Answer:
$1,500
Step-by-step explanation:
A 2.5% increase in the $60,000 average family income would be required:
0.025 × $60,000 = $1,500
Your annual income would have to increase by $1,500.
What is the slope of the line below
Answer:
The answer is option A
Slope of the line using points
( 2,0) and (0, 3)
Slope = 3 - 0 / 0 - 2 = -3/2
Hope this helps
Start at the y-intercept of 3 on the coordinate system.
Remember, when choosing points, chose clear
cut points where the line crosses them.
The next put is on the x-intercept and it's 2.
To get from (0,3) to (2,0), we go down 3 units and run 2 units.
Since our slope is going down, it's negative.
So the slope is -3/2.
Determine if the
following equation
represents a function:
y = 1/3x – 4
Answer:
Function
Step-by-step explanation:
y = 1/3 x - 4
Is a function because for every x, we will get only one value of y.
Answer:
Yes,is a function
We can obtain the points (0,-4)(6,-2)
I hope this help you :)......
Which equation gives the number of quarter inches that are in 23 inch? a) 23 ÷ 14 = 212 b)23 ÷ 14 = 83 c)14 ÷ 23 = 38 d)14 ÷ 23 = 122
Answer: The number of quarter inches in 23 inches is 4 × 23 = 92
None of the answers given is correct.
Step-by-step explanation:
The ÷ sign means divide.
There are 4 quarter inches in each inch, so you have to multiply 23 × 4
Dividing by 14 makes no sense.
23 ÷ 1/4 = 92 is also an equation that makes sense.
A residential complex has left for the recreation area a circular-shaped extension of 40 m radius. In this space, a basketball court 30 m long by 15 m wide will be built. Also, a trapezoid-shaped park will be left in the sand, 6 m with a larger base, 4 m with a lower base and 3.5 m in height. What is the area left in the circular zone, after building the basketball court and the sand park? NOTE: remember the value of π = 3.14
Answer:
Step-by-step explanation:
Area of the circular zone = [tex]\pi[/tex]r^2
= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2
Area of the basketball court = l × b
= 30 × 15 = 450 m^2
Area of the trapezium shaped park = ( 6 + 4 ) 3.5 / 2
= 35/2 = 17.5 m^2
∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )
= 5024 - ( 450 + 17.5 )
= 5024 - 467.5
= 4556.5 m^2
hope this helps
plz mark it as brainliest!!!!!!!
Kathy owns a farm house which contains 'birds and cows. There are 25 animals
which includes 70 legs. Find the number of birds.
Answer:
There are 10 cows and 15 birds :)
Step-by-step explanation:
4(10)+2(15)=70
Tara solved a quadratic equation. Her work is shown below, with Step 222 missing. What could Tara have written as the result from Step 222? \begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ &&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned} 2(x−3) 2 +6 2(x−3) 2 x−3 x=1 =14 =8 =±2 or x=5 Step 1 Step 2 Step 3 Step 4
Answer:
[tex](x-3)^2=4[/tex]
Step-by-step explanation:
Tara's work is shown below:
[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ &&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]
From the equation, we notice that in Step 1, Tara did:
[tex]2(x-3)^2+6=14\\2(x-3)^2=14-6\\2(x-3)^2=8[/tex]
She is trying to isolate the x-variable. Therefore, the next logical step will be to divide both sides by 2 and her Step 2 will therefore be:
[tex]\dfrac{2(x-3)^2}{2} =\dfrac{8}{2} \\\\(x-3)^2=4[/tex]
Tara could have written: [tex](x-3)^2=4[/tex] as her step 2 and we would then have her work as:
[tex]\begin{aligned} 2(x-3)^2+6&=14 \\\\ 2(x-3)^2&=8&\text{Step }1 \\\\ (x-3)^2&=4&\text{Step }2 \\\\ x-3&=\pm 2&\text{Step }3 \\\\ x=1&\text{ or }x=5&\text{Step }4 \end{aligned}[/tex]
Answer:
Step 2
Step-by-step explanation:
I did the Khan Academy.
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 30% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, what is the expected number of available places when the limousine departs?
Answer:
(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b) The expected number of available places when the limousine departs is 0.338.
Step-by-step explanation:
Let the random variable Y represent the number of passenger reserving the trip shows up.
The probability of the random variable Y is, p = 0.70.
The success in this case an be defined as the number of passengers who show up for the trip.
The random variable Y follows a Binomial distribution with probability of success as 0.70.
(a)
It is provided that n = 6 reservations are made.
Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:
P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)
[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]
Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b)
The formula to compute the expected value is:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]
Compute the expected number of available places when the limousine departs as follows:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]
Thus, the expected number of available places when the limousine departs is 0.338.
Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $180 monthly payment, 6.25% interest, 11 years
Answer:
The future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
Consider the provided information:
It is provided that monthly payment is $175, interest is 7% and time is 11 years.
The formula for the future value of the annuity due is:
Now, substitute P = 175, r = 0.07 and t = 11 in above formula.
Hence, the future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
And experiment consist of rolling a six sided dice to select a number between one and six and drawing a card at random from a set of 10 cards numbered one through 10 which event definition corresponds to exactly one outcome of the experiment
Answer:
1/60
Step-by-step explanation:
Since there are 6 possible outcomes for the first event and 10 possible outcomes for the second event, and they are independent of each other, one outcome of the experiment would have a 1/(6*10)=1/60 chance of happening. Hope this helps!
An urn contains 25 red marbles, 27 blue marbles, and 36 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?
Answer:
25/88
Step-by-step explanation:
25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles
P(red) = number of red/total
= 25/88
Answer:
Dear user,
Answer to your query is provided below
Probability of choosing a red marble is 0.28 or (25/88)
Step-by-step explanation:
Total number of marbles = 88
Number of red marbles = 25
Probability = 25/88
A basketball player scored 9 points in two games. What could her scores in each of the games be?
Answer: Her scores in one game may be 5 points and the other may be 4 points.
Step-by-step explanation:
You may think about dividing the 9 points into two to find how many points she made in each game. But after dividing you will have 4.5 which is not an accurate answer.In a basketball game you can't score have a point but you make whole points.
please very soon I offer the crown !!! + 10 points urgently !!!
I need help please help meeeeeeeee I don’t understand
Answer:
n-3
Step-by-step explanation:
Notice that the output is always 3 less than the input
output is input -3
f(n) = n-3
(Geometry) PLEASE HELP ASAP
Answer:
CD=72x=7please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Murphy made an art sculpture composed of 512 matchsticks and 760 uncooked penne pieces. What is the ratio of match sticks to penne pieces? Simplify your answer
Answer:
64/95
Step-by-step explanation:
Ok so unsimplified, you get 512 matchsticks to 760 penne pieces.
You can write ratios like 512:760, but since you want simplified, I assume you want a fraction.
Both 512 and 760 can divide by 8, so 512/760 simplifies to 64/95.
Hope this helps!
The ratio of the match sticks to penne pieces is 64:95
How to determine the ratio?The given parameters are:
Matchsticks = 512Penne pieces = 760Express as a ratio
Ratio = Matchsticks : Penne pieces
So, we have:
Ratio = 512 : 760
Simplify the ratio
Ratio = 64 : 95
Hence, the ratio of the match sticks to penne pieces is 64:95
Read more about ratios at:
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The final velocity (V) is given by the formula v = vo + at, where vols Initial velocity, v is final velocity, a is acceleration, and t is time.
Hola
A car moving at an initial velocity of 20 meters/second accelerates at the rate of 1.5 meters/second? for 4 seconds.
The car's final velocity is
meters/second
Answer:
[tex] \boxed{\sf Final \ velocity \ (v) = 26 \ m/s} [/tex]
Given:
[tex] \sf v = v_{0} + at[/tex]
[tex]\sf Initial \ velocity \ (v_{0}) = 20 \ m/s \\ \sf Acceleration \ (a) = 1.5 \ m/s^{2} \\ \sf Time \ (t) = 4 \ sec[/tex]
To Find:
Final velocity (v)
Step-by-step explanation:
[tex]\sf Substituting \ value \ of \ Initial \ velocity \\ \sf acceleration \ and \ time \ in \ given \ equation: \\ \\ \sf \implies v = v_{0} + at \\ \\ \sf \implies v = 20 + 1.5(4) \\ \\ \sf 1.5 \times 4 = 6 : \\ \sf \implies v = 20 + \boxed{6} \\ \\ \sf 20 + 6 = 26 : \\ \sf \implies v = 26 \: m/s[/tex]
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=55,
x=33,
p=0.55
p(3)=_________
Answer:
P(33) = 0.0826
Step-by-step explanation:
The binomial distribution in this case has parameters n=55 and p=0.55.
The probability that k successes happen with these parameters can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]
We have to calculate the probability fo X=33 succesess.
This can be calculated using the formula above as:
[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]
Pleassseeee hhheellppp
Answer:
a). Point A
b). 90°
c). Anticlockwise
Step-by-step explanation:
As it's clear from the picture attached,
Triangle XYZ has been rotated about a point A to form an image X'Y'Z'.
Angle of rotation is 90° about a point A.
a). Point which is the center of the rotation → point A.
b). Angle of rotation → 90°
c). Direction of rotation → Anticlockwise
Bryson hopes to win a three-day vacation in a drawing that is being held at his office. He purchased 40 raffle tickets. There were 500 raffle tickets sold. What is the theoretical probability of Bryson winning the trip?
Answer:
The probability would be 40 / 500 = 0.08.
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654
Answer:
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Step-by-step explanation:
Given first sample size n₁ = 677
First sample proportion
[tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]
Given second sample size n₂ = 3377
second sample proportion
[tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]
Null Hypothesis : H₀ : p₁ = p₂.
Alternative Hypothesis : H₁ : p₁ ≠ p₂.
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]
where
[tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]
P = 0.2036
Q = 1 - P = 1 - 0.2036 = 0.7964
[tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]
Z = 3.775
Critical value ∝=0.05
Z- value = 1.96
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
City Hoppa runs two buses starting
from the same bus-stop.
One bus has a route that takes 25
minutes.
The other bus has a route that takes
35 minutes.
Both buses leave the bus-stop at
6 a.m. and run continuously.
What is the next time that the buses
will be at the stop together?
?
Answer:
8:55 am.
Step-by-step explanation:
First we find the least Common Multiple of 25 and 35.
25 = 5 * 5
35 = 5 * 7
The LCM = 5 * 5 * 7 = 175 minutes
or 2 hours 55 minutes.
So the required time is 8:55 am.
Answer:
r < 37 or r ≥ 42
Step-by-step explanation:
the route, r?
than 37 minutes
she leaves after 7:00
then r= 37 or r ≥ 42
or
r < 37 or r ≥ 42
Please answer this correctly
Answer:
3/7 chance
Step-by-step explanation:
There are 3 numbers that are even out of the 7 numbers on the spinner.
This means that there is a 3/7 chance spinning an even number.
Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
90 34 41106 84 5355 48 4175 49 9792 73 7480 94 10256 83
Required:
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).
Answer:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
Step-by-step explanation:
Information given
90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
[tex]\bar X=71.35[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=22.48 represent the sample standard deviation
n=20 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=20-1=19[/tex]
Since the Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.093[/tex]
And replacing we got:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)
Answer: The distance of the shortest route of return is 400
Step-by-step explanation:
The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
BC² = 320² + 240²
BC² = 160000
BC = √160000
BC = 400
18 + 5k / 3
I need help asap please cuz my mom asked me to solve this in 2min
#aisanmoms #SOS
Answer:
Nothing can be further done to this equation. It has been simplified all the way.
How many parallel and perpendicular lines, are there in a trapezium?
Answer:
US
0 parallel linesoptionally, one or two (opposite) angles may be 90°World
2 parallel linesoptionally, one line perpendicular to the two parallel linesStep-by-step explanation:
It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.
A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.
__
A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.
In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.
A graduate student majoring in linguistics is interested in studying the number of students in her college who are bilingual. Of the 1,320 students at the college, 466 of them are bilingual. If the graduate student conducts a study and samples 50 students at the college, use a calculator to determine the probability that 17 or fewer of them are bilingual.
The result will be the probability that 17 or fewer out of the 50 sampled students are bilingual.
To determine the probability that 17 or fewer out of 50 sampled students are bilingual, we can use the binomial probability formula. Let's calculate it step by step:
First, we need to determine the probability of an individual student being bilingual. We can do this by dividing the number of bilingual students by the total number of students:
P(bilingual) = 466 / 1320
Next, we'll use this probability to calculate the probability of having 17 or fewer bilingual students out of a sample of 50. We'll sum up the probabilities for having 0, 1, 2, ..., 17 bilingual students using the binomial probability formula:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Where:
P(X = k) = (nCk) * (P(bilingual))^k * (1 - P(bilingual))^(n - k)
n = Sample size = 50
k = Number of bilingual students (0, 1, 2, ..., 17)
Now, let's use a calculator to compute these probabilities. Assuming you have access to a scientific calculator, you can follow these steps:
Convert the probability of an individual being bilingual to decimal form: P(bilingual) = 466 / 1320 = 0.353
Calculate the cumulative probabilities for having 0 to 17 bilingual students:
P(X ≤ 17) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 17)
Using the binomial probability formula, we'll substitute the values:
P(X ≤ 17) = (50C0) * (0.353)^0 * (1 - 0.353)^(50 - 0) + (50C1) * (0.353)^1 * (1 - 0.353)^(50 - 1) + ... + (50C17) * (0.353)^17 * (1 - 0.353)^(50 - 17)
Evaluate this expression using your calculator to get the final probability. Make sure to use the combination (nCr) function on your calculator to calculate the binomial coefficients.
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Using the central limit theorem, the probability that 17 or fewer of them are bilingual.
The following information is given in the question:
Population size N = 1320
Number of bilingual students = 466
Sample size n = 50
number of bilingual students in the sample = 17
Population proportion:
[tex]P =\frac{466}{1320}[/tex]
P =0.3530
Q= 1-3530
Q = 0.647
Sample proportion:
[tex]p = \frac{17}{50}[/tex]
p = 0.34
q = 1-0.34
q = 0.66
Since,
[tex]X \sim B(n, p)[/tex]
E(x) = np and var(x) = npq
Here, the sample size (50) is large and the probability p is small.
So we can use the central limit theorem, which says that for large n and small p :
[tex]X \sim (nP, nPQ)[/tex]
Where, P =0.3530
nP = 50 x 0.3530 = 17.65
and nPQ = 50x0.3530x0.647 = 11.41
Now, we want to calculate P(X≤17)
[tex]P(X\leq 17) = P(\frac{x-nP}{\sqrt{nPQ}}\leq \frac{17-17.65}{\sqrt{11.41}})[/tex]
[tex]P(X\leq 17) = P(z}\leq \frac{-0.65}{3.78}})[/tex]
[tex]P(X\leq 17) = P(z}\leq -0.172)[/tex]
[tex]P(X\leq 17) = P(z}\geq 0.172)[/tex]
[tex]P(X\leq 17) =1- P(z}\leq 0.172)[/tex]
[tex]P(X\leq 17) =1-0.56[/tex]
[tex]P(X\leq 17) =0.44[/tex]
Hence, the probability that 17 or fewer of the students are bilingual is 0.44.
Learn more about central limit theorem here:
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What system of equations would you use to solve the problem below?
The owner of a bike shop sells tricycles (3 wheels) and bicycles (2 wheels),
keeping inventory by counting seats and wheels. One day she counts 35
seats and 80 wheels. How many of each type of cycle are there?
Answer:
C.
Step-by-step explanation:
The seats are counted by 1 for both tricycles and bicycles, so t + b has to equal 35. The only answer choice that has t + b = 35 is C.
Suppose you are given a fair coin and an unfair.com, which
always comes out Head with probability 2/3. You chose one
at randoms of the Coins, tossed it twice and the outcomes were
both Heads. What is the probability that the com is fair
Answer:
9/25 or 36%
Step-by-step explanation:
The probability of selecting the fair coin is 1/2, and the probability of getting heads with the fair coin is 1/2.
P(fair) = 1/2, P(heads | fair) = 1/2
The probability of selecting the unfair coin is 1/2, and the probability of getting heads with the unfair coin is 2/3.
P(unfair) = 1/2, P(heads | unfair) = 2/3
P(fair and 2 heads) = 1/2 (1/2)²
P(fair and 2 heads) = 1/8
P(2 heads) = 1/2 (1/2)² + 1/2 (2/3)²
P(2 heads) = 1/8 + 2/9
P(2 heads) = 25/72
Therefore, the probability that you selected the fair coin, given that you flipped 2 heads, is:
P(fair | 2 heads) = (1/8) / (25/72)
P(fair | 2 heads) = (1/8) (72/25)
P(fair | 2 heads) = 9/25
The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than 0.003. The null hypothesis is
:__________
Answer:
Should not be rejected.
Step-by-step explanation: