Answer:
The expected value of X is 13.4.
Step-by-step explanation:
For each boox any time a ball is placed, there are only two possible outcomes. Either the ball is put into the box, or it is not. The boxes are independent. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
200 balls placed in boxes:
This means that [tex]n = 200[/tex]
For each box, the ball has 1/100 probability of being put there:
This means that [tex]p = \frac{1}{100} = 0.01[/tex]
The probability of a box being empty:
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.01)^{0}.(0.99)^{200} = 0.1340[/tex]
Let X denote the number of empty boxes at the end. What is the expected value of X?
Each box has a 0.1340 probability of being empty at the end.
There are 100 boxes.
So
0.1340*100 = 13.4
The expected value of X is 13.4.
In England,mass is measured in units called stones, one pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds does the cat weigh?
Answer:
Read below for the answer
Step-by-step explanation:
1 pound = 1/14 stone
[multiply by 14]
14 pounds = 1 stone
[multiply by 3]
42 pounds = 3 stone
[divide by 4]
42 / 4 pounds = 3/4 stone
[simplify]
21 /2 = 10.5 pounds = 3/4 stone
Answer: i dont now
Step-by-step explanation:
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample is $105. The population standard deviation is known to be $16. Calculate the value of the test statistic that you would use to test the hypothesis that the average room price is significantly different from $108.50. (Round your answer to two decimals.)
Answer:
9.76
Step-by-step explanation:
I am very smart
Triangle DEF is congruent to TriangleGHJ by the SSS theorem. Which rigid transformation is required to map TriangleDEF onto TriangleGHJ?
Answer:
Rotation
Step-by-step explanation:
Given:
Triangle DEF is congruent to Triangle GHJ by the SSS theorem
To find: transformation required to map Triangle DEF onto Triangle GHJ
Solution:
Two figures are said to be congruent if they overlap each other.
Two polygons are said to be congruent if they have same size and shape.
A rotation is a transformation that turns a figure about the center of rotation.
Rotation transformation is required to map Triangle DEF onto Triangle GHJ
Answer:
translation
Step-by-step explanation:
Estimate the square root to the nearest tenth.
0.39
The square root is approximately
Answer: 0.36 = 0.6
Step-by-step explanation:
What is the sum of a regular octagon?
A.) 540
B.) 360
C.) 1080
D.) 900
Answer:
The answer is C.
Step-by-step explanation:
(n-2) * 180
(8-2) * 180
(6) * 180
1080
What is the constant of proportionality in the equation? y = 5 x
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
The toxicity level of a lake is found by dividing the amount of dissolved toxins the lake water currently has per liter by the maximum safe amount of dissolved toxins that the water can hold per liter and then converting it to a percentage. If the river currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe amount of dissolved toxins is 1.04 milligrams per liter, what is the toxicity level of the lake water, to the nearest percentage? A. 86% B. 84% C. 83% D. 80% E. 79%
The toxicity level of the lake water is calculated by dividing the current level of toxins (0.86 mg per liter) by the maximum safe level (1.04 mg per liter) and then converting to a percentage, which results in approximately 83%.
Explanation:To determine the toxicity level of lake water, we need to divide the amount of dissolved toxins per liter by the maximum safe amount and convert it to a percentage.
Given that the lake currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe level is 1.04 milligrams per liter, we calculate the toxicity level using the following steps:
Therefore, the correct answer is C. 83%.
Maria has promised her neighbor to plant spring flowers in his garden. If the area is 250 square feet and she has completed 1/3 of it, how many square feet does she have left to plant flowers
Answer:
She still has 166.67 square feet does she have left to plant flowers
Step-by-step explanation:
The sum of total area planted, and the remaining area left to plant, is 100% = decimal 1.
She has planted 1/3 of the area. So
[tex]\frac{1}{3} + p = 1[/tex]
[tex]p = 1 - \frac{1}{3}[/tex]
[tex]p = \frac{3-1}{3}[/tex]
[tex]p = \frac{2}{3}[/tex]
So she still has to paint two thirds of the area.
The area is of 250 square feet.
2/3 of 250
[tex]250\frac{2}{3} = 166.67[/tex]
She still has 166.67 square feet does she have left to plant flowers
helphelphelphelphelphelphelphelphelphelphelp
The X-intercept (-250, 0)
The Y-intercept (0, 100)
These are the Y and X intercepts because this the first time the line intercepts. I hope I explained it well...
Have a good day!
The perimeter of a square is represented by 4x − 16. What is the length of a side of this square?
Answer:
(x-4)
Step-by-step explanation:
Since a square has 4 equal sides, the perimeter of a square is 4 times one of the sides (which is equal to adding all the sides together). So:
Perimeter = 4(a side) = 4x-16
a side = (4x-16)/4 = (x-4)
The length of a side of a square with perimeter 4x - 16 is x - 4.
perimeter of a square is represented as follows:
perimeter = 4lwhere
l = length
Therefore,
4l = 4x - 16
divide both sides by 4
l = x - 4
The length = x - 4
Note a square have all its side equal to each other.
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Construct a 90% confidence interval of the population proportion using the given information.
X= 175
n= 250
Tbe confidence interval marked the range of values for which the true population mean is estimated to be given a certain level of confidence. Hence, the confidence interval is (0.6523, 0.7477)
Since the sample size is large enough, we use the the Z distributuon :
Confidence interval is defined thus :
Mean ± margin of errorMargin of Error :
[tex] Z = Z* \sqrt{\frac{pq}{n}}[/tex] Mean, p = x/n = 175/250 = 0.7q = 1 - 0.7 = 0.3Zcritical at 90% = Z* = 1.645Hence,
Margin of Error = [tex] 1.645 \sqrt{\frac{0.7\times 0.3 }{250}} = 0.0477[/tex]Lower confidence boundary = 0.7 - 0.0290 = 0.6523
Upper confidence boundary = 0.7 + 0.0290 = 0.7477
Therefore, the confidence interval is (0.6523, 0.7477)
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To construct a 90% confidence interval for the population proportion, calculate the sample proportion, the standard error, and use the confidence interval formula.
Explanation:Step 1:
Calculate the sample proportion, which is X divided by n. In this case, it is 175 divided by 250, which gives us 0.7.
Step 2:
Calculate the standard error, which is the square root of (p*(1-p))/n, where p is the sample proportion. In this case, it is the square root of (0.7*(1-0.7))/250, which is approximately 0.0266.
Step 3:
Construct the confidence interval using the formula p ± z*(standard error), where p is the sample proportion and z is the z-score corresponding to the desired level of confidence. For a 90% confidence interval, the z-score is approximately 1.645. Therefore, the 90% confidence interval is 0.7 ± 1.645*0.0266, which becomes (0.658, 0.742).
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A pair of sunglasses is priced at $42.95. They are put on sale at 27% off the original price. Shane estimates the discounted price of the sunglasses to be around $36. Is this a reasonable estimate?
Answer:
no,
Step-by-step explanation:
1/4 of 40 is 10
40-10=30
It depends. The actual price would be $31.35. So it is not really reasonable since it is closer to the original price than it is to the discounted one... Just use your best judgement...
Can someone answer this plz ?
Two insurance policies, G and H, can each only submit one claim in a given month. For insurance policy G, there is a 45% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 5. For insurance policy H, there is a 35% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 9. For both policies, there is a deductible of 2 and they only reimburse 80% of the amount that exceeds the deductible. Calculate the difference between the expected reimbursements of the two policies for a given month.
To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
Explanation:To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
For policy G, there is a 45% chance of no claims, in which case the reimbursement is 0. If a claim is made, the loss amount follows an exponential distribution with a mean of 5. We need to find the expected value of the reimbursement in this case. Let X be a random variable representing the loss amount. The expected reimbursement for policy G is then given by:
Expected Reimbursement for Policy G = 0.45(0) + 0.55(0.8)(E(X) - 2)
Similarly, for policy H, there is a 35% chance of no claims and a 65% chance of a claim with a loss amount following an exponential distribution with a mean of 9. Let Y be a random variable representing the loss amount. The expected reimbursement for policy H is:
Expected Reimbursement for Policy H = 0.35(0) + 0.65(0.8)(E(Y) - 2)
To find the difference between the expected reimbursements, we subtract the expected reimbursement for policy H from the expected reimbursement for policy G:
Difference = Expected Reimbursement for Policy G - Expected Reimbursement for Policy H
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Roberta grows pea plants, some in shade and some in sun. She picks 8 plants of each type at random and records the heights. Shade plant heights (in.) 7 12 12 8 9 8 8 8 Sun plant heights (in.) 19 24 20 23 24 23 23 20
Answer: 2.6
Step-by-step explanation:
Step 1: Calculate the mean of Shade's plant heights.
= 7+12+12+8+9+8+8+8/8
= 72/8
=9
Step 2: Calculate the range of Shade's plant heights. Range is highest minus lowest number. This will be:
12 - 7 = 5
Step 3: Calculate the mean of Sun plant heights.
19+24+20+23+24+23+23+20/8
= 176/8
= 22
Step 4: Find the range of Sun plants height.
= 24 - 19 = 5
Step 5: Find the difference of means
= 22 - 9
= 13
Step 6: Divide the difference of means by the range.
= 13 ÷ 5
= 2.6
The difference in mean and range are 13 and 0 respectively.
We are to find the difference in mean and range of the plant height.
Given the Shade plant heights expressed as 7 12 12 8 9 8 8 8
Mean = 7 + 12+12+ 8+ 9+ 8+ 8+ 8
Mean = 72
Sample size = 8
Mean of shade heights plant = 72/8 = 9Range = Highest value - Lowest value
Range = 21 - 7
Range = 5Given the Sun plant heights expressed as 19 24 20 23 24 23 23 20
Mean = 19+ 24+ 20+ 23+ 24+ 23+ 23+ 20
Mean = 176
Sample size = 8
Mean of shade heights plant = 176/8 = 22Range = Highest value - Lowest value
Range = 24 - 19
Range = 5Evaluate the difference in mean
Difference in mean = 22 - 9
Difference in mean = 13
Evaluate the difference in range
Difference in range = 5 - 5
Difference in range = 0
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Solve the inequality |4x+2|<26
Answer:
-7<x<6
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variables
Mark me brainliest please!
kevin built a deck in his backyard. The length of the deck was 5x+1 units and the width of the deck was 4x-1 units. Write and simplify an expression to repersent the perimeter of kevins deck.
Answer:
Perimeter =
[tex]2(length + width) \\ 2(5x + 1 + 4x - 1) \\ 2(5x + 4x + 1 - 1) \\ 2(9x ) \\ 9 \times 2 \\ = 18[/tex]
In ΔFGH, f = 37 cm, ∠F=28° and ∠G=124°. Find the length of g, to the nearest 10th of a centimeter.
Answer:
65.3 cm
Step-by-step explanation:
The law of sines can be used for this.
g/sin(G) = f/sin(F)
g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)
The length of g is about 65.3 cm.
A circle with a diameter of 10 cm and a central angle of 30° is shown. What is the length, to the nearest tenth, of the arc formed by the 30° angle?
9514 1404 393
Answer:
2.6 cm
Step-by-step explanation:
The full circle is 360°, so an arc of 30° will have 30/360 = 1/12 of the measure of the circumference of the circle.
arc length = πd/12 = π(10/12) ≈ 2.6 cm
Which expression is the greatest common factor of the two addends in 18x + 30x2?
Step-by-step explanation:
I think common factors are
18 = 1 2 3 6 9 18
30 = 1 2 3 10 15 30
So highest common factor is 3
18x + 30x2
3x (6 + 10x)
Answer:
The answer is 6x
Step-by-step explanation:
A farmer owns a 100 acre farm and plans to plant at most three crops. The seed for crops A,B, and C costs $40, $20, and $30 per acre, respectively. A maximum of $3200 can be spent on seed. Crops A,B, and C require 1,2, and 1 workdays per acre, respectively, and there are maximum of 160 workdays available. If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C, how many acres of each crop should be planted to maximize profit
The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
Given that,
A farmer owns a 100-acre farm and plans to plant at most three crops. The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
A maximum of $3200 can be spent on the seed. Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
We have to find,
How many acres of each crop should be planted to maximize profit?
According to the question,
The farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
[tex]\rm P = 100A + 300B + 200C[/tex]
The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
And A maximum of $3200 can be spent on the seed.
[tex]\rm 40A + 20B + 30C \leq 3200[/tex]
Then, Sum of seed for crops costs = area of the farm
[tex]\rm A + B + C \leq 100[/tex]
Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
[tex]\rm A + 2B + C = 160[/tex]
Solving all the equations,
From equation 3,
[tex]\rm A = 100-B-C[/tex]
Substitute the value of A in equation 4,
[tex]\rm 100 - B - C+ 2B + C = 160\\\\100 + B = 160 \\\\B = 160 - 100\\\\B = 60[/tex]
Put B = 60 in the equation,
[tex]\rm A = 100-B-C\\\\A = 100-60-C\\\\A = 40-C[/tex]
Substitute the value of A in equation 2,
[tex]\rm 40(40-C) + 20\times 60 + 30C = 3200\\\\1600 - 40C + 1200 + 30C = 3200\\\\-10C + 2800 = 3200\\\\-10C = 3200-2800\\\\-10C = 400\\\\C = \dfrac{400}{-10}\\\\C = -40[/tex]
The area can not be negative then the value of C is +40.
And the value of A is,
[tex]A + B + C = 100\\\\A = 100 - 60 -40\\\\A = 100-100\\\\A = 0[/tex]
Then, Maximize profit is,
[tex]\rm P = 100A + 300B + 200C\\\\\rm P = 100(0) + 300(60) + 200(40)\\\\P =0+18000+8000\\\\P = 26000[/tex]
Hence, The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 80% salt. She wants to obtain 130 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?
Answer:
26 ounces of 55% solution104 ounces of 80% solutionStep-by-step explanation:
Let x represent the quantity of 80% solution. Then 130-x is the amount of 55% solution. The total amount of salt in the mix is ...
0.80x +0.55(130 -x) = 0.75·130
0.25x = 0.20·130 . . . . . . . subtract 0.55(130)
x = 0.20/0.25(130) = 104
130-x = 26
She should use 26 ounces of 55% solution and 104 ounces of 80% solution.
Final answer:
The scientist would need to use 26 ounces of Solution A and 104 ounces of Solution B to create 130 ounces of a 75% salt mixture.
Explanation:
To solve the problem of mixing two salt solutions of different concentrations to achieve a specific final concentration, we can set up a system of equations based on the amounts of salt and total solution. We know that Solution A is 55% salt and Solution B is 80% salt, and we want 130 ounces of a 75% salt mixture.
Let x be the amount of Solution A and y be the amount of Solution B. The first equation is based on the total amount of solution, and it is:
x + y = 130 ... (1)
The second equation is based on the amount of salt in the final mixture:
0.55x + 0.80y = 0.75(130) ... (2)
From equation (1), we can express y as y = 130 - x. Substitute this into equation (2) and solve for x:
0.55x + 0.80(130 - x) = 97.5
0.55x + 104 - 0.80x = 97.5
-0.25x = -6.5
x = 26 ounces (Solution A)
Substitute x back into equation (1) to find y:
x + y = 130
26 + y = 130
y = 104 ounces (Solution B)
So, to obtain 130 ounces of a 75% salt mixture, the scientist would use 26 ounces of Solution A and 104 ounces of Solution B.
A fifth grade class sets up 418 chairs for a graduation ceremony. Each row has 22 chairs.
How many rows of chairs does the class set up? Enter your answer in the box.
Answer:
19
Step-by-step explanation: all you have to do is divide 418 by 22, and u can use long division...Final answer:
The class set up 19 full rows of chairs for the graduation ceremony by dividing the total number of chairs, 418, by the number of chairs in each row, 22.
Explanation:
To determine how many rows of chairs the fifth grade class set up for a graduation ceremony, we divide the total number of chairs by the number of chairs in each row. They have set up a total of 418 chairs, and each row contains 22 chairs.
Divide the total number of chairs (418) by the number of chairs per row (22).
Perform the division: 418 ÷ 22 = 19.
The result is that they set up 19 full rows of chairs.
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should you run before jumping into the water in order to save the child? Round your answer to three decimal places.
The distance the lifeguard should run along the shore before jumping into the water, can be determined by minimizing the function of time, that is, the time it takes for the lifeguard to reach the child. This problem can be solved either by using calculus or the graphical method with a graphing tool.
Explanation:This problem can be solved using optimization of functions, which is a part of calculus. We would let 'x' be the distance along the shore that the lifeguard runs before jumping into the water. Then the total time taken to reach the child is given by the formula T = x/4 + sqrt((60-x)² + 40²)/1.1. We are looking for the minimum of T as a function of x. However, it would require knowledge of calculus to solve this problem. As an alternative, one can also use a graphing calculator or similar tool to graph the time function and then determine the minimum on the graph.
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Final answer:
To save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
Explanation:
To determine how far along the shore you should run before jumping into the water to save the child, you need to find the time it takes to run along the shore and then swim directly to the child.
First, calculate the time taken to run along the shore using the formula: time = distance / speed. In this case, the distance is 60 meters and the speed is 4 meters per second. So, the time taken to run along the shore is 60 / 4 = 15 seconds.
Next, calculate the time taken to swim directly to the child using the formula: time = distance / speed. In this case, the distance is 40 meters and the speed is 1.1 meters per second.
So, the time taken to swim directly to the child is 40 / 1.1 ≈ 36.364 seconds.
Therefore, the total time taken to save the child is the sum of the time taken to run along the shore and the time taken to swim directly to the child.
So, in order to save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
the histogram represents the number of gallons of gasoline that driver purchased weekly . how many driver represented by the histogram
Answer:
6
Step-by-step explanation:
I did it
Lindsay Electronics, a small manufacturer of electronic research equipment, has approximately 7 comma 000 items in its inventory and has hired Joan Blasco-Paul to manage its inventory. Joan has determined that 10% of the items in inventory are A items, 35% are B items, and 55% are C items. She would like to set up a system in which all A items are counted monthly (every 20 working days), all B items are counted quarterly (every 60 working days), and all C items are counted semiannually (every 120 working days). How many items need to be counted each day?
Answer:
108
Step-by-step explanation:
As per the given question the solution of items need to be counted each day is provided below:-
Here to reach the items needs to be counted each day first we need to find out the number of items which are as follows:-
[tex]For\ item\ A\ = Inventory\ A\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 10\% \times \ 7,000[/tex]
[tex]= 0.1 \times \ 7,000[/tex]
[tex]= \ 700[/tex]
[tex]For\ item\ B\ = Inventory\ B\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 35\% \times \ 7,000[/tex]
[tex]= 0.35 \times\ 7,000[/tex]
[tex]= \ 2,450[/tex]
[tex]For\ item\ C\ = Inventory\ C\ Percentage \times \ Number\ of\ inventory\ items[/tex]
[tex]= 55\% \times \ 7,000[/tex]
[tex]= 0.55 \times\ 7,000[/tex]
[tex]= 3,850[/tex]
Now, we will find out the items to be counted each day
[tex]Items\ to\ be\ counted\ each\ day\ = \frac{Item\ A}{Working\ Days\ of\ A} \ + \frac{Item\ B}{Working\ Days\ of\ B} \ + \frac{Item\ C}{Working\ Days\ of\ C}[/tex]
[tex]= \frac{700}{20} \ + \frac{2,450}{60}\ + \frac{3,850}{120}[/tex]
[tex]= \ 35\ + \ 40.83\ + \ 32.08[/tex]
[tex]= \ 107.92[/tex]
or
= 108
So, we have calculated the items to be counted for each day by using the above formula.
Given:
f(x) = x2 - 6x + 13
What is f (4)?
Answer:
5
Step-by-step explanation:
f(x) = x^2 -6x+13
Let x=4
f (4) = 4^2 -6(4) +13
= 16 -24 +13
= 5
The value of f(4) for the function f(x) = x^2 - 6x + 13 is 5.
Explanation:In order to find f(4) for the function f(x) = x2 - 6x + 13, we replace each x in the equation with 4. So, f(4) = (4)2 - 6(4) + 13. Squaring 4 gives us 16, and 6 times 4 gives us 24.
Therefore, our equation is now f(4) = 16 - 24 + 13. Solving for f(4), we subtract 24 from 16 to get -8, and then add 13 to get 5.
Thus, f(4) = 5.
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Determine whether each of the following LTIC systems is i) BIBO stable, ii) asymptotically stable, and iii) marginally stable. Explain why or why not. (a) d 3y dt3 − 3 dy dt − 2y(t) = df dt − f(t) (b) d 3y dt3 − 3 dy dt − 2y(t) = df dt − 2f(t) (c) d 2y dt2 + 3 dy dt + 2y(t) = df dt + f(t) (d) d 2y dt2 + 2 dy dt + 2y(t) = f(t) (e) d 2y dt2 + 2y(t) = f(t)
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D
Step-by-step explanation:
This function resembles that of the absolute value function, never going into the negative y values. Hope this helps!
What’s the first answer I’m it’s very easy I just need help thanks
Answer:121
Step-by-step explanation:
11 times 11.
Answer:
[tex]121[/tex]
Step-by-step explanation:
[tex]11^{2} \\ write \: the \: exponentiation \: as \\ multiplication. \\ \\ 11 \times 11 \\ multiply \\ \\ 121[/tex]