A cone has a volume of 98 cm3.
The radius of the cone is 5.13 cm.
Work out an estimate for the height of the cone.
Answer: Height is equal to approximately 3.56.
Step-by-step explanation:
FIND formula for finding height on a cone:3 * [tex]\frac{V}{\pi r^{2} }[/tex]
2. INSERT Volume and Radius
3 * [tex]\frac{98}{\pi 5.13^{2} }[/tex]
3.CALCULATE Height
Pi*5.13^2= 82.676979798 / 82.6769797= 1.185335995041.18533599504 * 3= 3.556007985133.55600798513 rounds to 3.56Answer:
3.6cm=h
Step-by-step explanation:
v=1/3πr^2h
input your values
98=1/3×22/7×5.13×5.13×h
98=(22*5.13*5.13*h)/21
cross multiply
98*21=22*5.13*5.13*h
2058=22*5.13*5.13*h/22*5.13*5.13
3.6cm=h
hope it helps, please mark brainliest
what the zero functions? f(x)=x^4-3x^3-4x^2
The zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.
What are zeroes of a function f(x)?
The zeroes of a function are the x - intercepts (the points where the graph cuts the x - axis) of the graph of the function f(x).
Given is a function f(x) as → f(x) = x⁴ - 3x³ - 4x²
In order to find the zeroes of the function → f(x) = x⁴ - 3x³ - 4x², we will plot the graph of the function. The graph is attached at the last. We can see that the graph cuts the x - axis at three coordinates → (- 1, 0) , (0, 0) , (4, 0). The x - intercepts will be → -1, 0, 4.
Therefore, the zeroes of the function f(x) = x⁴ - 3x³ - 4x² are x = -1 , 0 , 4.
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Josie makes fruit punch by mixing fruit juice and lemonade in the ratio 3 : 2 She needs to make 40 litres of punch for a party. How much of each ingredient does she need?
Fruit juice = litres
Lemonade = litres [4]
Answer:
Fruit Juice = 24 litres
Lemonade = 16 litres
Step-by-step explanation:
So, the ratio: [tex]3:2[/tex] really just means: "for every every 3 litres of fruit punch, there is 2 litres of lemonade.
Or in other words, every 3 litres of fruit punch, the entire mixture of both fruit punch and lemonade will be 5 litres, since there is 3 litres and 2 litres.
So dividing the 40 litres, by this 5 litres, we get 8. So we know there will be "8" of 3 litres of fruit punch, and "8" of 2 litres of lemonade.
Thus there will be 24 litres of fruit punch, and 16 litres of lemonade.
When you answer these, can you number them?
Use the words factor and quotient to describe related multiplication and.division facts
A quotient is an answer in the division. The divisor (denominator) and the quotient are the factors. The dividend (numerator) is the amount being divided — it doesn’t matter whether the dividend is larger or smaller than the divisor.
In elementary school, we refer to this process only in terms of fractions, so many people don’t realize that fractions are just division. If your fraction is proper, you will get a decimal number or simplified equivalent fraction. If the numerator (multiple) is the larger number, then the quotient will represent the other factor after dividing.
For example, in the equation x + 5 = 10, x is the unknown variable, and you want to find some number, which when added to 5 would result in 10.
Quotients are answers to a division problem.
For example, the quotient of 8÷2 would be 4.
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On Saturday, the bookstore sold x books. On Sunday, the bookstore sold 3 more books than on Saturday. The expression 2x + 3 represents the total number of books sold over the weekend.
What does the "2" represent in the expression 2x + 3?
A.the number of books sold on Saturday
B.how much more books were sold on Saturday
C.the total number of books sold
D.the number of days
a sequence is defined by f (n) =-4+2n for n is greater than or equal to 1. which of the following statements is the recursive definition of f?
a. f(1)=-2, f(n)=f(n-1) +2
b. f(1)=-4, f(n)=f(n-1) +2n
c. f(1)=-2, f(n)=f(n-1) + (-4)
d.f(1)=-4, f(n)=f(n-1) +2
EXPLAIN WHY
The recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2. (Correct choice: A)
What is the recursive definition of an arithmetic sequence?A recursive formula is a formula to find the value of an element in terms of previous elements of the same series. According to the statement, a sequence is defined by f(n) = - 4 + 2 · n. To derive the recursive definition, we must use algebra properties on the following difference:
Δf = - 4 + 2 · (n + 1) - (- 4 + 2 · n)
Δf = 2
n = 1
f(1) = - 4 + 2 · 1
f(1) = - 2
Then, the recursive definition of f is f(1) = - 2, f(n) = f(n - 1) + 2.
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Given f(x) = 2x - 1, g(x) = 3x^2 + 5, and h(x) = 4x+ 6 find h(g(f(x))).
Answer:
48x^2 - 48x + 38
Step-by-step explanation:
To get the composite function first understand the process of which a function inside another operates.
First solve one step at a time by trying to evaluate the inside before evaluating the outside using substitution.
For instance, h(g(f(x))) is the h function of g function of f.
Since f(x) is the inner component of the composite function, replace the x of g with the value of f(x).
Such that g(x) = 3x^2 + 5 → 3(f(x))^2 + 5 →
3(2x - 1)^2 + 5 → 3(2x - 1)(2x - 1) + 5 [foil] → 3(4x^2 - 4x + 1) + 5 → 12x^2 - 12x + 3 + 5 →
12x^2 - 12x + 8
Thus g(f(x)) = 3(f(x))^2 + 5 = 12x^2 - 12x + 8.
Finally to compute h(g(f(x))), using the process from the first composite function, same can be applied here:
Since h(x) = 4x + 6 →
h(g(f(x))) =
h(12x^2 - 12x + 8) =
4(12x^2 - 12x + 8) + 6 [distribute] →
48x^2 - 48x + 32 + 6 [combine like terms] →
48x^2 - 48x + 38
What is 2/3n plus 3/2n equals negative 13/4
Answer:
n=-2/3
Step-by-step explanation:
2/3n + 3/2n = -13/4
Make 2/3n and 3/2n into 4/6n and 9/6n so you can add them together.
13/6n = -13/4
Divide both sides by 13/6
n=-2/3
^ i hope thats what you were asking for :)
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 1, negative 3) and (0, 0). Everything to the right of the line is shaded. The second dashed line has a negative slope and goes through (negative 2, 3) and (1, negative 3). Everything to the right of the line is shaded.
A school is planning for an addition in some open space next to the current building. The existing building ends at the origin. The graph represents the system of equations that can be used to define the space for the addition. What is the system of equations that matches the graph?
y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1
Using linear functions, the system of inequalities that matches the graph is given by:
y ≥ 3x.y > -2x - 1.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Given two points, the slope is given by change in y divided by change in x. For the first line, the points are:
(-1, -3) and (0,0).
Hence the slope is:
m = (0 - (-3))/(0 - (-1))
m = 3.
When x = 0, y = 0, hence the y-intercept is of b = 0 and the line is given by:
y = 3x.
Everything to the right of the solid line is shaded, hence the values that are equal(line is solid) or greater than the line compose the inequality, as follows:
y ≥ 3x.
For the second line, the points are:
(-2,3) and (1,-3).
Hence the slope is:
m = (-3 - 3)/(1 - (-2)) = -6/3 = -2.
Then:
y = -2x + b.
When x = -2, y = 3, hence:
3 = -2(-2) + b
b = -1.
Hence the line is:
y = -2x - 1.
Everything to the right of the dashed line is shaded, hence the inequality is:
y > -2x - 1.
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Lorie ordered a shed to hold her gardening supplies. The shed had a length of 12.25 ft, a width of 10 ft, and a height of eight and one fifth ft.
Determine the volume, V, using the formula V = lwh.
30.45 ft3
100.45 ft3
960.05 ft3
1,004.5 ft3
The volume will be 1004.5 ft³.
How to calculate the volume?It should be noted that the volume is calculated as:
= Length × Width × Height
= 12.25 × 10 × 8.2
= 1004.5 ft³
Therefore, the volume will be 1004.5 ft³.
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If m ∠ F L G = 14 x + 5 ° and m ∠ H L G = 17 x − 1 ° , find m ∠ F L H .
The measure of angle FLH is 31x + 4
How to determine the measure of FLH?See attachment for the image that completes the question
The given parameters are
m∠FLG = 14x + 5°
m∠HLG = 17x − 1 °
The measure of FLH is calculated as
FLH = m∠FLG + m∠HLG
This gives
FLH = 14x + 5 + 17x - 1
Collect the like terms
FLH = 14x + 17x + 5 - 1
Evaluate the like terms
FLH = 31x + 4
Hence, the measure of FLH is 31x + 4
See attachment for the image that completes the question
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Graph each integer and its opposite on the number tin
hi!
lets try and further analyze this.
The integer -2 would be graphed directly on the "-2" point on the line. also marking positive 2 (2) as for that's its opposite. Positive 3 (3) would be marked on the 3 and so would -3. Then -5 and positive 5 (5) and lastly -1 and positive 1 (1).
hope this helps!
side note: for actually graphing the point just use a filled in dot indicating where you mark it.
which point on the number line represents the product (-4)(-2)(-1)?
Situation 1: A number cube has sides labelled 1-6. After rolling 15 times, Tyler records his data:
1,1,1,1,2,2,3,3,4,4,5,5,5,6,20
Is there an outlier? (yes/no)
If so, what is it? (write N/A if there is no outlier)
Should any data points be investigated or removed? (investigated/removed)
Why? (non-plausible/not representative)
Answer:
There is an outlier. The outlier is 20. 20 should be removed because a dice only has 6 faces, and there is no side numbered 20.
Step-by-step explanation:
solve
3*2^x+1-4^x=8
help me as soon as possible
Answer: 3.5
Step-by-step explanation:
If your trying to solve for X the answer would be 3.5 because you calculate 2 to the power of 1 and get 2 which then by now your equation should look along the lines of 3×2X+1−4^1 X=8
Calculate 4 to the power of 1 and get 4 then you Subtract 1 from both sides.
and then Subtract 1 from 8 to get 7. Combine all terms containing X which would make the equation come down to a standard form which then means you would have to divide both sides by 2, by dividing by 2 undoes the multiplication by 2. You should get 7/2 which then = 3 and 1/2 converted into 3.5
shift the graph right by 2 units and up by 3 units what cube root equation is it?
Where is making a frame to display a drawing she made. The frame 11 1/5 wide the frame has a rectangular shape and area of 560cm2
The Height of the frame having area of 560cm² is 50cm.
What is the area of the rectangle?By splitting a rectangle into two equal-sized right triangles, the formula for calculating the area of a rectangle may be obtained. For instance, a diagonal is drawn from vertex A to vertex C in the rectangle ABCD that is supplied.
The rectangle is split into two identical right-angled triangles by the diagonal AC.
(ABCD) Area = b × h
Given,
The area of the frame = 560cm²
Width of the frame = 11 1/5
Length = ?
Area of the rectangle = Length × Breadth
560 = 11 1/5 × L
⇒ L = 560 × 5/56
⇒ L = 50cm
The frame is 50cm tall.
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Correct question -
Claire is making a frame to display a drawing she made. The frame is 11 1/5 cm wide. The frame has a rectangular shape and an area of 560cm². How tall is the frame?
Use the laws of exponents to simplify the expression so that the base, x, appears once, and the exponent is positive. x^3/x^5
Here's a box plot that summarizes the average monthly rainfall of several cities.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 8, in increments of 0.5, labeled Monthly rainfall (centimeters). A left whisker extends from 3.5 to 5.5. The box extends from 5.5 to 7 and is divided into 2 parts by a vertical line segment at 6. The right whisker extends from 7 to 7.5. All values estimated.
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 8, in increments of 0.5, labeled Monthly rainfall (centimeters). A left whisker extends from 3.5 to 5.5. The box extends from 5.5 to 7 and is divided into 2 parts by a vertical line segment at 6. The right whisker extends from 7 to 7.5. All values estimated.
Find the range of the data.
The range of the data provided in the boxplot given the minimum number and the maximum number is 2.
What is the range of the data?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines known as the whiskers and a box. The left whisker represents the lowest number in the dataset. The right whisker represents the highest number in the dataset. The difference between these numbers is the range.
The box can be used to determine the first quartile, median and the third quartile. These values can be determined using the lines on the box.
The range of a data set is the difference between the highest number and the lowest number. Range is used to measure the variance of a dataset.
Range = highest number - lowest number
7.5 - 5.5 = 2
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How to do this exercise step by step?
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Consider a survey involving the cookie preferences of a sample of 1,214 adults. If 28% answered peanut butter" find the decimal and reduced fraction of that percentage
PRACTICE ANOTHER
The decimal fraction is 0.28 and reduced fraction is 7/25.
What is fraction?In mathematics, the fraction is generally a term which define the small part of something or amount of something. A fraction has generally two parts a numerator and a denominator.
The general syntax for fraction is : [tex]\frac{x}{y}[/tex]
where, x is the numerator part
y is the denominator part
The fraction has two types of notations:
Decimal notation : In the decimal notation of fraction the term is written as the decimal form of x / y. we generally try to reduce the decimal value upto the nearest tenth.Reduce notation: In the reduce notation the structure of term is x/y but in this we try to convert the fraction into smallest fraction form.In the question given,
Total number of samples = 1214
Adults who answered peanut butter = 28%
Now, the decimal fraction = 28 / 100 = 0.28
and, the reduce fraction = 28/100 = (7)(4) / (25)(4) = 7/25
Hence, The decimal fraction is 0.28 and reduced fraction is 7/25.
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A chef uses a recipe with the following ingredients then the chef decides to make more than 1 batch of recipe. if a total of 30 cups of mangoes and blueberries are used, how many batches of the recipe did the chef make? 3 cups used for 1 mango and 2 cups used for blueberries, 5 cups for apples and 1 cup used for blackberries
Answer:11 cups
Step-by-step explanation:
Srry if im wrong :)
RADICALS PLEASE HELP
(3√3 - 5√2) (2√3 + 5√2)
Answer: -32+5√6
Step-by-step explanation:
(3√3 - 5√2) (2√3 + 5√2)=
(3√3 * 2√3) + (3√3 * 5√2) - (5√2 * 2√3) - (5√2 * 5√2) =
(3*2*√3*√3) + (3*5*√3*√2) - (5*2*√2*√3) - (5*5*√2*√2)=
6*3 + 15*√(3*2) - 10*√(2*3) - 25*2=
18+15√6-10√6-50=
18-50+(15-10)*√6=-32+5√6
Tamara is a chef at a restaurant. She buys rice in bags
that weigh 20 pounds.
Each night, Tamara uses 0,4 pounds of rice. She needs to
order another bag when there are 1.6 pounds of rice left
in her bag.
Question: On Day 1 there are 20 pounds
of rice in her bag. On what day will
Tamara need to order a new bag of rice?
Using a linear function, it is found that Tamara will need to order a new bag after 46 days.
What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis(x = 0).The slope and the intercept in the context of this problem are given as follows:
Slope of -0.4, as she uses 0.4 pounds a day.Intercept of 20, as the bag initially has 20 pounds.Hence the weight of the bag after d days is given by:
W(d) = 20 - 0.4d.
He needs to order a new bag when W(d) = 1.6, hence:
1.6 = 20 - 0.4d.
0.4d = 18.4
d = 18.4/0.4
d = 46 days.
Hence she needs to order the new bag in 46 days.
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You have timed yourself and found that you can read 8 pages of a novel in 10 minutes. Your homework tonight is to read 42 pages in the novel. How many minutes should it take you? Round your answer to the nearest tenth if needed.
It will take 53 minutes to read 42 pages in a novel
Given,
The time taken to read 8 pages in a novel = 10 minutes
Therefore, the time taken to read 1 page = 10 ÷ 8 = 1.25 minutes
Now,
We have to find the time taken to read 42 pages of a novel.
Time to read 42 pages = 42 × 1.25
Time taken = 52.5 minutes
We can round it to nearest tenth, that is 53 minutes.
That is, the time taken to read 42 pages in a novel is 53 minutes.
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Can you guys help me on this one?
Answer:
The area is 12.57
The Circumference is 12.57
Step-by-step explanation:
One safe investment pays 10% per year, and a more risky investment pays 13% per year.
a. How much must be invested in each account if an investor of $100,000 would like a return of $10,780 per year?
b. Why might the investor use two accounts rather than put all the money in the 13% investment?
is invested in the 10% account.
is invested in the 13% account.
4
b. Why might the investor use two accounts?
a. S
OA. Although the 13% account earns more interest, the 10% account has no hidden fees.
B. The 13% investment is riskier than the 10% investment. There is a greater chance the investor will lose money if it is all placed in the 13% account.
C. Investing in two accounts always yields more money than investing in just one account.
Answer:
0.10x + 0.13y = 10780
x + y = 100000
x = 74000 --------------10%
y = 26000 --------------13% (more risky)
Ruguru wants to rent a car for 3 days. The cost,C , in dollars, for the rental is shown in the box, where D is the number of days the car is rented If Ruguru has 115, how much more will he need to rent a car for 3 days?
Ruguru need $15 more to rent a car for 3 days.
Given,
Number of days Ruguru wants to rent a car = 3 days
The amount Ruguru has with him = $115
The cost for the rental of the car:
C = 25 + 35D
Where,
D is the number of days
Now,
Lets find the total rent of the car for 3 days
C = 25 + 35D
C = 25 + 35 × 3
C = 25 + 105
C = 130
The total rent of a car for 3 days is $130
We have to find the amount needed by Ruguru to rent a car for 3 days.
That is,
Total rent - Amount Ruguru has = Amount needed
130 - 115 = 15
Therefore,
Ruguru need $15 more to rent a car for 3 days.
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A is the Midpoint of line RT. Find line RT if line RA= 3x and line AT= 5x-12
A. 6
B. 36
C.18
D. 30
[tex]\stackrel{3x}{R\rule[0.35em]{10em}{0.25pt}} A\stackrel{5x-12}{\rule[0.35em]{10em}{0.25pt}T} \\\\\\ 3x~~ = ~~5x-12\implies 3x+12=5x\implies 12=2x\implies \cfrac{12}{2}=x\implies \boxed{6=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE RT}}{3(6)~~ + ~~5(6)-12\implies 18+18\implies \text{\LARGE 36}}[/tex]