The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?
The answer is 9 but I don’t know how to get there.
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]
let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.
Related Questions
PLEASE PLEASE HELP NOW!!!!!
Givin: logam=x and logan=y
Prove: logamn=logam+logan
Drag the statements and reasons into the boxes to correctly complete the proof.
Answers
Answer:
2. ax=m and ay=n
4. mn=a(x+y)
6. power property of logarithms.
I took the quiz.
k12
i took the quiz this is the right answers
Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
Answers
The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.
Thus,
The rule to rotate a point P(x, y) after a rotation 270° counterclockwise around the origin is:
P(x, y) → P'(y, -x)
From the Graph,
In our case, we have the points
T = (4, -8)
U = (6, -8)
V = (9, -3)
W = (7, -3)
Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
P(x, y) → P'(y, -x)
T (4, -8) → T'(-8, -4)
U (6, -8) → U'(-8, -6)
V (9, -3) → V'(-3, -9)
W (7, -3) → W'(-3, -7)
Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
Learn more about Graph at
https://brainly.com/question/10712002
#SPJ1
M a t h (look at image)
Answers
Answer:
241
Step-by-step explanation:
9 x 12 = 108 m (area of square)
19 x 14 = 266 / 2 = 133 (area of triangle)
108 + 133 = 241
homer simpson is interested in studying the ratio of the various colors of sprinkles on lard lad donuts. to conduct his study, homer purchases three of each variety of donut they make and counts the sprinkles on them. what method did homer use to select his sample?
Answers
Stratified random sampling was the technique employed by Homer to choose his sample.
Given case;
Homer Simpson is fascinated with the proportion of the different sprinkled colors on lard lad doughnuts. Homer buys three of each type of donut they produce and counts the sprinkles on them to perform his research.
The method did homer use to select his sample is stratified random sampling. Because each variety is a stratum.
From there 3 3 samples are collected.
Stratified random sampling:
A crucial aspect of the sampling strategy known as stratified random sampling is the stratification of a population into smaller subgroups known as strata. During stratified random sampling, the strata are created based on the shared traits or features of the participants, such as level of education or income. Numerous uses and advantages of stratified random sampling include examining life expectancy and population demography.
The terms proportionate random sampling and quota random sampling are also used to describe stratified random sampling.
The method did homer use to select his sample is stratified random sampling.
To learn more about sampling click here:
brainly.com/question/12719656
#SPJ4
identify the error in the diagram below. what's wrong with it. 70pts
Answers
The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.
Describe the triangle.Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.
It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.
Here sides given are 3 m, 5 m, 9 m.
Let us add the sides length 3 m and 5 m
3 m + 5 m = 8 m
Compare this with the third-side length of the triangle
8 m < 9 m
So, the property does not hold true.
So, the triangle does not exist.
To know more about triangles, visit:
https://brainly.com/question/2773823
#SPJ1
each of ncustomers gives a hat to a hat-check person at a restaurant. the hat-check person gives the hats back to the customers in a random order. what is the expected number of customers that get back their own hat? derive your answer by using random variables and expected values of random variables.
Answers
The expected number of customers that get back their own hat is 1.
Define the term random variables?A random variable is called with an unspecified amount or a function that gives values to each of the results of an experiment. There are two types of random variables: discrete (having specified values) and continuous (value in a continuous range).Utilizing indicator random variables, we resolve this issue. For 1 ≤ i ≤ n,
Let .
Xi = I {Customer 'i' who gets his hat back itself}.
The number of clients that receive their own hats back should be the random variable X. We want to figure out E[X].
Clearly,
n
X = ∑ Xi
i=1
It is clear that 1/n represents the likelihood that customer 'I' will receive his own hat.
Due to the fundamental characteristics of indicator random variables, this means that E[Xi] = 1/n.
n
E[X] = E [ ∑ Xi ]
i=1
n
= ∑ 1/n
i=1
Put the limits.
E[X] = 1
As a result, 1 consumer is anticipated to have their own hats back.
To know more about the random variables, here
https://brainly.com/question/14356285
#SPJ4
what does it mean for a sample to have a standard deviation of zero? describe the scores in such a sample. when standard deviation is zero, no two scores are exactly the same. when standard deviation is zero, you cannot measure variability. when standard deviation is zero, the scores have no variability. when standard deviation is zero, there are no data points in the sample.
Answers
A sample to have a standard deviation of zero means the score has no variability.
When the score has no variability it points towards the standard deviation being zero, This is the case where all the scores in the sample have the exact same value. This means there is no spread in the data set at all. The data set is combined in a single clumped value. Since there is only one value it would be the mean of the data set. The standard deviation measures the spread of a quantitative data set. This number cannot be a non-negative real number.
To learn more about standard deviation and statistics,
https://brainly.com/question/16555520
#SPJ4
A train is moving along a
Straight track with a speed of 30ms^-1 when it reaches
point A.
the driver applies the brakes
and the train
decelerates at
a constant speed until it
comes to a stop
150m from point A.
a) what was the deceleration
of the train?
Answers
The deceleration of the train is -3 ms^-2.
Given:
A train is moving along a Straight track with a speed of 30 ms^-1 when it reaches point A. the driver applies the brakes and the train decelerates at a constant speed until it comes to a stop 150 m from point A
we know that:
v^2 - u^2 = 2as
where
v = 0
u = 30 ms^-1
s = 150 m
0^2 - 30^2 = 2a*150
0 - 900 = 300*a
-900 = 300*a
a = -900/300
a = -3 ms^-2
Negative acceleration is nothing but the deceleration so a = -3 ms^-2.
Learn more about the speed here:
https://brainly.com/question/7359669
#SPJ1
in a survey, 19 people were asked how much they spent on their child's last birthday gift. the results were roughly bell-shaped with a mean of $40.7 and standard deviation of $9.2. estimate how much a typical parent would spend on their child's birthday gift (use a 80% confidence level). give your answers to 3 decimal places.
Answers
The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
A sample mean is the result of a chance experiment. When we sample a random variable, we get one of its possible values. A sample is a specific value. The random variable's probability distribution determines the possible values and the likelihood of each.
Given that,
Point estimate = sample mean = X = 40.7
sample standard deviation = s = 9.2
sample size = n = 19
Degrees of freedom = df = n - 1 = 19 - 1 = 18
At 80% confidence level
α = 1 - 80%
α =1 - 0.80 =0.2
α/2 = 0.1
t α/2,df = t0.1,18 = 1.330
The margin of error = E = t /2, df x (s/√n)
= 1.330 x (9.2/√19)
= 1.330 x 2.110
= 2.8
Margin of error = E = 2.8
The 80% confidence interval estimate of the population mean is,
X ± E
= 40.7 ± 2.8
= (43.5, 37.9)
Therefore The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)
To learn more about sample mean visit
https://brainly.com/question/14127076
#SPJ4
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 peo
Answers
The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.
How to calculate the number of people?From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.
Let the number of days that the people can be fed when 18 people come be Illustrated as x.
Therefore, this will be illustrated as x. This will be:
x = (45 × 20) / 18
x = 900 / 18
x = 50
The number of days is 15 days.
Learn more about average on:
brainly.com/question/1307157
#SPJ1
Complete question
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?
Given that
7
x
−
3
y
=
23
Find
x
when
y
=
−
2
Answers
Answer: [tex]\frac{17}{7}[/tex]
Step-by-step explanation:
7x - 3y = 23
3y = -2 × 3 = -6
7x + 6 = 23
7x = 23 - 6
7x = 17
x = [tex]\frac{17}{7}[/tex]
Please help!!! Complete the flow proof given CM = YJ
Answers
f'(x) = 4f(x) and f(0) = 10
Answers
Answer:f(x)=10e^4x
Step-by-step explanation:
f(x)=C*e^4x
f(0)=c*e^4.0
10=C*e^4.0
10=C
f(x)=C*e^kx
f(x)=C*e^4x
Carly wants to buy 10 litres of paint and
only wants to go to one shop to buy it.
Home Stores sells 2 litre tins of paint for
£4.85 each.
Paint Supplies sells 1 litre tins of paint for
£3.60 each and it's 3 for 2.
The DIY shop sells 2.5 litre tins of paint for
£7.50 each, and it's buy 3 get 1 free.
What is the cost of getting 10 litres from
each shop?
Write down where Carly should buy her
paint from in the comment box.
Answers
Answer:
Home Stores
4.85×5
= 24.25
Paint Supplies
£18
Josie makes fruit punch by mixing fruit juice and lemonade in the ratio
She needs to make 35 litres of punch for a party.
How much of each ingredient does she need?
Fruit juice
7 litres
Lemonade =
28 litres
During the party Josie decides to make some more.
She has 3 litres of fruit juice left and plenty of lemonade.
How much xtra punch can she make?
litres
To make the second batch of punch go further Josie
adds 2 more litres of lemonade.
What is the ratio of fruit juice to
lemonade in the second batch?
Answers
Let the lemonade and fruit be Mixed in x ratio.
[tex]\therefore[/tex] Total mixture of fruit punch [tex]= 1\times x \ + \ 3\times x = 4x[/tex]
She needs to make 35 liters of punch.
Requirement of ingredients :
Fruit juice to be added [tex]= \frac{x}{4x} \times 35 = 8.75[/tex] liters of fruit juice
If 8.75 liters of fruit juice is to be added,
then,
lemonade required[tex]=35\ litres - 8.75\ litres = 26.25\ litres .[/tex]
Now ,
According to question she wants to make more fruit punch,
so , given that she had 2 liters of fruit juice.
Here ,
⇒x become 2.
⇒Lemonade required =[tex]2\times x[/tex]
⇒Lemonade required = [tex]2\times3 = 6\ liters[/tex]
There total fruit punch = [tex]6 + 3=9\ liters[/tex]
[tex]\therefore\\[/tex] ratio of fruit juice to lemonade in the second batch = 6:9 = 2:3.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
To know more about Ratio and Proportion:
https://brainly.com/question/12024093
#SPJ13
Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Answers
Our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
Given, The elevation of a sunken ship is 120 feet.
Your elevation is 58 of the ship elevation.
as it is given that the elevation of a sunken ship is 120 feet and our elevation is 58 of the ship elevation.
So, on using the concept of application of trigonometry we can conclude that our elevation is 58.
As, it is given that our elevation is 58 of the ship elevation.
So, our elevation is 120 + 58 = 178 feet.
Hence, our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
Learn more about Applications of Trigonometry here https://brainly.com/question/22972461
#SPJ4
10) Determine the value of 10 - t when t = 4.
11) Determine the value of 12 + m when m = 6.
12) Determine the value of a + 5.2 when a = 1.9.
13) Determine the value of 3.4 - b when b = 2.1.
Answers
Answer:
10) 6
11) 18
12) 7.1
13) 1.3
Step-by-step explanation:
all you have to do is substitute
10 - 4 = 6
12 + 6 = 18
1.9 + 5.2 = 7.1
3.4 - 2.1 = 1.3
Each month Edna spends all her income on rent, on travel and on other living expenses She spends 1/3 of her income on rent. she spends 1/5 of her income on travel. She spends $420 of her income on other living expenses. Work out her income each month.
Answers
Answer:I think $1064
Step-by-step explanation:
First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.
mike has 40 coins consisting of dimes and quarters. if the dimes were quarters and the quarters dimes he would have 90 cents more. how many quarters does he have?
Answers
In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.
A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation. Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:
x + y = 40
The amount of the total coins would be 0.1x + 0.25y.
If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.
Hence,
0.25x + 0.10y = 0.1x + 0.25y + 0.9
Solving,
0.25x – 0.1x = 0.25y – 0.1y +0.9
0.15x = 0.15y + 0.9
As x + y = 40, x = 40 – y
Substituting,
0.15 (40 – y) = 0.15y + 0.9
6 - 0.15 y = 0.15y + 0.9
0.15y + 0.15y = 6 – 0.9
0.3y = 5.1
y = 5.1/0.3 = 17
Hence, the number of quarters are 17.
Learn more about Word problem:
https://brainly.com/question/13818690
#SPJ4
when the auditors have chosen to test a control, what relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample?
Answers
Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.
Define sample.An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. Using samples, one can draw conclusions about populations. Since samples are useful, affordable, practical, and manageable, it is simpler to gather data from them. A crucial component of the scientific method is sampling, which enables researchers to demonstrate the validity of generalizable ideas using only a sample of particular facts. Additionally, sampling enables mathematicians to answer challenging paradoxes like the St.
Given,
Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.
To learn more about sample, visit:
https://brainly.com/question/13287171
#SPJ4
ben sat outside his school in cambridge and made a note of the colour of the first 100 cars that passed .
27 of them were red.
in britain there were around 35 million cars on the road.
use bens findings to give pout an estimate of how many cars on the road are red
Answers
The estimate for the number of cars that are red will be 9450000.
What is the estimate of the number of cars?From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.
Based on the above, the ratio of red cars to total cars is 27:100.
Therefore, if thee are 35 million cars, the red cars will be:
= Ratio of red cars × Total cars
= 27/100 × 3500000
= 9450000
The number of red cards is 9450000.
Learn more about ratio on:
brainly.com/question/2328454
#SPJ1
What is another way to write x^(x^2)? How do I work with this? I don't understand
Answers
The other ways of rewriting the expression are (xˣ)⁽²⁾ or xˣ²
How to rewrite the expression?From the question, we have the following expression that can be used in our computation:
x^(x^2)
Rewrite the expression properly
So, we have the following representation:
x⁽ˣ⁾⁽²⁾
The only ways the above expression can be rewriting the expression is by changing the positions of the brackets or removing the brackets entirely
Other than that, there are no other ways of rewriting the expression
So, we have
(xˣ)⁽²⁾ or xˣ²
Hence, the expressions are (xˣ)⁽²⁾ or xˣ²
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
Someone please help me with this question
Answers
Answer: D
Step-by-step explanation: Proportional relationship = relationships between two variables where their ratios are equivalent. 6:15 is equivalent with both 8:20 and 10:25. So D is the correct answer.
The variable p represents number of presents. If it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used. If there are 7 presents, how much ribbon is needed? Ribbon is sold in 15 feet packages. How many do you need to buy?
Answers
The number of ribbons that is needed for 7 presents is 73 ribbons.
She needs 5 packages.
What is an expression?An expression is simply used to illustrate the relationship between the variables.
In this case, it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used.
The ribbons needed for 7 presents will be:
= 10p + 3
= 10(7) + 3
= 70 + 3
= 73
Since it's sold in 15 feet packages, the number needed will be:
= 73 / 15
= 5
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
About 1 percent of the population has a particular genetic mutation. 100 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 100.
Answers
Answer:
1/100 or just 1
Step-by-step explanation:
$$$$$$$$$$$$$$$$$$$$$$$$
Please help!! 10 points
Answers
Answer:
y = - 2x + 4
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{4-1}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = - 2x + 4 ← equation of line
3. Elon is paid by the hour. He earned $50 for a 4 hour workday. How much
does he earn in one hour?
3b. How much does he earn for half an hour?
3c. How much does he earn in 5 hours?
Answers
Answer $12.5
$6.25
$62.5
PLEASE HELPPPP!!!
Simplify the imaginary number...
Answers
a cylindrical can is partially filled with sand. the radius of the cylindrical can is 15 cm. the height of the cylindrical can is 14 cm. if the volume of the sand is increasing at a rate of 555 cubic cm per second, what is the rate, in cm per second, at which the height of the sand is changing when the height of the sand is 5 cm?
Answers
The height of the sand is changing when the height of the sand is 5 cm is 0.7848 in cm/sec
What is meant by volume?Volume is a measure of three-dimensional space that is occupied. It is frequently quantified numerically using SI-derived units (such as the cubic metre and litre) or various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is related to volume. The volume of a container is commonly understood to be its capacity; that is, the amount of fluid (gas or liquid) that the container can hold, rather than the amount of space it occupies.
Volume was measured in ancient times using similar-shaped natural containers, and later, standardized containers. Arithmetic formulas can easily calculate the volume of some simple three-dimensional shapes. Volumes of more complicated shapes can be calculated using integral calculus if a formula is provided.
The volume of the cylindrical is,
V = πr²h
V = volume
r = base radius
h = height
Calculate the difference between both sides of the equation in relation to time t. Because the radius r does not change over time, we can consider it a constant:
dv/dt = πr²(dh/dt)
Given,
dv/dt =555 cubic cm per second
r = 15
solve dh/dt:
555 = π(15)²(dh/dt)
dh/dt = 555(7/22)(1/225)
dh/dt =0.7848
The height of the sand is decreasing at a rate of 0.7848 in cm/sec
To know more about volume, visit:
https://brainly.com/question/1578538
#SPJ4
1. 1/4 of a vegetable garden has broccoli and 2/3 of the garden has peppers. How much of the garden has vegetables growing in it?
2. Jessica and Maria are both making slime with different recipes. Jessica’s recipe calls for 1 1/2 cups of flour and Maria’s recipe calls for 2/3 cups of flour. How many cups of flour will they need in order to make both of their batches of slime?
3. Donnie has a pool and recently discovered a leak. He continues to patch the leak until someone can come out to repair it. After all the water has completely drained out of the pool due to the patch coming off, it takes him two days to fill the pool back up. It takes three days for the pool to drain completely. How long would it take to fill the pool if the patch is off while Donnie is refilling it?
4. I baked a cake for my sibilants. My brother ate 1/8 of the cake and my sister ate 3/4. How much of the cake is left for me?
5. Amanda is making oatmeal cookies with raisins and pecans for her club. The recipe makes seventeen oatmeal cookies. It takes 1/4 of a cup of nuts and 1/2 a cup of radon’s just for seventeen cookies! There are thirty-four members in Amanda’s club. If she makes exactly thirty-four cookies, how many cups of nuts will she need?
6. Felipe has a business where he builds and sells birdhouses. To build 12 birdhouses, he needs 5 1/4 meters of wood. During the holiday season, Felipe was asked to make 4 1/2 times the number of birdhouses he usually makes. How many meters of wood does Felipe need to make that many birdhouses?
7. It is Nadine’s birthday, and she is making walnut brownies for her sleepover. She invited eight of her friends to her party. The recipe that she is using makes twenty-four brownies, but she only wants to make eight. The recipe for twenty-four calls for 4 1/2 cups of walnuts. How many cups of walnuts will she need for eight people?
8. A candy bar is 5 1/3 inches long. If it is divided into pieces that are 1 1/4 inches long, then how many pieces of candy bar will there be?
9. A maple tree can grow in average to be 90 feet tall. Redwood trees can grow to be 2 2/3 times bigger than a maple tree. What is the average height of a Redwood tree?
10. A piece of rope is 24 1/2 feet long. How many 1/4- foot sections can be cut from it?
Answers
Broccoli and peppers occupy 11/12 of the gardenAs a result, 11/12 of the garden is filled with vegetables.
How can I determine how much of a garden's growing veggie there is?1,Let's add up those two fractions to determine how much of the entire garden contains broccoli and peppers since we know that 1/4 of the garden has broccoli and 2/3 of the garden contains peppers.
Consequently, 1/ 4 + 2/3 =?
It is necessary for the denominator to match.
Consequently, 1/4 x 3/ 3 = 3 / 12.
2/3 × 4 /4 = 8 / 12
Hence, 3 / 12 + 8 / 12 = 11 / 12
2 ,Amount of flour needed to complete both recipes =2+1/4+1
3, Baked cake 1 /8 +3/4,
6 , Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes
= 54 / 12 x 5¹/₄
= 23 ⁵/₈ meters
7, 24 brownies = 9/2 cups of walnuts
8 brownies =1 1/2 cups of walnuts
To learn more about solving for quantities needed refer
https://brainly.com/question/28605560
#SPJ13