A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,
in feet after t seconds is given by the function h=-167 + 120t + 10. How long does it take to
reach maximum height? What is the boulder's maximum height? Round to the nearest
hundredth, if necessary.
a. Reaches a maximum height of 235.00 feet in 3.75 seconds.
b. Reaches a maximum height of 10.00 feet in 7.50 seconds.
c. Reaches a maximum height of 7.58 feet in 3.75 seconds.
d. Reaches a maximum height of 15.16 feet in 7.5 seconds.

Answer:

35856

Step-by-step explanation:

12 times 83 is 996 and 996 times 36 is 35856

The pencil factory shipped 35,856 pencils this year.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A pencil factory puts 12 pencils in each box of pencils. The pencil factory sends out 83 boxes of pencils in each shipment.

So, The number of pencils in 83 boxes or one shipment is = (12×83).

= 996 pencils.

And This year, they sent out 36 shipments of pencils.

Therefore, The total number of pencils shipped this year is,

= (996×36).

= 35,856 pencils.

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Answer:

3 and 1/4

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

Divide your value by 2 if your given value is the length of the center line that creates the middle two triangles within the hexagon. The quotient is the length of the hexagon side. If this value is 25, then the length of one side of the hexagon is 25 divided by 2, which is 12.5. Then you multiply that by 6 for each side and get 75. Hopes this helps. : )

Answer:

y-intercept = (0, 2.5)

x-intercept = (2.143, 0)

Step-by-step explanation:

y - intercept:

This is when x = 0 so

-7(0) - 6y = -15

-6y = -15

y = -15/-6

y = 2.5.

x_intercept:

-7x - 6(0) = -15

-7x = -15

x = -15 /-7

= 2.143.

Answer:

unimodal skewed

Step-by-step explanation:

The given histogram is unimodal skewed.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

This histogram is unimodal skewed.

There are two parts to this answer. The first part has to do with the number of modes.

This would be the item that is occurring the most frequently.

In this case the mode is only 4.

It is occurring more than any other.

The second part of this has to do with the distribution of the data as it is displayed on the histogram.

There are 4 pieces of data that are only occurimg one time on the right of the histogram.

We call this skewing the data.

When both sides looks almost the same we say it is symmetric.

Hence, the given histogram is unimodal skewed.

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it's whatever the opposite is so if the slop is 3 the perpendicular would be -3

if the slope is 13 it perpendicular would be -13

Answer:

He will ride his bicycle for 72 hours and jog for 96 hours.

Step-by-step explanation:

David rode his bicycle for 6 hours and he jogged for 8 hours during the past 2 weeks.

We can say that per week, he rode his bicycle for 3hours and jogged for 4 hours.

Assuming that he continues at the same rate, in 24 weeks, he will ride his bike for:

24 * 3 = 72 hours

And he will jog for:

24 * 4 = 96 hours.

He will ride his bicycle for 72 hours and jog for 96 hours.

Answer:

72 all you need to do is 24  x 3 and you get 72. :)

Answer:

(0,8)

Step-by-step explanation:

Answer:

(0,8)

Step-by-step explanation:

Answer:

B    The fraction of oranges in the basket is greater than the fraction of any other type of fruit in the basket

Step-by-step explanation:

5 apples + 6 oranges is 11 fruits. witch means thare are 2 unidentified fruits tharefore C is wrong and D is wrong. and it couldn't be A because 5 is smaller than 6.

Answer:

The fraction of oranges in the basket is greater than the fraction of any other type of fruit in the basket.

Step-by-step explanation:

The oranges make up  [tex]\frac{6}{13}[/tex]

The apples make up  [tex]\frac{5}{13}[/tex]

The unknown rest of the fruit basket make up  [tex]\frac{2}{13}[/tex]

The oranges are the greatest fraction.

Answer:

[tex]\sqrt136[/tex] (option D)

Answer: 400

Step-by-step explanation:30+400+500=1200/3=400

Answer:

$400

Step-by-step explanation:

to find an average we add...

400+500+300=1200

then we divide..

$1200/3 months=

$400 per month

Hope this helps!

The total approximate surface area of Luther's rocket is 219.8 square inches.

Luther is building a model rocket and needs to calculate its surface area. His rocket consists of a cylindrical body with a nose cone. The diameter of the cylinder is 4 inches, the height of the cylindrical part is 12 inches (since the total height is 19 inches and the nose cone is 7 inches), and the height of the nose cone is 7 inches.

First, we calculate the surface area of the cylindrical body. The formula for the lateral surface area of a cylinder is 2πr*h, where r is the radius and h is the height. Half the diameter gives us the radius, which is 2 inches. Thus, the lateral surface area is 2π*2*12 = 48π square inches.

Next, we find the surface area of the two bases of the cylinder. The formula for the area of a circle is π[tex]r^2[/tex]. So, the area of one base is π*[tex]2^2[/tex] = 4π square inches. There are two bases, so we double this to get 8π square inches.

For the nose cone, we'll assume it is a cone whose slant height is the same as its height (because we do not have enough information to calculate the slant height if it were to differ). The surface area of a cone is πr*l, where l is the slant/linear height. Therefore, for the nose cone, we have π*2*7 = 14π square inches.

Now, we add the surface areas of the cylindrical part and the nose cone to get the total surface area of the rocket: 48π + 8π + 14π = 70π square inches.

Finally, multiplying 70π by approximately 3.14, we get the total approximate surface area of Luther's rocket: 70 * 3.14 = 219.8 square inches.

The correct answer is:

The surface area of the rocket is approximately [tex]\(48\pi + 2\pi(2 + \sqrt{53})\)[/tex] square inches, without numerical calculation.

To find the surface area of the rocket, we need to calculate the surface area of both the cylindrical body and the nose cone separately, then add them together.

1. Surface Area of the Cylindrical Body:

  The cylindrical body's surface area can be calculated using the formula for the lateral surface area of a cylinder: [tex]\( A_{\text{cylinder}} = 2\pi rh \)[/tex], where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.

  Given:

  - Diameter = 4 inches (radius = 2 inches)

  - Total height (including nose cone) = 19 inches

  - Height of the nose cone = 7 inches

  Radius r = 2  inches

  Height of cylindrical body = Total height - Height of nose cone = 19 inches - 7 inches = 12 inches

 [tex]\( A_{\text{cylinder}} = 2\pi \times 2 \times 12 = 48\pi \)[/tex] square inches

2. Surface Area of the Nose Cone:

  The surface area of a cone can be calculated using the formula: [tex]\( A_{\text{nosecone}} = \pi r_{\text{nosecone}}(r_{\text{nosecone}} + \sqrt{h_{\text{nosecone}}^2 + r_{\text{nosecone}}^2}) \), where \( r_{\text{nosecone}} \) is the radius and \( h_{\text{nosecone}} \)[/tex] is the height.

  Given:

  - Height of nose cone = 7 inches

  Since the diameter of the rocket is 4 inches, the radius of the nose cone is also [tex]\( \frac{4}{2} = 2 \)[/tex] inches.

[tex]\( A_{\text{nosecone}} = \pi \times 2 \times (2 + \sqrt{7^2 + 2^2}) = 2\pi(2 + \sqrt{53}) \)[/tex] square inches

3. Total Surface Area:

  The total surface area of the rocket is the sum of the surface areas of the cylindrical body and the nose cone.

  Total Surface Area = Surface Area of Cylindrical Body + Surface Area of Nose Cone

                      [tex]\( = 48\pi + 2\pi(2 + \sqrt{53}) \)[/tex] square inches

  Now, you can compute the numerical value.

Answer:

5 pizza rolls

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

[see picture]

Step-by-step explanation:

There were no given choices, but I did graph the equation using Desmos.

Choose the answer that is closest to this:

Answer:

B. ∠C = 69°

C. Jamie has positioned the ladder safely.

Step-by-step explanation:

A. In the figure attached length of ladder AC = 15 ft

   and the top of the ladder is at the point A 14 ft above the ground.

B. SinC = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

            = [tex]\frac{14}{15}[/tex]

        [tex]C=sin^{-1}(\frac{14}{15} )[/tex]

        C = 68.96°

        C ≈ 69°

C). For safety reasons, angle between the ladder and the ground should be less than 75°.

Existing angle between the ladder and ground is 69° which is less than the angle required for safety.

Therefore, Jamie has positioned the ladder safely.

Answer:

0.3333

Step-by-step explanation:

If so, there are two numbers less than 3: 1 and 2. There are 6 total possible results, so the probability of rolling a number less than 3 is 26 or 13 or 0.3333

Answer:

2/6 which can be simplified to 1/3

Answer:

$2,092.5 with $292.5 in interest.

Step-by-step explanation:

30 divided by 12 (to find the years/leftover months) [do this as an improper fraction to be a little simpler] 30/12 = 2 6/12 or 2 years 6 months

6.5% of 1800 is 117

117y = 117(2.5) = 292.5 [this is the interest]

1800 + 292.5 = 2,092.5

Answer:

THIS IS CORRECT I JUST ANSWERED

Step-by-step explanation:

Interest earned: $292.50

Balance: $2092.50

Answer:

B.) 24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

Area of rhombus = 8√3 m²

Step-by-step explanation:

Diagonal of rhombus is given as:

[tex] D_{1} [/tex] = 4 m

[tex] D_{2} [/tex] = 4√3 m

[tex]Area \: of \: rhombus = \frac{D_{1}D_{2}}{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{4 \times 4 \sqrt{3} }{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 4 \sqrt{3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8 \sqrt{3} {m}^{2} [/tex]

Step-by-step explanation:

Step 1:  Find the line

Option A

(y - y_1) = m(x - x_1)

(y - 5) = 2(x - (-4))

y - 5 = 2(x + 4)

Option C

y - 5 = 2x + 8

y = 2x + 13

Option D

2x - y = -13

-y = -13 - 2x

y = 2x + 13

I think Option A, C, D

Answer:

the answer is 2

Step-by-step explanation:

bc 3 is the y-intercept

Answer:

(0,16) or just 0 horizontally

Step-by-step explanation:

The x intercepts would be found by first setting these equations to equal zero!

[tex]x-4=0\\x+4=0[/tex]

Now we can add/subtract to solve for the zeros of the function!

[tex]x+4=0\\-4\\x=-4\\\\x-4=0\\+4\\x=4[/tex]

The mid-point between 4 and negative 4 is 0, so the vertex is at (4,-16)!

Answer:

1693.3 ft³

Step-by-step explanation:

The volume of a cylinder is given by; V = πr²h

For container A;

we are given;

Radius;r = 7ft

Height; h = 11 ft

Thus; Volume of container A = π•(7²)•11 = 1693.318 ft³

Similarly,

For container A;

we are given;

Radius;r = 6 ft

Height; h = 16 ft

Thus; Volume of container B = π•(6²)•16 = 1809.557 ft³

Now, since container A was full of water and all of it was pumped into container B, thus, the volume of the water in container B = Volume of container A = 1693.318 ft³

Approximating to the nearest tenth of cubic ft = 1693.3 ft³

Answer:

The area is [tex]78.54units^2[/tex]

The area would be 78.5[tex]units^2[/tex] (pi=3.14)

Step-by-step explanation:

The formula for the area of a circle is : [tex]\pi *radius^2[/tex]

To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.16.

The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.

The final step would be to divide the area of 314.16 by 4, this gives you 78.54. This is because we are using the area to work out the area of just one quadrant.

1) Multiply pi by 10 squared.

[tex]\pi*10^2=314.16^2[/tex]

2) Divide 360 by 90.

[tex]360/90=4[/tex]

3) Divide 314.16 by 4.

[tex]314.16/4=78.54^2[/tex]

Pi=3.14:

To work the area of this quadrant you would first need to work out the area of the circle. You can do this by multiplying pi by the radius of 10 squared, this gives you 314.

The next step is to work out how much of the circle we need to work out the area for. As this is a right angle (90°) we know that this is [tex]\frac{1}{4}[/tex] of a circle. This is because the total of a circle is 360, and that by dividing 360 by 90, this gives you 4. This tells that this is a quarter of a circle.

The final step would be to divide the area of 314. by 4, this gives you 78.5. This is because we are using the area to work out the area of just one quadrant.

1) Multiply pi by 10 squared.

[tex]\pi*10^2=314^2[/tex]

2) Divide 360 by 90.

[tex]360/90=4[/tex]

3) Divide 314.16 by 4.

[tex]314/4=78.5^2[/tex]

Answer:

c

Step-by-step explanation:

I subtracted 180 with 75 and I got 105.

The measure of angle ∠W is 50°. None of the answer choices match this result exactly.

To find the measure of angle ∠W, we can use the fact that the sum of the angles in a triangle is always 180 degrees. If we already know the measures of ∠X and ∠Y, we can find ∠W as follows:

m∠X + m∠Y + m∠W = 180°

Given:

m∠X = 55°

m∠Y = 75°

Now, plug in these values:

55° + 75° + m∠W = 180°

Combine the known angle measures:

130° + m∠W = 180°

To find the measure of ∠W, subtract 130° from both sides of the equation:

m∠W = 180° - 130°

m∠W = 50°

Therefore, the correct answer is not among the options provided.

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Answer:

one solution

Step-by-step explanation:

Answer:

Correct option: B -> (5 1/2) * 2

Step-by-step explanation:

We can observe the number of different distances she hiked:

5 1/4, 5 1/2, 6 1/4, 7 1/4, 7 1/2 and 7 3/4.

In Susannah's equation, we have only 5 parts, so it's missing one distance, that is 5 1/2.

In this distance there are 2 circles, so she hiked this distance two times. Then, the missing value that Susannah should sum is:

(5 1/2) * 2

Correct option: B

Answer:

The top of the tree house is 70.71ft high

Step-by-step explanation:

Kindly find attached rough sketch of the problem for your reference.

From the sketch we see that the rope at 45° and the tree house form a right angle triangle

Applying

SOH CAH TOA formula

using SOH

sin θ= h/100

h= sinθ*100

h= sin(45)*100

h= 0.7071*100

h= 70.71ft

Answer:

D.4.7%

Step-by-step explanation:

Answer:

MAYBE Italian tuna tomatoes and american cheese

Step-by-step explanation: