Answer:
Uncle Mike was 7 times as old as Sally 17 years ago.
Step-by-step explanation:
Let's call Uncle Mike's current age "x."
Sally is 12 years old, so x = 12 * 3 = 36 years old.
We are looking for years that must pass before Uncle Mike is only twice as old as Sally. So we need to find the age when x = 2 * (12 + n), where n is the number of years that have passed. Solving for n:
36 = 2 * (12 + n)
36 = 24 + 2n
12 = 2n
n = 6
So, six years must pass before Uncle Mike is only twice as old as Sally.
To find out how many years ago Uncle Mike was 7 times as old as Sally, we need to find the age when x = 7 * (12 - m), where m is the number of years ago. Solving for m:
36 = 7 * (12 - m)
36 = 84 - 7m
120 = 7m
m = 17
So, Uncle Mike was seven times as old as Sally 17 years ago.
What would have a greater effect on the volume of a cone: doubling
its radius or doubling its height? Explain?
The formula for the volume of a cone, V = (1/3)·π·r²·h, indicates that doubling the radius, quadruples the volume while doubling the height doubles the volume. Therefore;
Doubling the volume has a greater effect on the volume of a coneWhat is a circular cone?A cone is a three dimensional figure formed by lines that extend between a point and the circumference of the circular base, where the point is located on the a line perpendicular to and passing through the center of the circular base.
The formula for the volume of a cone is; V = (1/3) × π × r² × h
Where;
V = The volume of the cone
r = The radius of the cone
h = The height of the cone
Therefore;
When the radius is doubled, we get;
V₁ = (1/3) × π × (2·r)² × h = (1/3) × π × 4 × r² × h = 4 × (1/3) × π × r² × h
Therefore; V₁ = 4 × (1/3) × π × r² × h = 4·VWhen the radius of the cone is doubled, the volume of the cone increases 4 times the initial volume
When the height of the cone is doubled, we get;
V₂ = (1/3) × π × r² × 2·h = 2 × (1/3) × π × r² × h = 2·V
V₂ = 2·VWhen the height of the cone is doubled, the volume of the cone is doubled.
Therefore, doubling the radius of the cone which increases the volume to four times the initial volume has the greater effect on the volume of the cone than doubling the height which doubles the volume of the cone.
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Amir invests £785 for n years into a savings account.
Amir was paid 1.5% per annum compound interest.
At the end of the n years Amir had £1105.58 in the savings account.
Work out the value of n.
on=
Submit Answer
years
The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.
What is compound interest?Let 'A' is the amount, 'P' is the initial amount, 'r' is the rate of interest, and 'n' is the number of years.
Then the compound interest is written as,
A = P(1 + r)ⁿ
Then the equation is given as,
£1,105.58 = £785 × (1 + 0.015)ⁿ
1.40838 = (1.015)ⁿ
n log 1.015 = log 1.40838
n = 23 years
The number of years for the speculation to reach from £785 to £1,105.58 will be 23 years.
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A player hits the bullseye with a dart 8% of the time. Based on this relative frequency, how many times can the bullseye be expected to be hit when the player throws the dart 40 times. WRONG ANSWER = BLOCKED
The probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.
What is relative frequency?The quantity of occurrences of an event is referred to as its frequency. The concept of relative frequency is experimental rather than theoretical. It is experimental, therefore if we repeat the trials, we can get different relative frequencies. To determine the frequency, we must first:
Number of occurrences for the entire population
Frequency count for a particular demographic segment
If we know the two frequencies mentioned above, we can use the following formula to get the relative frequency probability. A subgroup's formula is as follows:
Subgroup Count / Overall Count: Relative Frequency
Given that, a player hits the bullseye with a dart 8% of the time.
The probability of hitting the dart is = 8/100.
Now, the probability of hitting the bullseye if the dart is thrown 40 times is:
p = 40 (8/100) = 3.2 times = 3 times.
Hence, the probability of hitting the bullseye if the dart is thrown 40 times is approx. 3 times.
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The measure of angle is less than times its complement. What is the measure of the complement of angle ?.
The measure of the complement of angle is 45 degrees.
Let's call the measure of the angle "x". The complement of the angle is defined as 90 degrees minus the measure of the angle, so the complement of the angle is 90 - x.
If the measure of the angle is less than its complement, then we can write the following inequality:
x < 90 - x
Now we can isolate x by subtracting x from both sides:
0 < 90 - 2x
And then dividing both sides by -2:
0 > -45 + x
Finally, subtracting x from both sides:
-x > -45
So, we have:
x < 45
So, the complement of the angle is 90 - x, which is greater than 90 - 45 = 45 degrees.
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7 cards were drawn from a standard deck of cards without replacement what is the probability of getting 4 hearts and 3 spades
Total No. of cards in a deck = 52
Total no. of suits = 4
Total number of cards in one suit = [tex]\frac{52}{4} \\[/tex] = 13
Ways of selecting combinations of 4 from 13 hearts (combination) = [tex]\frac{13!}{9! 4!}[/tex]
= 715
Ways of selecting combinations of 3 from 13 spades (combination) = [tex]\frac{13!}{10! 3!}[/tex]
= 286
Combining the two independent choices, there are 715×286=204490
ways to select a seven-card hand with 4 hearts and 3 spades.
Ways of selecting 7 cards from 52 cards = [tex]\frac{52!}{7! 45!}[/tex] = 133784560
Probability of getting 4 hearts and 3 spades on drwaing 7 cards from the deck = [tex]\frac{204490}{133784560}[/tex] = 0.0015285 (approx.)
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Total Surplus The sum of consumer surplus and producer surplus is called the total surplus; it is one measure economists use as an indicator of the economic health of a society. Total surplus is maximized when the market for a good is in equilibrium. A camera company estimates that the demand function for its new digital camera is and the supply function is estimated to be here is measured in thousands. Compute the maximum total surplus.
The total surplus at the equilibrium point is: $200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
To compute the maximum total surplus, we need to find the equilibrium quantity and price in the market for the digital camera, and then calculate the consumer and producer surplus at that point.
First, we need to set the demand and supply functions equal to each other to find the equilibrium quantity:
50 - 2P = 2P - 10
4P = 60
P = 15
Substituting this equilibrium price into either the demand or supply function, we can find the equilibrium quantity:
Q = 50 - 2(15) = 20
So the equilibrium price is $15, and the equilibrium quantity is 20,000 digital cameras.
Next, we can calculate the consumer and producer surplus at the equilibrium point. Consumer surplus is the difference between the maximum price a consumer is willing to pay for a good and the market price, summed over all consumers in the market. Producer surplus is the difference between the market price and the minimum price a producer is willing to accept for a good, summed over all producers in the market.
The demand function gives us the maximum price consumers are willing to pay for each quantity of digital cameras:
P = 25 - 0.5Q
So at the equilibrium quantity of 20,000 digital cameras, the maximum price consumers are willing to pay is:
P = 25 - 0.5(20) = 15
This is exactly the same as the market price, so there is no consumer surplus at the equilibrium point.
The supply function gives us the minimum price producers are willing to accept for each quantity of digital cameras:
P = 0.5Q - 5
So at the equilibrium quantity of 20,000 digital cameras, the minimum price producers are willing to accept is:
P = 0.5(20) - 5 = 5
The market price is $15, so the producer surplus is:
(15 - 5) * 20 = $200,000
Therefore, the total surplus at the equilibrium point is:
$200,000
This is the maximum total surplus that can be achieved in the market for the digital camera.
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Helppppppppppp meeee pleaseee
I don’t have an answer for number one but
2) Angle I = 59. From lowest to greatest it goes G,I,H
Answer:
Problem 1
From smallest to largest:
∠y , ∠w, ∠x
Problem 2
m∠I = 39°
Sides from shortest to longest
GH, HI, GI
Step-by-step explanation:
For question 1
The ratios of the sides of a triangle to the sine of the angle opposite them is the same
That means the ratios of the sides to each other is the same as the ratio of the sines of the angles opposite them
Since the sine of an angle increases with increasing angle value, the longest side will opposite the greatest angle measurement and the smallest length will be opposite the smallest angle measurement
So in order from smallest to largest
m∠y < m∠w < m∠x
For question 2
Since three angles of a triangle add up to 180°
Missing angle = 180 - (83 + 58)
= 180 - 141
= 39°
From shortest to longest it would be
Side GH < side HI < side GI
An international company has 12,700 employees in one country if this represents 18.7% of the company's employees how many employees does it have in total?
Round yiur answer to the nearest whole number
Answer:
67,914
Step-by-step explanation:
Let x = total employees.
18.7% of x = 12,700
0.187x = 12,700
x = [tex]\frac{12700}{0.187}[/tex] = 67914.438 → 67,914
This is the net of
triangular prism. To calculate the lateral surface area, you
should add the areas of which sides?
O A. A and D
• B. A, B, C, D, and E
• C. B, C, and E
O D. A, D, and E
To calculate the lateral surface area, you should add the areas of C. B, C, and E
What is a Triangular Prism?A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry.
If the sides of a right triangular prism are not rectangular, the prism is oblique.
We know that
The lateral area for a triangular prism is the sum of the areas of its side faces (which are 3 rectangles).,
From the given images, the side faces are B, C and E which is option C.
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Mrs. Smith asked her students to write a situation that could describe the relationship between all of the values of x and y in the table.
X 0 1 2 3
Y 8 9 10 11
Which situation best describes the relationship between all the values of x and y in the table?
A. Danee had eight dance classes per week.
B. Yolanda had eight books and bought one new book each week.
C. Lincoln started with zero stamps in his collection for the first 8 months and then started to collect one stamp per month.
D. Gavin caught one fish in the first minute of fishing and eight fish each minute after.
The solution is Option B.
The equation of line is y = x + 8 , where the slope is m = 1
Yolanda had eight books and bought one new book each week
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P (
Let the second point be Q (
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we getWhat is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 8 )
Let the second point be Q ( 1 , 9 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 9 - 8 ) / ( 1 - 0 )
Slope m = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 8 = 1 ( x - 0 )
On simplifying the equation , we get
y - 8 = x
Adding 8 on both sides of the equation , we get
y = x + 8
Hence , the equation of line is y = x + 8
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Answer: B
Step-by-step explanation:
For which intervals is the function increasing? Select each correct answer.
(2, ∞)
(1, 2)
(0, 1)
(-∞, 0)
Answer:
i think the answer may be (2,infinity)
(1, 2) and (-∞, 0)
===========================================================
Explanation:
The function curve is increasing when going uphill as you move to the right. This happens on the interval (-∞, 0) aka -∞ < x < 0 aka x < 0. This is why choice D is one of the answers.
The function is also increasing when 1 < x < 2 which translates to the interval notation (1,2). This is why choice B is the other answer.
Choices A and C are eliminated since they describe decreasing intervals.
Question content area top
Part 1
Mr.Curry has 264 pictures on 4 shelves in his house. He has the same number of pictures on each shelf. To find the number of pictures on each shelf, he divided 264 by 4. How many tens did he regroup as ones? How many pictures are on each shelf?
Question content area bottom
Part 1
Mr.Curry regrouped
enter your response here tens as
enter your response here ones.
If Mr.Curry has 264 pictures on 4 shelves in his house.
The number of tens did he regroup as ones is: 2 tens.The number of pictures that are on each shelf is 66 picturesHow to find the number of tens he regroup as ones is: 2 tens.The number of pictures on each shelf can be found by dividing the total number of pictures by the number of shelves:
264 ÷ 4 = 66
So, there are 66 pictures on each shelf.
To find the number of tens Mr. Curry regrouped as ones, we can use long division to see the process of dividing 264 by 4.
When dividing 264 by 4, the first step is to divide 2 by 4, which gives a quotient of 0 with a remainder of 2. Then, you bring down the next digit (6), and form the number 26. Dividing 26 by 4 gives a quotient of 6 with a remainder of 2. Finally, you bring down the last digit (4), and form the number 264. Dividing 264 by 4 gives a quotient of 66 with no remainder.
Therefore, Mr. Curry regrouped 2 tens as ones (or 20 as 10 + 10), which is the same as regrouping 20 ÷ 10 = 2 tens as ones.
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Find the height of a triangle that has a base of 5/4 and an area of 10 sq cm?
Answer:
Height = 16
Step-by-step explanation:
Area = (Base * Height) / 2
Height = (2 * Area) / Base
Height = (2 * 10) / (5/4)
Height = (2 * 10) / (5/4) * (4/4)
Height = (2 * 10 * 4) / 5
Height = (80 / 5)
Height = 16
The circle below has center K, and its radius is 7 yd. Given that m LKM = 60°, find the length of the major arc LNM
on solving the provided question we can say that length of the major arc angle is [tex](29/6)\pi or 4.83\pi[/tex].
what are angles?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. These are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.
circle with center K has an arc with a radius = 3 yards
angle subtended at the center = 70 degrees.
Angle = 360 - 70 = 290
Length of arc = (∅/360) x 2πr
Angle = 290,
r = 3,
Length of arc
[tex]= (290/360) X 2 X\pi X 3\\= (29/36) X 6\pi \\= (29 X \pi X 6)/36\\= 29\pi /6[/tex]
= (29/6)π or 4.83π
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Use the expression (10p+10)+(8p−1)
Simplify using properties of operations and then factor the expression using the GCF.
factored and simplified
answer :
9(2p+1)
steps
(10p+10)+(8p−1)
18p+9
9(2p+1)
chatgpt
Would anyone understand this?
Stuart has enough money to buy 4 kg of onions.
How do we calculate?we must first find the cost of 4 kg of onions.
We know that 2.5 kg of onions and 2 kg of carrots cost £2.36.
The cost of 15 2.5 kg of onions is 15 × 2.5 = 37.5 kg of onions.
The cost of 1 kg of onions is 2.36 ÷ 37.5 = 0.06293 = £0.063.
3 kg of carrots cost £1.74. and we need to find how much 1kg of carrots cost.
Therefore, the cost of 1 kg of carrots is 1.74 ÷ 3 = 0.58 = £0.58.
Now we can use the above information to find the cost of 4 kg of onions:
The cost of 1 kg of onions is £0.063.
Hence, the cost of 4 kg of onions is 4 × 0.063 = £0.252.
We then can say since Stuart has £2, and we have found that the cost of 4 kg of onions is £0.252. Stuart has enough money to buy 4 kg of onions.
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2 A customer applied for a loan for $15,000 to buy a motorcycle. The customer qualified for different loan options. Which loan option would allow the customer to pay the least amount of interest? (A A 3-year loan with an 7% annual simple interest rate B A 4-year loan with a 5% annual simple interest rate CA 5-year loan with a 4.5% annual simple interest rate A 6-year loan with a 3.7% annual simple interest rate
From the calculations, the best loan option is
A. 3-year loan with a 7% annual simple interest rate
How to find a better loan optionTo determine which loan option would allow the customer to pay the least amount of interest, we need to compare the amount of interest charged by each loan option.
For the 3-year loan with a 7% annual simple interest rate,
the interest charged would be $15,000 x 7% x 3 = $2,550.
For the 4-year loan with a 5% annual simple interest rate,
the interest charged would be $15,000 x 5% x 4 = $3,000.
For the 5-year loan with a 4.5% annual simple interest rate,
the interest charged would be $15,000 x 4.5% x 5 = $3,375.
For the 6-year loan with a 3.7% annual simple interest rate,
the interest charged would be $15,000 x 3.7% x 6 = $3,870.
From the calculations, it is clear that the 3-year loan with a 7% annual simple interest rate would result in the least amount of interest charged, with $2,550.
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The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
Answer:
60 square inches
Step-by-step explanation:
Measure of length in scale drawing = Measure of actual length
6 inches = 24 feet
∴ 1 inch = [tex]\frac{24}{6}[/tex] feet
∴Unit multiplier applied:
∴1 inch in scale drawing = 4 feet of actual measurement
Measure of width in scale drawing = Measure of actual width
x inches = 40 feet
∴ x inches = (40 feet) × ([tex]\frac{1 inch}{4 feet}[/tex])
Measure of width in scale drawing = 10 inches
Area of rectangular floor in the scale drawing = (Length) × (Width)
= (6 inches) × (10 inches)
= 60 square inches
In ΔXYZ, ∠X=81° and ∠Y=22°. ∠XWZ=90° and XY=180. Find the length of XW to the nearest integer.
The value of XW is 11
How to solve for thisXW = ZW/tan 81
= 0.158 ZW
We should recall that tan 81 = ZW/XW
WY = ZW/tan22
= 2.475ZW
We should recall that tan 22 = ZW/WY
XW = 0.158/0.158 + 2.475 + XY
= 0.158/2.633 x 180
= 11
Therefore, the value of XW is 11
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A rectangular prism measures 1 2/3 inches by 2 1/3 inches by 3 inches. How many cubes with edge length 1/3 inch fit in the prism?
Tricia needs to bring cookies and fruit to her class of 16 students. There will be a total of 48 items, including 1 piece of fruit for each student.
Using arithmetic equation, each students gets 2 cookies and 1 fruit.
What is arithmetic equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. That will be regarded as a phrase.
Given that, Total number of students are 16
total cookies and fruit are 48 items including 1 piece of fruit for each student
let each student get x cookies
16x + 16 = 48
subtract 16 from both side we get
16x = 48-16
16x = 32
both side divided by 16 we get
x = 32/16
x = 2
So that, each students gets 2 cookies and 1 fruit.
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You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 80.4%.
(Report answer accurate to three decimal places with appropriate rounding.)
Answer: To find the critical value for a 80.4% confidence interval for a normal approximation of a binomial distribution, we need to find the z-score that corresponds to the 80.4% confidence level. We can do this using a standard normal table or using a z-score calculator.
Using a z-score calculator, we can find that the z-score corresponding to 80.4% confidence level is approximately 0.931. This means that 80.4% of the data falls within 0.931 standard deviations of the mean.
So, the critical value that corresponds to a confidence level of 80.4% is approximately 0.931.
Step-by-step explanation:
Tina's 4 Kids ^drink 2 cups of Juice per day. In a 30-day month, how many gallers, will Tina's Ken Kids drink? AA = 8 cups each day in a
Answer:240
Step-by-step explanation:
8x30=240
Answer:
240
Step-by-step explanation:
30x2x8 so that is your answer
The weights of three children are in the properation 6:5:4 If the weight of the smallest chill is 25 Kg. find the weights of the other 2 Children.
The weight of the other children are 37.5 kg and 31.25 kg
How to calculate the weight of the other children?
The weight of the three children are 6:5:4
6x, 5x and 4x
The weight of the smallest child is 4x
4x= 25
x= 6.25
The weight of the other two children can be calculated as follows
6(6.25)
= 37.5
5(6.25)
= 31.25
Hence the weight of the other two children are 37.5 kg and 31.25 kg
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Which value of a would make a-5>-1 true?
A,2
b.-2
c. 3
d. 6
Answer:
d. 6
Step-by-step explanation:
Given, a-5> -1
Both sides add 5, and we get
a > 4
So a is 6.
how do you write 9.3E6 in standard form?
The question is in the picture.
The angles in the quadrilateral are as follows;
x = 77°
y = 103 degrees
z = 52 degrees
How to find angles in a quadrilateral?The diagram above is a quadrilateral. The angles x, y and z can be found as follows:
x + 103 = 180(sum of angles on a straight line)
x = 180 - 103
x = 77 degrees
Therefore,
y = 103 degree(vertically opposite angles)
Vertically opposite angles are congruent.
The sum of angles in a triangle is 180 degrees.
Therefore,
103 + 25 + z = 180
z = 180 - 128
z = 52 degrees.
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The grade of a highway up a hill is 26%, How much change in horizontal distance is there if the vertical height of the hill is 600 feet? Express the answer to the nearest foot.
The grade of a highway up a hill is 26%, therefore the amount of change in horizontal distance if the vertical height of the hill is 600 feet is 2307ft.
What is Distance?
This is referred to as the numerical or occasionally qualitative measurement of how far apart objects or points are.
First, express the grade as a decimal.
26% → 0.26
Grade = (change in vertical height) / (change in horizontal distance)
0.26 = (600 ft) / x
x = (600 ft) / 0.26 = 2307 ft
That is the change in horizontal distance.
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The radius of a cylinder is 3 inches, and the cylinder's height is 10 inches.
What is the exact volume of the cylinder?
Responses
1. 30π in³
2. 60π in³
3. 90π in³
4. 300π in³
Given:-
[tex] \rm{radius= \bold{ 3}}[/tex][tex] \rm{height = \bold{ 10}}[/tex][tex] \: [/tex]
To find:-
[tex] \rm{volume \: of \: the \: cylinder = \: ?}[/tex][tex] \: [/tex]
By using formula:-
[tex]\underline{ \boxed{ \rm{ \red{volume \: of \: the \: cylinder = πr²h}}}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{v = πr²h}[/tex][tex] \: [/tex]
[tex] \rm{v = π×( 3 )² × 10}[/tex][tex] \: [/tex]
[tex] \underline{\boxed{ \color{purple}{\rm{v = 90π in³}}}}[/tex][tex] \: [/tex]
The volume of the cylinder is 90π in³
[tex] \: [/tex]
hope it helps!:)
Select the subtraction problem represented by the fraction model.
The subtraction problem represented by the fraction model is given above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is a figure as shown in the image.
We can write the fractional problem as -
" A rectangle is divided into eight equal rectangles. Smith colored six of these rectangles. How much percentage fraction of the image is colored."
Therefore, the subtraction problem represented by the fraction model is given above.
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