The margin of error is approximately 0.3
To answer the question, we must figure out what margin of error corresponds to a 90% confidence level. The definition of the margin of error used to create confidence intervals for the population mean is as follows;
Mean = μ = 20.6
Standard deviation = σ = 2.7
Number of students = n = 225
the result of the sample mean's standard error and the accompanying z-score. The formula used to compute the sample mean's standard error is;
⇒ σ / √n
The z-score associated with a 90% confidence level:
From the given table z-score is 1.645
Therefore, the margin of error;
σ / √n * 1.645 = 2.7/√225 * 1.645
= 0.296
Hence, the margin of error is approximately 0.3
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Answer:
Approximately 0.3 of an error is allowed.
Given data in question
Confidentialevel=90%
Mean = μ = 20.6
2.7 as the standard deviation
N = 225 students are enrolled.
the outcome of the standard error of the sample mean and the corresponding z-score. The formula used to determine the standard error of the sample mean is;
⇒ σ / √n
The z-score for a 90% degree of confidence is:
Z-score for the provided table is 1.645.
Consequently, the error margin;
σ / √n * 1.645 = 2.7/√225 * 1.645
= 0.296
Consequently, the margin of error is roughly 0.3.
a triangle has 2 vertices at (1,10), (-5,2), and (7,2)
What is the circumcenter
The circumcenter of the triangle that has vertices at (1, 10), (-5, 2), and (7, 2) is (1, 3.75)
What is the circumcenter of a triangle?The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the three sides of the triangle.
The distance from the circumcenter to each of the three vertices are congruent.
The coordinates of the circumcenter can found using the as follows;
Let (x, y), represent the coordinates of the circumcenter, we get;
The distance of the circumcenter from the vertices of the triangle is the same for the three vertices, therefore;
The specified vertices of the triangle are; (1, 10), (-5, 2), and (7, 2)
The distance of the circumcenter, (x, y), from (1, 10), is therefore;
D₁ = √[(x - 1)² + (y - 10)²]
The distance of the circumcenter, (x, y), from (-5, 2), is therefore;
D₂ = √[(x - (-5))² + (y - 2)²]
The distance of the circumcenter, (x, y), from (7, 2), is therefore;
D₃ = √[(x - 7)² + (y - 2)²]
The properties of the circumcenter indicates that we get;
D₁ = D₂ = D₃
D₁ = √[(x - 1)² + (y - 10)²] = D₂ = √[(x - (-5))² + (y - 2)²] = D₃ = √[(x - 7)² + (y - 2)²]
D₁ = D₂ indicates;
√[(x - 1)² + (y - 10)²] = √[(x - (-5))² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - (-5))² + (y - 2)² = (x + 5)² + (y - 2)²
(x - 1)² + (y - 10)² = (x + 5)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² + 10·x + y² - 4·y + 29
According to the addition and subtraction properties of equality, we get;
x² - 2·x + y² - 20·y + 101 - (x² + 10·x + y² - 4·y + 29) = 0
12·x + 16·y - 72 = 0...(1)D₁ = D₃ indicates√[(x - 1)² + (y - 10)²] = √[(x - 7)² + (y - 2)²]
(x - 1)² + (y - 10)² = (x - 7)² + (y - 2)²
x² - 2·x + y² - 20·y + 101 = x² - 14·x + y² - 4·y + 53
x² - 2·x + y² - 20·y + 101 - (x² - 14·x + y² - 4·y + 53) = 0
12·x - 16·y + 48 = 0...(2)Equation (1) and (2) indicates;
12·x + 16·y - 72 = 12·x - 16·y + 48
12·x - 12·x + 16·y - (-16·y) = 48 - (-72) = 48 + 72 = 120
16·y - (-16·y) = 16·y + 16·y = 32·y = 120
y = 120 ÷ 32 = 3.75
y = 3.75
12·x - 16·y + 48 = 0...(2)
12·x - 16 × 3.75 + 48 = 0
12·x - 12 = 0
12·x = 12
x = 12/12 = 1
x = 1
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Caitlin had $385 in her bank account. She withdrew $14 each week to pay for a swimming lesson. She now has $245. How many swimming lessons did she pay for
The answer is 10 weeks of lessons she paid for using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Caitlin had $385 in her bank account. She withdrew $14 each week to pay for a swimming lesson.
She now has $245.
Total money spent 385-245 = 140
For 140 will pay 140/14 = 10 weeks
Hence total 10 weeks lessons she paid for.
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What is the midline equation of the function h(x)=-4\sin\left(x-\dfrac{\pi}{4}\right)h(x)=−4sin(x−
4
π
)h, left parenthesis, x, right parenthesis, equals, minus, 4, sine, left parenthesis, x, minus, start fraction, pi, divided by, 4, end fraction, right parenthesis?
x-axis or y = 0 is the midline equation of the function
h(x) = -4sin(x - π/4).
Given, a trigonometric function
h(x) = -4sin(x - π/4)
Now, we are asked the midline equation of the given function,
midline equation is the equation of a line that divides the given function into exactly two halves.
As, we have
h(x) = -4sin(x - π/4)
h(x) is obtained by transforming the function sinx.
Now, the midline equation of the function h(x) is,
y = 0 i.e. the x-axis.
Hence, x-axis or y = 0 is the midline equation of the function
h(x) = -4sin(x - π/4).
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Width: X
Length: 3x
Determine the lengths of the
sides of the rectangle using the
given area. Give answers both
exactly and approximately (to
the nearest tenth).
The area of the rectangle is 45
cm squared.
Answer:
[tex]3x \times x = 45 \\ {3x}^{2} = 45 \\ {x}^{2} = \frac{45}{3} \\ {x}^{2} = 15 \\ x = \sqrt{15} \\ x = 3.872983346 \\ x = 3.9[/tex]
Step-by-step explanation:
area of a rectangle is width a length
area of length already given as 45cm²
find the unknown x using a normal equation
26) Write the following exponential expression in an equivalent form:
The following exponential expression [tex]2^{2x+2}[/tex] in an equivalent form is [tex]4^{x} *4[/tex].
What is an exponential equation?
Any equation with exponents in which the exponent or a portion of the exponent is a variable is known as an exponential equation.
Given, [tex]2^{2x+2}[/tex] = [tex]2^{2x} *2^{2}[/tex]
= [tex](2^{2})^x*4[/tex]
= [tex]4^{x} *4[/tex]
Therefore, the exponential expression [tex]2^{2x+2}[/tex] in an equivalent form is [tex]4^{x} *4[/tex]
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Arlin takes out a mortgage of $160,000 from the bank for 20 years at 4.75%. Determine her monthly mortgage payment.
Answer:
Step-by-step explanation:
Hello, the solution to your problem can be found by using the PMT function in Excel.
The function would read: =PMT(.0475/12, 20*12, -160,000)
With this formula the monthly mortgage payment is: $1,033.96.
I have attached a screenshot file containing the correct answer as well; the formula in the bar also shows how to use the function for any other similar problems. I hope this helps. : )
Raíz cuadrada de 157
Answer:12.5
Step-by-step explanation:
is chicken good yes or no
Answer:
Chicken is highly nutritious and a good source of protein. Adding chicken to your diet may help support weight loss, muscle growth, and bone health.
Tell whether the value is a solution of the inequality r+4>8; r=2
Answer:
No, it is not a solution to the inequality.
Step-by-step explanation:
If r = 2, the equation would be 2 + 4 > 8.
2 + 4 = 6.
6 is NOT greater than 8.
start a penny (1 scent) on day one, and double it every day for one month (31 days) how much? will you have?
HELP ME PLEASEEE
Answer:2^(31-1)
Step-by-step explanation:
Solve the system by substitution. y=2x x+y=6 with solution
Answer:
The solution is x=2, y=4
Step-by-step explanation:
y = 2x
x+y = 6
Using substitution, we can substitute the first equation into the second equation
x + (2x) = 6
3x = 6
Divide by 3
3x/3 = 6/3
x = 2
Now we can find y
y = 2(2)
y = 4
The solution is x=2, y=4
5
Riley is saving up to buy a new television. She needs a total of $1,028.25. Riley has saved $200.39 already and earns $75.26 per
week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
OA. 10
OB. 12
OC. 9
OD.
11
Answer:
D. 11 weeksStep-by-step explanation:
Let the number of weeks Riley need to work is x.
She has $200.39 and will save $75.26 for x weeks to get $1028.25 total.
Set this as equation:
75.26x + 200.39 = 1028.25Solve it for x:
75.26x = 1028.25 - 220.3975.26x = 807.86x = 807.86/75.26x = 10.73 ≈ 11 (rounded to whole number)Correct choice is D
Answer:
d) 11
Step-by-step explanation:
Forming the equation,
→ 75.26w + 220.39 = 1028.25
Now the value of w will be,
→ 75.26w + 220.39 = 1028.25
→ 75.26w = 1028.25 - 220.39
→ 75.26w = 807.86
→ w = 807.86/75.26
→ w = 10.73425
→ [ w = 11 weeks ]
Hence, the answer is 11 weeks.
what is the value of 2/10 divided by 5/4
Divide. Round to the nearest tenth.
3.5÷2.29
Answer:
1.5
Step-by-step explanation:
look at the number after the 5 If that number is greater than 5, add 1 to the tenth value. If it is less than 5, leave the tenth place value as it is, and remove all the numbers present after the tenth's place
If triangle FGH is similar to triangle KJH, solve for x. show work please
Answer:
None of these
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so:
[tex]\frac{GH}{JH}=\frac{FH}{KH} \\ \\ \frac{x+8}{52}=\frac{4x-25}{32} \\ \\ 32(x+8)=52(4x-25) \\ \\ 32x+256=208x-1300 \\ \\ 256=176x-1300 \\ \\ 176x=1556 \\ \\ x=389/44[/tex]
in 10 seconds jamal travels 550 feet oh his bicycle at this speed how many feet can he travel in 1 minute
Answer:
Step-by-step explanation:
if you where to add up on the byesicle you would get 560 but if you multiply you would get 5,500
In 10 seconds Jamal travels 550 feet on his bicycle at this speed he can travel 3300 feet in 1 minute.
This can be solved with the help of unitary method:
In 10 seconds Jamal travels= 550 feet
In 1 second Jamal travels= 550/10 feet
In 1 minute or 60 seconds Jamal travels= 550/10×60=3300
So at the same speed Jamal can cover 3300 feet in 1 minute.
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A block i pulled 0. 90 meter to the right in 2. 5 econd. What i the block' average peed to the nearet hundredth of a meter/econd (m/)?
If a block is pulled 0.90 meter to the right in 2.5 second, then the average speed is 0.36 meter per second
The distance that he pulled the block = 0.90 meter
The time taken = 2.5 second
The average speed is defined as the total distance travelled by the total time taken
The average speed = Total distance / Time taken
Substitute the values in the equation
The average speed = 0.90 / 2.5
Divide the terms
= 0.90 / 2.5
= 0.36 meter per second
Hence, if a block is pulled 0.90 meter to the right in 2.5 second, then the average speed is 0.36 meter per second
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263 second grader and 198 third graders choose hot dogs to eat. How many hot dogs do the students eat choose to eat ?
Answer:
461 Hot Dogs.
Step-by-step explanation:
263+198=461 Hot dogs.
For the line maybe you can start at 0 then jump 200 then 60 then 3 then jump another 100 then 90 then 8 to get 461 Hot Dogs.
I hope this helps!
There are five times as many pink buttons as yellow buttons.
number of yellow buttons : number of blue buttons = 4 : 7
e button is selected at random.
ork out the probability that the button is either pink or blue.
ve your answer as a fraction in its simplest form.
Optional working
nswer:
Write your fraction in the form a/b
Answer:
please put the number of yellow buttons if you can
thank you.
the mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. the standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed. 4% of the time, the bolt is inserted in less than which time value? round to the nearest whole number.
4% of the time, the bolt is inserted in time less than 8 minutes.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
If the probability is 4%, then, using the z-table, the z-score would be -1.75287.
at p = 0.04 z = -1.75287
Using the formula for finding the z-score, solve for the data value, x.
z-score = (x – μ) / σ
where x = individual data value
μ = mean = 15
σ = standard deviation = 4.0
-1.75287 = (x - 15) / 4.0
x - 15 = -7.01148
x = 7.98852
Round off to the nearest whole number.
x = 8
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Mr. Thompon i buying 1 and 3/4 pound of turkey and 3/4 a much cheee a turkey at the deli
The correct option is D. Mr. Thompson is buying more turkey than cheese.
A fraction with a higher numerator than the denominator is said to be an improper fraction. A mixed fraction has a value that is consistently greater than 1. A mixed fraction has a proper fraction part and a whole number part.
Here, the values are given in both improper and mixed fraction formats. As a first step, convert the given mixed fraction to an improper fraction.
Then, we get 7/4 and 3/4.
To find which fraction is greater, follow the below steps.
Observe the denominator of the given values. Here, the denominator is the same, which is 4.Now compare the numerator of the given values. Here, one is 7 and another is 3. The fraction with a large numerator is greater than another. Therefore, [tex]\frac{7}{4} > \frac{3}{4}[/tex].So, the amount of turkey is greater than the amount of cheese.
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The complete question is -
Mr. Thompson is buying [tex]1\frac{3}{4}[/tex] pounds of turkey and [tex]\frac{3}{4}[/tex] as much cheese as turkey at a deli. Which of the following statements is true?
A. He is buying the same amount of turkey and cheese.
B. He is buying less turkey than cheese.
C. He is buying twice as much turkey as cheese.
D. He is buying more turkey than cheese.
In the triangle shown, what is the measure of QR?
Answer:
= (5sin(50°)) / sin(70°)
53=y−47.4 pls help sssssssssss
Answer:
5.6
Step-by-step explanation:
y = 53- 47.4=?
24. walking down jane street, ralph passed four houses in a row, each painted a different color. he passed the orange house before the red house, and he passed the blue house before the yellow house. the blue house was not next to the yellow house. how many orderings of the colored houses are possible?
The number of orderings of the colored houses is possible in 3 ways
There are 24 possible arrangements for the houses. The number of ways with the blue house next to the yellow house is [tex]$3! \cdot 2!=12$[/tex],
as we can consider the arrangements of B,Y, O, and R.
Thus there are [tex]$24-12$[/tex] arrangements with the blue and yellow houses non-adjacent.
Exactly half of these have the blue house before the yellow house by symmetry, and exactly half of those 6 arrangements have the orange house before the red house (also by symmetry), so our answer is
[tex]=$12 \cdot \frac{1}{2} \cdot \frac{1}{2}[/tex]
=3
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The equation 4/5d - 5 = 3/5d - 2 Represents the number of dimes, d, in a stack how many dimes are in the stack?
Answer:
d=10
Step-by-step explanation:
i hoped this helps
Answer:
15 dimes
Step-by-step explanation:
The equation 4/5d - 5 = 3/5d - 2 Represents the number of dimes, d, in a stack how many dimes are in the stack?
You are asked to solve for d:
4/5d - 5 = 3/5d - 2
subtract 3/5d from both sides:
4/5d - 5 - 3/5d = 3/5d - 2 - 3/5d
1/5d - 5 = -2
add 5 to both sides:
1/5d - 5 + 5 = -2 + 5
1/5d = 3
multiply both sides by 5:
5(1/5d) = 3(5)
d = 15
A survey was conducted in a classroom of 40 students. On the survey, 10 stated they were
fond of pineapple juice, 15 were fond of orange juice, and 7 liked to have both pineapple and
orange juice. Find how many students were neither fond of pineapple nor orange juice?
Answer: 8
Step-by-step explanation: Add 15, 10, and 7 together to get 32 students fond of OJ or Pineapple juice. then do 40-32 to get 8.
Mitchell buys a bag of cookies that contains 7 chocolate chip cookies, 8 peanut butter cookies, 4 sugar
cookies and 7 oatmeal cookies.
What is the probability that Mitchell reaches in the bag and randomly selects a sugar cookie from the bag,
eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Round your answer to four
decimal places.
The Probability of cookie is 0.0492
Describe probability.
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. The formula for computing probabilities in equiprobable sample spaces, the probability of the complementary event, etc., as well as the likelihood of two events joining together, are essential to understand in order to properly appreciate this branch of mathematics.
Given That:
chocolate chip cookies = 7
peanut butter cookies = 8
sugar cookies = 4
oatmeal cookies = 7
selecting a sugar cookie from the bag = [tex]\frac{4}{7+8+4+7}=\frac{4}{26}=\frac{2}{13}[/tex]
selecting a oatmeal cookie from the bag = [tex]\frac{8}{7+8+3+7} =\frac{8}{25}[/tex]
Over all probability = [tex]\frac{2}{13} *\frac{8}{25} = \frac{16}{325} =0.0492[/tex]
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consider the two jars below, which each contain 10 marbles. in jar a, 70% of the marbles are green and 30% of them are blue. in jar b, 30% of the marbles are green and 70% of them are blue. suppose a computer randomly chooses one of the jars, where there is a 15% chance it chooses jar a and a 85% chance it chooses jar b. the randomly chosen jar is shaken (shuffling its contents), and a marble is drawn out of it: the marble is green. what is the percent chance it came from jar a?
The likelihood that a green marble from jar A will be drawn out of it is 0.105.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
Here,
For jar A,
Total Marbles=10
Number of green marbles=7
Number of blue of marbles=3
For jar B,
Total Marbles=10
Number of green marbles=3
Number of blue of marbles=7
Probability of choosing jar A=15/100
Probability of choosing jar B=85/100
Probability that a marble is drawn out of it is the marble is green that came from jar a= 15/100*7/10
=105/1000
=0.105
Probability that a marble is drawn out of it is the marble is green that came from jar A is 0.105.
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Which triangle congruence postulate or theorem proves that these triangles are congruent?
Answer:
a squares + b squared = c squared
SHOW WORK FOR BRAINLIST
Answer:
x = -36, y = 25
Step-by-step explanation:
x + y = -11------>y = -11 - x
Substitute 11 - x for y into 2x - 3y = 3 and solve for x. Then find y.
[tex]2x - 3( - 11 - x) = 3[/tex]
[tex]2x - 33 - 3x = 3[/tex]
[tex] - 33 - x = 3[/tex]
[tex] - x = 36[/tex]
[tex]x = - 36[/tex]
[tex]y = - 11 - ( - 36) = - 11 + 36 = 25[/tex]
