The value of y is less than or equal to 0 (y ≤ 0).
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Given:
4y + 1/5 ≤ 4/5
We have to find the value of y.
Subtract 1/5 from both sides,
4y + 1/5 - 1/5 ≤ 4/5 - 1/5
4y ≤ 3/5
Multiply both sides by 1/4
4y x 1/4 ≤ 3/5 x 1/4
y ≤ 3/20
y ≤ 0.15
Hence, the value of y is less than or equal to 0 (y ≤ 0).
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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 136 millimeters, and a variance of 36. If a random sample of 50 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 1.9 millimeters
Answer:
0.025 = 2.5% probability that the sample mean would differ from the population mean by greater than 1.9 millimeters
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 diameter of 136 millimeters, and a variance of 36.
This means that [tex]\mu = 136, \sigma = \sqrt{36} = 6[/tex]
Sample of 50:
This means that [tex]n = 50, s = \frac{6}{\sqrt{50}} = 0.8485[/tex]
What is the probability that the sample mean would differ from the population mean by greater than 1.9 millimeters?
This is the probability that it is less than 136 - 1.9 = 134.1 millimeters or more than 136 + 1.9 = 137.9 millimeters. Since the normal distribution is symmetric, there probabilities are equal, which means that we can find one of them and multiply by two.
Probability that it is less than 134.1 millimeters:
This is the pvalue of Z when X = 134.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{134.1 - 136}{0.8485}[/tex]
[tex]Z = -2.24[/tex]
[tex]Z = -2.24[/tex] has a pvalue of 0.0125
2*0.0125 = 0.025
0.025 = 2.5% probability that the sample mean would differ from the population mean by greater than 1.9 millimeters
f(x) = 3x – 5
g(x) = –6x2 + 6x + 2
Find: f(x) · g(x)
Answer:
f(x) = 3x - 5
g(x) = 6x^2 + 2x
Find: g(f(x))
method: for each x in g, substitute (3x-5)
g[f(x)]=6(3x-5)^2+2(3x-5)
=6(9x^2-30x+25)+6x-10
=54x^2-180x+150+6x-10
Step-by-step explanation:
2. A meeting room has 8 rows of
chairs. Each row has 10 chairs.
The first people to arrive fil 2 rows.
How many chairs are not filled?
Answer:60
Step-by-step explanation:
There are 80 chairs in all because 8 rows x 10 chairs per row. The first people fill two rows which is 20 chairs because each row is 10 chairs so 60 chairs are left
The question is in the pic pls help
Answer:
pink
Step-by-step explanation:
Help if you can please
Answer:
10 coconut cupcakes
Step-by-step explanation: so, here is what we do since there is 8 cupcakes sold and 4 of them are coconut cupcakes we divide. this is hard to explain but we know that 8 divided by 4 is 2 so we have to multiply to 20 so like 2 times 10 which gives us 20. then we use the answer that we got from multiplying which is 10 as our answer if that makes sense.
The ring Zp^3 has exactly____maximal ideals
Discuss the various factors which lead to the formation of droughts
Step-by-step explanation:
Below average rainfall in a region for several months
Not enough rain to be absorbed into the ground before evaporating
Cutting down trees and overuse of land
Hot dry air masses blown into a region by westerly winds
Human activities that deplete the water table faster than it can be replaced
A parent believes the average height for 13-year-old girls differs from that of 13-year-old boys. The difference in the height between girls and boys using a 95% confidence interval is estimated to be 0.26 to 0.41 inches. Based on the results, is there a significant difference between the true mean height of 13-year-old girls and boys
Answer:
There is 0.15 difference so yes
Step-by-step explanation:
Helppppp !!! Quick I’ll mark u brainlist
Answer:
it is b approximately 163 yards
100 times 5 dino nuggie is how much
Answer:
500 dino nuggies.
Step-by-step explanation:
Hope this helps
Answer:
500 dino nuggies!!!
Step-by-step explanation:
please help me with this asap
Answer:
Upper left 10, upper right 2, lower left 3, lower right 3.
Step-by-step explanation:
they give us the upper left and lower right in the first two bullet points. Then “in total, 12 girls can sing”. 12 - the 10 who can sing and dance = 2 for upper right.
They also say there are 18 girls total. 18 - 10 - 3 = 3 for the lower left
Rewrite 24 + 48 using GCF and the distributive property.
a: 12(3+1)
b: 24(1+2)
c: 3(12+6)
d: 5(2+3)
Help fast i will make you the brainly thing if you get it right Which situation can be represented by the expression 3+(-7).
Choose 1 answer:
A Afootball team lost 3 yards on one play. The team gained 7 yards on the next play.
B
A football team gained 3 yards on one play. The team lost 7 yards on the next play.
A football team gained 3 yards on one play. The team gained 7 yards on the next play.
Answer:
I think it's B
Step-by-step explanation:
3 + (-7)
= 3 - 7
it's 3 - 7 because the positive and negative cancel each other out. A good example to think of intergers is with money, ex: If I borrow $7 from you and the next day I pay back $3, how much money do I still owe you?
(I'm not 100% sure)
Calculate the slope of a line that goes through points (3, 4) and (0, 0).
Question 5 options:
3/4
3
4
4/3
Answer:
4/3
Step-by-step explanation:
0-4/0-3
-4/0-3
-4/-3
4/3
Answer:
Step-by-step explanation:
3\4
solve -5 √x =-15
A. X= -9
B. X= -7
C. X= 9
D. X= 7
Solve the equation. Check your solution.
30) x/4 = 9
Answer:
x = 36
Step-by-step explanation:
x/4 = 9
multiply both sides by 4
x/4 (4) = 9(4)
x = 36
The answer is x = 36
We can check by plugging in x = 36 to the original equation:
x/4 = 9
(36)/4 = 9
9 = 9
Correct
I don’t know why there’s so many numbers to this help me
Answer:
806,350.307eight hundred six thousand three hundred fifty and three hundred seven thousandthsStep-by-step explanation:
You are asked to add up these numbers and describe the number in words. The given form is called "expanded form". It shows you the place value of each digit.
The sum is ...
800,000 +6,000 +300 +50 +0.3 +0.007 = 806,350.307
In word form, this is ...
"eight hundred six thousand three hundred fifty and three hundred seven thousandths"
PLEASE ANSWER ILL GIVE YOU BRAINLIEST
Answer:
80.07 in^2
Step-by-step explanation:
The equation is given: SA = 2πrh
h (height) = 8.5
r (radius is half the diameter) = 3 / 2 = 1.5
SA = 2π (1.5) (8.5) = 80.07
what are 4 major accomplishments in Will Smith's life?
Answer:
He first rapped as a duo named Dj Jazzy Jeff and the fresh prince in 1988, with the hit songs Summertime and Parents just don't understand
He then started his career as an actor with the hit sitcom The fresh prince of Bel-air in 1990
He then later gained more popularity in 1997 with hit songs like Gettin jiggy and Miami
He became a well-known actor for movies like Bad boys, Men in black, and the Aladin remake in 2019
Step-by-step explanation:
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How is solving a two-step INEQUALITY similar to and different from solving a two-step EQUATION?
Answer:
there both similar by using inverse operations to isolate the variable term by using addition or subtraction and multiplying or dividing to solve for the variable .
the difference is for an inequality if u multiply or divide by a negative number then u have to reverse the inequality symbol, for regular equations u don't have to do that , and for regular equations there is a equal sign and not a inequality symbol
Step-by-step explanation:
just explained it above
hope I helped ! pls mark me brainlest if I got it right thanks :)
Scores on a statistics final in a large class were normally distributed with a mean of 79 and a standard deviation of 12. Use the TI-84 PLUS calculator to answer the following. Round the answers to at least two decimals. (a) Find the 36th percentile of the scores. (b) Find the 70th percentile of the scores. (c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A
Answer:
a) The 36th percentile of the scores is of 74.68.
b) The 70th percentile of scores is 85.3.
c) The minimum score needed to get an A is 93.1.
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.
Mean of 79 and a standard deviation of 12.
This means that [tex]\mu = 79, \sigma = 12[/tex]
(a) Find the 36th percentile of the scores.
This is X when Z has a pvalue of 0.36. So X when Z = -0.36.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.36 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = -0.36*12[/tex]
[tex]X = 74.68[/tex]
The 36th percentile of the scores is of 74.68.
(b) Find the 70th percentile of the scores.
This is X when Z has a pvalue of 0.7, so X when Z = 0.525.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 0.525*12[/tex]
[tex]X = 85.3[/tex]
The 70th percentile of scores is 85.3.
(c) The instructor wants to give an A to the students whose scores were in the top 12% of the class. What is the minimum score needed to get an A?
The 100 - 12 = 88th percentile, which is X when Z has a pvalue of 0.88, so X when Z = 1.175.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.175 = \frac{X - 79}{12}[/tex]
[tex]X - 79 = 1.175*12[/tex]
[tex]X = 93.1[/tex]
The minimum score needed to get an A is 93.1.
Medical researchers are studying a certain genetic trait found in two populations of people, W and X. From an independent random sample of people taken from each population, the difference between the sample proportions of people who carried the trait (W minus X) was 0.22. Under the assumption that all conditions for inference were met, a hypothesis test was conducted using the following hypotheses.
H0 : pW=pXHa : pW > p XHo : pW= pX Ha: pW >pX
The p-value of the test was 0.03. Which of the following is the correct interpretation of the p-value?
a. The probability of selecting a person from population W who carries the trait is 0.22, and the probability of selecting a person from population X who carries the trait is 0.03.
b. If the proportions of all people who carry the trait are the same for both populations, the probability of observing a sample difference of at least 0.22 is 0.03.
c. If the proportions of all people who carry the trait are the same for both populations, the probability of observing a sample difference of 0.22 is 0.03.
d. If the difference in proportions of people who carry the trait between the two populations is actually 0.22, the probability of observing that difference is 0.03.
e. If the difference in proportions of people who carry the trait between the two populations is actually 0.03, the probability of observing that difference is 0.22.
Answer:
If the proportions of all people who carry the trait are the same for both populations, the probability of observing a sample difference of at least 0.22 is 0.03
Step-by-step explanation:
Given the hypothesis :
H0 : pW = pX
Ha : pW > pX
W - X = 0.22
Pvalue = 0.03
Since the Pvalue gives the probability of obtaining a value or result figure which is atleast as extreme as the observed value. The observed value here is 0.22 resulting from the difference in W and X (W - X).
This can thus be interpreted to mean ; going by the Null (difference between W and X) ; the probability of obtaining a value of atleast 0.22 as difference is 0.03
Find the missing values in the ratio table. Then write the equivalent ratios
What is the mean and MAD of this data set
Answer:
Option B will be your answer
Step-by-step explanation:
mean:6 gerbils
MAD:2.29
so its B
hope it helps
have a great day!!
k is decreased by 20
Solve for x to the nearest degree.
Answer: 22 degrees
Step-by-step explanation:
[tex]sin^{-1}[/tex]([tex]\frac{7}{19}[/tex])= 21.62 nearest degree= 22
What is the median for the data set below? 2 10 6.5 8.8 3 6 4.0 12.5
Answer:
Hi! The answer to your question is 6.25
Step-by-step explanation:
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- Brooklynn Deka
write an expression based on description; use grouping symbols
1:The sum of 11 and n decreased by 9
2:The product of y less than 16 and 5
Answer:
it's your answer and make me barinly least
PLS HELP
MATH ILL GIVE BRAINLIST
Answer:
D. g(x) = [tex]\frac{1}{4}x^{2}[/tex]
Step-by-step explanation:
The correct formula for g(x) is the following
g(x) = [tex]\frac{1}{4}x^{2}[/tex]
when dealing with the square of a variable, the lower the number that you multiply it by, the wider the parabola will be. In this case multiplying f(x) by 1/4 would give us the parabola that passes by point (2, 1). We can prove this by substituting 2 for x like so...
g(2) = [tex]\frac{1}{4} * 2^{2}[/tex]
g(2) = [tex]\frac{1}{4} * 4[/tex]
g(2) = 1
Which statement best explains whether △ABC is similar to △DEF?
A) The triangles are not similar because 613≠820.
B) The triangles are similar because 613=820.
C) The triangles are similar because 820=1025.
D) There is not enough information to determine whether the triangles are similar.
A). They are not similar, because 6/13 is not equal to 8/20
For triangles to be similar, the ratios of sides need to be the same (shortest to shortest, middle to middle, longest to longest). The shortest sides are 6 and 13, respectively, the middle ones are 8 and 20. Because 6/13 is not equal to 8/20, the triangles are not similar.
The statement best explains whether △ABC is similar to △DEF is (A) The triangles are not similar because 613≠820.
What are similar triangles?Similar triangles are triangles that have similar corresponding side lengths
The corresponding sides of the triangles are:
Triangle A Triangle B
6 13
8 20
10 25
Calculate the ratios
Ratio = 6/13
Ratio = 8/20
The ratios are not equal.
Hence, the triangles are not similar
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