Answer:
The answer are
A.
[tex] {f}^{ - 1} (x) = \frac{x + 3}{x - 2} [/tex]
B.
[tex] {f}^{ - 1} ( - 3) = 0[/tex]
Step-by-step explanation:
To find the infers we do that
[tex]f(x) = \frac{2 x + 3}{x - 1 } \\ (x - 1)f(x) = 2x + 3 \\ xf(x) - f(x) = 2x + 3 \\ xf(x) - 2x = f(x) + 3 \\ x(f(x) - 2) = f(x) + 3 \\ x = \frac{f(x) + 3}{f(x) - 2} \\ then \: \\ {f}^{ - 1} (x) = \frac{x + 3}{x - 2} \\ then \\ {f }^{ - 1} ( - 3) = \frac{ - 3 + 3}{ - 3 + 2} = 0[/tex]
A recent survey suggests that 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus. What is the probability that a randomly chosen college student either has a job or lives on campus
[tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability that a randomly chosen college student either has a job or lives on campus:
Given: 85% of college students have a job, 54% live on campus, and 42% have a job and live on campus.
So, out of 100 students, 42 students either has a job or live on campus.
43 college students have a job and 12 live on campus.
So, 43 + 42 + 12 = 85 + 54 - 42
85 + 12 = 139 - 42
97 = 97
Therefore, [tex]\frac{97}{100}[/tex] probability that a randomly chosen college student either has a job or lives on campus.
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If h (x)=√49-x², find h (0), h (-7) and h (9).
Answer:
Step-by-step explanation:
f(0) = √49 - x^2
f(0) means that wherever you see an x on the right, you put a zero.
so f(0) = √49 - 0^2
f(0) = √49
f(0) = 7
f(-7) = √49 - x^2
Again the meaning is that where you see an x on the right, you substitute - 7 for that x.
f(-7) = √49 - (-7)^2
f(-7) = 7 - 49
f(-7) = - 42
f(9) = √49 - (9)^2
f(9) = 7 - 81
f(9) = - 74
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever the sample size is large.
What is the Central limit theorem?The Central limit theorem says that the normal probability distribution is used to approximate the sampling distribution of the sample proportions and sample means whenever the sample size is large.Approximation of the distribution occurs when the sample size is greater than or equal to 30 and n(1 - p) ≥ 5.Thus, as a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when the sample size is large and each element is selected independently from the same population.
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how many hours will it take a plane to go 3 008 miles
Based on the speed of the plane, the number of hours it will take to fly 3,008 miles is 5.47 hours.
How long will the plane take to travel 3,008 miles?The speed of the plane is given as 550 miles per hour
In order to reach 3,008 miles, the plane should travel for:
= Distance / Speed
= 3,008 / 550
= 5.47 hours
Rest of the question is:
how many hours will it take a plane to go 3 008 miles if it travels at 550 mph
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An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 73%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 46%. A. What is the probability that they win both contracts
The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.
What is probability?Probability is the rate of successful outcomes to the total outcomes of an event.
P(E) = n(E)/n(S)
Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.
Calculation:It is given that,
An aerospace company has submitted bids on two separate federal government defense contracts.
The probability of winning the first contract is - 45%
The probability of winning the second contract if they win the first contract is - 73%
The probability of winning the second contract if they lose the first contact is - 45%
So, the probability that they win both contracts is
= (probability of winning the first contract) × (probability of winning the second contract)
= 0.45 × 0.73
= 0.3285 ≅ 0.33
⇒ 33%
Therefore, the probability that they win both contracts is 33%.
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Solve for x using common denominators.
2 over the quantity 3 times the binomial x minus 1 equals x over the quantity x minus 1
Answer: 2/3
Step-by-step explanation:
The common denominator would be 3(x-1). Thus, you need to multiply the expression on the right by 3/3 to achieve a common denominator. Then you would have 3x/3(x-1).
The equation then is 2/3(x-1) = 3x/3(x-1)
You can cancel out the denominators now, and you have 2 = 3x, so x = 2/3
Answer:
A
Step-by-step explanation:
The ratio of girls to boys at a party is 5:4. if there are 20 girls in the class, how many boys are there.
Answer:
16 boys
==========================
Let the number of boys be b and girls be g.
The ratio is:
g/b = 5/4And the number of girls is:
g = 20Substitute the number into ratio and find the value of b:
20/b = 5/4b = 20*4/5b = 16I feel like my answers are wrong someone please help
Using translation concepts, the equations are given as follows:
a) [tex]y = \sqrt{16 - 4x^2}[/tex]
b) [tex]y = 3\sqrt{16 - x^2}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]y = \sqrt{16 - x^2}[/tex]
In item a, when it is horizontally compressed by a factor of 2, it means that x -> 2x, hence:
[tex]y = \sqrt{16 - (2x)^2} = \sqrt{16 - 4x^2}[/tex]
In item b, the transformations are given as follows:
Vertical expansion by a factor of 3, hence y -> 3y.Reflected in the y-axis, hence x -> -x.Then:
[tex]y = 3\sqrt{16 -(-x)^2} = 3\sqrt{16 - x^2}[/tex]
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Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angles. In the figure, angle CAB measures 60°.
What is m∠ACB?
°
What is the length of segment AB?
What is the perimeter of the hexagon?
The perimeter of the hexagon is
the circumference of the circle.
The circumference of the circle is
.
The solution to the questions are:
The value of [tex]< ACB\ is\ 60\textdegree[/tex]. As a consequence, the radius of the circle is equal to the length of the segment AB.AB = BC =CA = R. As a consequence, the radius of the circle is equal to the length of the segment AB. The perimeter of the hexagon is equal to r times 6. As a result, the number 6r represents the hexagon's perimeter.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.P=6.28r. As a result, the diameter of the circle is a fraction of a unit bigger than.What is the length of segment AB?1) Generally, the equation for m∠ACB is mathematically given as
CA= CB
CA = radius of the circle
Therefore,
∠CAB =
[tex]\angle CBA = 60 \textdegree[/tex]
the sum of all the angles of a triangle
the sum of all the angles of a triangle is 180°
[tex]< CAB + < CBA + < ACB = 180 \textdegree[/tex]
[tex]60\textdegree + 60\textdegree + < ACB = 180\textdegree[/tex]
[tex]120\tetxtdegree + < ACB = 180\tetxtdegree[/tex]
[tex]< ACB = 60\textdegree[/tex]
The value of [tex]< ACB\ is\ 60\textdegree[/tex].
2. What is the length of segment AB?
In the same manner, as in ACB, all of the angles are the same. As a result, we may say that the triangle has equal sides.
In a triangle with equilateral sides, each of the triangle's three sides has the same length.
AB = BC =CA = R
As a consequence, the radius of the circle is equal to the length of the segment AB.
3. What is the perimeter of the hexagon?The formula for calculating the hexagon's perimeter is 6a, where an is the number of sides in the hexagon.
The circumference of the hexagon is equal to 6 times a.
The circumference of the hexagon is equal to six times each side (AB)
The perimeter of the hexagon is equal to r times 6.
As a result, the number 6r represents the hexagon's perimeter.
4. The perimeter of the hexagon is 6r the circumference of the circle.
the perimeter of the hexagon = 6rthe perimeter of the circle = [tex]2 \pi[/tex][tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a consequence of this, the hexagon's perimeter is less than the diameter of the circle.
5. The circumference of the circle is 6.28r.
the perimeter of the circle = [tex]2 \pi r[/tex]
[tex]P=2*\pi*r[/tex]
P=2*3.14*r
P=6.28r
As a result, the diameter of the circle is a fraction of a unit bigger than.
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Answer:
1. 60 degrees
2. r
3. 6r
4. slightly less than
5. slightly greater than 6r
Step-by-step explanation: I just did it on edge 2023. Hope this helps!
The rectangle pre-image has a length of 12 and width of 6. The rectangle image has a length of 6 and width of 3.
Find the scale factor of the dilation shown in the diagram.
1/2
1/3
2
3
Answer: 1/2
Step-by-step explanation:
Scale factor = (image)/(preimage) = 6/12 = 1/2
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
The triangles are similar by SAS principle.
How to know similar triangles?Similar triangles have the same shape but may have different sizes.
In similar triangles, corresponding sides are always in the same ratio.
The corresponding angles are congruent.
Therefore, using SAS ratio,
6 / 8 = 8 × 3 / 32
6 / 8 = 24 / 32 = 3 / 4
Therefore, the corresponding sides are a ratio of each other.
Therefore, the triangles are similar by SAS principles because the two triangles have two pairs of sides in the same ratio and the included angles are also equal
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A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet
The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.
How to calculate the volume of a hemisphere?The volume of the hemisphere is calculated by using the formula,
= [tex]\frac{2}{3}[/tex] × π × r³ cubic units
where r is the radius of the hemisphere.
Calculation:It is given that,
A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.
So, the volume of the bowl is
V = [tex]\frac{2}{3}[/tex] × π × (1)³
= [tex]\frac{2}{3}[/tex] × π cubic feets
The volume of each smaller hemisphere-shaped mold = [tex]\frac{2}{3}[/tex] × π × r³ cubic units
So, for 27 molds, the volume = 27 × [tex]\frac{2}{3}[/tex] × π × r³ cubic units
All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.
Then,
[tex]\frac{2}{3}[/tex] × π = 27 × [tex]\frac{2}{3}[/tex] × π × r³
⇒ r³ = 1/27
⇒ r = 1/3 ft
Therefore, the required radius of each of the smaller molds is 1/3 foot.
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How is 6.3 written in scientific notation? 6.3 times. 100 63 times. 10–1 6.3 times. 101 63 times. 100
The scientific notation of 6.3 is written as 6.3 × 10^0; option A
Scientific notationThe decimal points should be moved between the first digit and the next digit.When moving decimal point to the left in scientific notation; it is negative, that is, -When moving decimal point to the right in scientific notation; it is positive, that is, +Therefore, since there are only two significant number in 6.3, the decimal point can not be moved.
6.3 in scientific notation
= 6.3 × 10^0
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Answer: A
Explanation: 6.3 x 10^0
30 A club of 12 people would like to choose people for the offices of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office?
1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.
How many different ways are there to select the officers so that only one person holds each office?Total number of people in the club = 12
total number of positions = (president, vice president, secretary) = 3
From 12 people 3 people are taken at a time.
That is, using the formula for permutation we get,
ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]
Here n = 12 and x = 3
P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320
Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.
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x is directly proportional to w²
When w = 4, x = 48
y is inversely proportional to x³
When x = 2, y = 14
Find a formula for y in terms of w.
Give your answer in its simplest form.
The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³
Variationx = k × w²
w = 4, x = 48
48 = k × 4²
48 = k × 16
48 = 16k
k = 48/16
k = 3
So,
x = k × w²
x = 3 × w²
x = 3w²
y = k/x³
x = 2, y = 14
14 = k / 2³
14 × 2³ = k
14 × 8 = k
112 = k
So,
y = k/x³
y = 112/x³
y = (1/112)x³
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Find the roots of sin(x) which lie in [0, pi]
Answer:
Option (1)
Step-by-step explanation:
From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.
[tex]y = 6x + 3 \\ y = 6x - 4[/tex]
state whether each pair of lines are parallel or perpendicular
pls help
Answer:
The lines are parallel, this is because they both have the same slope/gradient of 6.
Answer:
parallel lines
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x + 3 ← is in slope- intercept form
with slope m = 6
y = 6x - 4 ← is in slope- intercept form
with slope m = 6
• Parallel lines have equal slopes
then the 2 given lines are parallel
A carpenter cuts the corners of a rectangle to make the trapezoid shown.
An isosceles trapezoid is shown. The top left angle is (9 x) degrees and the bottom left angle is (7 x + 4) degrees.
What is the value of x?
5.375
5.5
11
13
The value of x in the trapezoid is 11.
Properties of an isosceles trapezoidThe base angles are the sameThe sum of opposite angles is 180° or supplementary.The diagonals are the same in length.Therefore, the angle 9x and 7x + 4 are supplementary.
Hence,
9x + 7x + 4 = 180
16x + 4 = 180
16x = 180 - 4
16x = 176
x = 176 / 16
x = 11
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Answer:11
Step-by-step explanation:Easy
What is 3/4 divided 1/6
Answer:
Fraction form: 9/2
Mixed number form: 4 1/2
Decimal form: 4.5
Step-by-step explanation:
To divide the two number, follow these steps.
3/4÷1/6
3/4×6/1=18/4
Reduce.
18/4=9/2 or 4 1/2
Hope this helps!
Answer:
[tex]\dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex] \dfrac{3}{4} \div \dfrac{1}{6} = [/tex]
To divide a fraction by a fraction, rewrite the first fraction and multiply it by the reciprocal of the second fraction. To get the reciprocal of a fraction, flip it. The reciprocal of 1/6 is 6/1.
[tex] = \dfrac{3}{4} \times \dfrac{6}{1} [/tex]
[tex] = \dfrac{3 \times 6}{4 \times 1} [/tex]
[tex] = \dfrac{18}{4} [/tex]
[tex]= \dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Can someone please help me with this
Answer:
y = 0.5x
Step-by-step explanation:
y = rx
4.5/9 = 0.5
7/14 = 0.5
15/30 = 0.5
y = 0.5x
Travis jogged to his friend's house 10 miles away and then got a ride back home. It took him 2 hours longer to jog there than ride back. His jogging rate was 16 mph slower than the rate when he was riding. What was his jogging rate?
Answer asap please :)))
Using the relation between velocity, distance and time, it is found that his jogging rate was of 4.5 mph.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence:
[tex]v = \frac{d}{t}[/tex]
Jogging, his velocity was of v, while the time was of t + 2, for a distance of 10 miles, hence:
[tex]v = \frac{10}{t + 2}[/tex]
Riding, his velocity was of 16, while the time was of t, also for a distance of 10 miles, hence:
[tex]v + 16 = \frac{10}{t}[/tex]
Then, considering the first equation and replacing in the second:
[tex]\frac{10}{t + 2} + 16 = \frac{10}{t}[/tex]
[tex]\frac{10}{t} - \frac{10}{t + 2} = 16[/tex]
[tex]\frac{10t + 20 - 10t}{t(t + 2)} = 16[/tex]
16t² + 32t - 20 = 0 -> t = 0.5.
Then his jogging rate in mph was:
[tex]v = \frac{10}{0.5 + 2} = 4.5[/tex]
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On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). a point is at (2, 3). what is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x 2y = 4 x 2y = 8 2x y = 4 2x y = 8
The equation of the line that is parallel and passes through the point (2,3) is; x +2y =8.
What is the equation of the line that passes through (2,3)?If follows from the task content that the slope of the first line is; (-4-0)/(4-(-4)) = -1/2.
Hence, since the lines are parallel, they have the same slope and the equation of the second line is;
-1/2 = (y-3)/(x-2)
-x+2 = 2y -6
x +2y =8.
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Answer: b on edg
Step-by-step explanation:
A distribution in which two nonadjacent values occur more frequently than any other values in a set of data is called a(n):______distribution.
In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.
According to the statement
we have to tell about the that type of distribution in which two nonadjacent values occur more frequently than any other values in a set of data
A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution.
and from this definition we have clear that the in this distribution the values are repeated.
it shows the probability distribution with two peaks in the graphical mode.
Bimodal distribution show repeated value.
it is used in many types of data representation because of two peaks graphical representation than the simple graph.
it is the easiest method than the others distributions.
So, In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.
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D= [xlx is a whole number}
E = {xlx is a perfect square between 1 and 9)
F = (xlx is an even number greater than or equal to 2 and less than 9]
Which of the following is D n F?
O (4, 6).
O (2, 4, 6)
O (2,4,6,8)
O (2)
Answer: C: [tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Step-by-step explanation:
Let's first find the specific numbers that are in sets D and F.
[tex]D=\{0,1,2,\ldots\}[/tex], as D has all whole numbers.
[tex]F=\{2,4,6,8\}[/tex], as all of these numbers are even, greater than or equal to two, and less than nine.
Since all the numbers in F are whole numbers, all of them would be in D. Hence, the intersection of both would just be {2, 4, 6, 8}.
[tex]D\cap F = \{2, 4, 6, 8\}[/tex]
Oksana wrote the equation below on the whiteboard. 6 b 6 = 48 what is the value of b? 4 7 8 9
The correct answer is 7.
What is linear equation ?A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.
I am aware that this query's equation is,
6b + 6 = 48
subtract 6 from both side in the equation.
6b + 6 - 6 = 48- 6
6b = 42
now, divide by 6 from both side in the equation.
6b/6 = 42/6
b = 7.
Therefore, the correct answer is 7.
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I understand this is the question.
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
(a)4
(b)7
(c)8
(d)9
rewrite the equation to represent the resistance of resistor 2, r2, in terms of rt and r1.
The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.
In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]
We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.
To rewrite the equation, we do as follows:
[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]
Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].
Hence, the 3rd option is the right choice.
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For the complete question, refer to the attachment.
A process that behaves the same way as a procedure so that similar results are produced is called a _______.
A process that behaves the same way as a procedure so that similar results are produced is called a simulation.
In this question,
Simulations are used for finding probabilities for compound events. The probability model of a random phenomenon consists of a sample space of possible outcomes, associated events, random variables, and a probability measure that specifies probabilities of events and determines distributions of random variables.
Procedure is a method of analyzing or representing statistical data; a procedure for calculating a statistic. The goal of statistical analysis is to identify trends.
Hence we can conclude that a process that behaves the same way as a procedure so that similar results are produced is called a simulation.
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Find the volume of the cone.
either enter an exact answer in terms of it or use 3.14 for i and round your final answer to the nearest
hundredth.
The volume of the cone of radius 5 units and height 3 units is 78 cubic units.
Given radius of cone 5 units and height of cone be 3 units.
We are required to find the volume of cone.
Volume is the amount of substance that a container can hold in its capacity.
Formula of cone is 1/3 *π[tex]r^{2} h[/tex] in which r is radius and h is height of cone.
We have to just put the values in formula.
Volume=1/3 *π[tex]5^{2} 3[/tex]
=25*3π/3
=75π/3
=25π
Put π=3.14 as said in the question.
=25*3.14
=78.5 cubic units.
After rounding we will get 78.
Hence the volume of cone whose radius is 5 units and height is 3 units is to be 78 cubic units.
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Question is incomplete as it should include the figure.
Increase 320 mangoes by 5%
Answer:
336 mangoes
Step-by-step explanation:
If 320 mangoes = 100%
Increasing them by 5% means that we will need to work out 105%
32 mangoes = 10%
3.2 mangoes = 1%
336 mangoes = 105%
Our final answer is 336 mangoes
Hope this helped and have a good day
Have a question, solve it if you can?