Judy is planning a banquet-style dinner for her son Deon's
18th birthday. The equation C = 55g + 650 represents the
cost of the dinner.
Variables:
The C variable represents the choose your answer...
1.
2 The g variable represents the choose your answer...
Guests and Budget:
1. Each guest that attends costs type your answer... dollars.
2. The cost to rent the banquet venue is type your answer....
dollars.
3.
80 guests costs type your answer...
4. 105 guests costs
type your answer...
dollars.
dollars.
The parameters for the linear function in this problem are given as follows:
1. C is the total cost.
2. g is the number of guests.
3. Each guest costs $55.
4. The cost to rent the venue is of $650.
5. 80 guests cost $5,050.
6. 105 guests cost $6,425.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The function for this problem is given as follows:
C = 55g + 650.
Hence:
The slope of 55 represents the cost per guest.The intercept of 650 represents the cost to rent the venue.The costs are given as follows:
80 guests: C = 55 x 80 + 650 = $5,050.105 guests: C = 55 x 105 + 650 = $6,425.More can be learned about linear functions at https://brainly.com/question/24808124
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6. Imagine you are given the diameter of a circle and asked to find its volume. Circle the statement that describes what you should do. Draw a line through the incorrect statements.
Substitute the diameter value for r in the formula and calculate as usual.
Divide the diameter by 2 to find the radius, and then use the volume formula as usual.
Multiply the diameter by 2 to find the radius, and then use the volume formula as usual.
The formula for the volume of a circle is V = (4/3)πr³, where r is the radius obtained by dividing the diameter by 2.
First, it's important to understand what the diameter of a circle represents. The diameter is the distance across the circle, passing through the center. In contrast, the radius is the distance from the center of the circle to any point on the edge.
Now, let's consider the statements given:
Substitute the diameter value for r in the formula and calculate as usual.
This statement is incorrect because the formula for the volume of a circle involves the radius, not the diameter. If we substitute the diameter for the radius, we would end up with the wrong answer.
Divide the diameter by 2 to find the radius, and then use the volume formula as usual.
This statement is correct. Since the radius is half the diameter, dividing the diameter by 2 will give us the radius. We can then use the formula for the volume of a circle, which is V = (4/3)πr³, where r is the radius.
Multiply the diameter by 2 to find the radius, and then use the volume formula as usual.
This statement is incorrect. If we multiply the diameter by 2, we would end up with the diameter, not the radius. Again, we need to use the radius in the formula for the volume of a circle.
To summarize, when given the diameter of a circle and asked to find its volume, we should divide the diameter by 2 to find the radius and then use the volume formula as usual.
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What is tangent function.....???
PLS HELP
reposting this again pls help
Answer:
4/3x + y = -14/3
Step-by-step explanation:
Currently, the line we're given is in standard form, whose general form is
[tex]Ax+By=C[/tex]
We will need to find the slope of this line, since the slopes of perpendicular lines are negative reciprocals. This is shown by the formula:
[tex]m_{2}=-1/m_{1}[/tex], where m2 is the slope of the line we're trying to find and m1 is the slope of the line we're given.
Furthermore, we can find the slope of the line by converting the line from standard form to slope-intercept form, whose general form is
[tex]y=mx+b[/tex], where m is the slope and b is the y intercept:
[tex]3/4x-y=7/2\\-y=-3/4x+7/2\\y=3/4x-7/2[/tex]
Now, if we allow 3/4 to be m2 in the formula I provided, we can find the slope of the other line:
[tex]m_{2}=-1/(3/4)\\ m_{2}=-4/3[/tex]
Now, that we've found the slope of the new line, we can find the y-intercept by plugging in the slope and the point (-2, -2) for x and y in the slope-intercept form:
[tex]-2=-4/3(-2)+b\\-2=8/3+b\\-14/3=b[/tex]
Thus, the equation of the line passing through (-2, -2) and perpendicular to 3/4x - y = 7/2 is y = -4/3x - 14/3
In order to clear up confusion, we can convert this line to standard form so that it truly resembles the other line by simply isolating -14/3 (b in the slope-intercept form):
[tex]y=-4/3x-14/3\\4/3x+y=-14/3[/tex]
A flower garden is composed of 1/2 tulips and 3/10 of the tulips are pick.
How many pink tulips are in the garden? Type your answer like this: 1/2
There are 3/20 pink tulips
A flower garden is composed of 1/2 tulips
3/10 of this amount are the pink tulips
Therefore the number of pink tulips can be calculated as follows
= 1/2 × 3/10
= 3/20
Hence 3/20 of the tulips in the garden are pink
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solve the equation AND check your solution. Please show all of your work.
5/x^2-7x+12 - 2/x-3 = 5/x-4
EE 21-7 Jonick Company has sales of $740,000, and the break-even point in sales dollars is $547,600. Determine the company’s margin of safety as a percent of current sales.
Answer: Jonick Company's margin of safety as a percentage of current sales is 26.05%.
Step-by-step explanation: To find the margin of safety as a percentage of current sales, we need to first calculate the margin of safety, which is the amount of sales above the break-even point:
Margin of safety = Actual sales - Break-even point
We know that actual sales are $740,000 and the break-even point is $547,600, so:
Margin of safety = $740,000 - $547,600
Margin of safety = $192,400
Now that we know the margin of safety, we can calculate it as a percentage of current sales:
Margin of safety % = (Margin of safety / Actual sales) x 100
Plugging in the numbers, we get:
Margin of safety % = ($192,400 / $740,000) x 100
Margin of safety % = 26.05%
Therefore, Jonick Company's margin of safety as a percentage of current sales is 26.05%. This means that sales can drop by 26.05% before the company starts to incur losses.
three men visit a barber shop on their schedule, jack visits every 18 days, bryce visits every 8 days, and jadon visits every 9 days. If all visit on the same day, how many more days before they will visit on the same day again?
The three men will visit the barber shop on the same day again in 72 days.
Three men visit a barber shop on their schedule, jack visits every 18 days, bryce visits every 8 days, and jadon visits every 9 days
We have to find the how many more days before they will visit on the same day again
We want to find the least common multiple (LCM) of 18, 8, and 9.
First, we can find the prime factorization of each number:
18 = 2 × 3 × 3
8 = 2 × 2 × 2
9 = 3 × 3
Next, we can take the highest power of each prime factor that appears in any of the numbers:
2³ × 3² = 72
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what is the rational root theorem
Answer:
The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation
Step-by-step explanation:
A box has a base of 3 inches by 4 inches and a height of 12 inches. What is the length of the interior diagonal of the box, in inches?
The length of the interior diagonal of the box is .
Since, We know that;
In right triangles, the sum of the squares of the two legs a and b is equal to the square of the hypotenuse .
a² + b² = c²
Here, It is given that, a box has a base of 3 inches by 4 inches and a height of 12 inches.
We need to find the length of the interior diagonal of the box.
Now, we will find the length of the interior diagonal of the box by using the Pythagorean theorem.
So,
⇒ √3² + 4² + 12²
⇒ √9 + 16 + 144
⇒ √169
⇒ 13
Hence, 13 are the length of the interior diagonal of the box.
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The first four points in this table have been plotted on the scatter graph. Followers 20 240 270 90 130 Posts per month 40 160 170 110 180 Which of the points A-H shows where the last point should be plotted? Number of posts against number of followers on social media 200 A B XX .xx. C D Posts per month 100+ 0 X X 100 E F XX G H Followers 200 X 300
Since first four points in this table have been plotted on the scatter graph, the points that shows where the last point should be plotted is C.
What is an ordered pair?In Mathematics and Geometry, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
Based on the cartesian coordinate (grid) above, the coordinate points and quadrants should be identified as follows;
Point C ⇔ (130, 180) → quadrant I.
In conclusion, we can logically deduce that the each of the intervals on both the x-axis and y-axis is equal to 10 units.
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During 2022, Sam Reed purchased 350 shares of common stock issued by New Generation Electronics for $7800 including commission. Later in the same year, Sam sold the shares for $8400 after commission. Calculate the following. (Round all answers to two decimal places.)
1. Profit on this stock transaction: $
2. Percentage return on investment: %
The profit on this stock transaction is $600 and the percentage return on investment is 7.69%.
To calculate the profit on this stock transaction, we need to subtract the total cost from the total revenue:
Total cost = $7800
Total revenue = $8400
Profit = Total revenue - Total cost
Profit = $8400 - $7800
Profit = $600
Therefore, the profit on this stock transaction is $600.
To calculate the percentage return on investment
we need to divide the profit by the total cost and then multiply by 100 to get the percentage:
Percentage return on investment = (Profit / Total cost) x 100%
= ($600 / $7800) x 100%
= 0.0769 x 100%
= 7.69%
Therefore, the percentage return on investment is 7.69%.
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Will give Brainliest and extra points if correct!!!!
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
-2/3
-3/2
Answer:
The slope of a line can be calculated using the following formula:
```
m = (y2 - y1) / (x2 - x1)
```
where `m` is the slope, `y2` and `y1` are the y-coordinates of the two points, and `x2` and `x1` are the x-coordinates of the two points.
In this case, we have the following points:
```
(x1, y1) = (-3, -1)
(x2, y2) = (3, -10)
```
Plugging these values into the formula, we get the following:
```
m = (-10 - (-1)) / (3 - (-3)) = -9 / 6 = -3/2
```
Therefore, the slope of the line is **-3/2**. So the answer is (c).
Step-by-step explanation:
CNNBC recently reported that the mean annual cost of auto insurance is 1022 dollars. Assume the standard deviation is 272 dollars, and the cost is normally distributed. You take a simple random sample of 39 auto insurance policies. Round your answers to 4 decimal places. a. What is the distribution of X bar? X bar - N(
b. What is the distribution of x bar? x bar - N(
c. What is the probability that one randomly selected auto insurance is more than $990?
d. a simple random sample of 39 auto insurance policies, find the probability that the average cost is more than $990.
a. The distribution of X bar is x bar - N(1022, 43.45²).
b. The distribution of x bar is x bar - N(1022, 43.45²).
c. The probability that one randomly selected auto insurance is more than $990 is 0.1131.
d. a simple random sample of 39 auto insurance policies, the probability that the average cost is more than $990 is 0.887
a. The dispersion of X bar is ordinary with a cruel of 1022 dollars and a standard deviation of 272/√(39) dollars. In this way, X bar - N(1022, 43.45²).
b. The conveyance of x bar is additionally ordinary with the same cruel and standard deviation, so x bar - N(1022, 43.45²).
c. To discover the likelihood that one arbitrarily chosen auto protection is more than $990, able to utilize the z-score equation:
z = (990 - 1022) / 272/√(39) = -1.21. Looking up the comparing region beneath the standard typical dissemination bend, we discover a likelihood of 0.1131.
d. To discover the likelihood that the normally taken toll of a simple random test of 39 auto protections approaches is more than $990, we got to discover the z-score for this test cruel:
z = (990 - 1022) / 272/√(39) = -1.21. Employing a standard typical dispersion table, we discover that the likelihood of a z-score less than -1.21 is 0.1131. Hence, the likelihood of a test cruel more prominent than $990 is 1 - 0.1131 = 0.8869, or 0.887 (adjusted to 3 decimal places).
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of 100 athletes 31 like to run 65 like to walk ans 22 neither like to walk nor run .how many athletes like to both run or walk
There are 22 athletes who like both running and walking.
Let R be the set of athletes who like to run, and
let W be the set of athletes who like to walk.
Then we want to find the size of the intersection R ∩ W.
We know that there are 31 athletes who like to run,
65 athletes who like to walk, and
22 athletes who like neither.
Therefore, the total number of athletes who like to run or walk (or both) is:
31 + 65 - 22 = 74
This number includes athletes who like both running and walking, as well as athletes who like only running or only walking.
Now we can use the formula:
|A ∪ B| = |A| + |B| - |A ∩ B|
So |R ∪ W| = |R| + |W| - |R ∩ W|
Substituting the known values, we get:
74 = 31 + 65 - |R ∩ W|
Simplifying, we get:
|R ∩ W| = 22
Therefore, there are 22 athletes who like both running and walking.
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what is the approximate shortest distance between the treasure chest driftwood ?
A. 2.6 yards
B. 2.8 yards
C. 3.2 yards
D. 3.3 yards
The approximate shortest distance between the treasure chest and driftwood is 3.2 yards
The correct answer is an option (C)
From the attached figure of the coordinate plane,
the coordinates of the palm tree = (1, 2),
the coordinates of the treasure chest = (5, 8)
and the coordinates of the driftwood = (8, 7)
We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
We need to find the distance between the treasure chest and driftwood.
Let (x₁, y₁) = (5, 8)
and (x₂, y₂) = (8, 7)
Using distance formula, the approximate shortest distance between the treasure chest and driftwood would be,
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(7 - 8 )² + (8 - 5)²]
d = √[(-1)² + (3)²]
d = √[1 + 9]
d = √(10)
d = 3.1622
d ≈ 3.2 yards
This is the required distance between the treasure chest and the driftwood.
Therefore, the correct answer is an option (C)
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Find the complete question below.
What is the mean (rounded to the nearest hundredth) of
90.75
99.17
71.80
100.00
97.33
79.58
92.58
87.09
81.59
91.86
and 94.18
Solve the equation for y
X=4y-2
Answer:y=1/4x+1/2
Step-by-step explanation:
4y=x+2
y=1/4x+1/2
At noon, to begin a study, a petri dish had 2500 bacteria cells. Each hour since, the number of cells has increased by 11%.
Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
An exponential function showing the relationship between y and t is y = 2500(1.11ˣ)
To write an exponential function for this situation, we can start with the initial number of cells (2500) and then multiply by 1.11 for each hour that has passed. We can use the variable t to represent the number of hours since the start of the study, and the variable y to represent the number of bacteria cells. Then, our exponential function is:
y = 2500(1.11ˣ)
This function tells us that the number of bacteria cells (y) is equal to the initial number of cells (2500) multiplied by 1.11 raised to the power of the number of hours since the start of the study (x).
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Please help fast
Here is a new container without a top lid. How much popcorn
It can hold 200 unit³ of popcorn.
The amount of paper used is 150 unit².
We have,
b = 8 unit
h = 5 unit
l = 10 unit
So, Volume of Triangular prism
= 1/2 x b x h x l
= 1/2 x 8 x 5 x 10
= 40 x 5
= 200 unit³
and, the amount of paper used
= 6 x 5 + 8 x 5 + 10 x 5 + 1/2 x 6 x 10
= 30 + 40 + 50 x 30
= 150 unit²
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What is the arc length of arc STR 
The arc length SR is 6.98ft
What is arc length?Arc length is the distance between two points along a section of a curve. An arc is a cut out section of a circumference of a circle.
The arc angle = sector angle in the diagram
The length of an arc is expressed as;
l = tetha/360 × 2πr
where r is the radius and tetha is the angle between the two radii.
l = 100/360 × 2 × 4 × 3.14
l = 314 × 8/360
l = 2512/360
l = 6.98( nearest hundredth)
therefore the length of the arc is 6.98 ft
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simplify log_3+log_5+log_2 32
The simplified expression of log_3+log_5+log_2 32 is 5log_3(20) by properties of logarithms
Using the logarithmic identity that states log (a × b) = log a + log b
we can simplify the expression as follows:
log_3+log_5+log_2 32 = log_3(2⁵) + log_5(2⁵) + log_2(2⁵)
= 5log_3(2) + 5log_5(2) + 5log_2(2)
= 5(log_3(2) + log_5(2) + log_2(2))
using the property that log_b(a) + log_b(c) = log_b(a × c)
= 5(log_3(2 × 5× 2))
= 5(log_3(20))
Therefore, the simplified expression is 5log_3(20).
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HELP PLEASE will mark brainliest
Eighteen middle-aged women with platelet readings between 120,000 platelets per microliter and 150,000 platelets per microliter of blood were selected randomly from the population of similar female patients at a large local hospital. Nine of the 18 women were assigned randomly to group A and received a placebo. The other nine women were assigned to group B and received a new platelet drug. After four months, posttreatment platelet readings were taken for all 18 women and were compared with pretreatment readings. The reduction in platelet level (Pretreatment reading − Posttreatment reading) for each woman in the study is shown here.
Group A (placebo) increase (in platelets per microliter): 2,000, 5,000, 7,050, 10,125, 12,345, 17,350, 13,250, 12,200, 9,125
Group B (platelet drug) increase (platelets per microliter): 28,450, 23,438, 36,380, 12,450, 16,100, 21,350, 39,400, 41,000, 14,325
Create and interpret a 95% confidence interval for the difference in the placebo and the new drug.
The blood platelet count is an illustration of normal distribution,
Approximately 95% of the data lies within 2 standard deviations of the mean.
There are approximately 99.7% of women with platelet count between 65.2 and 431.8.
Given parameters are:
μ = 248.5
σ = 61.1
(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7,
Start by calculating the z-score, when x = 126.3 and x = 370.7
Z = x-μ / σ
Therefore,
Z = 126.3-248.5/61.1
Z = -2
Also,
Z = 370.7-248.5/61.1
Z = 2
The empirical rule states that:
Approximately 95% of the data lies within 2 standard deviations of the mean.
Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.
(b) The percentage with platelet count between 65.2 and 431.8
Start by calculating the z-score, when x = 65.2 and x = 431.8
Z = 65.2-248.5/61.1
Z = -3
And,
Z = 431.8-248.5/61.1
Z = 3
The empirical rule states that:
Approximately 99.7% of the data lies within 3 standard deviations of the mean.
Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8.
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6. Aisha's test scores are 74, 86, 67, and 76.
What score does she need on the last test in
order to average 80 on her tests?
Solve the equation:
10x^2 + x - 21 = 0
the cone and cylinder above have the same radius and height. the volume of the cone is 162 cubic inches what is the volume of the cylinder.
The volume of the cylinder is 623.17 cubic inches.
We have,
The volume of a cone is given by the formula V = (1/3)πr²h,
where r is the radius of the base and h is the height.
The volume of a cylinder is given by the formula V = πr²h,
where r is the radius of the base and h is the height.
Since the cone and cylinder have the same radius and height, we can set the equations for their volumes equal to each other:
(1/3)πr²h = πr²h
We can simplify this equation by multiplying both sides by 3:
πr²h = 3(1/3)πr²h
Simplifying further, we get:
πr²h = πr²(3h/3)
πr²h = πr²(3/1)
πr²h = 3πr²
Canceling the πr² from both sides, we get:
h = 3
We now know that the height of the cone and cylinder is 3.
We can use the given volume of the cone to solve for the radius:
V = (1/3)πr²h
162 = (1/3)πr²(3)
162 = πr²
r² = 162/π
r ≈ 6.4615
Now that we know the radius and height of the cylinder, we can use the formula for the volume of a cylinder to find its volume:
V = πr²h
V = π(6.4615)²(3)
V ≈ 623.17 cubic inches
Therefore,
The volume of the cylinder is 623.17 cubic inches.
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Julieta recorded the grade-level and instrument of everyone in the middle school School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar 12
Bass 3
Drums 10
Keyboard 5
Eighth Grade Students
Instrument # of Students
Guitar 4
Bass 3
Drums 6
Keyboard 2
Based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.
Note that the probability that a student chosen at random will play an instrument besides the guitar is 29/45.
How can you determine this?
To derive the probability, that a chosen at random will play an instrument other than guitar , we have to first find the sum total of all students who can play an instrument that is not a guitar.
From the table, we can se that this is:
3 + 10 + 5 = 18 on the 7th grade
while the 8th grade we have 3 + 6 + 2 = 11
18 + 11 = 29
So that total students in the middle school is
12 + 3 + 10 +5 + 4 + 3 + 6 + 2 = 45
hence the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form is 29/45
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4. Economists tend to classify a country as less developed if the country's average level of income is less
than
a. $9,500 per person
b. the average per-person-income of neighboring countries
c.
$3,040 per person
Od. a U.S. welfare recipient's income
5. Which of the following would not be considered a barrier to economic development?
a. high levels of political corruption
b. low population growth
Oc. low human capital
d. shortage of investment capital
Shortage of investment capital would not be considered a barrier to economic development.
All factors are considered for economic development except the following given .
Since Barriers to economic development are large population size, savings gap, large and inadequate capital accumulation, corruption, politics and poor governance, and the deficit in the foreign trade of goods and services.
Other factors lack of technological developments, climatic and weather disturbances, a decline of trade and commerce is considered to be one of the biggest drawbacks influencing this growth.
Institutional barriers like education, skill development, innovation, and access to equal opportunities.
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Find any Euler circuit on the graph above. Give your answer as a list of vertices, starting and ending at the same vertex. Example: ABCA
A Euler Circuit in the graph is ADGFACFIECBEHDBA.
What is a Euler circuit?When we describe an Euler circuit, we are describing a path in a diagram known as a graph that starts and ends at the same vertex.
While you can visit a vertex a number of time, you can only visits every edge of the graph once. This means that you cannot walk the path to a vertex more than once.
For the graph in the picture, ADGFACFIECBEHDBA is the Euler circuit. You can see that vertex like A was repeated three time, E, C and F, were repeated twice.
Can this graph be called Eulerian? No, because it does not fulfill the condition.
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f(x)=log(-5x+3) whats the domain
Answer: The domain of the function f(x) = log(-5x + 3) is the set of all real numbers x that make the argument of the logarithmic function positive.
Since the argument of the logarithmic function is -5x + 3, we must have:
-5x + 3 > 0
Solving for x, we get:
-5x > -3
x < 3/5
Therefore, the domain of the function f(x) = log(-5x + 3) is all real numbers x such that x < 3/5.
Step-by-step explanation: Hope this helps :D