Answer:
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]
The correct answer choice is a. (62.2, 113.8)
Step-by-step explanation:
Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with a standard deviation of $225.
Sample size = n₁ = 500
Sample mean = x₁ = $527
Standard deviation = s₁ = $225
Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with a standard deviation of $189
Sample size = n₂ = 500
Sample mean = x₂ = $439
Standard deviation = s₂ = $189
We are asked to find the 95% confidence interval for the difference between two means.
The given group of answer choices are
a. (62.2, 113.8)
b. (86.2, 120.5)
c. (10.3, 23.8)
d. (55.6, 67.8)
The confidence interval for the difference between two means is given by
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
Where [tex]\bar{x_{1} }[/tex] and [tex]\bar{x_{2} }[/tex] are the given sample means and margin of error is given by
[tex]$ MoE = z_{\alpha/2} \cdot \sqrt{\frac{s_{1}^2}{n_1} + \frac{s_{2}^2}{n_2}} $[/tex]
The z-score corresponding to 95% confidence level is given by
Significance level = α = 1 - 0.95 = 0.05/2 = 0.025
From the z-table at α = 0.025 the z-score is 1.96
[tex]$ MoE = 1.96 \cdot \sqrt{\frac{225^2}{500} + \frac{189^2}{500}} $[/tex]
[tex]MoE = 1.96 \cdot 13.14[/tex]
[tex]MoE = 25.75[/tex]
Finally,
[tex]CI = (\bar{x_{1} } - \bar{x_{2}} ) \pm MoE\\\\[/tex]
[tex]CI = (527 - 439) \pm 25.75\\\\CI = 88 \pm 25.75\\\\CI = 88 - 25.75 \:\: and \:\: 88 + 25.75\\\\CI = (62.2 \: ,\: 113.8 )[/tex]
Therefore, the correct answer choice is a. (62.2, 113.8)
How to use z-table?
In the z-table find the probability of 0.025
Note down the value of that row, it would be 1.9.
Note down the value of that column, it would be 0.06.
Add the two numbers together.
The z-score is 1.9 + 0.06 = 1.96
If ABC ~ DEF what is the scale factor of abc to def
Answer:
It might be 1/3 but I'm not 100% sure
The required scale factor of ABC to DEF is 1/3.
Scale factor of ABC to DEF to determine.
What is scale factor?The scale factor is defined as the ratio of modified change in length to
Here, Triangle ABC is similar to triangle DEF. So, the ratio of the same sides describe the scale factor.
Scale factor = EF/BC
= 7/21
= 1/3
Thus, the required scale factor of ABC to DEF is 1/3.
Learn more about Scale factor Here:
https://brainly.com/question/22312172
#SPJ5
Maddie is packing moving boxes. She has one 3 cubic-foot box and one 6 cubic-foot box. How many cubic feet of clothing can she fit in the two boxes?
8 9 10 12
Answer:
She can fit 9 cubic feet of clothing in the two boxes.
Step-by-step explanation:
She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.
3 + 6 = 9
Answer:
9 cu ft.
Step-by-step explanation:
That is the sum of the capacities of the 2 boxes
= 3 + 6
= 9 cu ft.
Complete this expression using the distributive property
5(4 + 8) =
O (5 + 4)(5 + 8)
O 5(4) + 8
O 5(4) + 5(8)
O (5+4) + (5 + 8)
Answer:
5(4) + 5(8)
Step-by-step explanation:
Through destributive property, 5 is multiplied by both 4 and 8
Answer:
the person above is right thank and five star them
Step-by-step explanation:
Help help , Please help! Brainliest if correct! What was the equation of the graph below before it was shifted to the left 1.5 units? A. G(x)=(x3)^3-(x-3) B. G(x)=(x-1.5)^3 C. G(x)=(x)^3 D.G(x)=x^3-x
Answer:
A. G(x) = (x -3)^3 -(x -3)
Step-by-step explanation:
The graph before it was shifted left will be a right-shift of the equation shown. That is accomplished by replacing x with (x-1.5). Then the right-shifted equation is ...
G(x) = ((x-1.5) -1.5)^3 -((x -1.5) -1.5)
G(x) = (x -3)^3 -(x -3) . . . . matches choice A
Classify the following triangle .check all that apply
Answer:
acute and scalene
Step-by-step explanation:
Answer:no entiendo esta en ingles
Step-by-step explanation:
Express each percent as a fraction in simplest form.
a. 85%
b. 5 72%
c. 12.55%
Answer:
(a) 17/20 b.5/18/25 c. 1.255
Find the equation of a line perpendicular to 2x-4y=1 that contains the point (-4, -2).
Answer:
y = -2x - 10
Step-by-step explanation:
1. rearrange to find the gradient.
the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.
2. substitute into y - y1 = m (x - x1)
y - (-2) = -2 (x - (-4))
y = -2x - 10
An amount was invested at r% per quarter. What value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
25.75 % interest rate
Step-by-step explanation:
Given:
Amount was invested = r% per quarter
Amount invested = P
Rate of interest = r % per quarter
Time (n) = 4 Quarters
Computation:
A = P(1 + r/100)ⁿ
According to question.
⇒ A = P + 1.5P = 2.5P
⇒ 2.5P = P(1 + r/100)⁴
⇒ 2.5 = (1 + r/100)⁴
⇒ 1 + r/100 = 1.2575
⇒ r/100 = 0.2575
⇒ r = 25.75
25.75 % interest rate
The mean weight of frozen yogurt cups in an ice cream parlor is 8 oz.Suppose the weight of each cup served is normally distributed withstandard deviation 0.5 oz, independently of others.(a) What is the probability of getting a cup weighing more than 8.64oz
Answer:
10.03% probability of getting a cup weighing more than 8.64oz
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this question, we have that:
[tex]\mu = 8, \sigma = 0.5[/tex]
What is the probability of getting a cup weighing more than 8.64oz
This is the 1 subtracted by the pvalue of Z when X = 8.64. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.64 - 8}{0.5}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a pvalue of 0.8997
1 - 0.8997 = 0.1003
10.03% probability of getting a cup weighing more than 8.64oz
6
Cheryl had 160 stickers more than Gareth. If Cheryl gave 185 stickers
to Gareth, Gareth would have 3 times as many stickers as Cheryl
How many stickers did Gareth have at first?
165
Answer:
260 stickers
Step-by-step explanation:
Let Gareth's stickers be x.
Hence Cheryl sticker is 160+x;
If Cheryl gave 185 stickers
to Gareth, it means:
Cheryl has at the moment;
160 + x - 185 = x - 25
At this time when Gareth receives 185 he now has:
x+ 185
Also when he receives x +185, he has 3 times Cherry's meaning:
x+185 =3(x-25)
x + 185 = 3x -75
185 + 75 = 3x-2x
260= x
x = 260.
Hence Gareth has 260 stickers
According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (Consumer fraud and, 2008). (7.1.2)
State the random variable, population parameter, and hypotheses.
Answer:
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
Step-by-step explanation:
Information provided
n=1432 represent the random sample taken
X=321 represent the number of complaints
[tex]\hat p=\frac{321}{1432}=0.224[/tex] estimated proportion of complaints in 2007
[tex]p_o=0.23[/tex] is the value to verify
z would represent the statistic
Random variable: for this case represent the number of complaints in 2007
Population parameter: represent the real proportion of complaints in 2007 p
Hypothesis to verify
We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:
Null hypothesis:[tex]p=0.23[/tex]
Alternative hypothesis:[tex]p \neq 0.23[/tex]
someone plz help asap plz
Answer:
a) 6
b) 10
Step-by-step explanation:
a) The area of a rhombus is half the product of the diagonals, meaning that the area of the shaded part is 4*3/2=6 square meters.
b) To find the area of the white background, you need to find the area of the full rectangle, and then to find the area of both rhombii. The area of the black rhombus is 2*4/2=4 square meters. The area of the full rectangle is 4*5=20 units. Subtracting the areas of the two rhombii, you get an area for the white background of 20-6-4=10 square meters. Hope this helps!
3. Set up an equation and use it to solve for x.
51°
(5x + 1)
Answer:
51 = 5x+1
x = 10
Step-by-step explanation:
The angles are vertical angles which means they are equal
51 = 5x+1
Subtract 1 from each side
51-1 = 5x+1-1
50 = 5x
Divide each side by 5
50/5 = 5x/5
10 =x
Answer:
10
Step-by-step explanation:
51 = 5x + 1
5x = 51 - 1
5x = 50
x = 10
Hope this helps!
What is the value of expression below? 7/2-4.5x3+8
Answer:-2
Step-by-step explanation:
Ok so I’m assuming the x stands for the multiplication sign
7/2-4.5*3+8
Use pemdas
Multiplication first
7/2-4.5*3+8
-4.5*3
7/2-13.5+8
Then addition
-13.5+8
Lastly subtraction
7/2-5
-2
Express loga 6 + loga 70 as a single logarithm
Answer:
logₐ(420)
Step-by-step explanation:
Answer:
The answer is
[tex] log_{a}(420) [/tex]
Step-by-step explanation:
You have to use Logarithm Law,
[tex] log_{a}(b) + log_{a}(c) ⇒ log_{a}(b \times c) [/tex]
* Take note, number b and c can only be multiplied when they have the same base, a
So for this question :
[tex] log_{a}(6) + log_{a}(70) [/tex]
[tex] = log_{a}(6 \times 70) [/tex]
[tex] = log_{a}(420) [/tex]
A Biology test contains 10 multiple choice questions each with 5 choices and one correct answer. If a law school student just randomly guesses on each of the 10 questions, i.e., the probability of getting a correct answer on any given question is 0.2. Assume that all questions are answered independently. (a) What is the probability that the student answers at least 9 questions correctly
Answer:
0.0004% probability that the student answers at least 9 questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. All questions are answered independently. This means that we use the binomial distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question, we have that:
[tex]n = 10, p = 0.2[/tex]
What is the probability that the student answers at least 9 questions correctly
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0.000004[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0 [/tex]
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.000004 + 0 = 0.000004[/tex]
0.0004% probability that the student answers at least 9 questions correctly
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Volume of sphere = (4/3)πr³
= 4/3(3.14)(d/2)³
= 4/3(3.14)(7/2)³
= 4/3(3.14)(3.5)³
= 4/3(3.14)(42.875)
= (1.33)(3.14)(42.875)
= 179.5 cm³
Answer:
The answer is 179.5 cm^2
Please answer this correctly
Answer:
4
Step-by-step explanation:
Set the height of the missing bar to 4 as there are 4 quantities between 21-25.
Write the value of the digit 5 in this number:178.25
I
Step-by-step explanation:
178.25
The number 5 is in the place of one's so the value of 5 is 5
(TEKS 2A.) EF has endpoints E (8,3) and F(-4,9). What is the distance of the given segment?
A 8.544
C 11.250
B 10.345
D 13.416
how to differentiate functions
Answer: see boxed answers below
Step-by-step explanation:
(i) multiply the exponent to the coefficient then subtract 1 from the exponent.
[tex]y=\dfrac{3}{5x^3}+3x^4+2x^2-20\\\\\\\text{rewrite it as follows}: y=\dfrac{3}{5}x^{-3}+3x^4+2x^2-20x^0\\\\\\y'=(-3)\dfrac{3}{5}x^{-3-1}+(4)3x^{4-1}+(2)2x^{2-1}-(0)20x^{0-1}\\\\\\y'=-\dfrac{9}{5}x^{-4}+12x^3+4x^1-0\\\\\\y'=\large\boxed{-\dfrac{9}{5x^{4}}+12x^3+4x}[/tex]
(ii) Use the division formula: [tex]y = \dfrac{a}{b}\rightarrow \quad y'=\dfrac{ab'-a'b}{b^2}[/tex]
[tex]a=5x^3+1\qquad \qquad a'=15x^2\\b=3x^5+4x^2\qquad \quad b'=15x^4+8x\\\\\\y'=\dfrac{(15x^2)(3x^5+4x^2)-(5x^3+1)(15x^4+8x)}{(3x^5+4x^2)^2}\\\\\\.\quad =\dfrac{45x^7+60x^4-75x^7-55x^4-8x}{(3x^5+4x^2)^2}\\\\\\.\quad =\large\boxed{\dfrac{-35x^7+5x^4-8x}{(3x^5+4x^2)^2}}[/tex]
A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920, 1290, 2220, and 1420. Find the z-scores that correspond to each value and determine whether any of the values are unusual
Answer:
A score of 1920 has a z-score of 1.27.
A score of 1290 has a z-score of -0.74.
A score of 2220 has a z-score of 2.23.
A score of 1420 has a z-score of -0.32.
The score of 2220 is more than two standard deviations from the mean, so it is unusual.
Step-by-step explanation:
When the distribution is normal, we use 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.
If X is 2 or more standard deviations from the mean, it is considered unusual.
In this question, we have that:
[tex]\mu = 1521, \sigma = 314[/tex]
Score of 1920:
X = 1920. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1920 - 1521}{314}[/tex]
[tex]Z = 1.27[/tex]
A score of 1920 has a z-score of 1.27.
Score of 1290:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1290 - 1521}{314}[/tex]
[tex]Z = -0.74[/tex]
A score of 1290 has a z-score of -0.74.
Score of 2220:
X = 1290. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2220 - 1521}{314}[/tex]
[tex]Z = 2.23[/tex]
A score of 2220 has a z-score of 2.23.
Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.
Score of 1420:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1420 - 1521}{314}[/tex]
[tex]Z = -0.32[/tex]
A score of 1420 has a z-score of -0.32.
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46
Rewrite the expression in the form z^n
[tex] \sqrt[5]{z {}^{4}z {{}^{ \frac{ - 3}{2} } } } [/tex]
Answer:
[tex]z^{0.5}[/tex]
Step-by-step explanation:
So first simplify inside:
[tex]z^4z^{-1.5}=z^{2.5}[/tex]
Now divide that by 5:
[tex]z^{0.5}[/tex]
* If you are given the measurements of two sides of a triangle,
what will be true about the triangles you make?
Answer:both sides will be equal
Step-by-step explanation:
What is the value of x to the nearest tenth? gradpoint
Answer:
5
Step-by-step explanation:
A local cable company claims that the proportion of people who have Internet access is less than 63%. To test this claim, a random sample of 800 people is taken and its determined that 478 people have Internet access. The following is the setup for this hypothesis test: H0:p=0.63 Ha:p<0.63 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
Answer:
Step-by-step explanation:
For the null hypothesis,
H0 : p = 0.63
For the alternative hypothesis,
Ha : p < 0.63
This is a left tailed test
Considering the population proportion, probability of success, p = 0.63
q = probability of failure = 1 - p
q = 1 - 0.63 = 0.37
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 478
n = number of samples = 800
P = 478/800 = 0.6
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76
From the normal distribution table, the area below the test z score in the left tail 0.039
Thus
p = 0.039
Answer:
-3.66
Step-by-step explanation:
Find the length of Line segment A C . Use that length to find the length of Line segment C D . Triangle A B C is shown. A perpendicular bisector is drawn from point A to point C on side B D. Angle A B C is 30 degrees and angle A D C is 25 degrees. The length of A B is 10 centimeters. What is the length of Line segment C D? Round to the nearest tenth. 2.3 cm 4.0 cm 10.7 cm 18.6 cm
Answer:
10.7 CM
Step-by-step explanation:
Correct on Edge 2020
Answer:
answer is C 10.7 cm
Step-by-step explanation:
got it right on edg 2020-2021
y = -9x - 2; (4, -37)
A. Yes it satisfies the equation
B. No the ordered pair does not satisfy the equation
Answer:
B. No the ordered pair does not satisfy the equation
Step-by-step explanation:
y = -9x - 2
Substitute the point in and see if it is true
-37 = -9(4) -2
-37 = -36 -2
-37 = -38
This is not true so the point is not a solution
