Answer:
a) 0.0985 = 9.85% probability that the thickness is less than 3.0 mm.
b) 0.0582 = 5.82% probability that the thickness is more than 7.0 mm.
c) 0.8433 = 84.33% probability that the thickness is between 3.0 mm and 7.0 mm.
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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Normally distributed, with a mean of 4.8 millimeters (mm) and a standard deviation of 1.4 mm.
This means that [tex]\mu = 4.8, \sigma = 1.4[/tex]
a) the thickness is less than 3.0 mm.
This is the pvalue of Z when X = 3. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3 - 4.8}{1.4}[/tex]
[tex]Z = -1.29[/tex]
[tex]Z = -1.29[/tex] has a pvalue of 0.0985
0.0985 = 9.85% probability that the thickness is less than 3.0 mm.
b) the thickness is more than 7.0 mm.
This is 1 subtracted by the pvalue of Z when X = 7. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7 - 4.8}{1.4}[/tex]
[tex]Z = 1.57[/tex]
[tex]Z = 1.57[/tex] has a pvalue of 0.9418
1 - 0.9418 = 0.0582
0.0582 = 5.82% probability that the thickness is more than 7.0 mm.
c) the thickness is between 3.0 mm and 7.0 mm.
This is the pvalue of Z when X = 7 subtracted by the pvalue of Z when X = 3. From questions a and b, we have these pvalues. So
0.9418 - 0.0985 = 0.8433
0.8433 = 84.33% probability that the thickness is between 3.0 mm and 7.0 mm.
Over 4 days, Krista deposited $45 into
her bank account, transferred $30 to a
friend, deposited $59, and withdrew
$18. What was the mean change per day
to Krista's account during that week?
Answer:
50
Step-by-step explanation:
45 - 30 = 15
15 + 59 = 74
74 - 18 = 56
The mean change per day to Krista's account during the week is $ 14
What is Average?
The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Given data ,
The total sum of money in Krista's account = $45 - $30 + $59 - $18
= $56
Total number of days = 4 days
Now ,
Mean change per day = Sum of money in Krista's account / Total number of days
Mean change per day = 56 / 4
= $ 14
Hence , The mean change per day to Krista's account during the week is $ 14
To learn more about average or mean click :
https://brainly.com/question/17160638
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What is the sixth term in the geometric sequence shown above?
A. 32
B. 24
C. -24
D. -32
So looking at the pattern you can tell that it is going by (-2)^(n-1)
if n=6 then we have (-2)^5 which is -32
The answers is D. -32
Each pattern below is made of six congruent
squares. Which pattern can be folded into a cube
that has a surface area of 96cm??
Step-by-step explanation:
im not sure have a good day stay safe and get a good grade
Please answer as soon as possible
Will give brainly
Which set of numbers shows the lower extreme, the lower quartile, the median, the upper quartile, and the upper
extreme for the box-and-whisker plot shown?
(14, 13, 28, 45, 54)
(6,12, 28, 44, 54)
(12, 20, 28, 44, 54)
(6,19,27, 44,54)
Will give brainly
Please help me
Solve the proportion.
10
15
a
24
a = [?]
help please I will give you brainliest!!
Let's solve your equation step-by-step.
10/a=15/24
Step 1: Cross-multiply.
10/a=15/24
(10)*(24)=15*a
240=15a
Step 2: Flip the equation.
15a=240
Step 3: Divide both sides by 15.
15a / 15 = 240/15
a=16
Help please I give brainliest and be serious
Answer:
you add all sides then you can calculate
Expand the following up to the term x⁴.
(2 + x)^-1
Answer:
Rewrite the expression using the negative exponent rule
rule b^-1 = 1/bn
1/2+x
Step-by-step explanation:
this is the correct answer you want.
A car travels 6 mile in 2 hours what is the unit rate
A 3 miles/ hour
B 1 mile/3 hour
C 3 /1 mile
D6 miles/ 1 hour
Answer:
A
Step-by-step explanation:
This is a fraction equal to
6 miles ÷ 2 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2
6 miles ÷ 2 2 hours ÷ 2= 3 miles1 hour= 3 miles hour = 3 miles per hour
Finding the area of each
Answer:
C.
HOPE THIS HELPS
-Todo <3
Step-by-step explanation:
2*2=4
PLEASE HELPP I REALLY NEED IT
Answer: Vertical angle proof
Step-by-step explanation: First off, this is really easy if you know how to do it. I think you should be able to figure it out. If you really are in collage. So Vertical angle proof, QPR is essentially (2x-30) but we need to find x. We know a triangle is 180 degrees and if it's a right angle then two angles add to 90.
So x+(2x+30)=90, 3x+30=90, 90-30=60, 3x=60, x=20. So there you have it. Now put x into the equation, 2(20)+30=70
70
What is -60a^2+642a-420
Answer:
The answer is −6(10a−7)(a−10)
Step-by-step explanation:
1) Factor out the common term 6.
[tex] - 6( {10a}^{2} - 107a + 70)[/tex]
2) Split the second term in 10a² - 107a + 70 into two terms.
[tex] - 6( {10a}^{2} - 7a - 100a + 70)[/tex]
3) Factor out common terms in the first two terms, then in the last two terms.
[tex] - 6(a(10a - 7) - 10(10a - 7))[/tex]
4) Factor out the common term 10a - 7.
[tex] - 6( 10a - 7)(a - 10[/tex]
Therefor, the answer is -6 ( 10a - 7) (a - 10).
help me pleeeeeeeeeeeeease
Answer:
1:9
Step-by-step explanation:
9/9 = 1 and 81/9 = 9
Thus, 9:81 ratio simplified is 1:9
please help me. this is my last problem and i’m clueless.
Answer:
-3
Step-by-step explanation:
so you SUBSTITUTE -2 in for z
ok i think they are trying to be tricky here
so
-1 - (-(-2))
inside parentheses, the two negatives are going to cancel eachother out.
now you have
-1 - (2)
which is
-1 - 2
-1 minus 2 is -3
please help me, its urgent ❗❗❗❗❗❗❗❗❗❗❗❗
Answer:
the answer to this one is A.
Step-by-step explanation:
Pls hurry I need an instant answer ASAP! Thank you
Answer:
A= -2
Step-by-step explanation:
Hope I helped!! Negitive 2
find the greatest 5 digit number which exactly divide by 16, 56 and 120
five-digitsinceStep-by-step explanation:
Ummm.....I have never done this before but I THINK what your supposed to do is find the lcm of all the pairs you can get from those 3 numbers.
so lcm(16,56)=112
lcm(56,120)=840
lcm(16,120)=240
Now take any number from this and take the lcm of that
lcm(112,840)=1680
that is the number if you take the lcm of any of them so it is the lcm of them all but it is not a number. so 16,56, and 120 are divisible by 2 I just multiplied 1680 by 2 until I got the highest possible 5 digit number which was 53760
Hope that helps :)
9514 1404 393
Answer:
99120
Step-by-step explanation:
The LCM of 16, 56, 120 can be found from their factors:
16 = 2^4
56 = 2^3 · 7
120 = 2^3 · 3 · 5
So, the least common multiple is 2^4×3×5×7 = 1680.
10^5/1680 = 59 r 880
The largest 5-digit number divisible by 16, 56, and 120 is 59×1680 = 99120.
Damian took out a car loan for $10,500 that has a 0% APR for the first 12
months and will be paid off with monthly payments over 3 years. For how
many months will Damian be charged interest?
A. 24 months
B. 48 months
C. 36 months
D. 12 months
Answer: 24 Months
Step-by-step explanation:
A- (x+4) (4x-1)
B- (x-4)(4x-1)
C-(x+4)(4x+1)
D-(x-4)(4x+1)
D-(x-4)(4x+1) is your answer
Answer:
4x²-15x-4
doing middle term factorization
4x²-16x+x-4
4x(x-4)+1(x-4)
(x-4)(4x+1)
help plz
The first four terms of a sequence are shown below:
9, 5, 1, −3
Which of the following functions best defines this sequence?
A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
B.) f(1) = 9, f(n + 1) = f(n) + 4; for n ≥ 1
C.) f(1) = 9, f(n + 1) = f(n) − 5; for n ≥ 1
D.) f(1) = 9, f(n + 1) = f(n) + 5; for n ≥ 1
Answer:
A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
Step-by-step explanation:
The first four terms of a sequence are shown below.
Let
f(1) = 9
f(2) = 5
f(3) = 1
f(4) = -3
Therefore we know that
f(2) - f(1) = 5 - 9
f(2) - f(1) = - 4
f(2) = f(1) - 4
f(3) - f(2) = 1 - 5
f(3) - f(2) = - 4
f(3) = f(2) - 4
f(4) - f(3) = -3 - 1
f(4) - f(3) = - 4
f(4) = f(3) - 4
Hence the answer is A.) f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
A brochure claims that the average maximum height a certain type of plant is 0.7 m. A gardener suspects that this estimate is not accurate locally due to soil conditions. A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m. Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m. Assume that the population standard deviation is 0.2 m.
Answer:
We accept the null hypothesis, that is, that the population mean is not different from 0.7.
Step-by-step explanation:
A brochure claims that the average maximum height a certain type of plant is 0.7 m.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 0.7[/tex]
A gardener suspects that this estimate is not accurate locally due to soil conditions.
Hypothesis test to determine whether the population mean is different from 0.7m, which means that the alternate hypothesis is:
[tex]H_{a}: \mu \neq 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.7 is tested at the null hypothesis:
This means that [tex]\mu = 0.7[/tex]
A random sample of 43 plants is taken. The mean height of the plants in the sample is 0.65m.
This means, respectively, that [tex]n = 43, X = 0.65[/tex]
Assume that the population standard deviation is 0.2 m.
This means that [tex]\sigma = 0.2[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.65 - 0.7}{\frac{0.2}{\sqrt{43}}}[/tex]
[tex]z = -1.64[/tex]
Pvalue of the test:
Since we are testing that the mean is different of a value, and z is negative, the pvalue of the test is 2 multiplied by the pvalue of z = -1.64
z = -1.64 has a pvalue of 0.0505
2*0.0505 = 0.101
Using a 1% level of significance, perform a hypothesis test to determine whether the population mean is different from 0.7m.
0.101 > 0.01, which means that we accept the null hypothesis, that is, that the population mean is not different from 0.7.
Simplify the expression: 2x+1+7x
Answer:
9x+1 is your answer
Step-by-step explanation:
2x+1+7x
2x+7x+1
9x+1
Answer:
9x+1
Step-by-step explanation:
2x+1+7x= 9x+1
can i have brainliest please
A trail is 2 miles long. There is a marker every 1/8 mile. How many markers are there?
Answer:
16
Step-by-step explanation:
Number of Markers =
[tex]2 \div \frac{1}{8} \\ = 2 \times 8 \\ = 16[/tex]
What is missing in the percent what is number 45 of 80
Answer:
35
Step-by-step explanation:
Find the area of the figure.
A) 96cm
B) 110cm
C) 120cm
D) 150cm
Answer:
A
Step-by-step explanation:
Answer:
209952=Area
56=Perimeter
Step-by-step explanation:
3*3*2*2*9*9*6*12=Area
3+3+2+2+9+9+6+12=Perimeter
a fair cube has 2 red sides, 2 blue sides, and 2 green sides what is the probability of rolling red or blue
Giving out the brainlest answer !!! help plsss ASAP !!!!!!!
Answer:
5
Step-by-step explanation:
As given
1/sqrt2=x/5sqrt2
5sqrt2/sqrt2=x Both sqrt will get cancelled
5=x
A rectangle has length of (5x+2) and a width of (3x-1) with an area of 308 units squared. Find the perimeter
Answer:
haach f,f msfmavfb
Step-by-step explanation:
Which expression is equivalent to (3x^2y)^2 (2x^4y^2)^2?
A. 10x^10y^6
B. 12x^24y^8
C. 24x^10y^7
D. 36x^12y^6
Pls help if not that’s fine just pls stop with the links
Answer:
C. 73 and 73
Step-by-step explanation:
An isosceles triangle has two angles that are the same, that narrows it down to C and D. The question states that there is only one 34° angle so it has to be C.
Answer:
C. 73° and 73°
Step-by-step explanation:
We know that the sum of interior angles in a triangle is equal to 180° and
Isosceles triangles has two angles with same measurement
it stated in the question that exactly one angle has measure of 34°
So the other two angles must be equal for the triangle to be isosceles
180 - 34 = 146 and this divided by 2
73° and 73° is the answer.
This Question: 1 pt
Determine whether the variation between the indicated quantities is direct or inverse.
The time required to defrost a frozen hamburger in a room and the temperature of the room.
Choose the correct answer below.
Inverse
Direct
Answer:
Inverse variation
Step-by-step explanation:
Required
What type of variation is described in the question
From the question, we understand that: the relationship is between time and temperature
The higher the time, the lower the temperature of the hamburger (to get freeze).
Hence, the relationship is an inverse variation.