A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ______ second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ______feet.
(Simplify your answer.)

The best way to decide on which group we should experiment with the population sample is through a random selection.

(B) Avoid bias and be sure the study you are executing is accurate:

Therefore, the best way to decide on which group we should experiment with the population sample is through a random selection.

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Answer:

x = 18

Step-by-step explanation:

ABCD ∼ JKLM

AB = 12        JK = x

AD = 6        JM = 9

6/9 = 12/x

2/3 = 12/x

2/3 = 12/18

2/3 = 2/3

Step-by-step explanation:

[tex]4(12xy - 8x - 21xy ^{2} + 14xy + 15y - 10)[/tex]

[tex]4( - 21 {xy}^{2} + 26xy - 8x + 15y - 10)[/tex]

[tex] - 84 {xy}^{2} + 104xy - 32x + 60y - 40[/tex]

The values of x =11.3° and y =10° as of given diagram.

A straight angle and a right angle are measured at 90° and 180°, respectively.

In the given diagram, ∠VRT = Right angle= 90°

i.e., (4y)° + (5y)° = 90°

(9y)° = 90°

y = 10°

∴ 4y = 40°

5y = 50°

Then, the line SRU is a straight line. The angle will be 180°;

i.e., (4y)° + (12x - 4)° = 180°

40° +  (12x - 4)° = 180°

12x - 4 = 180° - 40°

12x = 140° - 4°

x = 136° / 12

x = 11.3

Hence, the value of x =11.3° and y =10°

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The expression to a + bi form is [tex]=10-\sqrt{2i}[/tex]

Simply put, what is linear algebra?

The subject of linear algebra is linear combinations. To build new columns and arrays of numbers, arithmetic is used to arrays of numbers called matrices and columns of numbers called vectors. The study of the planes and lines, vector spaces, and mappings needed for linear changes is referred to as algebra.

What is nonlinear equations?
A nonlinear equation is one whose graph is not a straight line and whose greatest power of the variables is not 1.

Step-by-step explanation:

Given:

[tex]-\sqrt{4} + \sqrt{-72}+\sqrt{64}+\sqrt{-98}=2+8-7\sqrt{2i}+6\sqrt{2i}[/tex]
[tex]=10-\sqrt{2i}[/tex]

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the median of the data set is $60,260.00.To find the median of a set of data, we first need to put the values in order from lowest to highest. Then, if the number of values is odd, the median is the middle value.

what is median ?

In statistics, the median is a measure of central tendency that represents the middle value of a dataset. To find the median, you need to first arrange the values in order from lowest to highest (or from highest to lowest).

In the given question,

To find the median of a set of data, we first need to put the values in order from lowest to highest. Then, if the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

In this case, the values in order from lowest to highest are:

$56,250.00

$57,120.00

$57,120.00

$59,160.00

$61,360.00

$63,190.00

$65,370.00

$79,150.00

There are eight values, which is an even number, so we need to take the average of the two middle values, which are $59,160.00 and $61,360.00.

The average of these two values is:

($59,160.00 + $61,360.00) / 2 = $60,260.00

So the median of the data set is $60,260.00.

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As per the given percentage of 20, the total number of bees is 200 and on the second day, he caught 40 unique bees so the total unique bees are 140

Percentage:

Percentage refers the amount of something is expressed as if it is a part of the total which is a hundred. and the ratio can be expressed as a fraction of 100.

Given,

Sara wants to estimate the number of bees in a beehive. She catches 100 bees from the hive and marks each one with a dye. She then lets the bees go. The next day, Sara catches 50 bees from the hive. 10 of these bees have been marked with dye.

Here we need to determine the number of bees in the beehive.

Let us consider she catches 100 bees from the hive and marks each one with a dye. And then lets the bees go.

Then the next day, she catches 50 bees from the hive. 10 of these bees have been marked with dye.

So, the percentage of the dye bees in the hive will be

P = 10/50 x 100

P = 20%

Now, let the total number of the bees be x, then the total number of the bees will be

=> 100 x 2 = 200

Therefore, the total number of bees is 200.

Now, the number of unique bees will be

Unique bees = 100 + (50 - 10)

Then, the number of unique bees = 100 + 40

Therefore, the number of unique bees is 140.

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Step-by-step explanation:

try this option; all the details are in the attachment.

The area under the standard normal curve that lies to:

(a) to the left of z= -2.07

= 0.019226

(b) between z= -0.56 and z =1.2

= 0.17267

(c) between z = 0.08 and z =2.84

= 0.46586

(d) to the right of z =0.96

= 0.83147

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean is 0 and standard deviation is equal to 1.

Any normal distribution's values can be transformed into z scores to standardize it.

Z scores indicate the number of standard deviations each result is from the mean.

The area under the standard normal curve is gotten using the z table for the scores and the values are as follows

(a) to the left of z= -2.07

= 0.019226

(b) between z = -0.56 and z = 1.2

= z = -0.56 - z = 1.2

= 0.28774 - 0.11507

= 0.17267

(c) between z= 0.08 and z=2.84

= z = 0.08 - z = 2.84

= 0.46812 - 0.00226

= 0.46586

(d) to the right of z = 0.96

= 1 - z = 0.96

= 1 -  0.16853

= 0.83147

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Answer: 8 in²

Step-by-step explanation:

A diameter of a sweet potato pie is 8 inches

Hence a radius of a sweet potato pie is 8/2=4  inches

A=πr²

π=3.14159≈3    

r=4 inches

Hence,

A=3(4²)

A=3(4*4)

A=3(16)

A=48 in²

The area of each slice is:

48:6=

8 in²

Answer:

66 inch

Step-by-step explanation:

have great day

Answer: B and D

Step-by-step explanation:

y-4 = 2/3 (x-1)

y = 2/3 x - 2/3 + 4

y = 2/3 x - (-10)/3

y= 2/3x + 10/3

10/3 = 3  1/3

so the answers are B and D.

The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

O and R are the subsets of a Universal set, U, such that

U = {22,23,24,25,26,27,28,29,30}

O = {prime numbers} = {23, 29}

R = {even numbers} = {22, 24, 26, 28, 30}

The elements of (OUR)' will be given as,

(OUR)' = {23, 29}

The elements of (O∩R)' will be given as,

(O∩R)' = {22, 23, 24, 26, 28, 29, 30}

The elements of O∩R will be given as,

O∩R = 0

The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

The Venn diagram is given below.

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Answer:

46 = .90x + 2(.70x)

x = 20

Step-by-step explanation:

46 = .90x + 2(.70x)

46 = .90x + 1.4x

46 = 2.3x

20 = x

Applying vertical or opposite angles theorem the values of m∠1, m∠3 and m∠4 are 141°, 141° and 39° respectively

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °. The sum of the angles is 360° and they have made a full turn, and so the angles around a point add to equal 360° .

This implies that m∠1, m∠2, m∠3 and m∠4 all sum up to 360°

However, m∠2 = 39°

This can be used to find m∠4

m∠2 = m∠4 (Opposite or vertical angles are equal)

Therefore, m∠4 = 39°

But m∠1 and m∠3 are also equal by applying vertical angles theorem too.

Let them be represented by x

x + 39 + x + 39 = 360

Reason : Sum of angles at a point equals 360°

2x + 78 = 360

2x = 282

x = 141°

The values of m∠ 1 and m∠3 are 141° respectively

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The solution to the questions are:

From the question, we have the following parameters that can be used in our computation:

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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For the rotation in 90° counter clockwise, the rule that shows input and out of the of the rotation is (−y, x) and the new coordinates are (-1, -5)

Rotation:

Rotation defines the transformation in which the object is rotated about a fixed point.

Given,

Parallelogram ABCD

A is at (-5,1)

B is at (-4,3)

C is at (-1,3)

D is at (-2, 1).

Parallelogram ABCD is rotated 90° counterclockwise.

Now, we have to find the rule shows the input and output of the rotation, and what is the new coordinate of A′.

Here we need to find the rotation of A alone.

So, we have to take the point (-5,1) alone.

The rule, that is used for 90° counterclockwise rotation is states that "When rotating a point 90 degrees counterclockwise about the origin then the point A(x, y) becomes A'(-y, x)."

Based on the this rule, we have written the following as,

=> (-5,1) => (-(1), -5)

=> (-1, -5)

Therefore, the new coordinate of A' is (-1, -5)

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Confidence interval to estimate the population mean is 81.592< μ <96.408.

Confidence = 95%

Z-value = Z = 1.960

No. of sample = n = 28

Mean = X = $89

Standard deviation = S = 20

Confidence interval = CI = [tex]X+Z*(\frac{S}{\sqrt{N}})[/tex] or [tex]X-Z*(\frac{S}{\sqrt{N}})[/tex]

                                        = [tex]89+1.96(\frac{20}{\sqrt{28}})[/tex] or [tex]89-1.96(\frac{20}{\sqrt{28}})[/tex]

                                        = 89 + 7.408  or 89 - 7.408

                                        = 96.408 or 81.592

Hence, interval is 81.592< μ <96.408.

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The maximum of a/b to two decimal points after rounding off is 35.10.

According to the question,

We have the following information:

a = 730 (rounded to nearest 10)

b = 20.8 (rounded to 1 decimal point)

Now, we have to find the value of a divided by b and then we have to round off the final result to two decimal points.

So, we have the following expression for division:

a/b

730/20.8

35.0961

Now, when we will round off to two decimal points, we will increase 9 by adding 1 because the right next digit to 9 is greater than 5.

35.10

Hence, the maximum of a/b to two decimal points is 35.10.

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Answer:

i think D hope this helps :D

Step-by-step explanation:

Answer:

195

Step-by-step explanation:

Answer: ________________________________________________

f(x) = -1/2x

Answer:

Step-by-step explanation:

slope = y2-y1/x2-x1

-2-1/4-(-2)=-3/6=-1/2 or -0.5

Answer:

53 m

Step-by-step explanation:

4 times around a square means 16 sides

848 /16 = 53 m per side

Answer:

Step-by-step explanation:

(a) The probability that 10 or more are good is 1/10

(b) The probability that 5 or more are good is 1/25

(c) The probability that all are good is 3/25

Probability:

Basically, the possibility of the outcome of any random event is known as probability.

Given,

Approximately 75% of light bulbs are good.

Here we need to find If 15 light bulbs are chosen, then

(a) The probability that 10 or more are good

(b) The probability that 5 or more are good

(c) The probability that all are good

Let us consider that the total number of light bulbs are 100.

And 75% of the bulbs are good.

Which means there are 75 good bulbs in it.

So, the defective bulbs are

=> 100 - 75

=> 25

So, the probability that 10 or more are good is calculated as,

=> 10/100

=> 1/10

Similarly, the probability that 5 or more are good is

=> 5/100

=> 1/25

And the probability that all are good is,

=> 15/100

=> 3/25

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As per the concept of Poisson distribution ,

(a) The standard deviation of death in an army corps each year is 0.781

(b) The probability of exactly 3 deaths in an army corps in a given year is 0.069

(c) The probability of at most 2 deaths in an army corps over an 8-year period is 0.3425

Poisson distribution:

Basically, the process of estimating the occurrence of a specified event that happens during a particular period of time is known as Poisson distribution.

Given,

From a research paper, it is known that the number of soldiers who died annually by being kicked by a horse followed a Poisson distribution with an average of 0.61 death in an army corps each year.

Here we need to find the following:

(a) The standard deviation of death in an army corps each year

(b) The probability of exactly 3 deaths in an army corps in a given year

(c) The probability of at most 2 deaths in an army corps over an 8-year period

As per the given question, we have identified the following value,

The Poisson distribution average λ = 0.61

So, the standard deviation of the death

=> σ = √0.61

Therefore, the standard deviation is  0.781.

The probability of exactly 3 deaths in an army corps in a given year is  calculated as,

=> P(X = 3) = e⁻⁰°⁶¹ x (0.61³/3!)

=> P(X = 3) = e⁻⁰°⁶¹ x (0.2269/6)

=> P(X = 3) = e⁻⁰°⁶¹ x 0.0378

=> P(X = 3) = 1.8404 x 0.0378

=> P(X = 3) = 0.069

Therefore, the probability of exactly 3 deaths in an army corps in a given year is 0.069

Now, the probability of at most 2 deaths in an army corps over an 8-year period is calculated as,

=> P(X = 2) = e⁻⁰°⁶¹ x (0.61²/2!)

=> P(X = 2) = e⁻⁰°⁶¹ x (0.3721/2)

=> P(X = 2) = e⁻⁰°⁶¹ x 0.1861

=> P(X = 2) = 1.8404 x 0.1861

=> P(X = 2) = 0.3425

Therefore, the  probability of at most 2 deaths in an army corps over an 8-year period is 0.3425

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Answer:

10

Step-by-step explanation:

put 20 as the value for x and solve the equation:
(4/5) * 20 -6
= 4*20/5 - 6
= 80/5 - 6
= 16 - 6
= 10

Answer:

[tex]\huge\boxed{\sf f(20)=10}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x)=\frac{4}{5} x-6[/tex]

Put x = 20

[tex]\displaystyle f(20)=\frac{4}{5} (20)-6\\\\f(20)=4 \times 4 - 6\\\\f(20)=16-6\\\\f(20)=10\\\\\rule[225]{225}{2}[/tex]

Answer:

X=

Step-by-step explanation:

first you should substitute for X

Y=X-700

2X-y=800

2X-(X-700]=800

X+700=800

X=100

then you substitute for Y

Y=100-700

Y=-600

last you put in the equations to make sure all the numbers are right.

-600=100-700 good

200--600=800 good

X=100

Y=-600

The number of packs of mini cupcakes ordered by Mary are 15 approximately if she has $200 to spend and the cost of each pack is $12.75 and shipping cost is $14.50.

Total amount, Mary can spend = $200

Cost of one pack = $12.75

Total shipping cost = $14.50

Amount remaining after shipping cost = $200 - $14.50 = $185.50

Total packs Mary can order = $185.50/$12.75 = 14.54

Hence, Mary can order approximately 15 packs of mini cupcakes.

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Answer: SUCK

Step-by-step explanation:

From the calculation below, we have:

A) Current ratio = 1.31

(B) Acid test (quick) = 1.09

(C) Average day's collection = 37.39 days

(D) Asset turnover = 1.28 times

(E) Profit margin on sales = 14.63%

The requirements can be solved as follows:

A) Current ratio = Current Assets / Current Liabilities = $21,000 / $16,000 = 1.31

(B) Acid test (quick) = (Current Assets - Inventory) / Current Liabilities = ($21,000 - $3,500) / $16,000 = 1.09

(C) Average day's collection = (Accounts Receivable / Net Sales) * 365 = ($4,200 / $41,000) * 365 = 37.39 days

(D) Asset turnover = Net Sales / Total Assets = $41,000 / $32,000 = 1.28 times

(E) Profit margin on sales = Net Income / Net Sales = ($6,000 / $41,000) * 100 = 14.63%

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