The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $85.52 and a standard deviation of $10.81 are subsequently computed.
Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.
So, the 90% confidence interval for the true mean repair cost, μ is ;
⇒ P(-2.015 < t₅ < 2.015) = 0.90
{As the critical value of t at 5 degrees of freedom are -2.015 & 2.015 with P = 5%}
⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90
⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90
⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90
90% confidence interval for
⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))
Here, x = $85.52, s = $10.81, and n = 13
⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))
⇒ μ = (79.47, 91.56)
Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
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A forest covers 61,000 acres. A survey finds that 0.4% of the forest is old-growth trees. How many acres of old-growth trees are there?
Answer:
2,440 acres of old-growth trees.
Step-by-step explanation:
61,000*0.04=2,440
There are 2,440 acres of old-growth trees.
Hope this helps!
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Prove that cos 4θ = 8 cos⁴ θ - 8 cos² θ + 1
Answer:
Step-by-step explanation:
Answer is in the pic.
Answer:
See below for proof.
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]
Use the trigonometric identities to prove the given equation:
[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]
[tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]
please help!! (answer is NOT undefined)
[tex]-8\sqrt{-165} \\ \\ =-8\sqrt{-1}\sqrt{165} \\ \\ =\boxed{-8i\sqrt{165}}[/tex]
what is this equations value for x? |5-2x|>5
The value of equation for x is x > 0.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
|5-2x| > 5
To solve for let us take x on one side.
So, Subtracting 5 both the side we get,
|5 - 2x - 5| > 5 - 5
Simplifying we get,
|-2x| > 0
Extracting mod we get,
2x > 0
Now since 2 > 0 which is true,
Thus, x > 0
So, the value of equation for x is x > 0.
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what is the value of 32 ⅗ ?
Answer:
8
Step-by-step explanation:
I attached my answer........
write the algebraic expression for two less than for times a number
PLEASE SHOW WORK
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form..
Answer:
y = 4/5x + 27/5
or 5y = 4x + 27
or 5y - 4x = 27
Step-by-step explanation:
Look at (-3,3) and (2,7)
So the line rises 4 units and runs 5 units, then slope is 4/5
using m = 4/5, y = 3, x = -3
y = mx + b
3 = 4/5(-3) + b
3 = -12/5 + b
b = 15/5 + 12/5 = 27/5
so y = 4/5x + 27/5
or 5y = 4x + 27
or 5y - 4x = 27
in a random sample of 77 residents of the state of texas, the mean waste recycled per person per day was 1.01.0 pounds with a standard deviation of 0.290.29 pounds. determine the 98�% confidence interval for the mean waste recycled per person per day for the population of texas. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answer:
(0.63789 ; 1.38211 ) is the 98% confidence interval for the mean waste recycled per person per day for the population of texas and Tcritical = 3.143
In a random sample of 7 residents of the state of texas ,the mean waste recycled per person per day was 1.01 pounds and standard deviation 0.29 pounds
we have to find the 98% confidence interval for the mean waste recycled per person per day for the population of texas
Mean, xbar = 1.01
Standard deviation, s = 0.29
Sample size, n = 7
Confidence interval : xbar ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Degree of freedom (df) = n - 1 = 7 - 1 = 6
Hence Tcritical = 3.143
Margin of Error = 3.143 * 0.29/sqrt(6)
Margin of error = 0.37211
Lower boundary = (1.01 - 0.37211) = 0.63789
Upper boundary = (1.01 + 0.37211) = 1.38211
(0.63789 ; 1.38211 )
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Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary. Original price: $123.28 Tax rate: 7.5%
7.5% = 0.075
0.075 x 123.28 = 9.246
So, the tax will be $9.20.
Total cost would be $132.48.
the annual salaries of all employees at a financial company are normally distributed with a mean mu
The value of the Z - Score is a -1.5.
According to the statement
We have to find that the z-score of the company.
So, For this purpose, we know that the
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
From the given information:
The annual salaries of all employees at a financial company are normally distributed with a mean Mu = $34,000 and a standard deviation Sigma = $4,000.
Then
Let X = annual salaries of all employees at a financial company
And
The z score probability distribution for the normal distribution is given by:
Z - Score = Annual salary - mean / s.d.
Then substitute the values
Z - Score = 28,000 - 34,000/ 4000
Z -Score = -6/4
Z -Score = -1.5.
So, The value of the Z - Score is a -1.5.
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Insert <,>,or = to make the following sentence true. square root of 17 and 4
we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4
we have to solve the following sentence
[tex]\sqrt{17}[/tex] --- 4 ( insert <,>, = to make the following sentence true)
what is square root ?
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is [tex]\sqrt{}[/tex] .
we know that
square root of 17 is 4.12310563
which is 4+ 0.12310563
that is if we add 4+0.12310563 we get 4.12310563
therefore square root of 17 is greater than 4
that is [tex]\sqrt{17}[/tex] > 4
since 4.12310563 > 4
hence, we can insert > to make the following sentence true that is [tex]\sqrt{17}[/tex] > 4
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A scientist created a scatter plot to represent the heights of four plants over time. Then, she found a line of best-fit to model the height in centimeters of each plant after x days. The equations of each trend line are given in the table.
Trend Line Equations
Plant
Equation of trend line
1
y = three-halves x + three-halves
2
y = 2 x + 1
3
y = one-half x + 3
4
y = three-halves x + 1
According to the trend line equations, which plants are growing at the same rate per day?
The plants which are growing at the same rate are Plant 1 and Plant 4.
Both the plants are growing at the same rate because they have same slope when their growth rate is expressed in the form of equation. Slope may be defined as the amount of steepness of the graph when plotted on graph paper. The slope-intercept form of equation of line is given by y = mx + c where m is the slope of the line and c is the intercept formed by the line. The slope-intercept form of the growth rate equation of Plant 1 is given by y = 3/2x + 3/2 and the slope-intercept form of the growth rate equation of Plant 4 is given by y = 3/2x + 1.
If we compare them from the slope-intercept form of line, then both the Plants have same slope and thus their growth rate is same.
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Answer:
B. 1 and 4
Step-by-step explanation:
Edge 2023
Select all the expressions that are equivalent to –24 [tex]\frac{1}{2}[/tex] + 16.15 – 4.
The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex] .
In the question,
the given expression is [tex]-24\frac{1}{2} +16.15-4[/tex] , solving further we get
= -49/2 + 16.15 - 4 ...(as [tex]24\frac{1}{2} = \frac{49}{2}[/tex] )
= -24.5 + 12.15
= -12.35
In option(A) we have ,
=[tex]24\frac{1}{2} -16.15+4[/tex]
= 49/2 -16.15 +4
= 24.5 -16.15 +4
= 8.35 + 4
= 12.35
In option(B) we have ,
= 16.15 - 28.5
= -12.35
In option(C) we have ,
= -28.5 + 16.15
= -12.35
In option(D) we have ,
[tex]=-20\frac{1}{2} +16.5[/tex]
= -41/2 + 16.5 ...( as [tex]20\frac{1}{2} = \frac{41}{2}[/tex] )
= -20.5 + 16.5
= -4
In option(E) we have ,
[tex]=12.15-24\frac{1}{2}[/tex]
= 12.15 - 49/2
= 12.15 - 24.5
= -12.35
As we can see that from all the option , only option(B), option(C) and option(E) matches with the given expression .
Therefore , The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex] .
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Problem: Chrissy has 3 cats. Each cat weighs differently. The first and second cat weigh 7 kg altogether. The second and third cat weigh 8 kg altogether. The third and first cat weigh 11 kg altogether. What is the weight of each cat?
Answer:its a
Step-by-step explanation:
Find the distance between -55 and 63.
Answer:
The distance would be 118
Step-by-step explanation:
The easiest way I solve the distance between a negative number and a positive number is by adding the negative (but making it a positive) and the positive together. If you add 55 and 63 you would get 118. And 118 is the distance between -55 and 63.
I hope this helps!! :)
Mrs. Genebe worked all year and earned $23,400. How much did she earn per week?
Answer:
$448.766754 per week or $448
Step-by-step explanation:
i gotchu
theres 52.1429 weeks
divide 23,400 by 52.1429
u get $448.766754 per week
donald is studying the buying habits of all women attending his store. he samples the population by dividing the women into groups by age and randomly selecting a proportionate number of women from each group. he then collects data from the sample. which type of sampling is used?
According to the statement Donald is using Stratified sampling to collects data from the sample.
The correct option is A.
Briefing:A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.
The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.
What accomplishes stratified sampling?When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.
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I understand that the question you are looking for is:
Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?
a. Systematic sampling
b. Convenience sampling
c. Stratified sampling
d. Cluster sampling
Another circular section of the island to be used to count marine iguanas has
a'radius of 1 kilometer. Researchers will sample this area to draw conclusions
about the iguana population on the entire island. What is the area of this
section? Use an approximation of n to two decimal places. Place your
approximation of the area in the orange chart below.
The area of the circular section is 3.14 square units
How to determine the area of the circular section?The given parameters are:
Radius, r = 1 kilometre
Rewrite the above properly as follows
So, we have
r = 1 kilometre
The area of the circular section is:
A = πr^2
So, we have
A = 3.14 * 1^2
Evaluate the exponent
So, we have
A = 3.14 * 1
Evaluate the product
So, we have
A = 3.14
Hence, the area of the circular section is 3.14 square units
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find the solution to this equation:5(x-6)+8=7x-10
Answer:
x = -6
Step-by-step explanation:
Distribute where possible
5x - 30 + 8 = 7x - 10
Combine like terms
5x - 22 = 7x - 10
Subtract 7x from both sides and add 22 to both sides
-2x = 12
x = -6
A football team gained 6 yards on a first down, lost 15 yards on the second down, and gained 12 yards on the third down. How many yards did the team gain or lose?
9 yards
33 yards
21 yards
3 yards
AYUDA!! SE ME OLVIDO COMO RESOLVER GEOMETRÍA
P = 180 - (125 + 30)
P = 180 - 155
P = 25 degrees
Thus :
P = 25/180 n radian
P = 5/36 n
Which mean the first option is the correct answer.
25 points plus brainliest
Answer:
The first answer is correct
Step-by-step explanation:
y = mx + b is the slope intercept form of a line
15x - 5y = 30 Subtract 15x from both sides
-5y = -15x + 60 Divide both sides by -5
y = 3x -6 The -6 is your y-intercept. It is the point (0.-6) We could stop here because that is the only choice that shows (0,-6), but let's find the x intercept.
The x-intercept is when y = 0
y = 3x -6
0 = 3x - 6 Add 6 to both sides
6 = 3x Divide both side by 3
2 = x This is the point (2,0)
We could have taken the original equation and set x=0 and y=0
15x - 5y = 30
15(0) - 5y = 30
-5y = 30 Divide both sides by -5
y = -6
15x -5y = 30
15x - 5(0) = 30
15x = 30 Divide both sides by 15
x = 2
-
Simplify:
4(10+2³-5)
O a. 52
O b. 44
O c. 6892
O d. 17
Answer:
A. 52 is your answer
Step-by-step explanation:
Explained below
Answer:
Ans is a
First you solve the inside of the bracket u will get 4(13)
which will give u 52
17/21 + 1/3 - 5/7 thank you!
Answer:3/7
Step-by-step explanation:
Answer:
3/7
Step-by-step explanation:
change all denominators to 21
{21 is the lcd of all the numbers)
17/21 x 1= 17/21
1/3 x 7 = 7/21
5/7 x 3 = 15/21
17/21 + 7/21 - 15/21
24/21-5/21
9/21
reduce by three
9/21÷3
3/7
The expression for the nth term of a sequence is 5n^2
work out the third term in this sequence
Answer:45
Step-by-step explanation:
5n²
5(3)²
5(9)
∴ The third term in the sequence 5n² is 45
Simplify the ABSOLUTE VALUE of the number
sentence to solve:
| -4 | + | 1 |=
3
5
-5
-3
Answer:
5
Step-by-step explanation:
Every number from the absolute sign will be positive.
A number d is decreased by 5 and then doubled
Let us assume the given number is x.
If it is decreased by 5 and then doubled, then we can represent that event with an algebraic expression as:
= (x-5) × 2
Formation of equation:
The number decreased by 5 can be written as: x - 5
Now, to double it, we will multiply it by 2 = (x-5) × 2
Therefore, we have the algebraic form of the given condition as :
= (x-5) × 2
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what is the difference of - 3 - ( - 10)
Answer
(-3) - (-10) = 7
|7| = 7
7
jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. the area of the smaller lawn is 144 square feet. in the equation (x – 8)2
The dimensions of original lawn are a. 4 feet by 4 feet.
As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.
[tex](x - 8)^{2} = 144[/tex]
The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -
[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]
[tex]x^{2} + 64 + 16x = 144[/tex]
[tex]x^{2} + 16x + 64 - 144 = 0[/tex]
[tex]x^{2} + 16x - 80 = 0[/tex]
[tex]x^{2} + 20x - 4x - 80 = 0[/tex]
x (x + 20) -4 (x + 20) = 0
(x + 20) (x - 4) = 0
So, the two values of x that we get are:
x = 4 and -20.
The dimensions of lawn can not be negative. Hence, the value of x will be x.
Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.
The complete question is -
Jillian is trying to save water, so she reduces the size of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?
a. 4 feet by 4 feet
b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet
c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet
d. 20 feet by 20 feet
Solve problems on area of lawn -
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Given the definitions of f(x) and g(x) below, find the value of (gof)(-2).
f(x) = -2x + 7
g(x) = x² - 6x + 5
The value of (gof)(-2) for the given values of f(x) and g(x) is 60.
A Composite function may be defined as a function which is formed from the operation of combination of two functions. If f(x) and g(x) are two functions, then the composite functions of the given functions are fog(x) that is f(g(x)) and gof(x) that is g(f(x)).
It is given in the question that f(x) = -2x + 7 and g(x) = x² - 6x + 5.
Now, gof(x) = g(f(x)) = (-2x + 7)² - 6(-2x + 7) + 5
gof(x) = 4x² + 49 - 28x + 12x - 42 + 5
gof(x) = 4x² - 16x + 12
gof(-2) = 4(-2)² - 16(-2) + 12
gof(-2) = 16 + 32 + 12
=>gof(-2) = 60
Therefore, the value of gof(-2) is equal to 60.
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