Answer:
(y + 8) = -5.5(x + 8)
or
y = -5.5x - 52
Step-by-step explanation:
So find the slope first:
[tex]\frac{-8-3}{-8+10}=\frac{-11}{2} =-5.5[/tex]
Point - Slope Form: (y + 8) = -5.5(x + 8)
Slope - Intercept Form: y = -5.5x + b
-8 = 44 + b
b = -52
y = -5.5x - 52
Write a situation involving sales at an ice cream shop that could be reasonably modeled by the equation
4.50+0.50t=6.
Answer:
4.50 is for two scoops and a normal cone. Upgrades on cone is $0.50 and any additional toppings are also $0.50
Answer:5 × t = 6
Step-by-step explanation:
Step 1: 4.50 + 0.50 = 5
Step 2: We has 5t is 5 × t
Step 3: 5 × t = 6
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. F(x) = 0.4x² - 1
Step-by-step explanation:
→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.
→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.
This means answer choice, "B," is correct.
Answer:
The answer is B
Step-by-step explanation:
→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.
→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.
This means answer choice, "B," is correct.
Working on Summer Vacation. An Adweek/Harris (July 2011) poll found that 35% of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let x represent the number who do not work during summer vacation
a. For this experiment, define the event that represents a "success"
b. Explain why x is (approximately) a binomial random variable
c. Give the value of p for this binomial experiment
d. Find P(x = 3)
e. Find the probability that 2 or fewer of the 10 U.S. adults do not work during summer vacation
A becuase i worked it out and i got that so im really confident
The probability of obtaining a defective 10-year old widget is 66.6%. For our purposes, the random variable will be the number of items that must be tested before finding the first defective 10-year old widget. Thus, this procedure yields a geometric distribution. Use some form of technology like Excel or StatDisk to find the probability distribution. (Report answers accurate to 4 decimal places.) k P(X = k) 1 .666 Correct 2 3 4 5 6 or greater
Answer:
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
Step-by-step explanation:
The probability of obtaining a defective 10-year old widget is 66.6%
p = 66.6% = 0.666
The probability of obtaining a non-defective 10-year old widget is
q = 1 - 0.666 = 0.334
The random variable will be the number of items that must be tested before finding the first defective 10-year old widget.
The geometric distribution is given by
[tex]$P(X = k) = p \times q^{k - 1}$[/tex]
Solving manually:
For k = 1:
[tex]P(X = 1) = 0.666 \times 0.334^{1 - 1} = 0.666 \times 0.334^{0} = 0.666[/tex]
For k = 2:
[tex]P(X = 2) = 0.666 \times 0.334^{2 - 1} = 0.666 \times 0.334^{1} = 0.2224[/tex]
For k = 3:
[tex]P(X = 3) = 0.666 \times 0.334^{3 - 1} = 0.666 \times 0.334^{2} = 0.0743[/tex]
For k = 4:
[tex]P(X = 4) = 0.666 \times 0.334^{4 - 1} = 0.666 \times 0.334^{3} = 0.0248[/tex]
For k = 5:
[tex]P(X = 5) = 0.666 \times 0.334^{5 - 1} = 0.666 \times 0.334^{4} = 0.0083[/tex]
For k = 6:
[tex]P(X = 6) = 0.666 \times 0.334^{6 - 1} = 0.666 \times 0.334^{5} = 0.0028[/tex]
Using Excel function:
NEGBINOMDIST(number_f, number_s, probability_s)
Where
number_f = k - 1 failures
number_s = no. of successes
probability_s = the probability of success
For the geometric distribution, let number_s = 1
For k = 1:
=NEGBINOMDIST(0, 1, 0.666) = 0.6660
For k = 2:
=NEGBINOMDIST(1, 1, 0.666) = 0.2224
For k = 3:
=NEGBINOMDIST(2, 1, 0.666) = 0.0743
For k = 4:
=NEGBINOMDIST(3, 1, 0.666) = 0.0248
For k = 5:
=NEGBINOMDIST(4, 1, 0.666) = 0.0083
For k = 6:
=NEGBINOMDIST(5, 1, 0.666) = 0.0028
As you can notice solving manually and using Excel yields the same results.
A washer and a dryer cost $639 combined. The washer costs $61 less than the dryer. What is the cost of the dryer?
Answer:
$350
Step-by-step explanation:
Let d = price of dryer
Then d - 61 is the price of the washer.
The sum of the prices is $639.
d + d - 61 = 639
2d - 61 = 639
2d = 700
d = 350
The price of the dryer is $350
Two samples are randomly selected from each population. The sample statistics are given below.
n1 = 150 n2 = 275
x1 = 72.86 -x2 = 67.34
s1 = 15.98 s2 = 35.67
The value of the standardized test statistic to test the claim that μ1 > μ2 is _________.
-2.19
2.19
3.15
-3.15
Answer:
Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]
The statistic is given by:
[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]
And replacing we got:
[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]
And the best option would be:
2.19
Step-by-step explanation:
We have the following info given:
n1 = 150 n2 = 275
[tex]\bar x_1 = 72.86, \bar x_2 = 67.34[/tex]
s1 = 15.98 s2 = 35.67
We want to test the following hypothesis:
Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]
The statistic is given by:
[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]
And replacing we got:
[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]
And the best option would be:
2.19
A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off. Assuming both promotions can be applied at the same time how much more would you pay if you applied the coupon first?
Answer:
[tex]\$0.26[/tex] has to be paid more if the coupon is applied first
Step-by-step explanation:
Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.
To find: how much more would be paid if the coupon is applied first
Solution:
Let $ x denotes cost of hand soap
Case 1:
If the discount is given first,
cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]
If the coupon for $2.00 off is applied,
Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]
Case 2:
If the coupon for $2.00 off is applied first,
cost of hand soap = [tex]\$(x-2)[/tex]
If the discount is given then,
final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]
Here,
[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]
So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.
Answer:
$0.26
Step-by-step explanation: I took the test
A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
We have,
Given:
Total number of components (n) = 1000
Number of defective components (d) = 350
a.
P(A) is the probability that the first component drawn is defective:
P(A) = d/n = 350/1000 = 0.35
b.
P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:
Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.
P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349
c.
P(A ∩ B) is the probability that both the first and second components drawn are defective:
P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122
d.
P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:
[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:
[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65
Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.
P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228
e.
P(B) is the probability that the second component drawn is defective:
P(B) = Number of defective components / Total number of components
= 350/1000
= 0.35
f.
P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:
P(A|B) = P(A ∩ B) / P(B)
= (0.35 * 0.349) / 0.35
= 0.349
g.
To determine if A and B are independent, we need to compare
P(A) * P(B) with P(A ∩ B).
P(A) * P(B) = 0.35 * 0.35 = 0.1225
P(A ∩ B) = 0.122
Since P(A) * P(B) = P(A ∩ B), A and B are independent events.
It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.
The occurrence or non-occurrence of A does not impact the probability of B.
Thus,
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ4
There are 390 students at Walker Elementary this year. This is a 30% increase from the previous year. How many students were at Walker Elementary last year?
Answer:
There were 300 students
Step-by-step explanation:
Original * 30 = increase
Add the increase to get the new number
original + increase = 308
original + original*30% = 390
Factor out original number
original ( 1+30%) = 390
Change to decimal form
original ( 1+.30) = 390
original ( 1.30) = 390
Divide by 1.3
original = 390/1.3
=300
Suppose 90 geology students measure the mass of an ore sample. Due to human error and limitations in the reliability of the​ balance, not all the readings are equal. The results are found to closely approximate a normal​ curve, with mean 88 g and standard deviation 1 g. Use the symmetry of the normal curve and the empirical rule as needed to estimate the number of students reporting readings between 87 g and 89 g.The number of students reporting readings between 87 g and 89 g is:________
Answer:
The number of students reporting readings between 87 g and 89 g is 61
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 88g
Standard deviation = 1g
Percentage of students reporting readings between 87 g and 89 g
87 = 88-1
So 87 is one standard deviation below the mean.
89 = 88+1
So 89 is one standard deviation above the mean.
By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.
Out of 90 students:
0.68*90 = 61.2
Rounding to the nearest whole number:
The number of students reporting readings between 87 g and 89 g is 61
If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles
Answer:
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
Step-by-step explanation:
The question is incomplete:
Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 4 9 3 23 39
Disliked Crunchicles 5 27 28 64 124
No Preference 7 27 10 93 137
Total 16 63 41 180 300
One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .
If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.
The number that likes Crunchicles and are 55 and over is 23.
If we calculate the probability as the relative frequency, we have:
[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]
L: Likes Crunchicles.
The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.
(x-5)(x+1)=x-5 3(x+1) 3 For what values of x are the two expressions equal ?
Answer:
x=-77+5√ 231 x=-77-5√231
I got this answer for x and the both equations are equal
5. Si P(x)=2x+4a , Q(x)=4x-2 y P[Q(4)]=60 , Calcular el valor de a
Answer:
a = 8
Step-by-step explanation:
Explanation:-
Given P(x) = 2 x+4 a
Q(x)=4 x - 2
P( Q(4)) = 60
P(4 (4) - 2) = 60
P( 14 ) = 60
2 (14) + 4 a = 60
4 a + 28 = 60
Subtracting '28' on both sides , we get
4 a +28 - 28 = 60 - 28
4 a = 32
Dividing '4' on both sides , we get
a = 8
Which shows one way the equation can be represented in words?
Z-6=1.4
Answer:
6 less than a number is equal to 1 and 4 tenths
Step-by-step explanation:
(DONT REPORT OR ANSWER) pls don’t (what is -2 plus -2)
Answer:
I think it’s -4
Step-by-step explanation:
-2 plus -2 is -4
since 2 plus 2 is 4
Hope this helps ;)
Answer:
It is -4Step-by-step explanation:
It is because 2 plus 2 is 4
so -2 plus -2 is -4
hth!
Find the slope of the line: 3x-2y=6
Answer:
slope = 3/2
Step-by-step explanation:
3x-2y=6
Get this equation in the form y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x-2y=-3x+6
-2y = -3x+6
Divide each side by -2
-2y/-2 = -3x/-2 +6/-2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3
Answer:
3/2
Step-by-step explanation:
I got this answer by putting it in the form y=mx+b
Step 1: Subtract 3x from each side
-2y = -3x+6
Step 2: Divide each side by -2
y = 3/2x -3
The slope is 3/2 and the y intercept is -3 because m is the slope and b is the y-intercept.
x/2 = -5 solve for x
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
The arrival of customers at a service desk follows a Poisson distribution. If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?
Answer:
13.53% probability that no customers arrive in a five-minute period
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
They arrive at a rate of two every five minutes
This means that [tex]\mu = 2[/tex]
What is the probability that no customers arrive in a five-minute period?
This is P(X = 0).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
13.53% probability that no customers arrive in a five-minute period
Tom wants new carpeting for his bedroom. His room is a 9 metres by 7 metres rectangle.
How much carpeting does he need to buy to cover his entire bedroom floor
Answer:
63
Step-by-step explanation:
So just find the area of the carpet:
9 * 7 = 63
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
In the attached file
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Measure of arcURN = 270°
In radians:
270° = 270π/180
270° = 3π/2
Now
Area of sector = 1/2r²∅
= 1/2(10)²(3π/2)
= 50(3π/2)
= 75π
what’s the sum of x+x^2+2 and x^2-2-x ?
Answer: The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
________________________________
Hope this is helpful to you!
Best wishes!
________________________________
Answer:
The correct answer is: " 2x² " .
________________________________
Step-by-step explanation:
________________________________
We are asked: "What is the sum of: "x + x² + 2" and "x² − 2 − x" ?
Since we are to find the "sum" ;
→ We are to "add" these 2 (two) expressions together:
→ (x + x² + 2) + (x² − 2 − x) ;
Note: Let us rewrite the above, by adding the number "1" as a coefficient to: the values "x" ; and "x² " ; since there is an "implied coefficient of "1" ;
→ {since: "any value" ; multiplied by "1"; results in that exact same value.}.
→ (1x + 1x² + 2) + (1x² − 2 − 1x) ;
Rewrite as:
→ 1x + 1x² + 2) + (1x² − 2 − 1x) ;
Now, let us add the "coefficient" , "1" ; just before the expression:
"(1x² − 2 − 1x)" ;
{since "any value", multiplied by "1" , equals that same value.}.
And rewrite the expression; as follows:
→ (1x + 1x² + 2) + 1(1x² − 2 − 1x) ;
Now, let us consider the following part of the expression:
→ " +1(1x² − 2 − 1x) " ;
________________________________
Note the distributive property of multiplication:
→ " a(b+c) = ab + ac " ;
and likewise:
→ " a(b+c+d) = ab + ac + ad " .
________________________________
So; we have:
→ " +1(1x² − 2 − 1x) " ;
= (+1 * 1x²) + (+1 *-2) + (+1*-1x) ;
= + 1x² + (-2) + (-1x) ;
= +1x² − 2 − 1x ;
↔ ( + 1x² − 1x − 2)
Now, bring down the "left-hand side of the expression:
1x + 1x² + 2 ;
and add the rest of the expression:
→ 1x + 1x² + 2 + 1x² − 1x − 2 ;
________________________________
Now, simplify by combining the "like terms" ; as follows:
+1x² + 1x² = 2x² ;
+1x − 1x = 0 ;
+ 2 − 2 = 0 ;
________________________________
The answer is: " 2x² " .
Step-by-step explanation:
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1
Step-by-step explanation:
divide vertical drop by horizontal drop
or vertical increase by horizontal increase
for example, in the graph when y increases by 1 x increases by 1
1/1=1 and thus the gradient is 1
the whole equation is y=x+3
Answer:
The slope = 1.
Step-by-step explanation:
If we count squares down for the top arrow then left to the point where the line cuts the horizontal axis we get 10 and 10.
So the slope = 10/10 = 1.
Fuel Efficiency of Cars and Trucks Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean mileage of 28.1 mpg per vehicle. The population standard deviation is 4.7 mpg. Estimate the true mean gas mileage with 95% confidence.
Answer:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Step-by-step explanation:
Information given
[tex]\bar X= 28.1[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =4.7[/tex] represent the population standard deviation
n=40 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]
[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]
We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it. Square root of the quantity x + 6 end quantity - 4 = x.
Answer:
x = 2 is the solution of the given equation
Step-by-step explanation:
Step(i):-
Given equation
[tex]\sqrt{x+6-4} = x[/tex]
squaring on both sides , we get
[tex](\sqrt{x+2})^{2} = x^{2}[/tex]
⇒ x + 2 = x²
⇒x² - x -2 =0
Step(ii):-
Given x² - x -2 =0
⇒ x² - 2x + x - 2 =0
⇒ x ( x-2) + 1(x - 2) =0
⇒ (x + 1) ( x-2) =0
⇒ x = -1 and x =2
x = 2 is the solution of the given equation
Verification:-
[tex]\sqrt{x+6-4} = x[/tex]
Put x= 2
[tex]\sqrt{2+6-4} = 2[/tex]
[tex]\sqrt{4} = 2[/tex]
2 = 2
George is given two circles 0 and circles X as shown if he wants to prove that two circles are similar what would be the correct second step in his proof
Answer: Option A.
Step-by-step explanation:
Here we have two equations for the circumference, one for each circle:
C = 2*pi*r
C' = 2*pi*r'
now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:
C/C' = 2*pi*r/(2*pi*r') = r/r'
So we have the relation:
C/C' = r/r'
And this is obtained for the division property of equality.
IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.
Then the correct option is A.
Which is the population standard deviation of the data set: 53, 35, 40, 38, 42
Answer:
daddy wants some more dior
Step-by-step explanation:
Determine the number of ways three trumpet players out of 6 are chosen for 1st chair, 2nd chair, and 3rd chair.
Answer:
120 ways
Step-by-step explanation:
There are 3 spots and 6 options
_ _ _
1 2 3
6 ways for 1st chair to be chosen
5 ways for 2nd chair to be chosen (1st chair is chosen already, so there are 5 players left)
4 ways for 3rd chair to be chosen (1st and 2nd are already chosen, only 4 players left)
Multiply 6*5*4 to find the total number of ways (120)
In a manufacturing process, a machine produces bolts that have an average length of 5 inches with a variance of .08. If we randomly select five bolts from this process, what is the standard deviation of the sampling distribution of the sample mean
Answer:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
Step-by-step explanation:
For this case we have the following info given :
[tex] \mu= 5. \sigma^2 =0.08[/tex]
And the deviation would be [tex] \sigma = \sqrt{0.08}= 0.283[/tex]
For this case we select a sample size of n = 5 and the distirbution for the sample mean would be:
[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]
And replacing:
[tex] \mu_{\bar X}= 5[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]
And the distribution is given:
[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]
