Solve for d.
● Frank drove his car at an average speed of 43 mph for 2.5 hours.
Using your new equation, determine the distance, d, Frank drove.
Show all the steps.

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:

obtuse, scalene

Step-by-step explanation:

Answer:

obtuse, scalene

Step-by-step explanation:

I did the quiz

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:

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:

The Dryer cost is 450

Step-by-step explanation:

The washer cost $450. and together they have the cost is 787.

A washer and a dryer cost $809 combined.

Let the dryer cost x.

Then, the washer costs (x-91)

Together, they cost  (x) + (x-91) =809

        2x+91 = 809

We have to solve this equation

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

           2x = 718   .......          [subtract 97 from both sides]

            x = 359    .......         [divide both sides by 2]

The dryer cost $359.

Therefore, the washer cost $450.

Together, they cost,

450+359=$787

The washer cost $450. and together they have the cost is 787.

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Answer:

(a)6 Equilateral Triangles.

(b)30-60-90 triangle.

(c)See Attached Triangle in Figure 2

(d)Length of the short leg = 2cm.

(e)Length of the hypotenuse= 4cm.

(f)Length of the long leg=[tex]2\sqrt{3}cm[/tex]

(g)Apothem.

(h)Height of the Equilateral triangle=[tex]2\sqrt{3}cm[/tex]

(i)Area of One Equilateral triangle =[tex]4\sqrt{3}cm^2[/tex]

(j)Area of Hexagon =[tex]=24\sqrt{3}\:cm^2[/tex]

Step-by-step explanation:

(a)From Figure 1, there are 6 Equilateral Triangles.

(b)If we cut an equilateral down the middle (green line), we create a 30-60-90 triangle.

(c)Triangle Attached in Figure 2.

(d)The length of the short leg of one of the 30-60-90 triangle is 2cm.

(e)The length of the hypotenuse of one of the 30-60-90 triangle is 4cm.

(f)Length of the long leg

We use Pythagoras Theorem to find the length of the long leg of the right triangle.

[tex]4^2=2^2+l^2\\l^2=4^2-2^2=12\\l=\sqrt{12}=2\sqrt{3}cm[/tex]

(g)The vocabulary word for the long side of the 30-60-90 called in the polygon (green line) is Apothem.

It is line segment from the center to the midpoint of one of the sides of a polygon.

(h)Height of the Equilateral Triangle=[tex]2\sqrt{3}cm[/tex]

(i)Area of One Equilateral triangle

Base =4 cm, Height =[tex]2\sqrt{3}cm[/tex]

Area=0.5X4X[tex]2\sqrt{3}cm[/tex]

=[tex]4\sqrt{3}\:cm^2[/tex]

(j)Area of Hexagon =Area of One Equilateral Triangle X 6

[tex]=6X 4\sqrt{3}\\=24\sqrt{3}\:cm^2[/tex]

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:

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:

$56

Step-by-step explanation:

35 percent *160 =

(35:100)*160 =

(35*160):100 =

5600:100 = 56

Answer:

$56.

Step-by-step explanation:

Since it is 35% off, we can simply take 35% of the original price:

160 × 0.35 = $56.

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:

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:

The answer is A. 26

Step-by-step explanation:

26 is the only answer that makes sense becuase it is the only one less that 27. The answer is written as 26>27. All tho anwers dont make sense because they are less than 27.

PLUS I TOOK THE TEST

Answer:

the answer is 2

Step-by-step explanation:

bc 3 is the y-intercept

Answer:

D.4.7%

Step-by-step explanation:

Answer:

6 x 8 = 45 cans of cat food

4 x 2 = 8 cans of cat food

45 - 8 = 37

Sophie has 37 more cans of cat food than she does of dog food

Step-by-step explanation:

Answer:

I believe the answer is (x+3)(x-3)(x-4)(x-1)

Step-by-step explanation:

Notice both terms are perfect squares, therefore you can factor using the difference of squares formula:

(x²-9)(x²-5x+4)

For the first term, we get (x+3)(x-3) because x²-9 is a perfect square.

For the second term, we get (x-4)(x-1) because x²-5x+4 is a perfect square trinomial.

If you have any further questions about this problem, you can comment them down below and I'll try to answer them.

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]

Answer:

c = 11.3 yards

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (a + b)

where h is the perpendicular height and a, b the parallel bases

Here A = 416.955, h = 20.9, a = 28.6 and b = c, thus

[tex]\frac{1}{2}[/tex] × 20.9 × (28.6 + c) = 416.955, that is

10.45(28.6 + c) = 416.955 ( divide both sides by 10.45 )

28.6 + c = 39.9 ( subtract 28.6 from both sides )

c = 11.3 yards

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:

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:

The Answer would be 288 minutes

Step-by-step explanation:

So we have 9 people working to install a security system in an office building. they take about 96 minutes.

Today we have 3 people doing the same job.

yesterday we had 9 people doing the same job

so we would multiply 96 minutes by 3 because we divided the amount of people by 3

96x3= 288

3 people takes 288 minutes to do the same job.

To complete the installation of a security system that normally takes 9 people 96 minutes, three people would require 288 minutes given each person works at the same rate and the work is additive.

When a company usually sends 9 people to install a security system in 96 minutes, and today only has three people available for the same task, we need to calculate the expected time for completion. First, we assume that each person works at the same rate. With 9 people, it takes 96 minutes, so with one person, it would take 9 times longer, since the number of workers is inversely proportional to the time needed.

So, one person would take 9 × 96 = 864 minutes to do the job alone. Therefore, three people would take 864 ÷ 3 = 288 minutes to complete the installation of the security system.

This calculation is based on the assumption that the work done by each individual is additive and that they are working on the task continuously and independently without interruption.

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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Answer:

(-11, -4)

Step-by-step explanation:

this is the answer

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: 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!

Answer:

MAYBE Italian tuna tomatoes and american cheese

Step-by-step explanation:

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:

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:

(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)!