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
A Solve each problem.
1. Henry flies his plane at 240 mph for 3 hours. How far does he travel?
Distance = speed x time
Distance = 240 x 3 = 720 miles
Answer:
henry doesn't travel but plane travel
Step-by-step explanation:
240m×3hour240m×60×60sec2592000m/sA psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80. Suppose also that exactly 15% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
Answer:
The mean score is of 617.4.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80.
This means that [tex]\sigma = 80[/tex]
Suppose also that exactly 15% of the scores exceed 700.
This means that when X = 700, Z has a pvalue of 0.85. So X when X = 700, Z = 1.033. We use this to find [tex]\mu[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.033 = \frac{700 - \mu}{80}[/tex]
[tex]700 - \mu = 80*1.033[/tex]
[tex]\mu = 700 - 80*1.033[/tex]
[tex]\mu = 617.4[/tex]
The mean score is of 617.4.
Using the product of the means equals the product of the extremes, solve for x, to the nearest tenth. 4:9=x:6
Cross multiply:
4 x 6 = 9x
24 = 9x
Divide both sides by 9
X = 24/9
X = 2.7 ( rounded to the nearest tenth)
Find the area of the composite figure.
9 ft
4 ft
6 ft
Convert 400 meters (m) to feet (ft). Round your answer to two decimal places. (1 metre = 3.28084 feet)
Answer:
1m----------3.28084ft
400m---------xft
x=(400*3.28084)/1
x=1,312.33 ft
Step-by-step explanation:
Answer the following questions by choosing whether the first situation is less, equally, or more likely to happen than the second.
PART A
The probability of a chance event is 0.32, is likely to happen when compared to 1/3
Answer:
probably g
Step-by-step explanation:
Can someone explain how to do this
Answer:
28 x 6
Step-by-step explanation:
You times 28 with 6 snice, there are 6 sides.
28 x 6 = 168 meters
Answer: 168 meters
The management of KSmall Industries is considering a new method of assembling a computer. The current assembling method requires a mean time of 66 minutes with a standard deviation of 3.0 minutes. Using the new method, the mean assembly time for a random sample of 24 computers was 61 minutes.
a. Using the 0.10 level of significance, can we conclude that the assembly time using the new method is faster?
b. What is the probability of a Type II error? (Round "Critical values" to 2 decimal places and round your final answer to 4 decimal places.)
Answer:
Part a:
Since the calculated z= 8.1649 falls in the critical region z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.
Part b:
P (Type II Error)= 0.6628
Step-by-step explanation:
The null and alternate hypothesis are
H0: μ1 ≥ μ2 against the claim Ha: μ1 < μ2
This is left tailed test
The critical region for this test at 0.10 ∝ is z < ± 1.28
The test statistic
z= x1-x2/ s/√n
z= 66-61/ 3/√24
z= 5/0.61238
z= 8.16486
Since the calculated z= 8.1649 falls in the critical region z < ± 1.28 we reject H0 and conclude that the assembly time using the new method is faster.
Part b:
P (Type II Error) = P ( accept H0/ H0 is false)
z ( ∝)= X-u/s/√n
1.28= X-61/0.61238
X= 61.7838
So I will incorrectly fail to reject the null as long as a draw a sample mean that greater than 61.7838
The probability of a Type II error is given by
P (z> 61.7838-66/24)
P (z>- 0.42161)
From the tables
P (z>- 0.42161)= 0.6628
The catapults are 14.5 m, end text apart, as shown. From catapult A, there is a 96 degree angle between catapult B and the target. From catapult B, there is a 58°degree angle between catapult A and the target.
How far should catapult B throw the snowball to reach the target?
Do not round during your calculations. Round your final answer to the nearest tenth of a meter.
Thank you very much.
Answer:32.9 m
Step-by-step explanation:
Someone PLease help me
1. Find (f(g(2)) for f(x)= 3x² and g(x)= 5 - x.
Answer: 27
Step-by-step explanation:
Jackie bought a CD for $11.50. The sales tax is 6%. How
much did Jackie pay for the CD, including the sales tax?
$12.19
before the tax price is $11.50
and %6 is equal to $0.69
therefore if you add those together you'll get an answer of $12.19
What are some of the applications for exponential functions?
Designing identification tags
Conversion of measurements
Assigning phone numbers
Finding perimeter
Determining the number of subsets in a given set
Answer:
Option B and D are correct
Step-by-step explanation:
Exponential functions are really useful in the real world situation. They can be used to solve following
a) Population Models
b) Determination of area and perimeters
c) Determine time related things such as half life, time of happening of an event etc.
d) Useful for solving financial problems such as computing investments etc.
Hence, option B and D
You have been given the task of designing a study concerning the lifetimes of five different types of electric motor. The initial question to be addressed is whether there are differences in mean lifetime among the five types. There are 20 motors, four of each type, available for testing. A maximum of five motors can be tested in a day. The ambient temperature differs from day to day, and this can affect motor lifetime.
a. Describe how you would choose the five motors to test each day. Would you use a completely randomized design? Would you use any randomization at all?
b. If X;j represents the measured lifetime of a motor of type i tested on day j, express the test statistic for testing the null hypothesis of equal lifetimes in terms of the Xir
Answer:
a-As the only factor of interest is type of electric motor, thus instead of using 1-factor randomization, a randomized block design is used where at maximum one motor of each type is tested every day.
b- The test statistic is given as
[tex]F_{I-1,(I-1)(J-1)}=\dfrac{12\left(\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..}\right) }{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}[/tex]
Step-by-step explanation:
a-
This is done such that the days are considered as blocks and the randomization is only occuring within the block. The order of testing is random. However the condition is implemented such that one motor of each type is tested each day.
b-
The F-Value is given as
[tex]F-Value=\dfrac{MSA}{MSAB}[/tex]
Here MSA is given as
[tex]MSA=\dfrac{J\Sigma^I_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{I-1}[/tex]
Here
I is the number of types which is 5J is the number of motors of each type which is 4[tex]\bar{X}_{i.}[/tex] is the row-wise mean which is given as [tex]\bar{X}_{i.}=\dfrac{1}{J}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{..}[/tex] is the sample grand mean which is given as [tex]\bar{X}_{..}=\dfrac{1}{IJ}\Sigma^I_{i=1}\Sigma^J_{j=1}X_{ij}[/tex]Similarly MSAB is given as
[tex]MSAB=\dfrac{\Sigma^I_{i=1}\Sigma^J_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(I-1)(J-1)}[/tex]
Here
I is the number of types which is 5J is the number of motors of each type which is 4[tex]\bar{X}_{i.}[/tex] is the row-wise mean which is given as [tex]\bar{X}_{i.}=\dfrac{1}{J}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{..}[/tex] is the sample grand mean which is given as [tex]\bar{X}_{..}=\dfrac{1}{IJ}\Sigma^I_{i=1}\Sigma^J_{j=1}X_{ij}[/tex][tex]\bar{X}_{.j}[/tex] is the column-wise mean which is given as [tex]\bar{X}_{.j}=\dfrac{1}{I}\Sigma^I_{i=1}X_{ij}[/tex][tex]X_{ij}[/tex] is the any motor j of type iBy putting these values and simplifying, equation becomes:
[tex]F-Value=\dfrac{MSA}{MSAB}\\\\F-Value=\dfrac{\dfrac{J\Sigma^I_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{I-1}}{\dfrac{\Sigma^I_{i=1}\Sigma^J_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(I-1)(J-1)}}\\\\F-Value=\dfrac{\dfrac{4\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{5-1}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{(5-1)(4-1)}}\\\\[/tex]
This is further simplified as
[tex]F-Value=\dfrac{\dfrac{4\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{4}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\F-Value=\dfrac{\Sigma^5_{i=1}(\bar{X}_{i.}-\bar{X}_{..})^2}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\[/tex]
The numerator can be written as
[tex]F-Value=\dfrac{\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..}}{\dfrac{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}{12}}\\\\F-Value=\dfrac{12(\Sigma^{5}_{i=1}\bar{X}^{2}_{i.}-IJ\bar{X}^2_{..})}{{\Sigma^5_{i=1}\Sigma^4_{j=1}\left(X_{ij}-\bar{X}_{i.}-\bar{X}_{.j}+\bar{X}_{..}\right)^2}}\\[/tex]
A sweater costs $25. The store marks up the price by 85%. What is the selling price of the sweater?
Pls help me if u can
Answer:
523.33 cm³
Step-by-step explanation:
Formula of volume of sphere
[tex] = \frac{4}{3} \pi {r}^{3} [/tex]
The volume of the sphere
[tex] = \frac{4}{3} \times 3.14 \times {5}^{3} [/tex]
[tex] = \frac{1570}{3} [/tex]
[tex] = 523.3333333...[/tex]
= 523.33 cm³ (rounded to the nearest hundredth)
HELP PLEASE ILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
50%
- Animals
Home
Economics -
20%
30%
- Farm Mechanics
There were 2500 entries at the county fair. The circle graph tells what types of entries were made.
How many were Farm Mechanics entries?
Answer:
750 were Farm Mechanics.
Step-by-step explanation:
30% of 2500 is 750.
Hope this helps
A parallelogram has an area of 316.35 square inches and a base of 18.5 inches. What is the height
Answer:
17.1
Step-by-step explanation:
h=A/b
h= 316.35/18.5
h=17.1
Question 9 of 10
True or False? A circle could be circumscribed about the quadrilateral below.
Answer:
t
Step-by-step explanation:
A circle can be circumscribed about the given quadrilateral, the answer is: A. True.
We know that,
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral, the answer is: A. True.
Learn more about circumscribed polygon on:
brainly.com/question/1423054
#SPJ7
Find the surface area of the prism.
2 in.
2 in.
6 in.
Answer:
56 m^2
Explanation: L=2, H=2, W=2, d = 6.63324958 m, TSA = 56 m^2, LSA = 48 m^2, TSA = 4 m^2, BSA = 4 m^2, V = 24 m^3
Help ASAP
What is the highest common factor of 180 and 168
Answer:
Its 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
make a factor tree, find the product of the prime factors, it will be 12.
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Pleeeeeeeaaase answer quick. With explanation. Will give 40 points
Answer:
See attached
Step-by-step explanation:
Review the picture
Can someone help? I hate math so much lol I don’t understand
Answer:
±6
Step-by-step explanation:
Given the mathematical expression;
√36 < √42 < √49
But, √36 = 6 * 6 = 6²
√49 = 7 * 7 = 7²
Simplifying further, we would substitute the new values respectively;
±[6] < √42 < ±[7]
Therefore, evaluating √36 is equal to ±6.
hey I need help with my coordinates
Ok send the picture so I can help you.
Answer:
what is the question? I can help
Step-by-step explanation:
what is the midpoint of a segment with endpoints at (-4,-8) and (8,10)
Answer: Midpoint: (2, 1)
Step-by-step explanation:
Midpoint formula: ((x1 + x2)/2 , (y1 + y2)/2)
(-4 + 8)/2 = 2
(-8 + 10)/2 = 1
Answer: (2, 1)
What is sec 0 when cot 0 = -4/2?
Answer:
[tex]sec 0=\frac{\sqrt{66} }{8}[/tex]
Step-by-step explanation:
[tex]Cot0=-4\sqrt{2}[/tex]
[tex]sec0=\frac{\sqrt{33} }{4\sqrt{2} }[/tex]
[tex]=\frac{\sqrt{33} }{4\sqrt{4} } *\frac{4\sqrt{2} }{4\sqrt{2} }[/tex]
[tex]=\frac{4\sqrt{66} }{32}[/tex]
[tex]=\frac{\sqrt{66} }{8}[/tex]
--------------------
hope it helps...
have a great day!!
!NO LINKS, NO FILES!
please :)
Answer:
the area is 72
Step-by-step explanation:
14. On Monday, a work group eats at Ava's café,
where a lunch special is $8 and a dessert is
$2. The total is $108. On Friday, the group
eats at Bo's café, where a lunch special Is
$6 and a dessert is $3. The total is $90. Each
time, the group orders the same number of
lunches and the same number of desserts.
How many lunches and desserts are
ordered?
what the x and y value.
Answer:
no. who eat lunch special = 12
no. who eat dessert = 6
Step-by-step explanation:
Let x = no. who eat lunch special
y = no. who eat dessert
(1) 8x + 2y = 108 (2) 6x + 3y = 90
Divide thru by 2 Divide thru by 3
4x + y = 54 2x + y = 30
-2x - y = -30
2x = 24
x = 12 2(12) + y = 30
24 + y = 30
y = 6
PLSS HELP ASAP!!
13 points when answered:) Thank you!!
Answer:
The wright answer is A
Step-by-step explanation:
[tex] \sqrt{20} = 4.47 \\ \frac{14}{3} = 4.67 \\ 4.47 < 4.5 < 4.67[/tex]
