Sharon hits a golf ball off the ground. The function h represents the height of the golf ball, in feet, t seconds after it is hit. h(t) = -16(t − 3)2 + 144 Which of the following statements describes this situation correctly?

Answer:

[tex]P(A \cup B) = 0.75[/tex]

Step-by-step explanation:

There are two scenarios:

A - Rain

B - Fog.

The probability of rain or fog is determined by the Addition Rule, given that A and B are not mutually excluyent:

[tex]P(A\cup B) = P(A) + P(B) - P(A\cap B)[/tex]

[tex]P (A\cup B) = 0.75 + 0.25 - 0.25[/tex]

[tex]P(A \cup B) = 0.75[/tex]

Answer:

9

Step-by-step explanation:



Answer:

9 hours per night

Step-by-step explanation:

Assuming a week is 7 days

7 * 12 = 14 days

126/14=9

She slept 9 hours per night

Hey there! I'm happy to help! :D

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OVERVIEW

A complex number is a real number combined with an imaginary number (such as i, a number that will equal -1 when squared).

The complex plane is an interesting thing we use to graph complex numbers. The horizontal axis is where you plot the real part of the complex number, and the y-axis is where you plot the coefficient of the imaginary number.

For example, if I had the complex number 4+3i, I would plot the point (4,3) on the complex plane.

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MODULI

The modulus (plural is moduli) is the distance of a complex number from the origin on the complex plane. To find the modulus, you take the real number and the coefficient (basically the points of your graph), square them, add the results, and then you find the square root of that! Here's a little checklist so that you can always find the modulus of any complex number!

STEPS TO FIND MODULUS GIVEN COMPLEX NUMBER

STEP 1: PLOT THE COMPLEX NUMBER

Let's use our complex number 4+3i. If we plot it, the point will be (4,3)

STEP 2: TAKE YOUR VALUES OF X AND Y AND SQUARE THEM

4²=16

3²=9

STEP 3: ADD THESE SQUARES

16+9=25

STEP 4: SQUARE ROOT IT

√25=5

Therefore, the modulus (distance from the origin on the complex plane) of 4+3i is 5.

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SOLVING THE PROBLEM

In our case, we are given a modulus but not a point on the line. Our modulus is the square root of seventeen. We are going to have to the steps to find the modulus backwards to find our points. I will put the steps for finding a complex number given the modulus below.

STEPS TO FIND COMPLEX NUMBER GIVEN MODULUS

STEP 1: SQUARE THE MODULUS

√17²=17

STEP 2: FIND THE SQUARES THAT MAKE UP THE NUMBER

Before, we could just add things we found. Now, we have to find the things that were added! How do we know what things were added to find 17?  Well, we know that we added two squares to find the modulus, so we will subtract a square of some sort and hopefully come up with another square.

Let's see what squares exist that are less than seventeen.

1, 4, 9, 16

(Note that one is 1², 4 is 2², 9 is 3², and 16 is 4²)

Which of these can we add to get 17?

Well, we can do 1 and 16, so this is our result so far.

STEP 3: SQUARE ROOT THE RESULTS

Now, we just find the square roots of what we found in the last problem!

√1=1

√16=4

STEP 4: PLOT THE GIVEN NUMBERS ON THE PLANE AND FIND THE COMPLEX NUMBER

We can plot these either way because the modulus of 1+4i will be the same distance from the origin as 4+i because we only use the commutative property (adding order doesn't matter) when looking for the modulus. You can also have the negative version of either number because you immediately square it, so it can also be -4+i or 4-i! You can also rearrange the equation in tons of ways to figure it out. You could also have both be negative, flip the coefficient placement, etc.!

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SOLUTION

Therefore, the complex numbers that have a distance of √17 from the origin on the complex plane are ±4±i and ±1±4i. So, why did I write all of these funny plus and minus signs? Well, it's so that I didn't have to write all of the possible equations. I believe those equations actually represent 8 possible points we can create with the solution we got.

4+i

-4+i

4-i

-4-i

1+4i

-1+4i

1-4i

-1-4i

You can plug these complex numbers back in and find the modulus with my instructions to find the modulus given a complex number. Now, you will be able to deal with moduli and complex numbers for the rest of your life!

I hope that this helps! Have a wonderful day! :)

Answer:

option 4

Step-by-step explanation:

LA = πrl

Here, l ----> slant height

l= 21 ft

r = 12 ft

LA = 3.14*12*21  =  791.7 square ft

SA = πr(l + r)

= 3.14*12 *(12+21)

=3.14* 12 * 33

= 1244.1 square ft

Answer:

The sirt cost $7.5 before tax.

Step-by-step explanation:

Since the pair of slacks cost twice as much as the shirt, we have:

slacks = 2*shirt

And the total purchase was $22.5, so we have:

slacks + shirt = 22.5

We can create a system of equations such as:

slacks = 2*shirt

slacks + shirt = 22.5

If we apply the first formula on the second we can solve for the value of the shirt, we have:

2*shirt + shirt = 22.5

3*shirt = 22.5

shirt = 22.5/3 = 7.5

So the slacks cost:

slacks = 2*7.5 = 15

Answer:

The answer might be d.

Answer:

5

Step-by-step explanation:

We know that a^b^c = a^ (b*c)

1/25 ^(-2/3* 3/4)

1/25^ (-2/4)

1/25 ^ -1/2

Rewriting 1/25 as 5^-2

5^-2 ^-1/2

Again a^b^c = a^ (b*c)

5^(-2*-1/2)

5 ^ 1

5

Answer:

The equation of a circle is [tex](x-5)^2+(y+4)^2=4[/tex] .

Step-by-step explanation:

-The equation of a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex] (where center is [tex](h,k)[/tex], the point [tex](x_{1},y_{1})[/tex] and the radius known as [tex]r[/tex]).

-Use the center (5,-4) and the point (5,-2) for the equation:

[tex](5-5)^2+(-2+4)^2=r^2[/tex]

-Solve the equation:

[tex](5-5)^2+(-2+4)^2=r^2[/tex]

[tex]0 + (-2)^2=r^2[/tex]

[tex]4 = r^2[/tex]

[tex]\sqrt{4} = \sqrt{r^2}[/tex]

[tex]2 = r[/tex]

-After you found the radius, use the center (5, -4)  and radius 2 to get the equation of a circle:

[tex](x-5)^2+(y+4)^2=2^2[/tex]

-Then, after you have the equation, the radius needs to simplified by the exponent:

[tex](x-5)^2+(y+4)^2=4[/tex]

Answer:

The area of a rectangle is:

\sf A=lw

Plug in what we know:

\sf x^2-7x+10=l(x-5)

Factor the left side:

\sf (x-2)(x-5)=l(x-5)

Divide (x - 5) to both sides:

\sf l=\boxed{\sf x-2}

So the length is x - 2 meters.

Step-by-step explanation:

Answer:

Eva would have been better off selecting the 20-year term policy.

Step-by-step explanation:

Base on the scenario been described in the question, Eva would have been better off selecting the 20-year term policy. This reason is because assuming Eva bought the 20-year term policy, she wont be paying the new charge of extra 40% to her premium rate, compared to when she bought the 10-year term policy then renew the policy for another ten years.

Eva's best option would be to buy on a 20-year policy. This is better because she is able to evade the additional, 40% to her premium rate.

Premiums are percentages of the cost value charged by the insurance company for their services and benefits.

Read more on insurance premium;

https://brainly.com/question/9696972

Answer:

It would be 30

Step-by-step explanation:

6*5=30

Answer:

Hilda would pay $ 2,736.60   less interest

Step-by-step explanation:

The total interest payment is the total repayments for 5 years less the initial loan amount

If the interest rate is 10% Hilda repays $233.72  for 5 years multiplied by 12 months:

total repayment=$233.72*5*12=$ 14,023.20  

Interest =$14,023.20-$11,000.00=$3.023.20

If the interest rate is 18% Hilda repays $279.33 for 5 years multiplied by 12 months:

total repayment=$279.33*5*12=$ 16,759.80  

Interest =$16,759.80  -$11,000.00=$5759.8

Difference in interest payments=$5759.8 0-3.023.20=$ 2,736.60  

Answer:the length of MN is6 units

Step-by-step explanation:

It is correct

Lee sold 40 magazines

Step-by-step explanation:

Equation Model:

Let m be the number of magazines Lee sold.

150%-130%=20%, so if 0.2m=8 then m=40

Let me show another way: In the image above 20% is equal to 8 so if we use 8 and 20% and try to reach our way up to 100% (How much Lee sold in total) then we will get our answer.

20%=8

40%=16

60%=24

80%=32

100%=40

Therefore Lee sold 40 magazines.

Hope that makes sense! If you have any more questions or need further clarification then please comment down below or message me! Good luck!

Answer:

.im fully loaded

Step-by-step explanation:

Answer:

Since sine is equal to opposite over hypotenuse, you would create the fraction 8/10. 8 and 10 are both divisible by 2, so that fraction would reduce to 4/5, which is the answer.

Step-by-step explanation:

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Answer:

4/5 sine

Step-by-step explanation:

Answer:

-13/24

Step-by-step explanation:

find the common denominator then add

Answer:

Slant height = 33 inches

Step-by-step explanation:

r = 12 inches

Lateral Surface Area of cone = 396π square inches

πrl = 396π

π * 12 * l = 396π

[tex]l=\frac{396\pi }{12*\pi }\\[/tex]

l = 33 inches

Answer:

Step-by-step explanation:

The apples picked on Monday and Tuesday = 242 + 118 = 360

Apples sold on Wednesday = 360 - 109 =  521

Number of apples left = 251

Equation used: (242 + 118) - 109

Using the normal distribution, it is found that 0.35% of the testers scored a perfect score.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 20.9, \sigma = 5.6[/tex]

The proportion of scores above 36(perfect scores) is given by one subtracted by the p-value of Z when X = 36, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 20.9}{5.6}[/tex]

Z = 2.7

Z = 2.7 has a p-value of 0.9965.

1 - 0.9965 = 0.0035 = 0.35.%.

Hence, 0.35% of the testers scored a perfect score.

More can be learned about the normal distribution at https://brainly.com/question/24663213

#SPJ1

Answer:

Step-by-step explanation:

x three point shots: 8*3=24

x two point shots: 2*2=4

The point would Anthony score is : 24+4=28

I hope it'll help you much

Thank you for asking

Answer:

1.5

Step-by-step explanation:

Plug in numbers into the distance formula.

y2-y1

____

x2-x1

6 - 3.       3

____.     ___

3 - 5.       -2

3/-2=-1.5

Answer:

3.6 or Sqrt(13)

Step-by-step explanation:

plug into distance formula

(3-5)^2 + (6-3)^2

4 + 9

Sqrt(13)

Sqrt(13) is equal to 3.6055127546

^ is rounded up to 3.6

Answer:

He sold 7 more small boxes than large boxes

Step-by-step explanation:

Let x be the no of small boxes sold .

Cost of 1 small boxes of oranges = $5

Cost of x small boxes of oranges = 5x

Let y be the no. of large boxes sold

Cost of 1 large boxes of oranges = $9

Cost of y large boxes of oranges = 9y

He sold 17 boxes in all total for 105

So,x+y=17 ---1

So,5x+9y=105 ---2

Substitute the value of x from 1 in 2

5x+9(17-x)=105

5x+153-9x=105

153-105=4x

[tex]\frac{153-105}{4}=x[/tex]

12=x

Substitute value of x in 1

12+y=17

y=17-12

y=5

Difference in no. of boxes = 12-5 = 7

So, He sold 7 more small boxes than large boxes

Answer:

We equate the two expressions since they both pass through the center of the circle.

The coordinate of the center of the circle is (2,4)

Step-by-step explanation:

From circle theorem, we know that the perpendicular bisector of a chord passes through the center of the circle.

Since both equations would pass through the center of the circle, we equate them.

So, -2x+8 = 3x-2

Solving for x, we have

3x + 2x = 8 + 2

5x = 10

x = 10/5

x = 2

Substituting x = 2 into any of the equations, we find the y- coordinate of the center of the circle.

y = -2x + 8 = -2(2) + 8 = -4 + 8 = 4

So, the coordinate of the center of the circle is (2,4)

Personal Answer:

The perpendicular bisector of a chord passes through the center of the circle/plate, meaning that both expressions can contribute to the finding the center. By solving for x and y, one can find the coordinates of the center of the circle.

Plato Sample Answer:

Because the perpendicular bisector of any chord of a circle passes though the center of the circle, these two perpendicular bisectors intersect at that point. You can set up a system of equations and solve to find the coordinates of the center.

I hope this helps!

Answer:

6 put of 8, 3/4, or 75%

Step-by-step explanation:

Hope this helps ! :)  good luck

Answer:

5, 12, 13

Step-by-step explanation:

because if you use the pythagorean theorem, you will get 13 as the hypotenuse if you take the two shorter sides.

Answer:

2/5*180=72

360/72=5

as simple as that you just need to read on polygons

Step-by-step explanation:

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Answer:

Three or more points that lie on the same line are collinear points .

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

It is three because 3×5 is 15 and 3×3 is 9 so the greast common factore is 3.