The four possible times that car B could take to complete one lap are: 120 seconds, 90 seconds, 60 seconds, and 30 seconds.
The equation used to solve this problem is (150 - 30) = N * B, where N is the number of laps and B is the total number of seconds for car B to complete one lap. Therefore, the four possible times for car B to complete one lap are 120 seconds, 90 seconds, 60 seconds, and 30 seconds.
When solving for the total time, it is important to remember that the two cars start the race together and that their speeds remain constant. This means that the time it takes for car B to complete one lap must be a factor of 150 seconds. If car B takes a time that is not a factor of 150, then it will not be able to finish the race in 150 seconds.
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when lena arrived at her friend's birthday party there were 9 3/8 pizzas after lana and the other party guests had eaten pizza there was 2 5/8 pizzas left how much pizzas has eaten was eaten during the party
During the party, 6 3/4 pizzas were consumed.
To calculate the amount of pizza consumed during the party, subtract the remaining pizza from the original amount.
The original quantity of pizza was 9 3/8 pizzas, and the remaining quantity was 2 5/8 pizzas, resulting in:
6 3/4 pizzas = 9 3/8 - 2 5/8 pizzas
During the party, 6 3/4 pizzas were consumed.
This is the same as subtracting 2 and 5/8 from 9 and 3/8 and then reducing the result to the smallest fraction form.
The process of determining the difference between two fractions is known as fraction subtraction. To subtract two fractions, do the following:
Check that the fractions have a common denominator: If the denominators are not the same, you must find one. The least common multiple of two fractions' denominators is the smallest common denominator.
Subtract the numerators: Once the fractions have a common denominator, the numerators can be subtracted.
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Find the final value of an investment of £2500 that earns 0. 5% per month for the first six months but then depreciates at a rate of 0. 25% per month for the next 9 months
The final value of the investment is £2517.04.
Calculate the total amount earned over 6 months at 0.5% per month
At 0.5% per month, the investment of £2500 will earn £12.50 per month for six months.
Therefore, the total amount earned over 6 months is £12.50 x 6 = £75.
Determine the value of the investment after 6 months
The value of the investment after 6 months will be the initial investment plus the total amount earned over 6 months.
Therefore, the value of the investment after 6 months will be £2500 + £75 = £2575.
Determine the total amount lost over 9 months at 0.25% per month
At 0.25% per month, the investment of £2575 will lose £6.44 per month for nine months.
Therefore, the total amount lost over 9 months is £6.44 x 9 = £57.96.
Calculate the final value of the investment
The final value of the investment will be the value of the investment after 6 months minus the total amount lost over 9 months.
Therefore, the final value of the investment is £2575 - £57.96 = £2517.04.
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The final value of the investment would be £2491.97. To find the final value of the investment, we need to calculate the interest earned in the first 6 months.
When the rate was 0.5% per month, and then subtract the depreciation that occurred in the next 9 months when the rate was 0.25% per month.
First, calculate the interest earned in the first 6 months:
£2500 * (0.5/100) * 6 = £75Next, add this interest to the initial investment to get the value after 6 months:
£2500 + £75 = £2575Finally, calculate the depreciation in the next 9 months:
£2575 * (0.25/100) * 9 = £59.34Subtract the depreciation from the value after 6 months to get the final value:
£2575 - £59.34 = £2515.66 ≈ £2491.97.Learn more about Depreciation:
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Aviation A plane flies 500 kilometers with a bearing of 316° (clockwise from north) from Naples to Elgin. The plane then flies 720 kilometers from Elgin to Canton (see figure). Canton is due west of Naples. Find the bearing of the flight from Elgin to Canton.?
The bearing of the flight from Elgin to Canton is 231.23°. The solution has been obtained by using law of sines.
What is law of sines?
The ratio of the side length to the sine of the opposing angle is how the law of sines is typically defined. That is true for all three triangle sides, regardless of their sides and angles.
Let the angle formed at Canton be C.
The angle formed at Naples = 90 - 44 = 46°
Using law of sines,
⇒sin (46 ) / 720 = sin C / 500
⇒500 * sin ( 46 ) / 720 = sin C
⇒arcsin ( 500 * sin (46) / 720 ) = C
⇒C ≈ 38.77°
The bearing angle (clockwise from north) of the flight from Elgin to Canton is calculated as follows:
⇒270° - 38.77°
⇒231.23°
Hence, the bearing of the flight from Elgin to Canton is 231.23°.
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The figure of the question has been attached below.
Use the table to find the average rate of change over the interval [1,9]
Type your answer in the blank, with no spaces.
Answer:
1.6
Step-by-step explanation:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]
predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05
The number of people in a household with 2.5 pounds of waste are = 11
and we calculate this on the basis of question below
Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5
pound 0.27 ,1.41, 2.19 ,2.83 ,2.19 ,1.81 ,0.85, 3.05
people 2 3 3 6 4 2 1 5
so now the question is complete
in pound section we have to take care which value are greater than 2.5
so 2.83 and 3.05 is greater than 2.5 so here number of people who's home have greater than 2.5 pound of waste are 6+6=11
and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15
so final ans is 11.
so this question was in complete and this ans is valid for this Question only.
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Mrs. Thapa wishes to grow flowers on the hanging bowls at her home. She brings 16 hemispherical bowls from the market having internal diameter 21 cm and uniform thickness 0.5 cm each and fills the bowls with compost completely. (i) If 1 cm³ of compost weighs 2.31 gm, find the total weight of required compost (ii) If she covers outer curved surface of each bowl with polythene sheet, find the total amount of polythene.
Answer: (i) To find the total weight of compost required:
First, find the volume of one bowl: We can use the formula for the volume of a sphere to find the volume of one hemispherical bowl. The radius of the sphere is equal to half the diameter of the bowl, which is 21 cm / 2 = 10.5 cm. The volume of one hemispherical bowl is given by the formula (4/3)πr^3/2, where r is the radius. Plugging in the values, we get:
(4/3)π(10.5)^3/2 = (4/3) * (22/7) * (10.5)^3/2 = 532.8 cm³
Multiply by the number of bowls: To find the total volume of compost required, multiply the volume of one bowl by the number of bowls: 532.8 cm³ * 16 bowls = 8544.8 cm³
Multiply by the weight of compost per cm³: To find the total weight of compost, multiply the total volume by the weight of compost per cm³: 8544.8 cm³ * 2.31 gm/cm³ = 19824.9 gm = 19.82 kg
So, the total weight of compost required is 19.82 kg.
(ii) To find the amount of polythene required:
First, find the circumference of one bowl: The circumference of the circle is equal to 2π times the radius. So, the circumference of one bowl is 2π * 10.5 cm = 21π cm.
Find the length of the polythene: To find the length of the polythene, we need to find the length of the curved surface of the bowl. We can use the formula for the circumference of a circle, which is 2πr, where r is the radius. The curved surface of the bowl is half the circumference of the circle, so the length of the polythene is 21π cm / 2 = 10.5π cm.
Multiply by the number of bowls: To find the total length of the polythene, multiply the length of one bowl by the number of bowls: 10.5π cm * 16 bowls = 168π cm = 528 cm (rounded to the nearest cm)
So, the total amount of polythene required is 528 cm.
Step-by-step explanation:
f(x)=x2 g(x)=– 3x+1 Write your answer as a polynomial or a rational function in simplest form.
The simplest form of the polynomial is (x²)-3x+1.
A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.
In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.
The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.
This means that for any value of x, the polynomial will evaluate to the value given by the equation.
If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.
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4. The expression for sum of numbers a and b subtracted from their product is:
(a) a+b-ab
(b) ab-a+b
(c) ab - (a + b)
(d) ab+a-b
what’s the value of x
Check the picture below.
[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]
please help me I NEED HELP HELP
Bold = reason (in reasons 3 and 4 the formatting is odd and goes into the next line)
Statement Reason
1. line segment ʜᴏ is parallel to line segment EL, 1. Given
line segment HN intersects line segment OE at W,
the measure of HW is equal to the measure of NW*
2. angle HWO is congruent to angle NWE 2. Vertical angle theorem
3. angle OHW is congruent to angle WNE 3. alternate interior angles theorem
*4. line segment HW is congruent to line segment NW 4. definition of congruent
5. triangle HOW is congruent to triangle NEW 5. ASA postulate
*step 4 might not be needed; I don't know whether the "given" is saying that the measure of line segment HW is equal to the measure of line segment NW, or if it's saying that the two line segments are congruent
You might have to change the reasons for the statements, but this is the gist of how to prove it.
If you roll 2 dice, what is the exact binomial probability that the total number rolled will add up to 3 or less
The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.
What is the exact binomial probability?
The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;
The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).
The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;
The probability P = (1/36) + (2/36)
P = 3/36
P = 1/12
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Is there a relationship between the raises administrators at State University receive and their performance on the job? A faculty group wants to determine whether job rating (x) is a useful linear predictor of raise (y). Consequently, the group considered the straight-line regression model
y ^= β0 +β1x.
Using the method of least squares, the faculty group obtained the following prediction equation:
y ^= 14,000 - 2,000x
Interpret the estimated y-intercept of the line.
A) For an administrator who receives a rating of zero, we estimate his or her raise to be $14,000.
B) For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.
C) The base administrator raise at State University is $14,000.
D) There is no practical interpretation, since rating of 0 is nonsensical and outside the range of the sample data
Using the method of least squares, the faculty group obtained, the estimated y-intercept of the line is For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.
The relationship between the variables is calculated and represented as an equation in regression analysis. The dependent variable, independent variables, and line equation constants are all included in this equation. Variables may be related in ways that are linear, quadratic, polynomial, etc.
In this instance, the performance is the independent variable and the increase is the dependent variable. Simple linear regression is the name of the equation, which is shown as a straight-line equation.
Regression analysis makes use of the relationship between independent and dependent variables' relationship equation to forecast the values of the dependent variable y given the values of the independent variable x.
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referring to exercise 9, what is the probability that a person diagnosed as having cancer actually has the disease?
The probability that a patient who has been diagnosed with cancer truly has the illness 0.406
It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.
We wish to compute P(C | D) this time. Bayes rule is used in this process.
[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]
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In AMNO, the measure of 20=90°, MO = 8, ON = 15, and NM = 17. What ratio
represents the sine of /M?
Answer:
Step-by-step explanation:
To find the sine of angle M, we can use the sin function, which relates the sides of a right triangle to the sine of one of its angles. In this case, we have a right triangle with sides MO, NM, and ON, so we can use the following formula:
sin(M) = MO / ON
We know that MO = 8 and ON = 15, so we can calculate the sine of angle M as follows:
sin(M) = 8 / 15
So, the ratio that represents the sine of angle M is 8/15.
A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°.
If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.
How to find the metre the fire travelled?Distance = d = v * t
Let v represent speed of the fire .
Where :
t = time elapsed in seconds = 20 * 60 = 1200 seconds
Using the tangent function:
d / v = tan(6°) - tan(4°)
Simplify this expression using the identity:
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
Applying this to the above equation, we get:
d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))
Using a calculator to evaluate the tangent values
d / v = 26.64 / v
d = 26.64 * v
Substituting the value of t, we get:
d = 26.64 * v
= 26.64 * 1200
= 31,968 meters (rounded to the nearest meter)
Therefore the fire travelled 31,968 meters.
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The complete question is:
A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled m (to nearest metre)
Can you help me figure out the equation
The sine function for a specified range of angles is shown graphically in the sine graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is the sine function of that angle.
How is a sine graph drawn?To graph the sine function, we place the sine of each angle on the vertical y-axis and indicate the angles along the horizontal x axis.
The Sin Formula: What Is It?The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: hypotenuse/perpendicular = sin. sin(n+2) = sin for each n.
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Jack opens a savings account with $470. The account earns 4.4% annual interest compounded quarterly. Part A Enter a function to represent the balance A in the account after t years.
The function that represents the balance after t years is ,
FV = $470( 1.011)^4t
What is the function that represents the balance after t years?The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
here, we have,
given that,
P = Present value= $470.
R = interest rate = 4.4%/4 =
m = number of compounding =4
N = number of years = t
FV = $470( 1.011)^4t
Hence, The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t
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need help asap find x in the picture
Answer: 60
A triangle can only be 180 degrees so if one side is 60 so is the other two sides
When converting .000056 into scientific notation, the decimal point will move ___ spaces.
When converting 0.000056 into scientific notation, the decimal point will move 5 spaces to the right.
The resulting number in scientific notation would be 5.6 x 10^-5.
During a class election 28 people voted for candidate A. If there were 64 votes total, what is the ratio of votes for candidate B compared to candidate A?
In the number 455,025, which place value is 1000 times the value of the 2?
A. Hundreds
B. Thousands
C. Ten thousands
D. Hundred thousands
Answer:
Ten thousands
Step-by-step explanation:
20 x 1000 = 20,000 therefore, ten thousands
Factor this equation
Factorized form of polynomial is 3(−b²c+bc²−c²a+ca²−a²b+ab²).
What is factorization?This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions.
Given polynomial
(b - c)³ + (c - a)³ + (a - b)³
Factoring the polynomial
Calculation is attached below.
we get,
3(−b²c+bc²−c²a+ca²−a²b+ab²)
Hence,
3 and (−b²c+bc²−c²a+ca²−a²b+ab²) are factors of given polynomial.
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How many balls can one stack in a pile having a triangular base with 10 balls on each edge?
A. 220
B. 55
C. 550
D. 286
55 balls can be stacked in a pile with a triangular base having 10 balls on each edge. So, the answer is B. 55.
To determine the number of balls that can be stacked in a pile having a triangular base with 10 balls on each edge, we can use the formula for the triangular number sequence:
n(n+1) ÷ 2
where n is the number of balls on each edge of the triangular base. In this case, n = 10, so we have:
10(10+1) ÷ 2 = 55
So the answer is B. 55 balls can be stacked in a pile with a triangular base having 10 balls on each edge.
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At the beginning of the summer, Jenna had saved $166. To earn money over the summer, she is working part time at the local
community center. She will earn $23 per day of work. If x represents the number of days she works, which of the following
equations represents how much money she will have, including her savings?
Jenna will have total money, y= 166 + 23x.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Jenna had saved $166.
She will earn $23 per day of work
If x represents the number of days she works the she will earn
= 23x
So, She will have total
= 166+ 23x
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14 units to the right of-2 of a number line
Answer: 11 (Or I'm wrong)
Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
A pop quiz contains five questions: two
multiple choice questions with four options
each and three true-false questions. If Brad
randomly guesses, what is the probability
that he gets all five answers correct?
The probability that Brad gets all five answers correct is 1/128.
What is the probability that he gets all five answers correct?From the question, we have the following parameters that can be used in our computation:
true of false = 3
Multichoice = 2
For each multiple choice question, Brad has a 1/4 chance of getting the correct answer by guessing.For each true-false question, Brad has a 1/2 chance of getting the correct answer by guessing.So, the probability that Brad gets all five answers correct is (1/4)^2 * (1/2)^3 = 1/128.
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ASAP
A boat starts at point A. It travels a distance of 7 km on a bearing of 135° to point B. From B it travels 12 km on a bearing of 250° to point C. Using a scale of 1 cm: 1 km, draw a diagram to show these bearings and journeys.
The diagram that represent the distance and the journeys is added as an attachment
How to make the diagramFrom the question, we have the following parameters that can be used in our computation:
Initial point = ADistance of 7 km on a bearing of 135° to point B.From B it, travels 12 km on a bearing of 250° to point CUsing the above as a guide, we have the following:
Next, we create the diagram (see attachment)
The attached figure represents the required diagram
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The cost of producing t units is C = 3t2 + 8t, and the revenue generated from sales is R = 4t2 + t. Determine the number
of units to be sold in order to generate a profit.
A) t>0
B) t>9
D
t>7
t> 8
On solving the provided question, we can say that the equation are cost of producing t units is C = 3t2 + 8t, revenue generated from sales is R = 4t2 + t if t>0 then C = 43t and is t>7 then C =D = 32t
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation are
cost of producing t units is C = 3t2 + 8t,
revenue generated from sales is R = 4t2 + t
if t>0
then C = 43t
and is t>7
then C =D = 32t
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Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation ?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 20
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one third comma 0
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 40
A graph which represents this situation include the following: B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.What is y-intercept?In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this equation can be calculated as follows;
y = 30 + 10x
y = 30 + 10(0)
y = 30
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For summer Nicole charges a flat fee of $5, plus $20 per hour.
1. Write an equation for babysitting.
2. What is the slope
3.what does the slope represent
4.what is the y-intercept
5.what does the y-intercept represent
Answer:
The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.
The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).
The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.
The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.
The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.
Step-by-step explanation: