The volume of a cone is 88π cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown below.

Step 1: 88π = 1/3 πr² (8)
Step 2: 88π = 8/3 πr²
Step 3: 8/3 (88) = r²
Step 4: 234.7 = r²
Step 5: 15.3 =r

What is Fatima's error?
- In step 4, Fatima did not find the correct value of 8/3 (88).
- In step 2, Fatima should not have multiplied 1/3 and 8.
- In step 3, Fatima did not multiply 88 by the reciprocal of 8/3
- In step 1, Fatima did not substitute the correct value for the height in the formula.

Answers

Answer 1

To evaluate the radius of the cone we proceed as follows:
V=1/3 πr²h
plugging in the values, v=88π, h=8 ft
step 1
88π1/3πr²(8)
step 2
88π=8/3πr²
step 3
divide both sides by π
88=8/3r²
multiply both sides by 3/(8)
88(3/8)=r²
step 4
simplify
33=r²
step 5
get the square root
r=√33

Thus the mistake that Fatima made was:
In step 3, Fatima did not multiply 88 by the reciprocal of 8/3

Answer 2

Answer:

step 3

Step-by-step explanation:

took test

Related Questions

A weather satellite I'm circular orbit around earth completes one orbit every 5 hours. The radius of earth is about 6,400 km and the satellite is positioned 4,700 km above the earth. How far does the satellite travel in 1 hour?

Answers

To solve this problem you must apply the proccedure shown below:

1. You have that:

- It completes one orbit every 5 hours.
- The radius of earth is about 6,400 km.
- The satellite is positioned 4,700 km above the earth.

2. Then, you must use the following formula:

S=rθ

r=6,400 km+4,700 km
r=11,100 km

3. When you substitute the values, you obtain:

S=(11,100 km x 2π)/5
S=13,949 km

The answer is:13,949 km

Can someone answer for me please, if you're great at math.

The equation sin (35o) = 12/c can be used to find the length of AB. What is the length of AB? Round to the nearest tenth.

*A <35o ; CB = 12*

Answers

Assuming that c is the length of AB (as is usually the case in the angle-side notation for triangles):
If sin(35) = 12/c, we can transform by multiplying both sides by c, and dividing both by sin(35) to get
c = 12/sin(35)
Evaluating using a calculator gives 20.92 units.

What is the value after 7 years of a 2014 Ford Mustang that originally costs 25000 if it depreciates at a rate of 8% per year

Answers

$13,946.16

1. $25,000 is 100% of the cars original cost. You want to add an 8% depreciation rate per year, so you subtract 8%, to get 92%.

2. Move 92% over two decimal places to get .92, you can multiply this by the original price to find the price of the car after one year of depreciation. 25,000 * .92 = 23,000. The car cost $23,000 after the first year.

3. Repeat this process 6 more times to find the price of the car after 7 years.

The answer is $13,946.16

Answer:

The answer is 14000

Step-by-step explanation:

i need help on number 3 please. i don’t think my answer is correct

Answers

Your mistake was that you wrote 7x-5 and 9x-16 as 7x+5 and 9x+16. You have to add the expressions the way it is. It helps to put the parenthesis around it. So when you add (7x-5)+(9x-16)+(3x+11) you get 19x -10 =180. So 19x=190, so x=10.

You have the right idea: add up the three angles and set the sum equal to 180. However you misplaced a few signs. You wrote 7x+5 when it should be 7x-5. Also you wrote 9x+16 when it's actually 9x-16.

Think of the three angles as A, B, C
A = 7x-5
B = 9x-16
C = 3x+11
Adding up A,B,C will lead us to 180 degrees
A+B+C = 180
7x-5+B+C = 180 ... replace A with 7x-5
7x-5+9x-16+C = 180 ... replace B with 9x-16
7x-5+9x-16+3x+11 = 180 ... replace C with 3x+11

Now we solve for x
7x-5+9x-16+3x+11 = 180
19x-10 = 180
19x-10+10 = 180+10 ... add 10 to both sides
19x = 190
19x/19 = 190/19 ... divide both sides by 19
x = 10

Answer: 10

My answer for this question is Graph D, but it looks like Graph B could also be a candidate. B and D both show decreasing graphs, and I've chosen D simply because it "looks" like it is decreasing faster. At x = 0, the slope of Graph D is less than that of Graph B. I am guessing that Graph B shows a parabola whereas Graph D shows something exponential (i.e. with an increasing rate)?

Answers

Since we're looking for decreasing functions, the answer can be narrowed between B and D as we go downhill as we move along the curve from left to right.

Choice B starts off with a slow pace of decreasing and then speeds up in terms of how much is decreasing. In other words, it is accelerating in how fast it is decreasing. How can we tell? Because of the slope of the tangent line. The slope of the tangent line at x = -1 is much less steep compared to the slope of the tangent at x = 5. The more steep the line, the faster the amount of decrease.

Choice D is the opposite of choice B in a sense. It starts off with fast decrease and that decreasing pace slows down. So if it asked "decreasing at a decreasing rate", then choice D would be the answer.

Answer: Choice B

Edit: one example graph B could model is the amount of water left in a large container. If we had a small hole at the bottom, then the water would leak out slowly at first. If the hole progressively gets bigger (say the water eats at the hole), then the water would leak faster and faster, which makes the curve steeper and steeper.

What is 10/12 equivalent to

Answers

10/12 is equal to 5/6.

This can be found by dividing both to and bottom by 2, thus simplifying it into 5/6.

I hope this helps!

[tex] \frac{10}{12} [/tex] is equivalent to both [tex] \frac{5}{6} [/tex] and ≈ 0.833 repeated. In order to find out the fraction that is equivalent to [tex] \frac{10}{12} [/tex] you need to reduce the fraction with 2. Once you do this you're left with [tex] \frac{5}{6} [/tex],, making it the equivalent fraction. In order to find out a fractions equivalent decimal,, you need to divide the top of the fraction (10) by the bottom of the fraction (12) in which case you would get ≈ 0.8333333 repeated.
Let me know if you have any further questions.
:)

How would you solve the area

Answers

check the picture below.

so the composite is just 2 triangles, one rectangle and one parallelogram.

we know the height and base of the triangles and length and width of the rectangle.

now, the parallelogram, we can simply split in in two triangles and a rectangle, like you see the split in the middle, and that gives us two more triangles and one rectangle.

so, we can simply get the area of each of those figures and sum them up, and that's the area of the composite.

[tex]\bf \stackrel{\textit{left triangle}}{\cfrac{1}{2}(11)(8)}~~+~~\stackrel{\textit{left rectangle}}{11\cdot 9}~~+~~\stackrel{\textit{upper middle triangle}}{\cfrac{1}{2}(11)(2)} \\\\\\ +~~\stackrel{\textit{middle rectangle}}{7\cdot 11}~~+~~\stackrel{\textit{lower middle triangle}}{\cfrac{1}{2}(11)(2)}~~+~~\stackrel{\textit{right triangle}}{\cfrac{1}{2}(8)(9)}\\\\ -------------------------------\\\\ 44+99+11+77+11+36\implies 278[/tex]

List the following stocks and bonds in order from lowest default risk to highest default risk:

Bond in a stable foreign government
Preferred stock
Common stock

A. foreign government bond, common stock, preferred stock

B. foreign government bond, preferred stock, common stock

C. common stock, preferred stock, foreign government bond

D. preferred stock, common stock, foreign government bond

Answers

A foreign government bond is issued by a Country that needs money and borrows it from the investors, therefore, you would become a creditor of the government/Country.

Stocks represent part of the ownership of a corporation, but preferred stockholders get paid before the common stockholders, especially in case of insolvency of the corporation.

Therefore, the least risky investment is a bond of a foreign government, while the riskiest investment is a common stock.

Hence, the correct answer is B. foreign government bond, preferred stock, common stock.

Please Help! Will give Brainliest!! 1. ______________ is process that you can do over and over, where each result does not affect the next. Ex. Flipping a coin, rolling dice, choosing a card, etc. 2. ________________ are the possible results of an experiment. Example: Heads, tails; 1, 2, 3…; Ace, King, Queen…; etc. 3. ______________is the measure of how likely an event is. 4. An ________________ event has a 0% chance of occurring Example : Rolling a 7 on a 6 sided die. 5. A ________________ event has a 100% chance of occurring. Example: Picking a red ball from a bag of only red balls. 6._______________ probability is what you expect to happen. 7.________________ probability is what actually happened. 8.The ___________ is the average value of all data in a set.

Answers

Part 1:

In probability, an experiment is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes. Thus, an experiment is a process that you can do over and over, where each result does not affect the next. For example: Flipping a coin, rolling dice, choosing a card, etc. are all experiments.

Part 2.

Outcomes are the possible results of an experiment. For example: When a coin is tossed, you either get a Heads or a Tails. Thus, Head, Tail are the outcomes of tossing a coin The set of possible outcomes from an experiment is called the sample space of the experiment.

Part 3.

Probability is the measure of how likely an event is to occur. Probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur.

Part 4.

An impossible event has a 0% chance of occurring. Like stated in part 3 above, probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. A probability of 0 implies that the occurrence of the event is impossible. For example: It is impossible to roll a 7 on a 6 sided die.

Part 5.

A certain event has a 100% chance of occurring. Like stated in part 3 above, probability takes values between 0 and 1, where, 0 indicates impossibility and 1 indicates certainty. A probability of 1 implies that the occurrence of the event is certain. For example: It is certain that a ball picked from a bag containing only red balls will be red.

Part 6.

Theoretical probability is what you expect to happen. In theoretical probability, we do not conduct an experiment, rather we use our knowledge about a situation, some logical reasoning, and/or known formula to calculate the probability of an event happening. Theoretical probability is given by the number of favorable outcomes divided by the total number of possible outcomes.

Part 7.

Experimental probability is what actually happened. Experimental probability is when the probability of an event happening is calculated by conducting an experiment. Experimental probability is given by the numberof event occurrences divided by the number of trials.

Part 8.

The arithmetic mean is the average value of all data in a set. The arithmetic mean is a measure of central tendency calculated by adding all the data values in the data set and dividing the sum by the total number of observations.

The number 12,570 is divisible by 2, 3, and 6. True False

Answers

true because all of the numbers here divide and multiply back in to the original number 12,570.

Answer:

true have a amazing and blessed day god loves you

Step-by-step explanation:

Find the tangent of both angle A and angle B. Ignore what the picture says the numbers are the same.

Answers

For the angle A we have:
tan (A) = C.O / C.A
tan (A) = 10/24
Simplifying we have:
tan (A) = 5/12
For angle B we have:
tan (B) = C.O / C.A
tan (B) = 24/10
Simplifying we have:
tan (B) = 12/5
Answer:
The tangent of angles A and B is given by:
tan (A) = 5/12
tan (B) = 12/5

Plz Help

A survey asked males and females to watch two commercials and select the one they liked best. The results of the survey are shown in the two-way frequency table.

Commercial A Commercial B
Males 0.28 0.14
Females 0.33 0.25

What percent of the respondents were female?

Answers

0.58% it sure answer please smart me brainiest I've lost a lot of points and rankings because because nobody is marking the brainiest so if you mark me u and the to percents together and that's what I got 0.25 is,25% 0.33 is 33% then add or just plain 58% please mark brainiest I'm trying to get my brainiest points back up

Answer: There is 58% of female respondents.

Step-by-step explanation:

Commercial A Commercial B Total

Males 0.28 0.14 0.42

Females 0.33 0.25 0.58

Total 0.61 0.39 1.00

So, Percentage of the respondents were females is given by

[tex]\dfrac{0.58}{1}\times 100\\\\=58\%[/tex]

Hence, there is 58% of female respondents.

What is the next step in completing this construction?

Answers

The intent of the construction appears to be to produce tangents from point P to the circle O. There are several possible next steps:
• Name the point of intersection just created between the arc and circle O
• Draw a line (or segment) between points P and J
• Draw a line (or segment) between point P and the intersecting point just created on circle O.

Answer:

The next step in completing the construction is

Join P to cut arc on circle i.e join PJ.

Step-by-step explanation:

Given the construction of tangent from the external point.

we have to tell the next step in completing the construction shown in diagram.

The step for construction are

Step 1: Draw a line joining the point to center of the circle to any external point P.

Step 2: Construct the perpendicular bisector of that line .

Step 3: Place the compass on the midpoint, adjust its length to reach the point P, and draw an arc across the circle .

Step 4: Join P to cut arc on circle i.e join PJ.

The 4 step is required step to complete the construction.

Hence, the next step in completing the construction is

Join P to cut arc on circle i.e join PJ.

In how many ways can three married couples attending a concert be seated in a row of six seats if

Answers

i think it would be 30 ways

David is building a sandbox for his nephew. The dimensions are 10 ft. by 8 ft. and is 1.5 ft. deep. How much sand will the box hold? Give answer in terms of cubic feet.

Answers

So you are looking for the volume of the sand box so what you need to do is multiply the info you got. 10x8x1.5=120

so your answer would be 120 sf

Volume = Length x Width x Height

Volume = 10 x 8 x 1.5 = 120 ft³

Answer: The box can hold 120 ft³ of sand.

Find the surface area of a triangular prism that has a height of 11 meters and the following triangular base. All dimensions are in meters.

Answers

Area of base = 1/2 x 4 x 3.5 = 7 m²

Perimeter of the base = 4 + 4 + 4 = 12 m

Surface area = 7 + 7 + 12 x 11 = 146 m²

Answer: 146 m²

Answer:

146

Step-by-step explanation:

40 POINTS!

Any help would be greatly appreciated!

Answers

Look at the picture.
[tex]\cos x=\sin x[/tex]

[tex]x=\dfrac{\pi}{4}+k\pi;\ k\in\mathbb{Z}[/tex]

Identify the solution set of the inequality using the given replacement set. x < –4; {–5, –4.6, –4, –0.8, 1, 1.5}

Answers

The solution set is {-0.8, 1, 1.5}. You are just plugging in the values for x from the solution set. Then you see if it gives you a true mathematical statement. For example:

If you plug in -5 for x you get

[tex] - 5 < - 4[/tex]
which is not true, so it is not a solution. Therefore it is not apart of the solution set. Same for -4.6, and -4, as these values are not greater than -4. However when you substitute in -0.8 you get the solution:

[tex] - 0.8 < - 4[/tex]
which is true, and it is the same for 1 and 1.5, which is why these numbers would be considered as part of the solution set.

A house and a lot is appraised at $212,400. The value of the house is five times more the value of the lot. What is the house worth?

Answers

the house is worth $177,000
the lot is worth $35,400

Which situation is best modeled by the equation 9+x=16 ?
a.You have $16
left after spending $9
and some other amount.

b.Nine friends each pay the same amount to get into a theme park, and the total is $16.

c.The price of a water bottle, $9
, was decreased by some amount to $16.

d.You pay $9
for a burger and some amount for dessert for a total of $16.

Answers

Answer:

d. You pay $9 for a burger and some amount for dessert for a total of $16.

Step-by-step explanation:

We have the following equation:

[tex]9+x=16[/tex]

So the variable of this equation is the amount of money. According to the statement we have that:

A burger costs $9.A dessert costs $xThe total you pay is $16

If we solve this equation, we have that:

[tex]x=7[/tex]

So the dessert costs $7. Finally, you pay $16 for the burger and the dessert as follows:

You pay $9 for the burger.You pay $7 for the dessert.You pay a total amount of money = $16

Answer:

You pay $9

for a burger and some amount for dessert for a total of $16

Step-by-step explanation:

Brody is purchasing some tools for his workshop. He has a budget of $120 and needs to buy at least 14 tools. Each hammer costs $10, and each wrench costs $6. If the solution region represents the number of hammers and wrenches that Brody can buy given his budget, determine which graph represents the solution set to the system of inequalities representing this situation.

Answers

For this case, the first thing we must do is define variables:
x: number of hammers
y: number of wrenches
We write the system of inequations:
10x + 6y <= 120
x + y> = 14
We graph the system of inequations.
The solution set is given by the shaded region of the graph.
Answer:
see attached image.

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x------> the number of hammers

y------> the number of of wrenches

we know that

[tex]10x+6y\leq 120[/tex] -----> inequality A

[tex]x+y\geq 14[/tex] -----> inequality B

using a graphing tool

The solution of the system of inequalities is the shaded area

see the attached figure

given that A=43 degrees , B=82 degrees and c=28, solve triangle ABC. Round to the nearest hundredth. A) C= 93 degrees , b= 33.8 , a= 23.3 B) C= 55 degrees , b= 33.8 , a= 23.3 C) C= 55 degrees , b= 23.3 , a= 33.8 D) C= 93 degrees , b= 23.3 , a= 33.8

Answers

A=43°
B=82°
c=28

1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)

2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°

2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3

2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8

Answer: Option B) C=55°, b=33.8, a=23.3

The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden.

Answers

Comment
The gardens are square. There are two of them. The total is 18000 square feet. There is a relationship between smallest and largest square.

Development of the Equation.
Formula for a square = s*s

The first garden has a side of s
The larger garden has a side of 2s

The area of the first garden = s^2
The area of the 2nd garden = (2s)^2

The two areas together are
s^2 + (2s)^2 = 18000

Solve
s^2 + 4s^2 = 18000 Add the like terms on the left.
5s^2 = 18000 Divide by 5
s^2 = 18000/5
s^2 = 3600 Take the square root of both sides.
sqrt(s^2) = sqrt(3600)
s = 60 For the small garden

2s = 2*s = 2*60 = 120 for the large garden.

Answers
Small garden = 60 by 60
Large garden = 120 by 120

Check
Area of the small garden = 60 * 60 = 3600
Area of the large garden = 120*120 = 14400
Total Area = 18000 and it checks.

Abigail wants to measure the dimensions of a classroom to figure out how many desks can fit in the room. Which method could Abigail use to get the most accurate measurements?

Answers

weight and length but you need more variables

Answer:

Abigail could use a 50-foot tape measure to find the length of the classroom.

Please help asap 30 pts

Answers

D. If you were to graph this, the vertex would be at (9/8,101/4), or (1.13,25.25).

Find the area of this shape

Answers

You do A=1/2xhx(b1+b2)
A=1/2x3.6x(3.6+9)
A=1/2x3.6x12.6
A=1/2x45.36
A=22.68

If a tessellation is regular, how many sides can the tessellating regular polygon have?

Answers

For the answer to the question above, I think that only the regular polygons that tessellate are equilateral triangles, squares, and regular hexagons.
I hope my answer helped you. Have a nice day!

3, 4, 6 apex not sure if it is correct but i think it is

A cone with radius 5 units is shown below. Its volume is 105 cubic units. Find the height of the cone.

Answers

Answer:

height of the cone = 4.01273885 units

Step-by-step explanation:

Volume of a cone(V) is given by:

[tex]V = \frac{1}{3} \pi r^2h[/tex] ....[1]

where,

r is the radius and h is the height of the cone.

As per the statement:

A cone with radius 5 units and ts volume is 105 cubic units

⇒r = 5 units and V = 105 cubic units

Substitute these given values and use [tex]\pi = 3.14[/tex] in [1] we have;

[tex]105 = \frac{1}{3} \cdot 3.14 \cdot 5^2 \cdot h[/tex]

Multiply both sides by 3 we have;

⇒[tex]315 = 78.5 \cdot h[/tex]

Divide both sides by 78.5 we have;

[tex]4.01273885 = h[/tex]

h = 4.01273885 units

Therefore, the height of the cone is, 4.01273885 units

The height of the cone is 4 units.

What is the volume of a cone?

The volume of the cone is equal to;

[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h[/tex]

Where; B is the area of the circular base of the cone, and h is the height of the cone.

The base of the cone is given by;

[tex]\rm Base=\pi r^2[/tex]

Substitute all the values in the equation

[tex]\rm Volume \ of \ cone=\dfrac{1}{3} \times b \times h\\\\Volume \ of \ cone=\dfrac{1}{3} \times \pi r^2\times h \\\\ 105=\dfrac{1}{3} \times 3.14 \times 5^2\times h\\\\h = \dfrac{105\times 3}{25 \times 3.14}\\\\h=64[/tex]

Hence, the height of the cone is 4 units.

To know more about cone click the link given below.

https://brainly.com/question/12445166

#SPJ3

Juan makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours

Answers

I hour = $8
h hours = $8h

Answer: p = $8h

Juan's total pay p after working h hours is calculated using the equation p = 8h. This represents a direct relationship between hours worked and total earnings.

To represent Juan's total pay p after working h hours at a rate of 8 dollars per hour, we use the equation p = 8h. This equation shows that the total pay (p) is equal to the rate of pay per hour (8 dollars) multiplied by the number of hours worked (h).

For example, if Juan works for 8 hours a day, his total pay would be calculated as p = 8 * 8, which equals $64. If we consider a full day of work to be 8 hours producing a value of $160, we can see that Juan is being paid for only half the hours at that rate, since 8 hours' labor would have a value of $80 at his rate of pay.

Kevin is 39 years old and daniel is 3 years old.how many years will it take until kevin is only 4 times as old as daniel?

Answers

9 :)))))))))))))))))

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