Answer:
n = -7
Step-by-step explanation:
Use distributive property:
7n - 32n - 16 = 159
Combine like terms
-25n - 16 = 159
Add 16 to both sides to isolate variable n
-25n = 175
Divide both sides by -25 to isolate variable n
n = -7
Check your work:
7(-7) - 32(-7) - 16 = 159
-49 + 224 - 16 = 159
159 = 159
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining. A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. Assume that the population standard deviation for Compound 1 is 4414 miles, while the population standard deviation for Compound 2 is 2368 miles. Determine the 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2. Step 2 of 3 : Calculate the margin of error of a confidence interval for the difference between the two population means. Round your answer to six decimal places.
Answer:
The margin of error is of 623.2016.
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem, and subtraction between normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
A sample of 243 brakes using Compound 1 yields an average brake life of 37,866 miles. The population standard deviation for Compound 1 is 4414 miles.
This means that [tex]\mu_1 = 37866, s_1 = \frac{4414}{\sqrt{243}} = 283.16[/tex]
A sample of 268 brakes using Compound 2 yields an average brake life of 45,789 miles. The population standard deviation for Compound 2 is 2368 miles.
This means that [tex]\mu_2 = 45789, s_2 = \frac{2368}{\sqrt{268}} = 144.65[/tex]
Distribution of the difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.
The mean is:
[tex]\mu = \mu_1 - \mu_2 = 37866 - 45789 = -7923[/tex]
The standard deviation is:
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{283.16^2 + 144.64^2} = 317.96[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.96*317.96 = 623.2016[/tex]
The margin of error is of 623.2016.
The lower end of the interval is the sample mean subtracted by M. So it is -7923 - 623.2016 = -8546.2016
The upper end of the interval is the sample mean added to M. So it is -7923 + 623.2016 = -7299.7984
The 95% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-8546.2016, -7299.7984).
What is -13 decreased by 9
Answer:
-4
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
-13 - 9
When both the numbers have the same sign, we add them. After adding we put the same sign of the numbers to the answer
-13-9 = -22please help me here im begging you it won't let me just skip it
Answer:
ABCD in statement and the other in reasoning
Step-by-step explanation:
An inclined walkway leading to a new building is to rise 11 inches for each horizontal distance of 22 feet. Write this slope as a grade. (Round to the nearest tenth of a percent if necessary.)
Answer:
4.2%
Step-by-step explanation:
The horizontal distance, x (Run) = 22 feets
Rise, vertical distance, y = 11 inches
The slope is the ratio of the vertical to the horizontal distance, Rise to Run
Slope = Rise / Run
Converting to the same unit ;
Foot to inches
1 foot = 12 inches
Hence, x = 22 feets = (12 * 22) = 264 inches
Slope = Rise / Run = 11 / 264 = 0.04167
Slope = 0.04167 * 100% = 4.167%
9. What is 30% of 60?*
8
18
28
38
Answer:
It's 18
Step-by-step explanation:
30/100 x 60/1
180/100 =18
Answer:
18
Step-by-step explanation:
Here. We are going to multiply both sides of the equation by this fraction 100 over 30 100 over 30.
The rate at which a quantity M of a certain radioactive substance decays is proportional to the amount of the substance present at a given time. Which of the following is a differential equation that could describe this relationship?
1. dM/dt = -3.72 t^2
2. dM/dt = -0.11M
3. dM/dt = 0.08 t^2
4. dM/dt = 1.2M
Answer:
2. dM/dt = -0.11M
Step-by-step explanation:
Differential equations for proportional amouts:
A differential equation for proportional amounts is given by:
[tex]\frac{dx}{dt} = ax[/tex]
In which a is the constant rate. If the amount increases, a is positive. If it decays, b is positive.
In this question:
Decays, so a < 0.
Proportional to the amount of the substance present at a given time, which means that a multiplies the amount M.
This means that the correct answer is given by option 2.
K Write an expression for the sequence of operations described below. add y to z, then multiply 3 by the result
Answer:
3(y+z)
Step-by-step explanation:
y+z is added first so it is in parentheses and then multiply by the 3
Stock in Macy's costs $25.75 per share. Hector buys 200 shares of Macy's
through his broker who charges a commission of $25.75. How much did George
pay in total to purchase the stock?
Answer: $5175.75
Step-by-step explanation:
The amount that is paid in total to buy the stock will be gotten through the addition of the cost of the shares and the commission paid. This will be:
= (200 × $25.75) + $25.75
= $5150 + $25.75
= $5175.75
Therefore, the total amount that is paid to buy the stock will be $5175.75.
For his birthday , Aaron received four stamps for his collection . his collection already contained eight times that number of stamps. Before pasting the stamps into albums , Aaron divide them equally into three envelope. Which numerical expression models the number of stamps in each envelope? A 12÷3 B 4+32÷3 C (4+32)÷3 D 12×4÷4
Answer:
C
Step-by-step explanation:
Aaron received four stamps. He already had eight times as much. 32 + 4. Before pasting the stamps into albums, Aaron divides them equally into three envelopes. (32 + 4) ÷ 3.
A student formed a pattern in which each term is represented by a sum. The first four terms of the pattern are shown below Which expression can be used to determine the value of the sum in any term, n
Answer:
n2
Step-by-step explanation:i did this last year
A bag contains 2 red, 4 blue, and 4 yellow marbles. What is the probability of pulling a red marble, putting the marble back, and then pulling a blue marble?\
Answer:
Di ko po alam sorry
Step-by-step explanation:
Di ko alam putaenamo
Can someone here please help me out?
Answer:
hope you can now substitute and find y
PLZ FULL ANSWER
Maria has the following scores on exams in her social studies class: 86, 75, 97, 58, 94, and 58. Find the mean, median, and mode of the scores. Should Maria’s social studies teacher use the mean, median, or mode of the exam scores to convince Maria that she needs to study more regularly for her exams?
Answer:
The mean is 78
The Median is 80.5
And The Mode is 58.
Step-by-step explanation:
(Mean) 86,75,97,58,94, and 58 equal 468. Divide it by 6 (The Total Of All The Numbers) and it gives you 78.
(Mode) Find the number that occurs the most which would be 58.
(Median) Put the numbers in order. Order: 58,58,75,86,94,97. Next, your supposed to find the number in the middle, but since there are 2(75 and 86.)
Add them together and you get 161. After that, divide them by 2 and it'll give you 80.5
By the way, if the number of numbers in the problem add up to be an even number, divide it by 2 and find the average. If it's odd, divide it by 2 and round it up to get to the median.
So yes, the teacher should use the scores to convince Maria that she needs to study more regularly for her exams.
The mean, median, or mode of the exam scores is 78, 86 and 58
What is Mean, median and Mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
Given data: 58, 58, 75, 86, 94, 97
1. Mean= sum of observation/ Total number observation
= 58+58+75+86+94+97/6
=468/6
=78
2. Median,
Since, n is even
median= (n/2)+ 1
= 6/2 + 1
= 3+1
=4 th term= 86
3. Mode: Mode is the repeating data
mode= 58
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(2, -16)
plug in the correct variables in the equation below
y = mx + b
The Answer Is Y=-8x
This is because x is multiplied by -8 to find y.
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 754 hours. A random sample of 29 light bulbs has a mean life of 737 hours. Assume the population is normally distributed and the population standard deviation is 59 hours. At α=0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e)
Answer:
The calculated test |Z| = |-1.55| >1.405 at 0.08 level of significance
The null hypothesis is rejected at a 0.08 level of significance.
An Alternative hypothesis is accepted
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at most 754 hour
Step-by-step explanation:
Step(i):-
Given that the mean life of a certain type of light bulb is at least 754 hours
Given that the random sample size 'n' =29
Given that the mean life of sample x⁻ = 737
Given that the standard deviation of the Population = 59
Step(ii):-
Null hypothesis: H₀: μ≥ 754
Alternative Hypothesis:H₁: μ≤ 754
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{737-754 }{\frac{59}{\sqrt{29} } }[/tex]
Z = -1.55
The calculated test |Z| = |-1.55| >1.405 at 0.08 level of significance
The null hypothesis is rejected at 0.08 level of significance
Final answer:-
The calculated test |Z| = |-1.55| >1.405 at 0.08 level of significance
The null hypothesis is rejected at a 0.08 level of significance.
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at most 754 hour
A spinner has five sections labeled a,b,c,d,e. The spinner is spun 45 times
Answer:
40
Step-by-step explanation: pls I need points make brainpy
Bob the builder eat no fewer then three donuts. What is the inequality?
Answer:
3
Step-by-step explanation:
I think
Answer:
less than or equal to 3
Step-by-step explanation:
expanded form :32,456
Answer:
30,000 + 2,000 + 400 + 50 + 6
Step-by-step explanation:
[tex]\text{The expanded form of 32,456 would be 30,000 + 2,000 + 4,000 + 50 + 6.}[/tex]
[tex]\text{We would have to identify what each number stands for.}[/tex]
[tex]\text{For example, 3 in 32,456 stands for 30,000.}[/tex]
[tex]\text{Hence, following this rule, we can conclude that the answer above is correct.}[/tex]
[tex]\text{I hope I helped you suceed!}[/tex]
(05.03 LC) What is the equation of a horizontal line passing through the point (2, 10)? (5 points)
Answer:
y=10
Step-by-step explanation: a horizontal line has no slope
Write an equation for the sum of x and 3 minus 2 is 12
Answer:
x + (3-2) = 12
Step-by-step explanation:
x + (3-2) = 12
or x + 1 = 12
so x = 11
Jon throws a ball into the air off a platform. The height of the ball is given by y equal minus 2 x to the power of 2 plus 11 x plus 21 where y is the height, in feet, above the ground when the ball has traveled a horizontal distance of x feet. What is the factored form of the expression that could be used to find out how far the ball has traveled horizontally when it hits the ground?
A. (x+7)(-2X+3)
B. (x-7)(-2x-3)
C.(2x+7)(x+3)
D. (2x-7)(-x-3)
Answer:
B (-2x - 3 )(x - 7) = (x - 7)(-2x - 3 )
Step-by-step explanation:
y = -2x² + 11x + 21
find x when y is zero (the ground)
(-2x - 3 )(x - 7) = 0
(-2x - 3 ) = 0, (x - 7) = 0
x = -1.5 and x = 7 since Jon did not throw the ball behind him (remember he is standing on a platform) the only possible answer is 7 feet in front of him, but they the question didn't ask for x, so I would answer B. The answer I got and multiplicans are in reverse order from their choice.
The factored form of the expression that could be used to find out how far the ball has traveled horizontally when it hits the ground is (x-7)(-2x-3)
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² +bx+c=0. with a ≠ 0 .
Given that Jon throws a ball into the air off a platform.
The height of the ball is given by y equal minus 2 x to the power of 2 plus 11 x plus 21
y= -2x² + 11x + 21.
Let us factor out the equation by quadratic equation
-2x² + 11x + 21
When we factor out the equation becomes as (x-7)(-2x-3)
Let us verify the solution by applying distribution property
-2x²-3x+14x+21
-2x²+11x+21
Hence, (x-7)(-2x-3) is the factored form of the expression that could be used to find out how far the ball has traveled horizontally when it hits the ground.
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Select the statement that correctly describes a normal distribution.
a. It is a negatively skewed distribution, as the extreme values are less than the median.
b. It is a symmetric distribution, as the mean and the median are the same.
c. It is a positively skewed distribution, as the extreme values are greater than the median.
d. It is a uniform distribution, as all of the values have equal frequency.
Answer:
b. It is a symmetric distribution, as the mean and the median are the same.
Step-by-step explanation:
Normal distribution:
The biggest characteristic of the normal distribution is that it's symmetric, that is, 50% of the values are below the mean and 50% are above, which means that the mean is the same as the median.
This means that the correct answer is given by option b.
Suppose {an) is an arithmetic sequence with a16=12 and a7=30. Find a9.
Answer:
a9 = 26
Step-by-step explanation:
nth term of an arithmetic sequence an = a + (n-1)d
a16 = a+15d = 12.... 1
a7 = a+6d = 30.....2
Subtract
15d - 6d = 12 - 30
9d = -18
d =-18/9
d = -2
Substitute d = -2 into 1
a + 15d = 12
a+15(-2) = 12
a - 30 = 12
a = 12 + 30
a = 42
Get a9;
a9 = a+8d
a9 = 42+8(-2)
a9 = 42 - 16
a9 = 26
hence the 9th term of the sequence is 26
Write equivalent fractions for 1 2/3 and 1 7/8 using 24 as the common denominator 2 24 7 1 0
Answer:
2×8=16
7×3=21
2/3 + 7/8 = 16/24 + 21/24
GIVING BRAINLIEST
Explain your reasoning.
3(n + 2) = 9(6 - n)
Answer: n = 4
Step-by-step explanation:
Divide both sides by 3
n+2=3(6−n)
Expand
n+2=18−3n
Subtract 2 from both sides
n=18−3n−2
Simplify 18−3n−2 to −3n+16.
n=−3n+16
Add 3n to both sides
n+3n=16
Simplify n+3n to 4n
4n=16
Divide both sides by 4
n= 4/16
Simplify 16/4 to4
n=4
Determine the median of the following numbers: 8, 11, 11, 12, 13, 15, 16, 16, 18, 21
Answer:
The median of the following numbers is 14
Step-by-step explanation:
PLEASE TELL ME PLEASE
Answer: D!! also 35% are spotted
Answer:
The answer is a.
Step-by-step explanation:
This is because the percent is out of 100 and the flock of spotted sheep is placed in the numerator.
The first step in the process for factoring the trinomial x2-3x - 40
Answer:
List all the factors of 40
Step-by-step explanation:
the sum of the first four terms of an A.p is 62.if the difference between 4 terms and 2nd terms is 14. find the first term and common difference
Answer:
-2 -4 -6 -8
Step-by-step explanation:
I got the answer off of khan academy
If the given figure is rotated 180° around the origin, what are the new coordinates of point Z?
please I really need help with this.
Answer:
New coordinates of the point Z are (-6, 9)
Step-by-step explanation:
If a point (x, y) is rotated 180° about the origin, coordinates of the image point is given by the rule,
(x, y) → (-x, -y)
Coordinates of the vertex Z → (6, -9)
Following the same rule,
Z(6, -9) → Z'(-6, 9)
Therefore, coordinates of the new (image) point will be (-6, 9).