IF three coins are thrown. What is the probability of obtain at least one head

Answer:

you will get no solutions

Answer:

No Solution

Step-by-step explanation:

Answer:

...

Step-by-step explanation:

Answer:

its D

Step-by-step explanation:

got it right

The slope of the line that passes through the points (-5, 6) and (-9, -6) is 3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Let the given points as shown:

(x1,y1)= (-5, 6) and (x2,y2)= (-9, -6)

Slope = m = (y2-y1) /( x2-x1)

                 = (-6-6) /(-9-(-5))

                 = -12/-4

                 = 3

So, the slope of the line that passes through the points (-5, 6) and (-9, -6) is 3

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Answer:

First choice, 75%

Step-by-step explanation:

Add all the numbers together:

15 + 8 + 10 + 12 + 15 = 60

So the probability that you'll get a lose a turn card is 15/60 which simplified is 1/4, 1/4 in decimal form is 0.25 which is 25%. % means out of 100 so to double check: 1/4 times 100 = 100/4 = 25%

There's a 25% chance that you will draw the lose a turn card so

100% - 25% = 75%

So there's a 75% probability you will not draw the lose a turn card

Answer: 1331

Step-by-step explanation: v=lwh

The volume would be 1,331 cm cubed. I hope this helps, have a good day!

Using the given equations and the fact that A, B, C, D, E, and F are greater than zero, we can set the following inequalities:

Therefore, C is greater than 2 numbers of the list and smaller than 2 numbers on the list, then C could be 3 or 4.

Substituting the first equation in the third equation we get:

Therefore:

Since F is an integer greater or equal than 1 and smaller or equal than 6, necessarily F=6.

Now, If C=3, from the third equation we get that E=3, which is false because the 6 letters represent different numbers. Therefore C=4.

Answer: C represents 4.

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

There are 221 hot dogs and 169 hamburgers

Step-by-step explanation:

(If you need me to explain a little clearer, please comment so I can edit!)

17 : 13 = 30

x : y = 390

390 ÷ 30 = 13

17 · 13 = x

221 = x

13 · 13 = y

169 = y

Answer:

221 hotdogs

169 hamburgers

Step-by-step explanation:

Let 17x = no. of hotdogs

and 13x = no. of hamburgers

17x + 13x = 390

30x = 390

x = 13

17x = 17(13) = 221 hotdogs

13x = 13(13) = 169 hamburgers

Answer:

y= 1/2x+3.5

Step-by-step explanation:

Answer:

y= 1/2x+3.5

I took the test this is right

Step-by-step explanation:

Answer:

31874

Step-by-step explanation:

I think that's right?

please tell me

Answer:

C = 100 + 40n

The independent variable is n (number of months) and the dependent variable is C ( total cost)

Step-by-step explanation:

Let the total cost of the fitness center = C

Given fixed cost = $100

given cost per month = $40

let number of month = n

The total cost of the fitness center in a given 'n' month is calculated as;

C = 100 + 40n

From the above equation;

the independent variable is n (number of months) and

the dependent variable is C ( total cost)

C = 100 + 40n The independent variable is n (number of months) and the dependent variable is C ( total cost)

Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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Answer:

A Is the Answer to this problem

Step-by-step explanation:

B is true. C is true. D is true because the are parallel

Answer:

slope is 1

Step-by-step explanation:

rise / run = 5 / 5

the slope is 1

Answer: Well I can tell you that your answer is right, the answer is one.

Step-by-step explanation:

Pick two points on the line and determine their coordinates.

Determine the difference in y-coordinates of these two points (rise).

Determine the difference in x-coordinates for these two points (run).

Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

Answer:

Root under 39

Step-by-step explanation:

Just multiply the times like 5, 5.25, 5.50, 5.75, 6, 6.25 , 6.50....in such way and calculate...

Answer:

D. \(\sqrt{39}\)

Step-by-step explanation:

You don’t even need a calculator for this task.

You can see that the dot is 6.2, but lets just think what number should give us 6 in \(\sqrt{x}\), and we know it’s \(\sqrt{36}\), but since our dot equal 6.2, we see from our choise that the best answer is \(\sqrt{39}\).

In this question, we are given that common blood types are determined genetically by the three alleles A, B, and O. A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous.

The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is modeled by P(p,q,r)=2pq+2pr+2qr where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population and p+q+r=1 (the sum of the three must equal 100%).We are to use the fact that p+q+r=1 to show that the maximum proportion of heterozygous individuals in any population is 2/3.In the given expression:$$P(p, q, r) = 2pq + 2pr + 2qr$$We know that p + q + r = 1The number of alleles per person is 2 since we have a diploid genome (one set of chromosomes from each parent).So, the total of all the individual allele frequencies must be 2.

We have:p + q + r = 1A person with two alleles (homozygous) has a frequency of:p² or q² or r²Similarly, a person with one allele of each type (heterozygous) has a frequency of:2pq or 2pr or 2rqTo show that the maximum proportion of heterozygous individuals in any population is 2/3, we will use the AM-GM inequality which states that the arithmetic mean is greater than or equal to the geometric mean.\($$ AM \geq GM $$\)The AM-GM inequality can be rewritten as:\($$ \frac{a+b}{2} \geq \sqrt{ab} $$\)where a and b are any two positive numbers.

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Answer: We can cut 6 \(\dfrac23\) sections  out of each piece of wood.

Step-by-step explanation:

Given: A piece of wood is 4 feet long.

Number of \(\dfrac23\) sections = \(4\div\dfrac23\)

\(=4\times\dfrac{3}{2}\ \ \ \ [\because \dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}]\\\\=2\times3\\\\=6\)

i.e. Number of \(\dfrac23\) sections = 6

Hence, we can cut 6 \(\dfrac23\) sections  out of each piece of wood.

Answer:

Please show the graph, and i will be able to answer it for you.

Step-by-step explanation:

Answer: Fourth Choice. -46.08

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

s = 2.4

b=-7.2

t=4.8

n=-9.6

Given expression

(s - b) (n + t)

Substitute values into the expression

= (2.4 - (-7.2)) (-9.6 + 4.8)

Simplify values in the parentheses

= (2.4 + 7.2) (-4.8)

=(9.6) (-4.8)

Simplify by multiplication

= \(\boxed{-46.08}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

s = 2.4

b = - 7.2

t = 4.8

n = - 9.6

Substituting the given values in the equation :-

= > ( s - b ) ( n + t )

= > ( 2.4 - ( - 7.2 ) ) ( - 9.6 + 4.8 )

= > ( 2.4 + 7.2 ) ( -4.8 )

= > ( 9.6 ) ( - 4.8 )

= > - 46.8

In a simple graph with a shortest cycle of length 4, there can be at most one vertex with degree n-1.



Suppose G is a simple graph on n vertices, and the shortest cycle in G has length 4. Let v be a vertex of G. If v has degree n-1, then all other vertices must be adjacent to v. In particular, any two non-adjacent vertices u and w must be adjacent to v in order to form a cycle of length 4. However, this contradicts the assumption that the shortest cycle in G has length 4, since there exists a cycle of length 3 (u-v-w).

Hence, if the shortest cycle in G has length 4, no vertex can have degree n-1. Now suppose there are two vertices, u and w, with degree n-2. If there exists a path from u to w of length greater than 2, we can add u-w to this path to form a cycle of length greater than 4, which contradicts the assumption. Therefore, the only possibility is that u and w are adjacent. But this means there exists a cycle of length 3 (u-v-w), again contradicting the assumption.

Therefore, if the shortest cycle in G has length 4, G can contain at most one vertex of degree n-1.

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Answer:

Step-by-step explanation:

For angle C,

cos(∠C) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\) = 0.97

sin(∠C) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\) = 0.26

tan(∠C) = \(\frac{\text{Adjacent side}}{\text{Adjacent side}}\) = 0.27

Therefore, from the triangle ABC,

cos(∠A) = cos(90° - ∠C)

             = sin(∠C)

             = 0.26

sin(∠A) = sin(90 - ∠A)

            = cos(∠A)

            = 0.97

tan(∠A) = \(\frac{\text{sinA}}{\text{cosA}}=\frac{0.97}{0.26}\)

            = 3.73

Angle        \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)                 \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)                    \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

  A                    0.26                       0.97                             3.73

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

The given proof that all horses are the same color is a fallacy of circular reasoning or proof by induction.                                

   Here’s why: There is a fallacy in the statement given in the proposition P(k) is true, so that all the horses in any set of k horses are the same color. The fallacy is that it assumes the truth of the proposition to be proven by circular reasoning. By saying that all horses in any set of k horses are the same color, it means that all horses in a set of 1 horse, which is the basis step, are the same color. But this is false because a horse, as a solitary individual, can be of any color.                                

So, the statement, "all horses in any set of k horses are the same color" assumes the conclusion to be proven. This flaw invalidates the entire proof by induction. Therefore, the "proof" that all horses are the same color is wrong.

What is induction?                                                                                                                                                                                                             Induction is the process of establishing a general statement or principle by looking at examples or instances. It involves a specific observation or case that leads to a general conclusion. It is useful in mathematical proofs, scientific inquiry, and problem-solving.
The issue with this "proof" that all horses are the same color lies in the inductive step. To clarify, let's go through the proof by induction process:

1. Basis Step: P(1) is true since there is only one horse, and it must be the same color as itself.
2. Inductive Step: Assume P(k) is true for some arbitrary k (all k horses have the same color).

Now, proof consider a set of k + 1 horses. You claimed that the first k horses have the same color and the last k horses have the same color. However, this argument fails when k = 1. In this case, you would have a set of 2 horses (k+1), and there is no overlap between the first horse and the second horse, so you cannot conclude that they have the same color based on the induction assumption.

Thus, the inductive step does not hold for all cases, and the proof that all horses are the same color is incorrect.

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There are 70 ways to choose four toppings from the eight choices at the salad bar.

In mathematics, permutation refers to the arrangement of objects in a specific order. A permutation is an ordered arrangement of a set of objects, where the order matters and repetition is not allowed. It is denoted using the symbol "P" or by using the notation nPr, where "n" represents the total number of objects and "r" represents the number of objects chosen for the arrangement.

Permutations are commonly used in combinatorial mathematics, probability theory, and statistics to calculate the number of possible arrangements or outcomes in various scenarios.

To determine whether to use a permutation or a combination, we need to consider if the order of the toppings matters or not.

In this situation, the order of the toppings does not matter. You are simply selecting four toppings out of eight choices. Therefore, we will use a combination.

To solve the problem, we can use the formula for combinations, which is nCr, where n is the total number of choices and r is the number of choices we are making.

Using the formula, we can calculate the number of ways to choose four toppings from eight choices:

\(8C4 = 8! / (4! * (8-4)!) = 8! / (4! * 4!) = (8 * 7 * 6 * 5) / (4 * 3 * 2 * 1) = 70\)

So, there are 70 ways to choose four toppings from the eight choices at the salad bar.

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The final value is:

f(-5) = (-5)^2 = 25.

f(-5) = (-5)^2 - 1 = 24.

f(-5) = (-5)^2 + 1 = 26.

We can solve this problem by using the fact that the derivative of a function gives us the slope of the tangent line at any point. We can then use this information to find the equation of the function that satisfies the given derivative and the additional information about the function's values at certain points.

A) To find f(-5) if f(0)=0, we need to integrate the derivative f'(x)=2x with respect to x, since integration is the inverse operation of differentiation.

∫f'(x)dx = ∫2xdx = x^2 + C

where C is the constant of integration.

Since f(0)=0, we can find C by substituting x=0:

f(0) = 0^2 + C = 0

C = 0

Thus, the equation of the function is:

f(x) = x^2

So, f(-5) = (-5)^2 = 25.

B) To find f(-5) if f(1)=0, we can use the same method:

∫f'(x)dx = ∫2xdx = x^2 + C

Since f(1)=0, we can find C by substituting x=1:

f(1) = 1^2 + C = 0

C = -1

Thus, the equation of the function is:

f(x) = x^2 - 1

So, f(-5) = (-5)^2 - 1 = 24.

C) To find f(-5) if f(-4)=17, we can again use the same method:

∫f'(x)dx = ∫2xdx = x^2 + C

Since f(-4)=17, we can find C by substituting x=-4:

f(-4) = (-4)^2 + C = 17

C = 1

Thus, the equation of the function is:

f(x) = x^2 + 1

So, f(-5) = (-5)^2 + 1 = 26.

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Answer:

where is the question

Step-by-step explanation:

Four of the unit rates of 1/4 equals 16.

What is the fraction?

A fraction is a mathematical representation of a number that expresses one quantity relative to another. It is written as two numbers separated by a horizontal or diagonal line, with the number above the line known as the numerator and the number below the line known as the denominator.

To find the unknown value in the equation /16 = 3/12 using a unit rate, we can start by simplifying the fraction on the right side of the equation to a unit fraction with a denominator of 1.

3/12 = (3 ÷ 3)/(12 ÷ 3) = 1/4

So, we now have the equation /16 = 1/4.

To solve for the unknown value represented by the variable "/", we can use cross-multiplication:

/16 = 1/4

4 x /16 = 4 x 1/4

4/4 = /16

1 = /16

Therefore, the unknown value represented by "/" is 1.

Using a unit rate of 1/4, we can also see that 16/4 = 4, which means that four of the unit rates of 1/4 equals 16.

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1) General solution for second order differential equation, y" – 2y' + y = 0, is y = (c₁x + c₂)eˣ .

2) General solution for differential equation, 9y" + 6y' + y = 0, is y =(c₁x + c₂)e⁻³ˣ.

3) General solution for differential equation, 4y"- 4y'- 3y = 0, is y = c₁ e⁶ˣ+ c₂e⁻⁴ˣ.

4) General solution for differential equation, 4y" + 12y' +9y = 0, is y = (c₁x + c₂)e⁻⁶ˣ.

5) General solution for differential equation, y" – 2y' + 10y = 0, is y = eˣ (c₁cos(6x) + c₂sin(6x)).

6) General solution for differential equation, y" – 6y' +9y = 0 is y = (c₁x + c₂)e³ˣ.

7) General solution for differential equation, 4y" + 17y' + 4y = 0, is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) General solution for differential equation, 16y" + 24y' +9y = 0, is y = (c₁x + c₂)e⁻¹²ˣ.

9) General solution for differential equation, 25y" – 20y' + 4y = 0, is y = (c₁x + c₂)e¹⁰ˣ.

10) General solution for differential equation, 2y" + 2y' + y = 0, is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

General solution is also called complete solution and complete solution = complemantory function + particular Solution

Here right hand side is zero so particular solution is equals to zero. Therefore, evaluating the complementary function will be sufficient to determine the general solution to the differential equation.

1) y"-2y' + y = 0, --(1)

put D = d/dx, so (D² - 2D + 1)y =0

Auxiliary equation for (1) can be written as, m² - 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula,

\(m =\frac{-(- 2) ± \sqrt { 4 - 4}}{2}\)

=> m = 1 , 1

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)eˣ .

2) 9y" + 6y' + y = 0 or (9D² + 6D + 1)y =0 Auxiliary equation can be written as, 9m² + 6m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (6) ± \sqrt {36 - 4×4}}{2}\)

=> m = - 6/2

=> m = -3 , -3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻³ˣ.

3) 4y"- 4y'- 3y = 0

put D = d/dx, so (4D² - 4D - 3)y = 0

Auxiliary equation can be written as, 4m² - 4m - 3 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(-4) ± \sqrt {16 - 4×4×(-3)}}{2}\)

=> m = (4 ± 8)/2

=> m = -4 , 6

The roots of equation are real and equal. So, general solution is y = c₁ e⁶ˣ + c₂e⁻⁴ˣ.

4) 4y" + 12y' +9y = 0 or (4D² + 12D + 9)y= 0

Auxiliary equation can be written as, 4m² + 12m + 9= 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{-(12) ± \sqrt{144 - 4×4×9}}{2}\)

=> m = -12/2

=> m = -6 , -6

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻⁶ˣ.

5) y" – 2y' + 10y = 0 or (D² - 2D + 10)y = 0 Auxiliary equation can be written as, m² - 2m + 10 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-2) ± \sqrt {4 - 4×1×10}}{2}\)

=> m = (2 ± 6i)/2 ( since, √-1 = i)

=> m = 1 + 6i , 1-6i

The roots of equation are imaginary and unequal. So, general solution is y =eˣ (c₁cos(6x) + c₂sin(6x)).

6) y" – 6y' +9y = 0 or (D²- 6D + 9)y =0

Auxiliary equation can be written as, m² - 6m + 9 = 0 , a quadratic equation

solving it by using quadratic formula,

\(m =\frac{ - (-6) ± \sqrt {36 - 4×1×9}}{2}\)

=> m = 6/2 = 3,3

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e³ˣ.

7) 4y" + 17y' + 4y = 0 or (4D²+ 17D + 4)y=0

Auxiliary equation can be written as, 4m² + 17m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{- (-17) ± \sqrt {16 - 4×4×17}}{2}\)

=> m = ( -17 ± 15)/2

=> m = (-17 + 15)/2, (- 17 - 15)/2= -1, -16

The roots of equation are real and unequal. So, general solution is y = c₁e⁻ˣ + c₂e⁻¹⁶ˣ.

8) 16y"+24y'+9y =0 or (16D²+ 24D + 9)y= 0

Auxiliary equation can be written as, 16m² + 24m + 9 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (24) ± \sqrt {576 - 4×9×16}}{2}\)

=> m = (-24 ± 0)/2

=> m = -12,-12

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e⁻¹²ˣ.

9) 25y"- 20y' +4y =0 or (25D²-20D + 4)y = 0

Auxiliary equation can be written as, 25m²- 20m + 4 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (-20) ± \sqrt {400 - 4×4×25}}{2}\)

=> m = 20/2

=> m = 10 , 10

The roots of equation are real and equal. So, general solution is y = (c₁x + c₂)e¹⁰ˣ.

10) 2y" + 2y' + y = 0 or (2D²+ 2D + 1)y =0

Auxiliary equation can be written as, 2m² + 2m + 1 = 0 , a quadratic equation solving it by using quadratic formula, \(m =\frac{ - (2) ± \sqrt {4 - 4×1×2}}{2}\)

=> m = (- 2 ± 4i)/2 ( since, √-1 = i)

=> m = -1 + 2i , -1 - 2i

The roots of equation are imaginary and unequal. So, general solution is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)). Hence, required solution of differential equation is y = e⁻ˣ (c₁cos(2x) + c₂sin(2x)).

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Answer:

The tangent segments whose endpoints are the points of tangency and the fixed point outside the circle are equal. In other words, tangent segments drawn to the same circle from the same point (there are two for every circle) are equal.

Step-by-step explanation: