Answer:
1.4Step-by-step explanation:
The formula for calculating the standard error of the mean is expressed as shown below;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma[/tex] is the standard deviation and n is the sample size.
Given [tex]\sigma[/tex] = 14 and n = 100
Substituting this values into the formula fr calculating the standard error of the mean;
[tex]SE = \frac{14}{\sqrt{100} } \\\\SE = \frac{14}{10} \\\\SE = 1.4[/tex]
Hence, standard error of the mean is 1.4
PLZ HELP ITS 20 POINTS Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
The answer is (1,-5). (i.e x=1 and y=-5).
Hope it helps..
Answer:
(1,-5)
Step-by-step explanation:
Helppppppp ASAP pleaseee
Answer:
True
Step-by-step explanation:
Inverse variation on a graph is depicted by the movement of the graph diagram (line) in a downward motion
Answer:true
Step-by-step explanation:
A 5-ounce container of Greek yogurt contains 140 calories. Find the unit rate of calories per ounce
Answer:
28
Step-by-step explanation:
140 calories over 5 ounce
= 28
The unit rate of calories per ounce will be 28 calories/ ounce
What is proportion ?
A proportion is an equation based on the equality of two ratios.
It is given that 5-ounce container of Greek yogurt contains 140 calories and it is to calculate for one ounce calories contain in Greek yogurt :
[tex]\begin{aligned}5 \text{\:ounce}&\rightarrow 140 \text{\:calories}\\1 \text{\:ounce}&\rightarrow \frac{140}{5}\text{\:calories} \\&\rightarrow 28 \text{\:calories}\end{aligned}[/tex]
Therefore, the unit rate of calories per ounce will be 28 calories/ ounce
Read more about ratio at:
https://brainly.com/question/17869111
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Below are some of the scores on a math quiz given last week,
{82, 73, 74, 78, 46, 73}
What will happen to the mean of the quiz scores if the outlier is removed?
A
The mean will decrease.
OB
The mean will increase
C
There is not enough information given.
OD
The mean will not change.
Answer:
B: The mean will increase
Step-by-step explanation: The outlier is 46, which is way below all the other numbers, which is the definition of an outlier. If we remove a really low number from the set, then the mean(average) will increase.
6th grade math, help me please.
Answer:
a) [tex]\frac{2}{3} \,\frac{lb}{bread}[/tex]
b) [tex]1\frac{1}{4} \,\frac{in}{domino}[/tex]
Step-by-step explanation:
Part a:
every 4 lbs of flour, she makes 6 loaves of bread. this as a rate in simplest fraction form is:
[tex]\frac{4}{6} \,\frac{lb}{bread} = \frac{2}{3} \,\frac{lb}{bread}[/tex]
Part b:
every 10 inches , 8 dominoes can be placed. then the rate can be written as:
[tex]\frac{10}{8} \,\frac{in}{domino} = \frac{5}{4} \,\frac{in}{domino} =1\frac{1}{4} \,\frac{in}{domino}[/tex]
The value of y varies inversely as the square of x, and y = 16, when I = 3.
Find the value of x when y = 1.
Answer:
x = 12Step-by-step explanation:
The statement
The value of y varies inversely as the square of x is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of proportionality
To find the value of x when y = 1 first find the formula for the variation
y = 16 x = 3
k = yx²
k = 16(3)²
k = 16 × 9
k = 144
The formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
We have
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
We have the final answer as
x = 12Hope this helps you
The ratio of oranges in a fruit salad to people it will serve is 9/40, or 9:40. If Lisa wants to serve 800 people, how many oranges will Lisa use?
The correct answer is 180 oranges
Explanation:
In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:
[tex]\frac{9}{40} = \frac{x}{800}[/tex] - 1. Multiply 9 x 800 and 40 x x (cross multiplication)
[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40
[tex]\frac{7200}{40} = x[/tex]
[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which can be expressed as 180: 800
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $6.00 for adults and $3.00 for students. However, this situation has two constraints: The theater can hold no more than 240 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
Answer:
160 adults and 80 students
Step-by-step explanation:
With the information from the exercise we have the following system of equations:
Let x = number of students; y = number of adults
I want to maximize the following:
z = 3 * x + 6 * y
But with the following constraints
x + y = 240
y / 2 <= x
As the value is higher for adults, it is best to sell as much as possible for adults.
So let's solve the system of equations like this:
y / 2 + y = 240
3/2 * y = 240
y = 240 * 2/3
y = 160
Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.
On moving day, Guyton needs to rent a truck. The length of the cargo space is , and the height is less than the width. The brochure indicates that the truck can hold . What are the dimensions of the cargo space
On moving day, Guyton needs to rent a truck. The length of the cargo space is 10 ft , and the height is 1 ft less than the width. The brochure indicates that the truck can hold 420 ft3 . What are the dimensions of the cargo space? Assume that the cargo space is rectangular shape.
Answer:
The dimensions; width w is 7 ft and height is 6 ft
Step-by-step explanation:
L = 10 ft the length of the cargo space
w = the width of the cargo space
h = the height of the cargo space the height is 1 ft less than the width
h = w - 1
The truck can hold 420 ft^3 - this means the volume of the space V = 420 ft^3
But V = L*w*h
Substitute h = w - 1 into the Volume equation
Therefore,
10*w*(w - 1) = 420
10w^2 - 10w - 420 = 0
By Using quadratic equation formula to solve and considering positive answer,
w = {-b +- √(b^2 - 4ac)}/2a
Where;
a = 10, b = -10 and c = -420
w = {-(-10) +- √(-10^2 - 4(10)(-420)}/2(10)
w = {-(-10) +- 130}/20
w = (10 + 130)/20 = 140/20 = 7
Or
w = (10 -130)/20 = -120/20 = -6
Here,
I take positive answers and the width is 7 ft
Also, from h = w - 1
height = 7 - 1 = 6 ft
As per the question on a moving day, the Guyton is renting a truck and the length of his cargo the height of which is less than the width. The brochure indicates the trick that he can hold.
How much width and height does Guyton need in cargo space?The dimension of the cargo will be based on the amount of capacity of the cargo and the amount of cargo that needs to be moved. On the day of the move, he rent a truck. The L of all cargo space is given as 10 feet, and that of height is 1 foot which is less than the width. This brochure tells us that the truck can hold 420 feet.
Find out more information about the length of the cargo space.
brainly.com/question/1170096.
|x–5|=|x+5| If you answer this question before 2:35 pm on July 28, 2020, I will give 10 points!!
Answer:
[tex]\boxed{x=0}[/tex]
Step-by-step explanation:
[tex]|x-5|=|x+5|[/tex]
Solve absolute value.
There are two possibilities.
First possibility:
[tex]x-5=x+5\\0=10[/tex]
No solution.
Second possibility:
[tex]x-5=-(x + 5)\\x-5=-x-5\\2x=0\\x=0[/tex]
The floor of a shed given on the right has an area of 44 square feet . The floor is in the shape of a rectangle whose length is 3 less than twice the width. Find the length and width of the floor of the shed.
Answer:
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
Step-by-step explanation:
Given that the shape of the shed is a rectangle, the expression for the area is:
[tex]A = w \cdot l[/tex]
Where [tex]w[/tex] and [tex]l[/tex] are the width and length of the shed, measured in feet. In addition, the statement shows that [tex]l = 2\cdot w - 3\,ft[/tex]. Then, the equation of area is expanded by replacing length:
[tex]A = w\cdot (2\cdot w - 3)[/tex]
[tex]A = 2\cdot w^{2} - 3\cdot w[/tex]
If [tex]A = 44\,ft^{2}[/tex], then, a second-order polynomial is formed:
[tex]2\cdot w^{2}-3\cdot w - 44 = 0[/tex]
The roots of this equation are found via General Equation for Second-Order Polynomials:
[tex]w_{1} = \frac{11}{2}\,ft[/tex] and [tex]w_{2} = -4\,ft[/tex]
Only the first roots is a physically reasonable solution. Then, the length of the shed is:
[tex]l = 2\cdot \left(\frac{11}{2}\,ft \right)-3\,ft[/tex]
[tex]l = 8\,ft[/tex]
The length and width of the floor of the shed are 8 feet and 5.5 feet, respectively.
What is the y-intercept of the line described by the equation below? Y=3x - 6
We are given the equation y = 3x - 6
The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.
The b value in this equation is -6, thus the y-intercept is -6.
Let me know if you need any clarifications, thanks!
A student is using the elimination method to solve the system of equations below. What is the best first
step?
4x - 5y = 2
2x + y = -3
Answer:
The best first step would be to multiply the second equation by -2
Step-by-step explanation:
The best first step would be to multiply the second equation by -2
then you would have the following
[tex]\ \ \ \ \ \ 4x - 5y = 2 \\-2*(2x)+ (-2)*y = (-2)*3[/tex]
and when you multiply it is easy to eliminate because you will get
[tex]4x - 5y = 2 \\-4x -2y = 6[/tex]
and if you sum the equations you get
-7y = 8
so that is a single variable equation which is easier to solve.
A congressman wants to measure the level of support in his district for campaign finance reform and determine if there is a gender gap among voters with respect to this issue. One aid suggests that they find separate confidence intervals for the percent of men and the percent of women who favor reform and then see if the intervals overlap. Another aid suggests that they find a confidence interval for the difference in the proportions of men and women who favor reform. The question is: Is there a gender gap
Answer:
Campaign Finance Reform
Gender Gap among Voters in the District
There is a gender gap among women and men who favor campaign finance reform.
Step-by-step explanation:
In issues such as the above, a gender gap always exist between women and men who think that there is the need to reform the campaign finance. Women ordinarily favor a reduction in the campaign finance. On the other hand, men do not mind so much about the candidate expenditure in campaigns. Reducing the huge campaign finance will ensure that political campaigns and aspiration to political offices are not left to money bags. Many women would like to get involved, but they are limited by funding. So, anytime the issue of reforming the whole electoral system, especially with respect to campaigns, women favor the reforms more than men. The gap is always there. The main issue is how would this gap be measured?
1000 randomly selected Americans were asked if they believed the minimum wage should be raised. 600 said yes. Construct a 95% confidence interval for the proportion of Americans who believe that the minimum wage should be raised.
a. Write down the formula you intend to use with variable notation).
b. Write down the above formula with numeric values replacing the symbols.
c. Write down the confidence interval in interval notation.
Answer:
a. p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex]
b.0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. { -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
Step-by-step explanation:
Here the total number of trials is n= 1000
The number of successes is p` = 600/1000 = 0.6. The q` is 1 - p`= 1- 0.6 = 0.4
The degree of confidence is 95 % therefore z₀.₀₂₅ = 1.96 ( α/2 = 0.025)
a. The formula used will be
p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ( z with the base alpha by 2 (α/2 = 0.025))
b. Putting the values
0.6 ± 1.96 [tex]\sqrt \frac{0.6* 0.4}{1000}[/tex]
c. Confidence Interval in Interval Notation.
{ -1.96 ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ 1.96} = 0.95
{ -z( base alpha by 2) ≤ p`± z₀.₀₂₅[tex]\sqrt{ \frac{p`q`}{n}[/tex] ≥ z( base alpha by 2) } = 1- α
One angle of a right triangle measures 31° what is the measure of the other angle
Answer:
59°
Step-by-step explanation:
A triangle adds up to 180°. A right triangle has a 90° angle.
1. Set up the equation
90 + 31 + x = 180
2. Simplify
121 + x = 180
3. Solve for x by subtracting 121 from both sides
x = 59
What is the following simplified product? Assume x>0
2 square root 8x^3(3 square root 10x^4-x square root 5x^2
Answer:
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]
Step-by-step explanation:
The product [tex]2\sqrt{8x^3} (3\sqrt{10x^4} - x\sqrt{5x^2})[/tex] can be simplified as follows:
Step 1: Use the distributive property of multiplication
[tex]2\sqrt{8x^3}(3\sqrt{10x^4)} - 2\sqrt{8x^3}(x\sqrt{5x^2})[/tex]
[tex] 2*3\sqrt{8x^3*10x^4} - 2*x\sqrt{8x^3*5x^2} [/tex]
[tex] 6\sqrt{80x^7} - 2x\sqrt{40x^5} [/tex]
Step 2: simplify further
[tex] 6\sqrt{16*5*x^3*x^3*x} - 2x\sqrt{4*10*x^4*x} [/tex]
[tex] 6*4*x^3\sqrt{5*x} - 2x*2*x^2\sqrt{10*x} [/tex]
[tex] 24x^3\sqrt{5x} - 4x^3\sqrt{10x} [/tex]
-2x(x+3)-(x+1)(x-2)=
Answer:
-3x^2 -5x +2
Step-by-step explanation:
-2x(x+3)-(x+1)(x-2)=
Distribute
-2x^2 -6x -(x+1)(x-2)
Foil
-2x^2 -6x -(x^2 -2x +x -2)
Combine like terms
-2x^2 -6x -(x^2 -x -2)
Distribute the minus sign
-2x^2 -6x -x^2 +x +2
Combine like terms
-2x^2 -x^2 -6x +x +2
-3x^2 -5x +2
Answer:
[tex]\huge\boxed{-2x(x+3)-(x+1)(x-2)=-3x^2-5x+2}[/tex]
Step-by-step explanation:
[tex]-2x(x+3)-(x+1)(x-2)[/tex]
Use the distributive property: a(b + c) = ab + ac
and FOIL: (a + b)(c + d) = ac + ad + bc + bd
[tex]=(-2x)(x)+(-2x)(3)-\bigg[(x)(x)+(x)(-2)+(1)(x)+(1)(-2)\bigg]\\\\=-2x^2-6x-\bigg(x^2-2x+x-2\bigg)=-2x^2-6x-x^2-(-2x)-x-(-2)\\\\=-2x^2-6x-x^2+2x-x+2[/tex]
Combine like terms:
[tex]=(-2x^2-x^2)+(-6x+2x-x)+2=-3x^2+(-5x)+2\\\\=-3x^2-5x+2[/tex]
Write the first 4 terms of the sequence defined by the given rule f(n)=n2 -1
Answer:
0, 3, 8, 15Step-by-step explanation:
Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:
f(1) = 1² - 1 = 1 - 1 = 0
f(2) = 2² - 1 = 4 - 1 = 3
f(3) = 3² - 1 = 9 - 1 = 8
f(4) = 4² - 1 = 16 - 1 = 15
The chart below lists the original and sale prices of items at a clothing store.
Clothing Prices
Original price Sale price
$7.99
$5.59
$10.99
$7.69
$12.99
$9.09
$15.99
$11.19
$24.99
$17.49
$29.99
$20.99
Which statement best describes why the sale price is a function of the original price?
As the original price increases, the sale price also increases.
The sale price is always less than the original price.
For every original price, there is exactly one sale price.
The sales price is never less than zero.
Answer: C) For every original price, there is exactly one sale price.
For any function, we always have any input go to exactly one output. The original price is the input while the output is the sale price. If we had an original price of say $100, and two sale prices of $90 and $80, then the question would be "which is the true sale price?" and it would be ambiguous. This is one example of how useful it is to have one output for any input. The input in question must be in the domain.
As the table shows, we do not have any repeated original prices leading to different sale prices.
Answer:
C STAY SAFE!!!
Step-by-step explanation:
Ok we know this cant be A the reason is It says tha the original price is increasing so thats FALSE... its trying to trick you so no
The second choice says The sale price is always less than the original price. well take a look at the sale prices are they? Obiously not so False
Ok the third option For every original price, there is exactly one sale price. well this is true ask yourself each it helps.
Last option The sales price is never less than zero. erm FALSE OBIOUSLY THIS IS TRUE JUST NOT TRUE ITS WRONG
THE ANSER IS C
TWhich equation has the same solution as this equation. X^2 - 8x + 12 = 0
x² - 8x + 12 = 0
First of all we need to find the roots
Δ = b² - 4.a.c
Δ = (-8)² - 4 . 1 . 12
Δ = 64 - 4. 1 . 12
Δ = 16
Has 2 real roots
x = (-b +- √Δ)/2a
x' = (--8 + √16)/2.1
x'' = (--8 - √16)/2.1
x' = 12 / 2
x'' = 4 / 2
x' = 6
x'' = 2
So our equation can be solved with x = 6 and x = 2, therefore we can create two other equations with the same roots
x - 6 = 0
and
x - 2 = 0
Answer:
(x – 4)2 = 4
Step-by-step explanation:
CORRECT ANSWER WILL GET BRAINLIEST EO
Use the graph of f(x) to find the indicated function values.
ty
8
If x = 0, then f(0) =
4
If f(x) = 0, then x =
A
-3
-2
2
Done
Intro
Answer:
Step-by-step explanation:
if x=0 then f(x)=2 (0,2)
if f(x)=0 then x=-1 (-1,0)
If x = 0, then f(0) =
✔ 2.25
.
If f(x) = 0, then x =
✔ –1
.
A recipe for 1 batch of muffins used 2/3 of blueberries. Amir made 2 1/2 batches of muffins. How many cups of blueberries did he use? A. 1 4/6 B. 1 5/6 C. 2 2/6 D. 3 1/6. Please show your work.
Answer:
A. 1 4/6 cups of blueberries
Step-by-step explanation:
1 -- 2/3
Proportion, Batches to Blueberries
1*(2 1/2) -- (2/3)( 2 1/2)
Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion
2 1/2 -- (2/3)( 5/2 )
2 1/2 -- 5/3
2 1/2 -- 1 2/3
Simplify
On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6
Hope that helps! Tell me if you need more info
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.) f(x) = x2 − 7x + 5
Answer:
F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]
Step-by-step explanation:
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = [tex]\int\limits{f(x)} \, dx[/tex]
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = [tex]\int\limits {(x^2 - 7x + 5)} \, dx[/tex]
F(x) = [tex]\frac{x^3}{3} - \frac{7x^2}{2} + 5x + c[/tex]
Where c is the constant of the integration (antiderivative).
PS: The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
13. If 6 times the 6th term of an A.P. is equal to
13 times the 13th term, prove that 19th term
of this A.P. is zero.
please give the answer as fast as you can
please
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
6(a₁ + 5d) = 13(a₁ + 12d) ← distribute parenthesis on both sides
6a₁ + 30d = 13a₁ + 156d ( subtract 13a₁ from both sides )
- 7a₁ + 30d = 156d ( subtract 30d from both sides )
- 7a₁ = 126d ( divide both sides by - 7 )
a₁ = - 18d
Now
a₁₉ = a₁ + 18d = - 18d + 18d = 0 ← as required
174 people ate lunch at Alice’s restaurant yesterday, and 1/3 of them had dessert. How many people had dessert after lunch?Explain how you got your answer. (90 points!!!)
Answer:
58 people
Step-by-step explanation:
174 people ate lunch.
1/3 of the 74 people had dessert after lunch.
Multiplying 1/3 and 174.
1/3 × 74
= 58
58 people had desert after lunch.
Answer:
[tex]\boxed{ 58\ people}[/tex]
Step-by-step explanation:
People who ate lunch = 174 people
People among among them who had desserts = 1/3 of the total
(Remember "of" means to "multiply")
=> 1/3 * 174
=> 1 * 58
=> 58 people
What the answer fast
Answer:
HI = 13
Step-by-step explanation:
The triangle that is shown is a 45-45-90 triangle, so we know that GH = GJ = 9 and IJ = 13, we are able to solve for HI.
Technically, IJ = HI, since both triangles are congruent. Both IJ and HI will be 13.
Find the 12th term of the following geometric sequence.
10, 30, 90, 270,
Answer:
The 12th term is 1771470Step-by-step explanation:
Since the above sequence is a geometric sequence
An nth term of a geometric sequence is given by
[tex]A(n) = a(r)^{n - 1} [/tex]
where a is the first term
r is the common ratio
n is the number of terms
From the question
a = 10
To find the common ratio divide the previous term by the next term
That's
r = 30/10 = 3 or 90/30 = 3 or 270/90 = 3
Since we are finding the 12th term
n = 12
So the 12th term is
[tex]A(12) = 10( {3})^{12 - 1} [/tex]
[tex]A(12) = 10 ({3})^{11} [/tex]
A(12) = 1771470Hope this helps you
Use a graphing calculator to sketch the graph of the quadratic equation and then give the coordinates for the x-intercepts (if they exist) y=x2+7x+10 A (-2,0),(5,0) B (2,0);(-5,0) C (2,0);(5,0) D (-2,0);(-5,0)
Answer:
Option D.
Step-by-step explanation:
The given quadratic equation is
[tex]y=x^2+7x+10[/tex]
We need to draw the graph of given equation by using graphing calculator as shown below.
From the graph it is clear that the parabola intersect the x-axis at points (-2,0) and (-5,0). So, the x-intercepts are (-2,0) and (-5,0).
Therefore, the correct option is D.
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If = 4 cm, what is the smallest diameter of wrapper that will fit the candy bar?
Answer:
Step-by-step explanation:
No figure supplied, so lots of assumptions needed.
Assume side length of triangle is 4 cm.
( If = 4 cm means ??)
Assume ABC is equiangular, all three angles are 60 degrees.
(This is a cross-sectional view, but don't see any)
Side length = 4
altitude of triangle = 4 sin(60) = 2sqrt(3)
radius of circumscribed circle of equilateral triangle
R = (2/3) altitude
= (2/3)*2sqrt(3)
= (4/3)sqrt(3)
Diameter
D = 2R
= (8/3) sqrt(3)
Answer: 8 cm
Step-by-step explanation:
The figure in the image attached below shows that there are two specific angles that are congruent to each other, angles AD and CD.
We are given the length of one of these angles:
AD= 4 cm so we must multiply 4 by 2, since there are TWO angles measuring 4 cm.
4 cm x 2 angles (AD and CD) =8 cm.
Proof of answer is shown below!