Answer:
standard deviation=4.47
Step-by-step explanation:
We have to find the standard deviation of the data set:
13 17 9 21
Now we calculate the mean of the data .
We know that mean is the average of the data values and is calculated as:
[tex]Mean=\dfrac{13+17+9+21}{4}\\ \\Mean=\dfrac{60}{4}\\\\Mean=15[/tex]
Now we find the difference of each data point from the mean as:
Deviation:
13-15=-2
17-15=2
9-15=-6
21-15=6
Now we have to square the above deviations we obtain:
4 4 36 36
now we calculate the mean of the above sets:
[tex]variance=\dfrac{4+4+36+36}{4}\\ \\Variance=\dfrac{80}{4}\\\\Variance=20[/tex]
now standard deviation is the positive square root of variance
so, standard deviation=√(20)=4.47
Final answer:
To find the standard deviation for Omar's work hours, we first calculate the mean of the data, then compute the squared differences from the mean, sum these, divide by the sample size minus one, and take the square root of this result, which is approximately 5.16 hours.
Explanation:
To calculate the standard deviation for Omar's recorded work hours: 13, 17, 9, 21, we follow these steps:
First find the mean (average) of the sample. Mean = (13 + 17 + 9 + 21) / 4 = 60 / 4 = 15 hours.
Next, subtract the mean from each data point and square the result:[tex](13-15)^2[/tex] = 4,[tex](17-15)^2[/tex] = 4, [tex](9-15)^2[/tex]= 36,[tex](21-15)^2[/tex] = 36.
Now, find the sum of these squared differences: 4 + 4 + 36 + 36 = 80.
Since this is a sample (not the full population), we divide by the sample size minus 1, which is 3: 80 / 3 ≈ 26.67.
Finally, take the square root of this quotient to find the standard deviation: √26.67 ≈ 5.16 hours.
Therefore, the standard deviation for the data is roughly 5.16 hours.
Suppose you want to cut 1515 identical boards of length 33 feet. the procedure is to measure and cut the first board, then use the first board to measure and cut the second board, then use the second board to measure and cut the third board, and so on. answer parts a and
b.
a. what are the possible lengths of the 1515th board if, each time you cut a board, there is a maximum error of plus or minus±one third 1 3 inch? the board could be as short as nothing inches or as long as nothing inches. (simplify your answer. type integers or decimals rounded to the nearest hundredth as needed.)
The lengths of the 1515th board could range from 32.51 feet to 33.49 feet, considering the maximum measurement error of plus or minus one third inch per cut.
Explanation:To find the possible lengths of the 1515th board, we need to consider the maximum error in each board measurement. Each time a board is cut, there is a maximum error of plus or minus one third inch. So, the 1515th board could be as short as 33 feet minus 1515 multiplied by one third inch, and as long as 33 feet plus 1515 multiplied by one third inch. Simplifying this, the 1515th board could be as short as 32.51 feet and as long as 33.49 feet.
What is the markup for a pair of hiking boots that the store buys for $80 each if the markup rate is 15%?
Final answer:
To find the markup on a pair of hiking boots with a cost of $80 and a 15% markup rate, multiply the cost by 0.15 to get a $12 markup. The selling price would then be $80 + $12, totaling $92.
Explanation:
To calculate the markup for a pair of hiking boots that the store buys for $80 with a markup rate of 15%, first convert the percentage to a decimal by dividing by 100.
Markup rate as a decimal: 0.15
Next, multiply the cost price by the decimal.
Markup amount = Cost price × Markup rate
Markup amount = $80 × 0.15
Markup amount = $12
So, the markup on the hiking boots is $12. To find the selling price, you add the markup to the cost price:
Selling price = Cost price + Markup amount
Selling price = $80 + $12
Selling price = $92
The store would sell the hiking boots for $92.
Two angles are supplementary. One angle measures 50 degrees more than the other angle. Find the measure of the larger angle?
Final answer:
Using algebra, the larger of two supplementary angles, where one is 50 degrees more than the other, is found to be 115 degrees.
Explanation:
To solve for the measure of the larger angle in a pair of supplementary angles, where one angle measures 50 degrees more than the other, we can use algebra. If we let x represent the measure of the smaller angle, then the larger angle will be x + 50 degrees. Since supplementary angles sum up to 180 degrees, we can set up the equation x + (x+50) = 180.
Solving this equation:
Combine like terms: 2x + 50 = 180
Subtract 50 from both sides: 2x = 130
Divide by 2: x = 65
Since x is the measure of the smaller angle, the larger angle measures x + 50, which is 65 + 50 = 115 degrees.
Therefore, the measure of the larger angle is 115 degrees.
One of the events at the circus starred Gabriella the Human Cannonball. On Saturday she performed in four shows. Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters. What was the total distance Gabriella flew that day?
The total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters is,
⇒ 51.44 meters
The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that,
On Saturday she performed in four shows.
Shot from a cannon, her distances measured 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters.
Now, To find the total distance Gabriella flew that day with distances measuring 8.05 meters, 17.71 meters, 14.38 meters, and 19.35 meters we can add all the distances,
⇒ 8.05 m + 17.71 m + 14.38 m + 19.35 m
⇒ 51.44 meters
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What is the equation of the line that goes through (3,11) and is parallel to the line 2x-y=5
What percentage of the participants lie within one standard deviation unit of the mean (i.e., on both sides of the mean) in a normal distribution?
What is 45122 to the nearest ten thousand
Solve the equation. 0.7+y=−1.34
Just subtract 0.7 from 1.34
y = -2.04
Hope this help
Answer: The required solution is x = -2.04.
Step-by-step explanation: We are given to solve the following linear equation :
[tex]0.7+y=-1.34~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation, we must find the value of the unknown variable y.
The solution of equation (i) is as follows :
[tex]0.7+y=1.34\\\\\Rightarrow y=-1.34-0.7\\\\\Rightarrow y=-2.04.[/tex]
Thus, the required solution is x = -2.04.
multiply 5 × 381 using place value and expanded form
The distance between Maggie’s home and her school is 5,280 yards. (Hint: 1 mile = 1,760 yards.)
Answer:
The answer is 10,560 yards and 6 miles. The 5,280 yards is just from her home to the school. So you multiply it by 2 and divide by 1760.
Step-by-step explanation:
By showing your work what is the answer to 0.96÷0.144=
Answer:
Recognize that both 0.96 and 0.144 are divisible by 12:
(0.96/12) / (0.144/12) = 0.08 / 0.012. This reduces to 0.02 / 0.003, or
20/3 or approx. 6.666.
You could also begin by eliminating the decimal fractions. Mult. 0.96 and 0.144 each by 1000 results in 960/144.
Since both 960 and 144 can be divided evenly by 24, we get 40 and 6.
40/6 = 20/3, or approx. 6.666, as before.
Step-by-step explanation:
(2.03)
Below are the steps to solve an equation:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
Which of the following is a correct next step to solve the equation? (1 point)
Olivia has taken out a $13,100 unsubsidized Stafford loan to pay for her college education. She plans to graduate in four years. The loan has a duration of ten years and an interest rate of 7.6%, compounded monthly. By the time Olivia graduates, how much greater will the amount of interest capitalized be than the minimum amount that Olivia could pay to prevent interest capitalization? Round all dollar values to the nearest cent.
a. $654.45
b. $477.27
c. $995.60
d. $354.22
If Olivia wants to prevent interest capitalization, she must pay the accrued interest each month. That amount is
... I = Prt = $13,100×0.076×(1/12) = $82.97
Over 4 years (48 months), these payments total $82.97×48 = $3982.56.
_____
If no payments are made, the loan balance grows by the multiplier (1 +r/12) each month. Then the amount of interest that will be capitalized at the end of 48 months is ...
... $13,100×((1 +0.076/12)^48 -1) = $4637.01
The difference in these amounts is ...
... $4637.01 -3982.56 = $654.45 . . . . . matches selection a.
Answer:
A
Step-by-step explanation:
654.45
Estimate the value of 9.9 squared x 1.79
The estimation of 9.9 squared multiplied by 1.79 is 180.
To estimate the value of 9.9 squared multiplied by 1.79, use rounded numbers to simplify the calculation.
First, round 9.9 to 10 and calculate 10 squared, which is 100.
Next, we round 1.79 to 1.8.
Now, we can perform the multiplication:
100 x 1.8 = 180
Therefore, an estimation is 180.
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The value of 9.9 Squared x 1.79 is 175.59
Let's calculate
[tex]9.9^{2}[/tex]×1.79 let's break it down step by step:
[tex]9.9^{2}[/tex] means 9.9 [tex]\times[/tex] 9.9 multiplied by itself:
9.9×9.9, which equals 98.01
Now, multiply
98.01 × 1.79 = 175.5879
Rounded to a reasonable precision, the value is approximately
175.59
The process involves squaring
9.9 first and then multiplying the result by
[tex]1.79.9.9^{2}[/tex] gives us 98.01 and then that result is multiplied by
1.79 to obtain 175.59.
The explanation illustrates the order of operations: performing the exponentiation before the multiplication. This follows the basic principles of arithmetic, ensuring each step is carried out accurately to arrive at the final result.
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Solve for A, 4(2a+3)=-3(a-1)+31
Suppose Georgette buys 400 shares of Google at $250 a share. She sells them at $350 a share. What is her capital gain?
Math Please Help!!!!
290 in expanded notation
This is the answer. 200 + 90 + 0
The place value chart can help us to write a number in expanded notation. When we put 290 into the place value chart, we can recognize that our number is equal to
2 hundreds + 9 tens + 0 units
Image is provided.
is math related to science ?
Factor the polynomial completely
24x^2y-6y
You have a 5 question multiple choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?
Type your answer below using complete sentences.
WORLD'S HARDEST MATH QUESTIONS
Scientists released 6 rabbits into a new habitat in year 0. Each year, there were four times as many rabbits as the year before. How many rabbits were there after x years? Write a function to represent this scenario.
what is
4 group of _ tenths is 2.8
What's the value of the 8's in 88,000
A rectangular piece of gift wrap is 5.5 inches by 2.1 inches what is the area of the gift wrap? ( Hint: use A=lxw
chose the graph that represents the equation y=|x-4|
Answer:
V shape.
Vertex at (4,0)
Intersect with y axis at (0,4)
Step-by-step explanation:
In order to solve this you just ahve to search fo the graph that grows like a V because when you deal with functions that have absolute values you can have negative and positive values for the independent variable but not for the dependent, in this case x is the independent so x will have negative and positive values while Y will only grow in the postives, now the vertex of the function is found where Y=0 so to calculate that you equal the function to 0
y=|x-4|
0=|x-4|
x=4
So the vertex will be at (4,0) and the intersect with the y axis will be located where x=0, so you evaluate the function for 0:
y=|x-4|
y=|o-4|
y=|-4|
y=4
So the intersect with the y axis will be at (0,4).
The nurse researcher is reading about linear regression. what is linear regression
There are two lakes in town of Roxbury. Lake Big Rock is 1650 ft longer than Little Lake Rock. Together, they are 5273 ft long. How long is each lake? Please show work.
Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.
Let's use algebra to solve this problem.
Let L be the length of Little Lake Rock in feet, and let B be the length of Lake Big Rock in feet.
We are given two pieces of information:
Lake Big Rock is 1650 ft longer than Little Lake Rock: B = L + 1650.
Together, they are 5273 ft long: B + L = 5273.
Now, we have a system of two equations with two variables:
B = L + 1650
B + L = 5273
We can use the first equation to express B in terms of L and then substitute this expression into the second equation:
B = L + 1650
Now, substitute B in the second equation:
(L + 1650) + L = 5273
Combine like terms:
2L + 1650 = 5273
Subtract 1650 from both sides:
2L = 5273 - 1650
2L = 3623
Now, divide by 2 to find the length of Little Lake Rock (L):
L = 3623 / 2
L = 1811.5 feet
Now that we know the length of Little Lake Rock, we can find the length of Lake Big Rock using the first equation:
B = L + 1650
B = 1811.5 + 1650
B = 3461.5 feet
So, Little Lake Rock is 1811.5 feet long, and Lake Big Rock is 3461.5 feet long.
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Juanita is making necklaces to give as presents. She plans to put 15 beads on each necklace. Beads are sold in packages of 20. What is the least common number of packages she can buy to make necklaces and have no beads left over?
Answer: 3
Step-by-step explanation:
Given : Juanita is making necklaces to give as presents.
She plans to put 15 beads on each necklace. Beads are sold in packages of 20.
To find the least common number of packages she can buy to make necklaces and have no beads left over, First we need to find the least common multiple of 15 and 20.
Since , [tex]15=3\times5\\\\20=2\times2\times5[/tex]
Then least common multiple of 15 and 20 =[tex]2\times2\times3\times5=60[/tex]
Now, the least common number of packages she can buy to make necklaces and have no beads left over =[tex]\dfrac{60}{20}=3[/tex].
Hence, the least common number of packages she can buy to make necklaces and have no beads left over=3
Suppose you randomly select a letter from BURGER AND STARBIRD. Imagine writing these letters on Ping- Pong balls—one letter per ball—then putting them all in a barrel and remov- ing one. What is the probability of pulling out an R?