Step-by-step explanation:
s1 = 3
s2 = 3×2 = 6
s3 = 6×2 = 12
s4 = 12×2 = 24
s5 = 24×2 = 48
sn = sn-1 × 2 = s1 × 2^(n-1)
s17 = 3 × 2¹⁶ = 3 × 65,536 = 196,608
A consumer advocate agency is concerned about reported failures of two brands of MP3 players, which we will label Brand A and Brand B. In a random sample of 197 Brand A players, 33 units failed within 1 year of purchase. Of the 290 Brand B players, 25 units were reported to have failed within the first year following purchase. The agency is interested in the difference between the population proportions, , for the two brands. Using the data from the two brands, what would be the standard error of the estimated difference, Dp = A – B, if it were believed that the two population proportions were, in fact, equal (i.e., )?
Answer:
The standard error of the estimated difference is of 0.0313.
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Brand A:
33 out of 197, so:
[tex]p_A = \frac{33}{197} = 0.1675[/tex]
[tex]s_A = \sqrt{\frac{0.1675*0.8325}{197}} = 0.0266[/tex]
Brand B:
25 out of 290, so:
[tex]p_B = \frac{25}{290} = 0.0862[/tex]
[tex]s_B = \sqrt{\frac{0.0862*0.9138}{290}} = 0.0165[/tex]
What would be the standard error of the estimated difference?
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.0266^2+0.0165^2} = 0.0313[/tex]
The standard error of the estimated difference is of 0.0313.
How many faces are there?
A. 7
B. 10
C. 15
D. not enough information
The polyhedron has 7 faces.
To find the faces of the figure.
What is polyhedron?A polyhedron is a 3D shape that has flat faces, straight edges, and sharp vertices (corners). The regular polyhedron are the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. when many flat surfaces are joined together they form a polyhedron.
Given that:
The given figure,
By the use of Euler's formula to find the faces.
F + V - E = 2
Where F = Faces, V = Vertices and E = Edges
Given, V = 10 and E = 15
F + 10 - 15 = 2
F - 5 = 2
F = 5 + 2 = 7
Therefore, the polyhedron has 7 faces.
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Write a linear equation in point-slope form for the line that goes through (1, -3) and (3,9).
A. y+3 = -6(x-1)
B. y- 9 = 6(x - 3)
C. y- 9 = 2(x-3)
D. y + 3 = 6(x-1)
Two identical lines are graphed below. How many solutions are there to the
system of equations?
5
A. Infinitely many
B. Zero
C. One
D. Two
Two identical lines have, A. Infinitely many solutions.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables,
The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given are two identical lines,
Now we know the solution of two lines is where they intersect.
We also know that a line is made up of infinite points, So if two lines are identical every point of one line lies with every other point of the other line.
Therefore they have an infinite number of solutions.
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Estimate the average rate of change from x 1 to x = 4. Enter your estimate as a decimal number (not as a fraction), rounded to one decimal place. Average rate of change = Number
Answer:Mark brainliest please
Answer is - 0.5
Step-by-step explanation:
The average rate of change is -0.5 which is the average rate of change from x 1 to x = 4 the answer is -0.5.
What is the rate of change?It is defined as the change in values of a dependent variable with respect to the independent variables.
As we know an average is a single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a graph of functions shown in the picture.
Estimate the average rate of change from x 1 to x = 4.
At x = 1,
y = 5
At x = 4
y = 3.5(approx)
The average rate of change = (3.5 - 5)/(4 - 1)
The average rate of change = -1.5/3
The average rate of change = -0.5
Thus, the average rate of change is -0.5 which is the average rate of change from x 1 to x = 4 the answer is -0.5.
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plzzzzz helppp i will give brainlyist
Answer:
C. (2)
Step-by-step explanation:
an integer is a WHOLE NUMBER
have an amazing day :)
Answer:
2 is an integer
Step-by-step explanation:
An integer is a whole number, it does not have a fractional part
If b < 0 and a/b > c/b, then what is the relationship between a and c?
Answer:
a < cStep-by-step explanation:
Given inequality:
a/b > c/bSince b is negative, when multiplied by b, the inequality changes to opposite direction:
b(a/b) < b(c/b)a < cletter A represents the decimal
Answer:
answer is 0.4
Step-by-step explanation:
in the figure above, three congruent circles are tangent to eachother and have centers that lie on the diameter of a larger circle. if the area of each of these small circles is 9pi, what is the area of the larger circle?
a) 36pi
b) 49pi
c) 64pi
d) 81pi
The area of the larger circle is 81π square units.
Congruent circles are circles that are similar in pattern.
The formula for calculating the area of a circle is expressed as:
[tex]A = \dfrac{\pi d^2}{4}[/tex]
Given that the area of each of the small circles is 9π, then:
[tex]9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units[/tex]
This shows that the diameter of one of the small circles is 6units.
Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;
Diameter of the larger circle = 3(6) = 18units
Get the area of the larger circle:
[tex]A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi[/tex]
Hence the area of the larger circle is 81π square units.
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For the specified margin of​ error, confidence​ level, and educated guess for the observed​ value, obtain a sample size that will ensure a margin of error of at most the one specified​(provided, of​ course, that that observed value of the sample proportion is further from 0.5 than the educated​ guess).
Margin of errorequals= 0.04​
Confidence levelequals=95%
Educated guessequals=0.32
n=?
Answer:
The appropriate answer is "523".
Step-by-step explanation:
Given:
Margin of error,
E = 0.04
Confidence level,
= 95%
Educated guess,
[tex]P_g[/tex] = 0.32
According to the question,
[tex]\alpha = \frac{100-95}{100}[/tex]
[tex]=0.05[/tex]
[tex]\frac{\alpha}{2} = \frac{0.05}{2}[/tex]
[tex]=0.025[/tex]
[tex]Z_{0.025} = 1.96[/tex]
The sample size will be:
⇒ [tex]n=P_g (1-P_g) (\frac{Z_{\frac{\alpha}{2} }}{E} )^2[/tex]
By substituting the values, we get
[tex]=0.32(1-0.32)(\frac{1.96}{0.04} )^2[/tex]
[tex]=0.32\times 0.68\times (49)^2[/tex]
[tex]=0.32\times 0.68\times 2401[/tex]
[tex]=522.4576[/tex]
or,
[tex]=523[/tex]
Below is the justification for the formula for area of a circle. Which word, when placed in the blank, best completes this argument?
Answer:
B half the circumference or pi r
Step-by-step explanation:
The base of the parallelogram is pi r
To form the parallelogram the triangles are removed from the bottom half of the circle and moved to flip the gaps in the top half.
Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.
Answer:
(-14.8504 ; 0.5644)
Step-by-step explanation:
Given the data:
Population 1 : 30 35 23 22 28 39 21
Population 2: 45 49 15 34 20 49 36
The difference, d = population 1 - population 2
d = -15, -14, 8, -12, 8, -10, -15
The confidence interval, C. I ;
C.I = dbar ± tα/2 * Sd/√n
n = 7
dbar = Σd/ n = - 7.143
Sd = standard deviation of d = 10.495 (using calculator)
tα/2 ; df = 7 - 1 = 6
t(0.10/2,6) = 1.943
Hence,
C.I = - 7.143 ± 1.943 * (10.495/√7)
C.I = - 7.143 ± 7.7074
(-14.8504 ; 0.5644)
Elmo likes music. He wondered if listening to music while studying will improve scores on an exam. Fifty students who were to take the midterm in a week agreed to be part of a study. Half were randomly assigned to listen to classical music while studying for the exam. The other half were told not to listen to any music while studying for the exam. A hypothesis test is to be performed to determine if the average scores of those listening to music while studying for the exam were higher than those who did not listen to any music while studying for the exam. Which of the following hypothesis tests should be used?
A. a two-sample z-test.
B. a chi-square test.
C. a two-sample t-test.
D. a one-sample t-test.
E. a two-sample z-test for proportions.
The hypothesis tests should be used is A. a two-sample z-test.
What is Alternative Hypothesis ?An Alternative Hypothesis is the one that disproves the Null Hypothesis in that it believes that indeed there is a change in the dependent variable due to a change in the independent variable.
The Alternative Hypothesis is essentially aims to prove the assertion of the Researcher that there is an effect as a result of the introduction of a variable.
Null Hypothesis believes that no significant difference exists between a change in a dependant Variable as a result of a change in an independent one.
This is the alternative hypothesis because it believes that there was a change in the exam results due to reading while studying.
Therefore, the hypothesis tests should be used is A. a two-sample z-test.
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ASAP! Plssssss
Tysm.
Answer:
4×10⁶ is the answer.........
Answer:
[tex]4 \times {10}^{6} [/tex]
Step-by-step explanation:
[tex] \frac{8 \times {10}^{24} }{2 \times {10}^{18} } [/tex]
[tex] \frac{4 \times {10}^{24} }{ {10}^{18} } [/tex]
[tex] = 4 \times {10}^{6} [/tex]
The 3rd and 7th terms of an arithmetic progression are 6and 30 respectively determine the common difference, first term,10th term.
Answer:
d = 6 , a₁ = - 6 and a₁₀ = 48
Step-by-step explanation:
The nth term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 6 and a₇ = 30 , then
a₁ + 2d = 6 → (1)
a₁ + 6d = 30 → (2)
Subtract (2) from (1) term by term to eliminate a₁
4d = 24 ( divide both sides by 4 )
d = 6
Substitute d = 6 into (1)
a₁ + 2(6) = 6
a₁ + 12 = 6 ( subtract 12 from both sides )
a₁ = - 6
Then
a₁₀ = - 6 + (9 × 6) = - 6 + 54 = 48
----------------------------------------------------
Answer:
d=6
a=-6
Step-by-step explanation:
use the formula for the nth term which is
Tn=a+(n-1)d..you will have to create two equations then solve them as a simultaneous equation
T3=6 and T7=30
T3=a+(3-1)d
6=a+2d........... first equation
T7=a+(7-1)d
30=a+6d.......... second equation
then solve them as a simultaneous equation
a+2d=6
a+6d=30
-4d/-4=-24/-4
d=6
a+2d=6
a+2(6)=6
a=6-12
a=-6
I hope this helps
find the probability that in a random arrangements of the letters of the word 'science' that all vowels may never be together.
Answer:
i dont know
Step-by-step explanation:
In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1
Answer:
A. 0; 1
Step-by-step explanation:
Required
Mean and standard deviation of a standardized normal distribution
A standardized normal distribution is represented as:
[tex](\mu,\sigma) = (0,1)[/tex]
This implies that:
[tex]\mu = 0[/tex] -- mean
[tex]\sigma = 1[/tex] --- standard deviation
Hence, (a) is true
find the area of the figure. all corners are right angles
Answer:
L(4)
Step-by-step explanation:
It is L(4)because all sides are equal
Use the following data obtained from ages of the last six U. S. Presidents at the time of their inauguration to answer the following questions:
Ages of Last 6 Presidents at Inauguration
Ronald Reagan 69
George Bush 64
Bill Clinton 46
George W. Bush 54
Barack Obama 47
Donald Trump 70
a. Find the mean of the data set. (Round to one decimal place.)
b. Find the standard deviation of the data set. (Do not round until the final answer. Round final answer to 1 decimal place.)
c. What percentage of presidents' ages fall within one standard deviation of the mean
Answer:
a) The mean of the data set is 58.3.
b) The standard deviation of the data-set is of 10.8.
c) 50% of presidents' ages fall within one standard deviation of the mean
Step-by-step explanation:
Question a:
Sum of all values divided by the number of values.
[tex]M = \frac{69 + 64 + 46 + 54 + 47 + 70}{6} = 58.3[/tex]
The mean of the data set is 58.3.
Question b:
Square root of the sum of the difference squared between each value and the mean, divided by the number of values subtracted by 1. So
[tex]S = \sqrt{\frac{(69-58.3)^2 + (64-58.3)^2 + (46-58.3)^2 + (54-58.3)^2 + (47-58.3)^2 + (70-58.3)^2}{5}} = 10.8[/tex]
The standard deviation of the data-set is of 10.8.
Question c:
Between 58.3 - 10.8 = 47.5 and 58.3 + 10.8 = 69.1.
3 out of 6(Reagan, Bush and W. Bush), so:
3*100%/6 = 50%
50% of presidents' ages fall within one standard deviation of the mean
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320
The ball hits the ground after____ seconds
Answer:
28 seconds ..............
evaluate (5^0-4^-1)×3/4
Answer:
[tex](5^{0} -4^{-1} )(\frac{3}{4} )\\\\=(1-\frac{1}{4^{1}} )(\frac{3}{4} )\\\\=(\frac{4}{4} -\frac{1}{4} )(\frac{3}{4} )\\\\=(\frac{3}{4} )(\frac{3}{4} )\\\\=\frac{9}{16}[/tex]
The height and weight of several adults were recorded:
Using this model, what would be the weight of someone who is 5.8 ft tall? Round your answer to the nearest tenth. You must find the quadratic regression equation first.
Weight of someone who is 5.8ft tall is 149.8 lbs.
What is a quadratic equation?A quadratic equation is a method of representation of a unknown variable by some variable of degree upto 2.
How to find the weight?a=5.607,b=-12.009,c=30.648
Let, y= weight(lbs) and x=height(ft)
y=5.61*x*x-12x+30.65
y=5.61*5.8*5.8-12*5.8+30.65
y=149.77
y≈149.8lbs.
Weight of someone having height 5.8ft tall is 149.8lbs.
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Please help me please! I really need it! Thank you so much!!!!!!!!!!! Sorry Quality is really bad
Answer:
7[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
- 2[tex]\frac{1}{3}[/tex] - ( - 10[tex]\frac{1}{6}[/tex] ) = - 2[tex]\frac{1}{3}[/tex] + 10[tex]\frac{1}{6}[/tex] = - 2[tex]\frac{2}{6}[/tex] + 10[tex]\frac{1}{6}[/tex] = ( 10 - 2 ) + ( [tex]\frac{1}{6}[/tex] - [tex]\frac{2}{6}[/tex] ) = 8 - [tex]\frac{1}{6}[/tex] = 7 + ( [tex]\frac{6}{6}[/tex] - [tex]\frac{1}{6}[/tex] ) = 7[tex]\frac{5}{6}[/tex]
Situation 1 Riverbed Cosmetics acquired 10% of the 215,000 shares of common stock of Martinez Fashion at a total cost of $12 per share on March 18, 2020. On June 30, Martinez declared and paid $74,000 cash dividend to all stockholders. On December 31, Martinez reported net income of $127,600 for the year. At December 31, the market price of Martinez Fashion was $13 per share.
Situation 2 Marin, Inc. obtained significant influence over Seles Corporation by buying 30% of Seles's 31,300 outstanding shares of common stock at a total cost of $9 per share on January 1, 2020. On June 15, Seles declared and paid cash dividends of $36,600 to all stockholders. On December 31, Seles reported a net income of $80,100 for the year.
Prepare all necessary journal entries in 2020 for both situations. (Credit account titles are automatically indented when amount is entered. Do not indent manually. If no entry is required, select "No Entry" for the account titles and enter for the amounts.)
Answer:
Riverbed Cosmetics and Martinez Fashion
March 18, 2020:
Debit Investment in Martinez Fashion $2,580,000
Credit Cash $2,580,000
To record the acquisition of 10% of the 215,000 shares of common stock
June 30, 2020:
Debit Cash $7,400
Credit Dividend Income $7,400
To record dividend income received ($74,000 * 10%).
December 31, 2020:
Debit Investment in Martinez Fashion $215,000
Credit Unrealized Gain $215,000
To record the unrealized gain from the increase in share price.
Situation 2:
Marin, Inc. and Seles Corporation
January 1, 2020:
Debit Investment in Seles Corporation $84,510
Credit Cash $84,510
To record the 30% of Seles's 31,300 shares acquired at a total cost of $9 per share.
June 15, 2020:
Debit Cash $10,980
Credit Investment in Seles Corporation $10,980
To record the 30% of $36,600 dividends paid to all stockholders.
December 31, 2020:
Debit Investment in Seles Corporation $24,030
Credit Retained Earnings $24,030
To record the company's share of the net income.
Step-by-step explanation:
a) Data and Analysis:
Riverbed Cosmetics and Martinez Fashion
March 18, 2020: Investment in Martinez Fashion $2,580,000 Cash $2,580,000 10% of the 215,000 shares of common stock
June 30, 2020: Cash $7,400 Dividend Income $7,400 ($74,000 * 10%)
December 31, 2020: Investment in Martinez Fashion $215,000 Unrealized Gain $215,000
Situation 2:
Marin, Inc. and Seles Corporation
January 1, 2020: Investment in Seles Corporation $84,510 Cash $84,510
30% of Seles's 31,300 outstanding shares of common stock at a total cost of $9 per share
June 15, 2020: Cash $10,980 Investment in Seles Corporation $10,980
30% of $36,600 paid to all stockholders.
December 31, 2020: Investment in Seles Corporation $24,030 Retained Earnings $24,030
Because the P-value is ____ than the significance level 0.05, there ____ sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α= 0.05.
Do the results suggest that imported lemons cause carfatalities?
a. The results suggest that an increase in imported lemons causes car fatality rates to remain the same.
b. The results do not suggest any cause-effect relationship between the two variables.
c. The results suggest that imported lemons cause car fatalities.
d. The results suggest that an increase in imported lemons causes in an increase in car fatality rates.
Answer:
H0 : correlation is equal to 0
H1 : correlation is not equal to 0 ;
Pvalue < α ;
There is sufficient evidence
r = 0.945 ;
Pvalue = 0.01524
Step-by-step explanation:
Given the data :
Lemon_Imports_(x) Crash_Fatality_Rate_(y)
230 15.8
264 15.6
359 15.5
482 15.3
531 14.9
Using technology :
The regression equation obtained is :
y = 16.3363-0.002455X
Where, slope = - 0.002455 ; Intercept = 16.3363
The Correlation Coefficient, r = 0.945
H0 : correlation is equal to 0
H1 : correlation is not equal to 0 ;
The test statistic, T:
T = r / √(1 - r²) / (n - 2)
n = 5 ;
T = 0.945 / √(1 - 0.945²) / (5 - 2)
T = 0.945 / 0.1888341
T = 5.00439
The Pvalue = 0.01524
Since Pvalue < α ; Reject the Null and conclude that there is sufficient evidence to support the claim.
Word problem help please
Answer:
C(M) = 0.65*M + 22.55
Step-by-step explanation:
We know that the cost to rent and drive for M miles is given by:
S(M) = 0.40*M + 17.75
And the insurance, also a function of M, is given by:
I(M) = 0.25*M + 4.80
We want to find the equation of the total cost for a rental that includes insurance.
This would be just the sum of the two above functions:
C(M) = S(M) + I(M)
C(M) = (0.40*M + 17.75) + (0.25*M + 4.80)
Now we just need to simplify this:
Taking M as a common factor, we get:
C(M) = (0.40 + 0.25)*M + 17.75 + 4.80
C(M) = 0.65*M + 22.55
Then the total cost equation, as a function of M, is given by:
C(M) = 0.65*M + 22.55
solve this set of equation, using elimination or substitution method.
Answer:
X =224
Y= -10
Step-by-step explanation:
To solve this question it's better to convert the fractions to decimals this way it will be easy to solve.
0.25x+0.6y= -4
0.2x+0.25y=-0.9
0.2(0.25x+0.6y=-4)
0.25(0.2x+0.25y=-0.9)
0.05x+0.12y=-0.8
0.05x+0.06y=-0.225
0.0575y/0.0575=-0.575/0.0575
Y=-10
To find x you replace the value of y in any of the equations
0.25x+0.6y=-4
0.25x+0.6(-10)=-4
0.25x=-4+60
0.25x/0.25=56/0.25
X=224
I hope this helps and sorry if it's wrong
The hiking trail 2600 miles long and passes through fourteen states. Because it is their first time hiking the trail, Janet and kellen plan to start hiking in Georgia and hike 416 miles. What percent of the trail will they hike?
Answer:
They will hike 16% of the trail in Georgia.
Step-by-step explanation:
We have that:
The hiking trail is of 2600 miles.
416 of those miles are in Georgia?
What percent of the trail will they hike?
Georgia distance multiplied by 100% and divided by the total distance. So
416*100%/2600 = 16%
They will hike 16% of the trail in Georgia.
Express -6 as the sum of a negative integer and a whole number
What is the volume of the prism?
227.0 cubic inches
169.1 cubic inches
177.9 cubic inches
157.5 cubic inches
Answer:
B. 169.1 cubic inches
Step-by-step explanation:
Volume of the prism = base area × height
Base area = s²
Where,
s = 5.4 in.
Base area = 5.4²
Base area = 29.16 in.²
height = 5.8 in.
Volume of the prism = 29.16 × 5.8
= 169.128
≈ 169.1 cubic inches (to nearest tenth)
