A rocket is launched in the air. Its height in feet is given by h(t)= -16t^2+88t where t represents the time in seconds after launch. How long is the rocket in the air?


Answer: ___ seconds

The expression's factored version, which employs the greatest common factor, is -z(12z-16z3 + 3z).

The largest number that can be split into exactly two or more other numbers. It is the "best" thing for making fractions simpler!

Given the expression below

-12z+16z^4 - 3z²

We are to factor the expression using the greatest common factor

Find the factors of each terms

-12z = -12 * z

16z^4 = 16 * z * z^3

-3z^2 = -3 * z * z

Since -z is common to the factors, hence the factored form of the expression using the greatest common factor is -z(12z-16z^3 + 3z)

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The potential energy of an object is given by the equation:

PE = mgh

where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height.

Rearranging this equation, we get:

h = PE / (mg)

Substituting the given values, we get:

h = 16800 J / (68.0 kg x 9.81 m/s^2)

h = 24.8 meters

Therefore, the cliff-jumper is standing 24.8 meters above the base of the cliff.

Answer:

h

Step-by-step explanation:

The probability that at least two of the four cards dealt have the same numeric value (1 through 20) is approximately 0.907.

To calculate the exact probability, we need to consider the different ways that two or more cards could have the same numeric value. If two cards have the same numeric value, there are 19 ways to choose that value and 2 ways to choose the two cards with that value. The probability of this happening is 19 * (2 / 20 * 19 / 19) * (18 / 18 * 17 / 18) * (16 / 17 * 16 / 17) * (15 / 16 * 15 / 16) = 19 * (1/190) = 0.1.

Similarly, we can calculate the probability of three or four cards having the same numeric value. Adding these probabilities, we get an estimate of 0.907 for the probability that at least two of the four cards dealt have the same numeric value.

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The amount of paper used to create the label was approximately 201.06 cm². This was calculated by multiplying the diameter of 16 cm by the height of 8 cm and then multiplying the result by 3.14 (T).

The amount of paper used to create the label for an 8 cm tall cylinder can with a diameter of 16 cm can be calculated by using the formula for the lateral surface area of a cylinder (T*r*h). T is the constant pi, which is equal to 3.14. r is the radius of the cylinder, which is equal to half of the diameter (16 cm/2 = 8 cm). h is the height of the cylinder, 8 cm. Therefore, the lateral surface area of the cylinder can is calculated by multiplying 3.14 by 8 cm (radius) by 8 cm (height). This results in 201.06 cm² of paper needed to create the label. The label can be wrapped around the cylinder, covering the whole surface area of the can.

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The value of the expression is -5/6.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Given:

An expression,

7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6).

Solving further with the help of PEMDAS,

7/5 × 1/3 + 3/5 × (- 2/9) + 7/5 × (- 5/6)

= 7/15 - 6/45 - 35/30

= (42- 12 - 105)/90

=  -75/90

= -5/6

Therefore, the value is -5/6.

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The equations that represent direct proportion are

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

The list of options

A proportional linear equation is represented as

y = kx

Where

The constant of proportionality is k

Using the above as a guide, we have the following:

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Kweku would save $180 in a year buying electricity for the Desla electric compared to buying gas for the Deswagon.

To make up for the higher sale price,

it will take him more than 66 years.

Subtraction is a mathematical operation. Which is used to remove terms or objects in the expression.

Given:

Deselectric costs $11900 more than the Deswagon.

Unit cost:

Deselectric: $0.11 per mile.

Deswagon: $0.12 per mile.

Kweku drives about 18,000 miles a year.

That means

the cost for each car;

Deselectric: 18000 x 0.11 = $1980

Deswagon: 18000 x 0.12 = $2160

The more cost is,

= $2160 - $1980

= $180 of savings in a year.

Now, the make-up for the higher sale price,

= 11900/180

= 66.11 in years.

Therefore, it will take him more than 66 years.

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You would expect a total of 2560 extra credit points to be rewarded (rounded to the nearest integer).

You must multiply the total number of extra credit points awarded by the number of pupils in order to find the answer to this question.

The equation would be as follows, assuming that each student receives the same number of extra credit points:

Total Extra Credit Points = Amount of Extra Credit Points per Student * Total Amount of Students

Therefore, in this case, the total amount of extra credit points to be rewarded would be:

Total Extra Credit Points = 10 * 256 = 2560

Therefore, If all 256 students from the in-person and online STA 381 classrooms choose to participate in the game, you can anticipate receiving a total of 2560 extra credit points (rounded to the nearest integer).

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Answer:

2 in

Step-by-step explanation:

Hope it helps.

On math thing

If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median.

A boxplot is a visual representation of the distribution of a set of data, and it typically consists of a box, two whiskers, and possibly some outliers. The box represents the interquartile range (IQR), which is the range between the first and third quartiles of the data. The median (or second quartile) is usually represented by a line within the box.

If there is no line in the box to indicate the median, it is possible that the median has not been calculated or that the data set is too small to provide an accurate representation of the median. With only 20 students, it is possible that the median may not be a meaningful representation of the central tendency of the data, especially if there are extreme outliers or skewed distributions. In such cases, it is best to consult other measures of central tendency, such as the mean or mode, to get a better understanding of the data.

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Answer:

The total number of counters in the bag is 150.

Step-by-step explanation:

There are 90 red counters and the ratio of red to blue is 3:5, which means that for every 3 red counters there are 5 blue counters. Thus, 90 red counters would mean that there are 5/3 times as many blue counters, or 150/3 = 50 blue counters. Therefore, 90 red counters + 50 blue counters = 150 counters in total.

We can conclude for the pair of number (a, b), where {b > a} -

Given is a pair of numbers.

Since the numbers are not given, assume the pair to be (a, b).

Let -

{b} = x% of {a}

{b} = {x/100} x {a}

x =  (100b/a)

Now, we can write {b} is (100b/a)% of {a}.

Then, we can write that {a} will be {100 - 100b/a}% less than {b}.

Therefore, we can conclude for the pair of number (a, b), where {b > a} -

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The area of the given figure is 66 square miles.

As we can see in the figure, we have 2 different rectangles attached to one another. So the total area of the figure will be the area of the vertical rectangle plus the area of the horizontal rectangle.

Area of the horizontal rectangle = L₁ × W₁

L₁ = 9 mi

W₁ = 2 mi

∴ Area = 9 mi × 2 mi

= 18 square miles

Area of the vertical rectangle = L₂ × W₂

L₂ = 12 mi

W₂ = 4 mi

∴Area = 12 mi × 4 mi

= 48 square miles

Now, the total area of the figure = the area of the vertical rectangle + the area of the horizontal rectangle.

= 48 square miles + 18 square miles

= 66 square miles.

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Answer: 11, 16, 26, 41

Step-by-step explanation:

As a result, the measurements of angles KAG and JAF are both 90, and the measure of arc KG is 2 * 90 = 180. Angle HAE and angle HAF are both 90 degrees.

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.

Here,

In the diagram, since KG, JF, AE, and AH intersect at point A, we know that angle KAG = angle JAF (both are inscribed angles and intercept the same arc), and angle HAE = angle HAF (both are alternate interior angles and are equal in measure).

To find the value of x, we need to use the angle relationships. Since angle KAG = angle JAF, and they are both inscribed angles, they are equal to half the measure of the intercepted arc KG. We also know that angle HAE = angle HAF, so we can use them to find the measure of KG.

Let's call the measure of KG = 2x. Then, angle KAG = angle JAF = x, and angle HAE = angle HAF = x.

Adding the measures of angle KAG and angle HAE, we get x + x = 2x = 180. Solving for x, we get x = 90.

So, the measures of angle KAG and angle JAF are 90, and the measure of arc KG is 2 * 90 = 180. The measures of angle HAE and angle HAF are also 90.

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Answer:

361.3 m²left

Step-by-step explanation:

10 kattha =3386.3sqm

sq pond of 55m side, area = 55*55 =3025

so 3386.3 - 3025 = 361.3 m²left

A confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

What does confidence interval mean?

If you repeat your experiment or resample the population in the same manner, the confidence interval is the range of values you expect your estimate to fall within a specific proportion of the time.

In point a:

The confidence interval will not provide convincing proof that only the two population prolongations differentiate because a 99 percent confidence interval for both the difference throughout the true promotion around -0.020 and 0.120 is included 0.

In point b:

This confidence interval gives strong evidence also that two population proportions were identical because there is a confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

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The complete question is -

A CBS News poll asked 606 randomly selected women and 442 randomly selected men, "Do you think putting a special tax on junk food would encourage more people to lose weight?" 170 of the women and 102 of the men said "Yes." A 99% confidence interval for the difference (Women – Men) in the true proportion of people in each population who would say "Yes" is –0.020 to 0.120.

a. Does the confidence interval provide convincing evidence that the two population proportions are different? Explain your answer.

b. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

These polygons have the following areas:

Case 9: 67

Case 10: 72

Case 11: 84

Case 12: 87.5

Case 13: 90

The walkway seal has a cost of $ 774.

In this question we need to determine the areas of irregular polygons and polygonal sections, these areas can be obtained in terms of sums and triangles and rectangles, whose formulas are introduced below:

Triangles

A = 0.5 · w · l

Rectangles

A = w · l

Where:

Now we proceed to determine the areas of each polygon:

Case 9

A = 0.5 · 3 · 4 + 0.5 · 6 · 4 + 0.5 · 2 · 7 + 0.5 · 2 · 7 + 5 · 7

A = 6 + 12 + 7 + 7 + 35

A = 67

Case 10

A = 4 · 0.5 · 3² + 9 · 6

A = 18 + 54

A = 72

Case 11

A = 0.5 · 3 · 12 + 3 · 12 + 0.5 · 3 · 12 + 0.5 · 1 · 4 + 0.5 · 5 · 4

A = 18 + 36 + 18 + 2 + 10

A = 84

Case 12

A = 0.5 · 7 · 3 + 7² + 0.5 · 3 · 4 + 0.5 · 3 · 4 + 4²

A = 10.5 + 49 + 6 + 6 + 16

A = 87.5

Case 13

A = 0.5 · 5 · 3 + 0.5 · 1 · 5 + 10 · 8

A = 7.5 + 2.5 + 80

A = 90

Case 14

A = 4 · 0.5 · (12 ft) · (10 ft) + 2 · (18 ft) · (12 ft) + 2 · (10 ft) · (18 ft)

A = 240 ft² + 432 ft² + 360 ft²

A = 1032 ft²

And the seal cost is:

C = (0.75 $ / ft²) · (1032 ft²)

C = $ 774

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Answer:

The y and m2 and the m (0, 2) when x=3

Step-by-step explanation:

Answer: 506,150

First we must divided 0.9 into 530,000 to find out how much of the population will decrease each year.

0.9% of 530,000 is 4770. Which means that each year, 4,770 people will move the District of Columbia. From 2010 to 2015, that is 5 years, which means that we have to multiply 4,770 by 5.

4770 x 5 is 23850.

Next we have to subtract the amount of people who moved.

530,000- 23,850 is 506,150

This means by 2015, the expected population will be 506,150 in the District of Columbia.

I hope this helped & Good Luck <3 !!!

Answer:

(f + g)(x)= -x + 6.

Step-by-step explanation:

The sum of two functions, f(x) and g(x), is given by (f + g)(x) = f(x) + g(x).

So, for f(x) = 4x + 6 and g(x) = -5x,

(f + g)(x) = f(x) + g(x) = (4x + 6) + (-5x) = -x + 6.

The result is a linear function and is already in the simplest form, so it cannot be further simplified.

The new check register balance of $131.35 now matches the bank statement balance of $161.96.

A bank balance is the amount of money a person or organization has in their account at a financial institution such as a bank. It reflects the amount of money that is available for spending or withdrawal, taking into account any transactions that have been made or are pending. The bank balance is an important aspect of managing finances, and individuals and businesses monitor their balances regularly to ensure that they have enough money to cover their expenses and to make sure that their accounts are in good standing.

To reconcile the checking account, you need to find out the reason for the difference between the check register balance ($107.87) and the bank statement balance ($161.96).

Add the interest earned of $0.43 to the check register balance: $107.87 + $0.43 = $108.30

Add the ATM deposit of $56 to the check register balance: $108.30 + $56 = $164.30

Subtract the incorrect amount of Check 307 ($32.95 instead of $35.29) from the check register balance: $164.30 - $32.95 = $131.35

The new check register balance of $131.35 now matches the bank statement balance of $161.96. This means the checking account has been reconciled.

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The value of k is given as follows:

k = 2.

The polynomial for this problem is defined as follows:

P(p) = p^4 + p² + p - k.

We have that p - 1 is a factor of the polynomial, meaning that according to the Factor Theorem, P(1) = 0.

Hence, considering that when p = 1, P = 0, the value of k is obtained as follows:

1^4 + 1² + 1 - k = 1

3 - k = 1

k = 3 - 1

k = 2.

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Answer:

Step-by-step explanation:

The circumference of the circle in a basketball court that has to be painted which has a radius of a feet is 2π.

The circumference of a circle is the distance around its edge. It is a key measurement of a circle and is used in many applications, such as finding the length of a rope needed to go around a circular object.

The formula for the circumference of a circle is given by C = 2πr, where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The constant π is used to represent the relationship between the diameter and the circumference of a circle.

In this case, the circle has a radius of a feet, so the circumference of the circle can be calculated as follows:

C = 2π

The units of measurement for the circumference will be the same as the units of measurement for the radius, in this case feet.

So, the circumference of the circle with a radius of a feet is 2π feet, expressed in terms of π.

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The measure of angle PSR in a kite PQRS, is equals to the 60°.

We have a kite PQRS, present in above figure. The measure of angle QPO = 50°

The measure of angle QRO = 70°

We have to determine the measure of angle PSR. As we see in figure, there is four right angled triangles as ∆POQ, ∆OQR , ∆POS and ∆OSR.

measure of angle POS = measure of angle SOR = 90°

measure of angle SPO = measure of angle QRO = 70° ( Since alternative angles)

Similarly, measure of angle SRO

= measure of angle QPO = 50° ( Alternative angles )

So, measure of angle PSR = measure of angle PSO + measure of angle RSO --(1)

Measure of angle RSO = 180° - measure of angle ROS - measure of angle SRO

= 180° - 90° - 50° = 40°

Also, Measure of angle PSO = 180° - measure of angle POS - measure of angle SPO = 180° - 90° - 70° = 20°

So, from equation (1),

measure of angle PSR = measure of angle PSO + measure of angle RSO

= 40° + 20°

= 60°

Hence, required measure of angle is 60°.

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Complete question:

The above figure completes the question. In kite PQRS, measure of angle QPO=50° and measure of angle QRO=70°. Find measure of angle PSR.

Answer:

Since the residual is very close to 0 and residual= actual y value so it is 8.

Please give me Brainlest:)

Step-by-step explanation:

The mean height of the hexagon is 21.33 in.

To find the length of the sides of a regular hexagon with a perimeter of 372 inches, you must divide the perimeter by 6. This gives you a result of 62 inches for the length of each side. The other steps are:

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Since LMNO is a parallelogram, opposite angles are congruent, which means that angle L is congruent to angle N and angle M is congruent to angle O.

Since angles L and M are adjacent angles in a parallelogram, they are supplementary, which means that their sum is 180 degrees. Therefore, the sum of the measures of angles L and M is:

L + M = 180 degrees.

Answer: 180 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

So and L and M add up to 180 degrees.