.27 margin of error, then 16 Americans must be surveyed.

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