You throw a rock and the equation of the function that models the height as a function
of time is h (t) = -16t² +32t+6. Explain how you find the maximum height of the
rock.

Answer:

D. Graph C

Step-by-step explanation:

Step 1:  Identify the parts of the point-slope form to find the correct graph:

Currently, y - 1 = 2(x + 2) is in point-slope form, whose general equation is given by:

y - y1 = m(x - x1), where

Answer:

Joan has 78 Stickers left

Step-by-step explanation:

Joan gave 74 stickers to Sally: 263 - 74 = 189

Remaining Stickers: 189

Joan gave 51 stickers to her sister: 189 - 51 = 138

Remaining Stickers: 138

Joan gave 60 stickers to Jason: 138 - 60 = 78

Remaining Stickers: 78

Step-by-step explanation:

\( \frac{5gb}{110} = \frac{2.3gb}{x} \)

→ x = 2.3 ×110÷5 = 50.6 $ Aaron pay

→Brian = 1.1 × 110 ÷5=24.2$

Caleb = 110 - ( 24.2 + 50.6 ) = 110 -74.8 = 35.2$

Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.

To split the bill among the three brothers in proportion to the data they used, we need to calculate the fraction of the total data used by each brother and allocate the bill accordingly.

The total data used by the three brothers is 2.3gb + 1.1gb + 1.6gb = 5gb.

Now, let's calculate the fraction of the bill that each brother should pay based on their data usage:

Aaron's fraction = 2.3gb / 5gb = 0.46

Brian's fraction = 1.1gb / 5gb = 0.22

Caleb's fraction = 1.6gb / 5gb = 0.32

The sum of these fractions should equal 1, representing the entire bill.

To allocate the bill, we multiply each brother's fraction by the total bill amount:

Aaron's payment = 0.46 * $110 = $50.60

Brian's payment = 0.22 * $110 = $24.20

Caleb's payment = 0.32 * $110 = $35.20

Therefore, Aaron should pay $50.60, Brian should pay $24.20, and Caleb should pay $35.20 to split the bill in proportion to the data they used.

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The lateral faces of the given prism are rectangles and thus prove that it is a right prism, we need to have certain information about its properties and dimensions.

The term "right prism" means that the prism has rectangular bases that are perpendicular to the lateral faces or sides. This means that all the lateral faces must also be rectangles, as stated in the question.It also does not provide any angles or other measurements that can help us determine if the faces are rectangles or not.
We could make some assumptions based on the definition of a right prism and the fact that it is a commonly used shape in geometry and engineering. We could assume that the prism has right angles at all of its corners and that its lateral faces are parallel to each other.

The lateral faces of the prism are rectangles, its dimensions and properties. This could be provided through measurements or diagrams that show the shape and angles of the prism, or through mathematical calculations that demonstrate that the faces must be rectangles based on the given dimensions.

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The line AB is not a perpendicular bisector of CD.

Perpendicular bisectors are lines that divides another line into two equal parts.

From the diagram, we can see that line CD cuts AB at the centre. Hence we can say that CD is a perpendicular bisector of AB.

The same is not applicable to line AB passing through CD. The line AB did not bisect (divide equally) line CD.

Hence we can conclude that line AB is not a perpendicular bisector of CD.

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Answer:

x=3

Step-by-step explanation:

An equation's omitted factors are the values of x for which the result is unknown. This indicates that if the denominator or x(x-3) equals 0, your solution is undefined.

Set up this equation and solve for the potential possibilities of x to find these numbers: x(x-3)=0

Divide both sides by (x-3) to find one of the values:

x(x-3)/(x-3)=0(x-3)

Because (x-3) cancels on the left side of the equation and everything divided by 0 is zero on the right, you should get: x=0.

Now that you've determined one of the excluded values, work out the other:

To begin, split both sides by x:

x(x-3)=0

x-3=0

Finally, multiply both sides by -3 to get: x=3

The relative frequency of an 8th grader that has a cell phone but no tablet is given as follows:

0.21.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The relative frequency of an event is equals to the probability of the event.

Out of 100 8th graders, 21 have a cellphone but no tablet, hence the relative frequency is given as follows:

21/100 = 0.21.

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The complement rule states that (C) P(A) = 1 - P(A')

The complement rule states that the probability of an event A occurring is equal to 1 minus the probability of the event A not occurring (the complement of A).

Mathematically, the complement rule is represented as:

P(A) = 1 - P(A')

where:

P(A) is the probability of event A,

P(A') is the probability of the complement of event A (not A).

The complement rule is based on the fact that the sum of the probabilities of an event and its complement must equal 1. In other words, if there are only two possible outcomes (A and not A), then the probability of A happening plus the probability of not A happening should equal 1.

By using the complement rule, we can determine the probability of an event indirectly by finding the probability of its complement and subtracting it from 1. This can be useful when calculating probabilities, especially when it is easier to calculate the probability of the complement of an event rather than the event itself.

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Answer:

$6 per hour

Step-by-step explanation:

27/4.5=6

Answer:

volume = 174.8 sq. units.

Answer:

61.5752159 units³

Step-by-step explanation:

The height of a cone can be found using the following formula:

\(v=\frac{1}{3} \pi r^2h\)

We know that the height is 14.7 and the radius is 2.

\(h=14.7 \\r=2\)

Substitute the values into the formula.

\(v=\frac{1}{3} \pi (2)^2(14.7)\)

Evaluate the exponent.

⇒ 2²= 2*2 = 4

\(v=\frac{1}{3} \pi (4)(14.7)\)

Multiply 4 and 14.7

\(v=\frac{1}{3} \pi (58.8)\)

Multiply 1/3 and pi.

\(v=1.04719755*58.8\)

Multiply the two numbers together.

\(v=61.5752159\)

Add appropriate units. Volume is cubic units, and we aren't given units. So, we should use cubic units.

\(v=61.5752159 units^3\)

The volume of the cone is 61.5752159 cubic units.

In the given triangle,

sides vx and vw are equal,

and ∠v = 40°

∠w = ∠x (Adjacent angles of the equal sides of a triangle are equal)

Also, ∠v + ∠w + ∠x = 180° (Angle sum property of a triangle)

⇒ 40° + ∠x + ∠x = 180°

⇒ 2∠x = 140°

⇒∠x = 70°

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Answer:

Non - linear as for it is not a straight line.

Step-by-step explanation:

To the second power it would make a curve not straight line.

Answer:

Do you mean y = (x-6)^2? If yes, it is NONLINEAR FRACTION

Step-by-step explanation:

If you graph it, it forms a parabola so it is considered as nonlinear fraction/function

The value of the integral ∫4|x - 2| dx from 0 is equal to 20.

To evaluate the integral ∫4|x - 2| dx from 0, we can interpret it in terms of areas.

The integrand |x - 2| represents the absolute value of the expression (x - 2).

Geometrically, this implies that the function will always be positive and symmetrical about the y-axis.

The interval of integration is from 0, which means we are only concerned with the region to the right of the y-axis.

To evaluate the integral, we need to consider two cases:

When x ≥ 2:

For x ≥ 2, the absolute value of (x - 2) is equal to (x - 2) itself. Therefore, we can rewrite the integral as ∫4(x - 2) dx from 2 to 4.

When x < 2:

For x < 2, the absolute value of (x - 2) is equal to -(x - 2).

Therefore, we can rewrite the integral as ∫4(-(x - 2)) dx from 0 to 2.

Now, let's evaluate each case separately:

Case 1: When x ≥ 2

∫4(x - 2) dx from 2 to 4:

= 4∫(x - 2) dx from 2 to 4

\(= 4[(x^2/2 - 2x) |_2^4]\)

= 4[(16/2 - 8) - (2/2 - 4)]

= 4[(8 - 8) - (1 - 4)]

= 4(0 - (-3))

= 4(3)

= 12

Case 2: When x < 2

∫4(-(x - 2)) dx from 0 to 2:

= -4∫(x - 2) dx from 0 to 2

\(= -4[(x^2/2 - 2x) |_0^2]\)

= -4[(4/2 - 4) - (0/2 - 0)]

= -4[(2 - 4) - (0 - 0)]

= -4((-2) - 0)

= -4(-2)

= 8

Now, we can sum up the results of both cases:

12 + 8 = 20.

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Answer:

4

Step-by-step explanation:

Evaluate f(3) and g(2)

f(3) = 2(3) - 4 = 6 - 4 = 2

g(2) = - 3(2)² + 5(2) = - 3(4) + 10 = - 12 + 10 = - 2

Then

f(3) - g(2) = 2 - (- 2) = 2 + 2 = 4

B

It is quite obvious. America is capatalist, we are relatively free here. No laws regulate competing against other people nor regulating the ability to make a large profit from real estate.

if you were confused with C, the word bartering basically means trading goods. In order to acquire good most people use money, we do not have to trade things like bread for steak n stuff.

Hope it helps

Answer:

$12.50

Step-by-step explanation:

Look at the graph down below \/

U can also mark where the pounds is so right at 25 pounds it would be about $12~

Answer: on the screenshot

Step-by-step explanation: linear function should go down or up(straight line)

Answer:

Always

Step-by-step explanation:

Answer:

never.

Step-by-step explanation:

Using technology, the weighted average ROR of the investment, rounded to the nearest tenth of a percent is 2.1%

What is the weighted average ROR?

The weighted average ROR means the rate of return of the four investments combined together to give a single return, which is computed as the sum of the RORs multiplied by the percentage of total portfolio invested in each security.

total investment=$2600+$3700+$575+$1225

total investment=$8100

% invested in each security=amount invested in each security/total investment

weighted average ROR=(1.7%*$2600/$8100)+(3.2%*$3700/$8100)+(12.9%*$575/$8100)+(-5.6%*$1225/$8100)

weighted average ROR=2.1%

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Answer: 9(x−4)

Step-by-step explanation: Hope this help :D

Answer:

1361 ft.

Explanation:

The circumference of the wheel times the number of rotations equals distance travelled

\(C = d\pi\)

Answer:

Step-by-step explanation:

One rotation is same distance as:

Total distance traveled:

Convert inches to feet:

Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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Answer:

2nd graph is a function

Step-by-step explanation:

To find graph is a function or not, draw a vertical line. if that line cuts your graph more than once, then it's not a function.

If you draw a vertical line through circled graph, it will cut your graph at two points. so it's not a function

If you draw a vertical line through 2 nd graph it will cut your graph at only one point. therefore it's a function.

Answer:

The coordinate of T is -3:2

Answer:

T' (3, -2) i believe.

Step-by-step explanation:

hope this helps!

Answer:

16

Step-by-step explanation:

22-6=16 16+6=22

hope this helps! :)

Therefore, the 90% confidence interval for the mean repair cost for the VCRs is ($82.40,$90.12).

Subject to the exclusions outlined in this clause, the repair cost is defined as the cost of the parts and labor required to fix or replace any covered component as a result of a covered mechanical breakdown. We reserve the right to substitute components of comparable sort and quality, whether they are new, OEM, swapped, rebuilt, remanufactured, or used. The suggested retail price of a part of a like type and quality, or the manufacturer's indicated retail price for Your Vehicle, whichever is higher, may not be exceeded when pricing out parts. A current, widely used flat-rate labor guide will be used to calculate labor costs. According to state-specific rules, the Repair Cost includes the necessary taxes related to the covered Mechanical Breakdown.

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The volume of the solid y = 13 √sin x for y = 13 , x= 0 generated when r is revolved around x-axis is equal to 338π ( π/2 - 1 )cubic units.

Height of each shell is represented by the difference between the y-coordinates of the upper and lower bounds of the region.

Height = 13 - 13 √sin x.

Volume of each shell is :

dV = 2π(13 √sin x)(13 - 13√ sin x)dx ___(1)

When y = 13

y = 13√sinx

⇒ 13 = 13√sinx

⇒ sinx = 1

⇒ x = π/2

Volume of the solid is

Integrate (1) both the sides over 0 to π/2 we get

V = \(\int_{0}^{\pi /2}\) 2π(13 √sin x)(13 - 13√ sin x)dx

  =2π \(\int_{0}^{\pi /2}\) ( 169√sinx - 169sinx ) dx

  = 338π\(\int_{0}^{\pi /2}\) ( √sinx - sinx ) dx

  = 338π ( π/2 - 1 )cubic units

Therefore the volume of the solid generated where r revolved about x-axis is equal to 338π ( π/2 - 1 )cubic units.

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The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

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