Answer:
0.64%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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.
Mean of 75 grams and a standard deviation of 22 grams.
This means that [tex]\mu = 75, \sigma = 22[/tex]
Sample of 144:
This means that [tex]n = 144, s = \frac{22}{\sqrt{144}} = 1.8333[/tex]
More than 80 or less than 70:
Both are the same distance from the mean, so we find one probability and multiply by 2.
The probability that it is less than 70 is the pvalue of Z when X = 70. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{70 - 75}{1.8333}[/tex]
[tex]Z = -2.73[/tex]
[tex]Z = -2.73[/tex] has a pvalue of 0.0032
2*0.0032 = 0.0064.
0.0064*100% = 0.64%
The probability is 0.64%.
Solve for angle x help plz
Answer:
123 degrees
Step-by-step explanation:
Answer:
123°
Step-by-step explanation:
360 - 114 - 43 - 80 = 123
What is
7(2b + 3) - 2b
Pls I need help fast
Answer:
b= = - 7/4 or -1.75
Step-by-step explanation:
14b +21 -2b=0
12b +21=0
12b= -21
b= -21/12
b= - 7/4 or -1.75
Answer:
i dont know what you neccesarily want but here are two answers b=-7/4 or -1 3/4 other answer is 12b+21
Step-by-step explanation:
first, you have to set this question equal to 0.
7(2b+3)-2b=0
now you have to distribute the 7 to everything inside the parentheses.
14b+21-2b=0
combine like terms
12b+21=0
you can stop here and take this answer if this is the one you want
now subtract each side by 21
12b=-21
divide each side by 12
b=-21/12
simplify
b=-7/4
hope this helps! have a nice day :)
Maya read 3535 pages in \frac{4}{5}
5
4
of an hour. If she continues reading at the same rate, how many pages will she read in an hour?
Question for the Poster: Can I get brainliest,Thanks.Please type your questions with correct spelling so you can get your question answered to the best of everyone's ability
Answer:Maya reads 43 and 3/4 or 43.75 pages in 1 hour(or 44 pages per hour)
The area of a triangle is 92 square inches. The base is 23 inches. What is the height in inches? Do not include units in your answer.
Answer:
34,5 ?? I am not good at this but I did 92-23 that's 69 ÷ 2 = 34.5 ?
Answer:
Step-by-step explanation:
We can use the formula for the area of a triangle, to help us find the height:
Area=12⋅b⋅h
Using the formula for area, we can solve for the height by plugging in the information we have about the area and the base:
92=12⋅23⋅h
Isolate h by multiplying both sides by 2 and dividing both sides by 23.
hh=2⋅9223=8
The height is 8 inches.
Combine like terms:
7x + 3x + 4y - X+.5y
Answer:
9x + 4.5y if .5y is a decimal point, 9x + 9y if the dot is a typo
Step-by-step explanation:
If the dot is real,
7x + 3x + 4y - x + 0.5y
10x + 4y - x + 0.5y
10x - x + 4y + 0.5y
9x + 4.5y
If the dot is a typo,
7x + 3y + 4x - x + 5y
10x + 4y - x + 5y
10x - x + 4y + 5y
9x + 9y
Answer:
the answer is 9x + 9y
7x + 3x + 4y - x + 5y
7x + 3x - x + 4y + 5y
10x - x + 4y + 5y
9x + 9y
How many inches is in 5 1/4 feet
Answer:
63 in.
Step-by-step explanation:
Answer:
There is 63 inches in 5 1/4 feet :)
Solve and check each equation below . show all work . 24=g+14. f-9=12
Answer:
g = 10
f = 21
Step-by-step explanation:
Given equations:
24 = g + 14
f - 9 = 12
24 = g + 14
Subtract 14 from both sides
24 - 14 = g + 14 - 14
10 = g
g = 10
Check:
24 = g + 14
24 = 10 + 14
24 = 24
f - 9 = 12
Add 9 to both sides
f - 9 + 9 = 12 + 9
f = 21
Check:
f - 9 = 12
21 - 9 = 12
Tyler has 2 1/3 cups of yogurt to make smoothies. Each smoothie uses 1/3 cup of yogurt. How many smoothies can Tyler make with the yogurt?
Answer:
7 smoothies
Step-by-step explanation:
change 2 1/3 into improper fraction => 7/3
divide 7/3 by 1/3:
=> 7/3 × 3
=> 7
Answer:
2 1/3
Step-by-step explanation:
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 26 engines and the mean pressure was 6.6 pounds/square inch with a standard deviation of 1.0. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer:
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
The null hypothesis is accepted at 0.01 level of significance
The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch
Step-by-step explanation:
Step:-1
Given that mean of the population (μ) = 6.5 pounds/ square inch
Given that the sample size 'n' = 26
Given that mean of the sample ( x⁻) = 6.6 pounds/ square inch
Given that the standard deviation of the sample (σ) = 1.0
t₀.₀₁ = 2.7874
Step:-2
Null hypothesis:H₀: μ = 6.5
Alternative Hypothesis:H₁: μ ≠6.5
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{6.6-6.5}{\frac{1.0}{\sqrt{26} } }[/tex]
t = 0.510
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
Final answer:-
The calculated value t = 0.510 < 2.7874 at 0.01 level of significance
The null hypothesis is accepted at 0.01 level of significance
The engineer designed the valve such that it would produce a mean pressure of 6.5 pounds/square inch
The window above Matt's front door is shaped like a triangle.
How many equal-length sides does the window have?
Enter the correct answer in the box.
PLEASE HELP
Answer:
It has 2 equal side lengths
Find the median and mean of the data set below: 40,45,7,21,31 40,45,7,21,31
Answer:
mean=28.8
median=31
Step-by-step explanation:
mean=sum of all values/number of all values
mean=40+45+7+21+31+40+45+7+21+31/10
=288/10
mean=28.8
Median
arrrange in order
7,7,21,21,31,31,40,40,45,45
in case of even ungrouped data median is the average of middle two values
= (31+31)/2
median =31
can someone give me a simple answer to this problem
10.) Find values of x and y for which ABCD must
be a parallelogram.
A x=2 y=4
B x=2 y=6
C x=2 y=16
D x=6 y=2
Answer:
B x=2 y=6
Step-by-step explanation:
For ABCD to be parallelogram, following conditions should be satisfied:
2x - 0 = x + 2 & 4y - 8 = y + 10
2x - 0 = x + 2
2x - x = 2
x = 2
4y - 8 = y + 10
4y - y = 10 + 8
3y = 18
y = 18/3
y = 6
2. Half of Robert's piece of wire is equal to of Maria's wire. The total length of their wires is 10 feet. How much longer is Robert's wire than Maria's?
Step-by-step explanation:
Given that,
Half of Robert's piece of wire is equal to of Maria's wire i.e.
[tex]\dfrac{R}{2}=M[/tex] ....(1)
Total length of the wires = 10 feet
ATQ,
[tex]R+M=10[/tex] ....(2)
Use equation (1) in (2).
[tex]R+\dfrac{R}{2}=10\\\\\dfrac{3R}{2}=10\\\\R=\dfrac{20}{3}\\\\R=6.67\ ft[/tex]
So,
[tex]M=\dfrac{6.67}{2}\\\\M=3.33\ ft[/tex]
Hence, this is the required solution.
On the day of a child's birth, a parent deposits $30,000 in a trust fund that pays 3% interest, compounded continuously. Determine the balance in this account on the child's 24th birthday.
Answer:
3/100 × 30000 is the answer to your question.
Sheila had one gallon of milk. She used gallon of milk to make ice cream. She used another gallon of milk to make cookie dough. How much of a gallon of milk does Sheila have left?
Answer:
Step-by-step explanation:
we know that
1) Sheila had 1 gallon of milk
2) she used 1/4 of a gallon of milk ------> 1-1/4-----> 3/4 gallon left
3) she used 1/6 of a gallon of milk------> 3/4-1/6---> (6*3-4*1)/24---> 14/24
14/24-----> 7/12 gallon
A company manufacturing a roadside lighting system wants to estimate the average illuminance (brightness) at sunset. The illuminance at sunset for the past 10 days was as follows: 406, 385, 389, 383, 352, 379, 388, 343, 368, 387 lux. Construct a 95% confidence intervals for the average illuminance at sunset. Assume that the illuminance at sunset is approximately normally distributed.
Answer:
(364.595 ; 391.405)
Step-by-step explanation:
Given the sample data:
406, 385, 389, 383, 352, 379, 388, 343, 368, 387
Using calculator :
Sample mean, xbar = 378
Standard deviation, s = 18.74
Confidence interval :
Xbar ± Margin of error
Margin of Error = Tcritical * s/√n
TCritical at df = 24 ; 0.05 = 2.262
Margin of Error = 2.262 * 18.74/√10 = 13.405
Lower boundary = (378 - 13.405) = 364.595
Upper boundary = (378 + 13.405) = 391.405
(364.595 ; 391.405)
Rewrite as an exponential equation.
In7 = y
Please be correct, HELP ASAP!!!!
[tex] \displaystyle \: x_{ \text{lesser}}= - 18.16\\ x _{ \text{greater}} = - 11.84[/tex]
Step-by-step explanation:
we are given a equation
we want to figure out x
add 10 to both sides:
[tex] \displaystyle \: (x + 15 {)}^{2} = 10[/tex]
square root both sides:
remember that,
[tex] \displaystyle \: a = \pm \sqrt{b} [/tex]
by that
[tex] \displaystyle \: x + 15 = \pm\sqrt{10} [/tex]
cancel 15 from both sides:
[tex] \displaystyle \: x = \pm\sqrt{10} - 15[/tex]
so
[tex] \displaystyle \: x_{ \text{lesser}}= - 18.16\\ x _{ \text{greater}} = - 11.84[/tex]
Lilly was working on a report on Italian and Spanish scientists. She decided to find a 96 percent confidence interval for the difference in mean age at the time of significant scientific discoveries for Italian versus Spanish scientists. She found the ages at the time of science discovery of all the members of both groups and found the 96 percent confidence interval based on a t-distribution using a calculator. The procedure she used is not appropriate in this context because
The entire population is measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used.
The sample sizes for the two groups are not equal.
Age at the time of science discovery occurs at different intervals in the two countries, so the distribution of ages cannot be the same.
Age at the time of science discovery is likely to be skewed rather than bell shaped, so the assumptions for using this confidence interval formula are not valid.
Age at the time of science discovery is likely to have a few large outliers, so the assumption for using this confidence interval formula is not valid.
A t statistic was used to conduct a test of the null hypothesis H0: µ = 11 against the alternative Ha: µ ? 11, with a p-value equal to 0.042. A two-sided confidence interval for µ is to be considered. Of the following, which is the largest level of confidence for which the confidence interval will NOT contain 11?
A. A 90% confidence level
B. A 92% confidence level
C. A 96% confidence level
D. A 97% confidence level
E. A 98% confidence level
Answer:
The answer is "Option A and Option B".
Step-by-step explanation:
In question 1:
In all cases, the entire population is measured so that the actual medium discrepancy could be measured as well as an interval of trust cannot be used.
This issue would be that she calculated the ages with all representatives of both classes, such that she measured a whole population. It's not necessary.
In question 2:
When the p-value is 0.042. At 90% trust and 92% trust level 11 (p-value below 0.10 and 0.08) are not included. however the biggest confidence level of 92%. Consequently, the largest trust level where the 11 is Not included in the trust interval is 92% trust.
area of circle if circumference is 132m
Answer:
1386 cm²
Step-by-step explanation:
Here's your answer!
Hope it helps :)
Answer:
1386.56m²
Step-by-step explanation:
A=C2
4π
Circumference^2/4(3.14)
if f(x)=k g(x), what is the value of k
Answer:
the y intercept
Step-by-step explanation:
the k in algebra is the y intercept :))
10 POINTS FOR THE CORRECT ANSWER PLEASE HELP ME
Answer:
10.3
Step-by-step explanation:
6²+b²=9²
36+b²=81
b²=81-36
b²=45
b=√45
b=6.7
So CE is 6.7.
6²+b²=7²
36+b²=49
b²=49-36
b²=13
b=√13
b=3.6
so EA is 3.6
AC = CE+EA = 6.7+3.6 = 10.3
4. Complete the number sentence below: *
x 102 = 2,500
Help me please !!!
Directions: Find the perimeter and area of each figure below.
HELPPPP ASPPP
Answer:
17) [tex]6a^{3}b^{2}[/tex]
18) [tex]40m^{4} n^{10}[/tex]
19) 14x³y²
20) [tex]9x^{2} y^{6}[/tex]π
Step-by-step explanation:
17)
Area of triangle = 1/2*b*h
A = 1/2(4a²b)(3ab)
A = 6(a³b²)
18)
A = 1/2(4mn⁵)(20m³n⁵)
A = (40)(m⁴n¹⁰)
19)
A = 2 (1/2)(2xy)(3x²y)
A = (6x³y²) + (4x²y*2xy)
A = 6x³y² + 8x³y²
A = 14x³y²
20)
A = (3xy³)²
A = 3² x² (y³)²
Find the solutions of :
-3X + 2 2 14
Give 5 solutions
Answer:
-3(x - 738)
Step-by-step explanation:
-3x+2214
-3x+3 . 738
-3(x-738)
What is the absolute value of point J on the number line?
_------_-----_-----_-----_-----_-----_-----_-----_-----_-----_-----_----J
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
A -6
B 0
C 3
D 6
Answer:
D (6)
Step-by-step explanation:
you must place a number on a number line starting from the smallest (negative number ) to the bigger number (positive number ).
the number that is represented by J is 6
Round to one billion place. Drop the zeros.
28,436,297,825
30,943,267,101
45,831,246,935
Answer:
28,436,297,825
30,943,267,101
45,000,000,000
Step-by-step explanation:
ur welcome
PLEASEEE HELP I WILL MARK YOU BRAINIEST!!!
Answer:
26
Step-by-step explanation:
duh....
Which statements are true about the expression that y +92 Choose ALL that apply.
I uploaded the answer to a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3a8Nt8n
Answer:
A, C, D, and F