The graph shows a line and two similar triangles.
What is the equation of the line?
A) y=3x
B) y=1/3x
C) y=1/3x+2
D) y=3x+2
Two containers designed to hold water are side by side, both in the shape of a
cylinder. Container A has a radius of 7 feet and a height of 11 feet. Container B has a
radius of 6 feet and a height of 16 feet. Container A is full of water and the water is
pumped into Container B until Container A is empty.
After the pumping is complete, what is the volume of water in Container B, to the
nearest tenth of a cubic foot?
please help!!
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
An account earns simple annual interest.
$1800 at 6.5% for 30 months
a. Find the interest earned.
b. Find the balance of the account.
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
A 100-foot rope from the top of a tree house to the ground forms a 45 degree angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot
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
a washer and a dryer cost $809 combined. the washer costs $91 less than the dryer. what is the cost of the dryer?
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
What is the 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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a. Jamie has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 14 ft above the ground.
Draw a picture of the ladder leaning against the wall and label the lengths listed in the problem:
b. Use Trigonometry to find the angle formed between the ground and the ladder using your diagram and values from part 1a. Round to the nearest whole number. Show your work:
c. For safety reasons, Jamie wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe the way she has it positioned?
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.
3 Polnis
-
Trevor has a $1000 bond with a 4.5% coupon. Trevor purchased this bond for
$965. What is the yield of this new bond?
O A. 5%
OB. 5.1%
C. 4.5%
D. 4.7%
Answer:
D.4.7%
Step-by-step explanation:
Here is the histogram of a data distribution.
5
4
3
2
1
1
2
9 '10
Which best describes the shape of this distribution?
Answer:
unimodal skewed
Step-by-step explanation:
The given histogram is unimodal skewed.
What is Graph?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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Jonas has 5 apples and 6 oranges in a fruit basket. The basket contains 13 pieces of fruit. Which statement is true
regarding the contents of the fruit basket?
The fraction of apples in the basket is greater than the fraction of any other type of fruit in the basket.
The fraction of oranges in the basket is greater than the fraction of any other type of fruit in the basket
There are 3 other pieces of fruit in the basket
There are 6 types of fruit in the basket.
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.
David rode his bicycle for 6 hours and he jogged for 8 hours during the past 2 weeks. If he continues bicycling and jogging at the same rate, how many hours will he ride his bicycle and jog in 24 weeks?
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. :)
You roll a number cube. How likely is it that you will roll a number less than 3? Explain.
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
Find the slope of the line perpendicular to the line graphed.
A) -3
B) -
1
3
C)
1
3
D) 3
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
Luther is building a model rocket for a science fair project. He attaches a nose cone to a cylindrical body to
form the rocket's fuselage. The rocket has a diameter of 4 inches and a total height (including the nosecone)
of 19 inches. The nosccone is 7 inches tall. What is the surface area of the rocket?
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.
Please help!!! I will give 20 points and brainliest answer to the correct answer!!
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.
Classify the triangle using its angles and sides
(choose 2)
A.) Acute
B.) Obtuse
C.) Scalene
D.) Equilateral
Answer:
obtuse, scalene
Step-by-step explanation:
Answer:
obtuse, scalene
Step-by-step explanation:
I did the quiz
Susannah made the line plot below to show the distances she hiked each day in the past two weeks.
Distances Hiked
Then she wrote this sum to find the total number of miles she hiked
(5+ x 3) + (6 + x 5) + (74 x 2) (74 x 1) + (73 x 1)
Which of the following must be added to the sum to get the correct total?
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
If m∠X = 55° and m∠Y = 75°, then m∠W = A) 20°. B) 35°. C) 105°. D) 130°.
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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Find the area of the rhombus.
4√3 m
4 m
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]
A pencil factory puts 12 pencils in each box of pencils. The pencil factory sends out 83 boxes of pencils in each shipment. This year, they sent out 36 shipments of pencils. How many pencils did they ship this year?
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.
What is a unitary method?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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A company lost $400 dollars in March, $500 in April, and $300 in May. Write an integer for the average loss per month
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!
what is the midpoint of the x intercepts of f(x)= (x-4) (x+4)
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)!
which picture shows the correct graph of |x|=3?
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:
In deciding where to have lunch, a group of friends
looks at the websites for 2 pizzerias, 3 drive-throughs,
and 2 diners.
How many choices are the friends considering?
Answer:
5 pizza rolls
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
Question 5:
Factor (x^2 – 9) (x^2 – 5x + 4) completely.
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.
Plz help i will give brainliest
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.
This is for geometry and I am very confused.
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. : )
A company usually sends 9 people to install a security system in an office building, and they do it in about 96 minutes. Today, they have only three people to do the same size job. How much time should be scheduled to complete the job?
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.
Explanation: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.
i need help with this
Answer:
MAYBE Italian tuna tomatoes and american cheese
Step-by-step explanation:
What is the slope in the equation
Screenshot attached
Answer:
the answer is 2
Step-by-step explanation:
bc 3 is the y-intercept
help with question 17 pls
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