What is the volume of the cone below?
A. 112 units3
B. 5671 units 3
C. 16811 units 3
D. 3367 units3
Answer:
B
Step-by-step explanation:
3367unit 3 unit 3
The volume of the cone with the given radius and height in terms of constant pi is 112π units³.
Hence option A) 112π units³ is the correct answer.
What is a Cone?A cone is simply a 3-dimensional solid geometric shape having a circular base and a pointed edge, it has a single face and a vertex.
The volume of a cone is expressed as;
V = (1/3)πr²h
Where r is the radius, h is height and π is constant pie
Given the data in the image below;
Height of the cone h = 21Radius r = 4Volume of the cone V = ?We substitute our given values into the expression above.
V = (1/3)πr²h
V = (1/3) × π × (4 units)² × 21 units
V = (1/3) × π × 16 units² × 21 units
V = 112π units³
the volume of the cone with the given values of radius and height in terms of constant pi is 112π units³.
Hence option A) 112π units³ is the correct answer.
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Zak is going to buy some bookcases and some lamps to sell in his shop. Each bookcase costs £16 Each lamp costs £12 Zak has a maximum of £360 to spend. He is going to buy x bookcases. He is going to buy y lamps. Show that 4 x + 3 y ≤ A where A is a constant to be found
Answer:
He can buy 8 bookcases and 6 lamps
Step-by-step explanation:
4(16) + 3(12)
64 + 36 = 100
360- 100 = 260
260-100=60
4*2=8 3*2=6
Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.
Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”
Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”
Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”
Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”
Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem
Answer:
Option D.
Step-by-step explanation:
The given equation is
[tex]32g+8g-10g=150[/tex]
It can be written as
[tex](32+8-10)g=150[/tex]
To solve this equation, add 32 and 8.
[tex](40-10)g=150[/tex]
Subtract 10 from 40.
[tex]30g=150[/tex]
Divide both sides by 30.
[tex]\dfrac{30g}{30}=\dfrac{150}{30}[/tex]
[tex]g=5[/tex]
The value of g is 5 and wilhem is correct.
Therefore, the correct option is D.
Answer:
The correct answer is d. wilhem
Given that the measure of ∠x is 60°, and the measure of ∠y is 110°, find the measure of ∠z.
Answer:
∠z = 10°Step-by-step explanation:
A triangle is always 180 degrees.
If ∠x is 60°
and ∠y is 110°,
110 + 60 = 170
∠z = 10 degrees
Answer:
50
Step-by-step explanation:
Find which term in the geometric sequence 1, 3, 9, 27, ... is the first to exceed 7,000.
hint (use a table)
Answer:
10th term
Step-by-step explanation:
3ⁿ⁻¹ > 7000
log₃ 7000 = 8.05
n - 1 > 8
n > 9
10th term
check: 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683
You have a package of 20 assorted thank-you cards. You pick the four cards shown. How many of the 20 cards would you expect to have flowers on them?
what is shows in the picture:
2 with thank you's then one with flowers that says thank you than on with a dragon fly that says thank you for you kindness
this is the question: You would expect ___cards to have flowers on them.
Out of 20 there are 5 cards which have flowers on them.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have total 20 thank-you cards.
Now, we choose four cards.
Out of 4 cards 2 with thank you then one with flowers that says thank you than on with a dragon fly
So, We choose pair of 4 cards 5 times.
Then, we get total cards with flower
= 1 x 5
= 5
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A discount clothing store is selling a $99 sport jacket for $11 off the regular price. What is the discount rate?
Answer:
jacket is $99 at a discount of $11 off regular price
add the discount back on to get regular price which is $99+$11=$110
$110x.10=$11
therefore the jacket is sold at a 10% discount
Step-by-step explanation:
Pharrell wants to write equations in the form y = mx + b for the lines passing through point P that are parallel and perpendicular to line w. First he finds the slope of line w and line v to be 1/2 and the slope of line n to be -2. Point P is located at (-4, 2). Which step could he use to find the y-intercepts?
A. Multiply the slope, -2, by the x-coordinate, -4, and add the y-coordinate, 2, to the product.
B. Substitute the slope, -2, and the coordinates of point P (-4, 2) in y = mx + b and then solve for b. Repeat using the slope 1/2 for the second equation.
C. Multiply the slope, -2, by the y-coordinate, 2, and subtract the result from the x-coordinate, -4. Repeat for the slope 1/2 for the second equation.
D. Solve the proportion m/b = y/x for b, where m = -2, y = 2, and x = -4. Then solve the proportion m/b = y/x for b, where m = 1/2, y = 2, and x = -4.
Answer:
B. Substitute the slope, -2, and the coordinates of point P (-4, 2) in y = mx + b and then solve for b. Repeat using the slope 1/2 for the second equation.
Step-by-step explanation:
In which month was the peak, the largest deposit, made?
A January. B June. July. D August
Answer: It was made in B June
Step-by-step explanation: The following transactions occurred in June through August 2020. June 1 After much thought, Natalie sells a mixer to Curtis on credit, terms n/30, for $1,150 (cost of mixer $620). 30 Curtis calls Natalie. He is unable to pay the amount outstanding for another month, so he signs a one-month, 8.35% note receivable. July 31 Curtis calls
Answer:
C. July
Step-by-step explanation:
It's the tallest one in the plot.
I hope this helped. B)
The table shows the relationship "Mason rode 15 miles per hour on his bicycle."
Hours (h)
1
2
3
4
Miles (m)
15
30
45
60
75
Which statements are correct? Check all that apply.
The variable m is the independent variable.
The number of miles increases as time increases.
The number of hours causes a change in the number of miles ridden.
The variable h is the independent variable.
NE
Save and Exit
The statements which are correct are-
The number of miles increases as time increases. The number of hours causes a change in the number of miles ridden. The variable h is the independent variable.Step-by-step explanation
The above table displays the relationship between the time taken in hours ("h") by Mayon to cover the distance (miles "m").
It means that the distance is dependent on time in hours. Hence, the variable "m" is a dependent variable since it depends on time "h" for which bicycle is being ridden.
Similarly, the variable "h" is an independent variable.
As seen from the table, the value of "m" continuously increases for the value of "h" and thus the number of hours causes a change in the distance ridden.
Answer:
The number of miles increases as time increases.
The number of hours causes a change in the number of miles ridden.
The variable h is the independent variable.
The variable m is the dependent variable.
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
I also did the quiz, and got it correct.
Good luck!
11. Find the next 4 numbers in the pattern. 21, 24, 19, 22, 17, 20,
Answer:
The answer is 23???....?
Answer:
16,19,15,18
Step-by-step explanation:
rule=+3,-4
At a New Car Dealership a particular model comes in 4 trims levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?
Answer:
60 different versions
Step-by-step explanation:
4 times 5 times 3 is 60.
The number of different versions of this car model that can be created from these options is 60.
Number of different versions:Using this formula
Number of different versions=Trims levels×Different colors×Different Interior
Where:
Trims levels=4
Different colors=5
Different Interior=3
Let plug in the formula
Number of different versions=4×5×3
Number of different versions=60
Inconclusion the number of different versions of this car model that can be created from these options is 60.
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What is the equivalent of 4 meters?
q= r/2 (s +t) for t.
Answer:
t=2Q-sr/r
Step-by-step explanation:
We are to make t the subject of formula from the given question
Q=r/2 (s+t)
Q=Sr+tr/2
Cross multiply
2Q=Sr+tr
2Q-sr=tr
t=2Q-sr/r
f(x)=-x^2-9x-4 find f(10)
The value of the given expression f(x)=-x² - 9x - 4 is -194.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given expression f(x)=-x² - 9x - 4 will be solved as below:-
f(x)= -x² - 9x - 4
f(x)= -( 10 )² - 9x(10) - 4
f(x) = -100 - 90 - 4
f(x) = -194
Therefore, the value of the given expression f(x)=-x² - 9x - 4 is -194.
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The length of a rectangle is four times the width. The
perimeter of the rectangle is 40 inches. What is the area of
the rectangle (in square inches)?
Answer:
Step-by-step explanation:
let the width=x
length=4x
P=2(l+w)=2(4x+x)=10x
10x=40
x=40/10=4
width=4 in
length=4×4=16 in
area=16×4=64 square inches.
The required area of the given rectangle is given as 64 inch².
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
Here,
As mentioned in the question,
The length of a rectangle is four times the width.
l = 4w
Now,
The perimeter of the rectangle is 40 inches.
2 [l + w] = 40
2 [4w + w] = 40
5w = 20
w = 4 inches
Length,
l = 4(4) = 16 inches
Area of rectangle = l × w
= 16 × 4 = 64 inch²
Thus, the required area of the given rectangle is given as 64 inch².
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what is the y intercept of f(x)=2x^2+8x+6
Answer:
6 is the y intercept
Step-by-step explanation:
Avery received $80 in cash for mowing lawns. She did the following with the $80. Put 20% of the $80 into a bank account. Spent 1/4 of the $80. Kept the rest of the $80 in cash. How much of the $80 did Avery keep as cash?
Answer:
$48
Step-by-step explanation:
To start off, we know that Avery put 20% of the $80 in her bank account. We can figure out how much 20% of 80 is by multiplying 80 by 20% and then subtracting that number from 80. Remember to switch 20% to its decimal form (20% -> .2).
Step 1) 80 x .2 = 16
Step 2) 80 - 16 = 64
Next, we have to figure out how much 1/4 of the remaining $64 would be. We just simply divide 64 by 4 to figure out how much Avery spent.
Step 3) 64 / 4 = 16
Lastly, since we know Avery spent 16 dollars, we can subtract the 16 from 64 to get our final answer.
Step 4) 64 - 16 = 48
Avery kept $44 of the $80 as cash after putting 20% into a bank account and spending 1/4 of it.
Avery received $80 in cash for mowing lawns. Let's calculate how much she kept after her transactions. First, she put 20% of the $80 into her bank account. Calculating 20% of $80 involves multiplying $80 by 0.20, resulting in $16. Next, Avery spent 1/4 of the $80, which equals $20, as $80 divided by 4 gives $20. To find the amount Avery kept as cash, we subtract the amounts she put in her bank and spent from the original $80.
$80 - $16 - $20 = $44
Therefore, Avery kept $44 of the $80 as cash.
5. A 200 pound person weighs 33 pounds on the moon.
a. How much did the person's weight decrease?
Answer:
Step-by-step explanation:
The answer will be 167
Final answer:
The weight of a 200-pound person decreases by 167 pounds on the moon due to the weaker gravitational force. Weight varies with gravity, but mass remains constant.
Explanation:
If a 200-pound person weighs 33 pounds on the moon, the person's weight has decreased by 167 pounds. The weight decrease can be calculated by subtracting the weight on the moon from the original weight on Earth.
Weight decrease = Original weight on Earth - Weight on moon
Weight decrease = 200 pounds - 33 pounds
Weight decrease = 167 pounds
This calculation shows how weight varies with the acceleration due to gravity, which is weaker on the moon. Therefore, the gravitational force acting on a person on the moon is less, resulting in a lower weight, although the person's mass remains constant.
Scott paid 19.99 for a 7.98-kg bag of dog food. A few weeks later, he paid 20.38 for an 8.39-kg bag at a different store. What is the unit price for each bag
Answer:
Store 1: 19.99/7.98 = 2.51
Store 2: 20.38/8.39 = 2.43
Step-by-step explanation:
unit price is per 1 kg...so you will divide
Store 1: 19.99/7.98 = 2.51
Store 2: 20.38/8.39 = 2.43
The unit price of the first bag of dog food is $2.50 per kg, and the unit price of the second bag is $2.43 per kg.
Explanation:
To determine the unit price for each bag of dog food, we need to divide the total cost of the bag by the weight of the bag. The unit price will tell us the cost per kilogram of dog food. Let's calculate the unit price for each bag.
For the first bag:
Cost = $19.99
Weight = 7.98 kg
Unit price = Cost ÷ Weight
Unit price = $19.99 ÷ 7.98 kg
For the second bag:
Cost = $20.38
Weight = 8.39 kg
Unit price = Cost ÷ Weight
Unit price = $20.38 ÷ 8.39 kg
Let's perform the calculations:
First bag's unit price: $19.99 ÷ 7.98 kg = $2.50 per kg (rounded to two decimal places)Second bag's unit price: $20.38 ÷ 8.39 kg = $2.43 per kg (rounded to two decimal places)So the unit prices are $2.50 per kg for the first bag and $2.43 per kg for the second bag.
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A pack of 4 chocolate bars costs £1.20
What is the price per unit?
Answer:
30 cents
Step-by-step explanation:
Since 4 bars cost 1.20 pounds, divide 1.20 by 4
Simplify using exponential notation. (9a^3)^6
A circular plate has circumference 16.3 inches. What is the area of this plate? Use 3.14 for pi.
The area of this plate is about " blank" square inches
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest thousandth as needed.)
Plz answer will give brainiest to the person who answers this plz help!!!!!!!
Answer:
The area of this plate is about 21 in².
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Geometry
Circumference Formula: C = 2πr
r is radiusArea of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify given.
C = 16.3 in
Step 2: Find Radius r
[Circumference Formula] Substitute in C:Step 3: Find Area
[Area of a Circle Formula] Substitute in r:∴ we have found the area of the plate.
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Topic: Geometry
a rectangle field has an anrea of 40cm^2. if one side of the field is 3m longer than the other side, find the new area of the field where the length of each side is increased by 10%
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex].
Step-by-step explanation:
The given is,
A rectangle field has an area of 40 [tex]cm^{2}[/tex]
If one side of the field is 3 cm longer than the other side
The length of new area in each side is increased by 10%
Step:1
Let,
[tex]b[/tex] - One side of rectangle
[tex]l[/tex] - Other side of rectangle
From given.
[tex]l[/tex] - [tex]b[/tex] +3
Formula for area of rectangle,
[tex]Area, a = lb[/tex]
40 = ( b+3) × b
40 = [tex]b^{2}[/tex] + 3b
Solving the above the equation,
b = 5 cm
l = 8 cm
Step:2
If the area of rectangle increased by 10%,
l = 8 + ( 8 × [tex]\frac{10}{100}[/tex] )
= 8.8
b = 5 + ( 5 × [tex]\frac{10}{100}[/tex] )
= 5.5
Area of rectangle is,
a = ( 8.8 × 5.5 )
= 48.4 square centimeters
Result:
The area of the field where the length of each side is increased by 10% is 48.4 [tex]cm^{2}[/tex], if a rectangle field has an area of 40 square centimeters and one side of the field is 3 cm longer than the other side.
Ella deposited $2500 into a savings account. The relationship between the time, t, in years, since the account was first opened, and Ella's account balance, B(t), in dollars, is modeled by the following function.
B(t)=2500⋅e^0.025t
What will the balance of Ella's savings account be after 4 years?
Answer:
She will have $2762.927
Step-by-step explanation:
The modeled function is
B(t) = 2500*e^0.025t
Where t represent the time in years. In four years, her account would be
B(t) = 2500 * e^0.025(4)
B(t) = 2500 * e^0.1
B(t) = 2762.927
In four years, Ella would have $2762.927 in her account
Answer:
2762.927
Step-by-step explanation:
The lines below are perpendicular the slope of the red line is -2 what is the slope of the green line
Answer:
The slope will be 1/2.
Step-by-step explanation:
Sine the lines are perpendicular, the slope of the green line will be the negative reciprocal of the slope of the red line. To find the negative reciprocal of -2, first change the sign. Since the slope is negative, make it positive 2. Then to find it's reciprocal, divide 1 by your answer. 1 divided by 2 is one half, s that is your answer.
HELPPPppp MEEEEEEeeee
Hi, What is 678 divided by -4 times 56xs then added 7h.
Answer:-9492xs+7h
Step-by-step explanation:if you do 678 divided by -4 it would be -169.5 then multiply that by 56 witch would be -9492 then times s would be -9492xs then that added to 7h would be -9492xs+7h and your final answer
Which expression represents 22 more than the difference between 95 and 63
A. (22+95)
B. 22+(95+63)
C. (95-63)+22
Answer:
C
Step-by-step explanation:
Difference: 95 - 63
22 more: (95 - 63) + 22
Answer:
C. (95-63)+22
Step-by-step explanation:
difference means subtraction
95-63
more than means add after
(95-63) +22
Meghan unfolded a three dimensional solid and formed the two dimensional figure below. Select all the statements that apply to this figure
Answer:
The statements that apply to this figure are:
3. The surface area is the lateral area plus the area of the two circles.4. This is the net of a cylinder.
5. The lateral area is the circumference of the circle multiplied by the height of the solid.
Explanation:
First, analyze the 2D figure and imagine what it is in 3D: you may bend the left circle 90º, then roll it along the line of the rectangle all the way up and then bend the other circle 90º.
The rectangle will become the lateral walls of a cylinder and each circle a base.
Thus, the net corresponds to a cylinder.
Now, check every statementÑ
1. This is the net of a cone
FALSE. It is a cylinder2. The volume is found by adding up the areas of the circles and the rectangle.
FALSE. By adding up the areas of the circles and the rectangle you get the area of the cylinder.
3. The surface area is the lateral area plus the area of the two circles.
TRUE. The lateral area of the cylinder is equal to the area of the rectangle. The area of the two circles is the area of the bases of the cylinder.
By adding the lateral area and the area of the bases you get the total surface area of the cylinder.
4. This is the net of a cylinder.
TRUE. Explained above
5. The lateral area is the circumference of the circle multiplied by the height of the solid.
TRUE. The circumference of the circle is equal to the length of the rectangle. Thus, by multiplying this by the height of the rectangle, which is the same height of the solid, you get the area of the rectangle and that is the lateral area of the cylinder.
6. The solid has 3 faces, 6 edges and 4 vertices.
FALSE. The only edges of the cylinder are the rims of the bases and a cylinder does not have vertices.
Hence, the true statements that apply in the figure are:
The surface area is the lateral area plus the area of the two circles.This is a net of a cylinder.The lateral area is the circumference of the circle multiplied by the height of the solid.Cylinder:A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases are normally circular in shape (like a circle) and the center of the two bases are joined by a line segment, which is called the axis. The perpendicular distance between the bases is the height, [tex]'h'[/tex] and the distance from the axis to the outer surface is the radius [tex]'r'[/tex] of the cylinder.
Here this unfold is of a cylinder as it has [tex]2[/tex] circulars bare and [tex]1[/tex] rectangle side of the surface.
Total surface area is equal to= Surface area of lateral area + 2 circular area.
Lateral area= height[tex]\times[/tex]circumference of the circle.
This solid has 3 faces, 2 edges then, option 3,4,5 is true.
Volume of area[tex]=\frac{1}{3} \pi r^{2}h[/tex] [[tex]r=4 cm\\h=13 cm[/tex]]
[tex]=\frac{1}{3}\pi (4) ^{2} h\\=217.817 \ cm^{2} \\\simeq 218 \ cm^{2}[/tex]
Volume of cylinder[tex]=\pi r^{2} h[/tex]
[tex]=251.32 \ cm^{2} \\\simeq 251 \ cm^{2}[/tex]
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