The critical value is 2.069 and the margin of error is 1.294.
Given data:
To find the margin of error (ME) for a 95% confidence interval estimate for the population mean using the Student's t-distribution, determine the critical value (t*) and the standard error (SE).
The critical value (t*) can be obtained from the t-distribution table.
For a 95% confidence level with 23 degrees of freedom (n-1), the critical value is approximately 2.069.
The standard error (SE) is calculated using the formula:
SE = sample standard deviation / √(sample size)
[tex]SE = \frac{3}{\sqrt{23}}[/tex]
Now, calculate the margin of error (ME):
ME = t* * SE
[tex]ME = 2.069 *\frac{3}{\sqrt{23}}[/tex]
On simplifying the equation:
[tex]ME=1.294[/tex]
Hence, the margin of error is 1.294.
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If a coin is tossed 5 times, and then a standard six-sided die is rolled 4 times, and finally a group of three cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer: 5,499,187,200
Step-by-step explanation:
A coin is tossed 5 times.
There are two options (heads or tails) so the possible outcomes are: 2⁵
A six-sided die is rolled 4 times.
There are six options so the possible outcomes are: 6⁴
A group of 3 cards are drawn (without replacement).
The first outcome has 52 options, the second has 51 options, and the third has 50 options: 52 x 51 x 50
Now if we want the coin AND the die AND the cards, we have to multiply all of their possible outcomes:
2⁵ x 6⁴ x 52 x 51 x 50
= 32 x 1296 x 132,600
= 5,499,187,200
Rhea obtained a CO-OP credit working at a computer store. They have now hired her for a summer job with the store. She makes $8/hour, plus a 5% commission on sales.
Which expression best describes Rhea's total earnings? Explain.
a) E = 8h + 5s b) E = 8h + .50s
c) E = 8h + .005s d) E = 8h + 0.05s
Rhea worked 15 hours last week and made $260 in total. What were her total sales in computers for the week?
Why do you think employers offer commissions to their employees? Do you think there are any potential problems with this form of earnings?
Answer:
d) E = 8h + 0.05s
Her total sales in computers for the week is $2800.
Step-by-step explanation:
Let Rhea's hourly pay =h
She makes $8/hour, therefore sales for h hours =$8h
Let the volume of sales = s
She also earns 5% commission on sales = 5% of s = 0.05s
Therefore, the expression which best describes Rhea's total earnings:
(D) E=8h+0.05s
Rhea worked 15 hours last week and made $260 in total.
h=$15
From the formula
260=8(15)+0.05s
0.05s=260-8(15)
0.05s=140
s=2800
Her total sales in computers for the week is $2800.
Employers offer commissions to their employees to motivate them to seek to make sales rather than just passing time.
In so far as the sales commission do not eat up the profit of the business, there are no potential problems with this form of earnings
Which of the x-values are solutions to the following inequality? 17 > x Choose all answers that apply: (A) x = 7 (B) x = 12 (C) x = 17
Answer:
7 and 12
Step-by-step explanation:
7 and 12 are ok
17 is not
hope this helps
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The inequality is given below.
x < 17
The solution of the inequality x < 17 will be all the real numbers less than 17. Then the correct options are A and B.
More about the inequality link is given below.
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There are 1,596 fans at a football match. 3/7 of them are children. How many adults attended the football match?
Which is the better buy? Store A: $250 of 20% off Or Store B $280 at 25% off
Show your work
Answer:
Store A
Step-by-step explanation:
So. What we are going to want to do here is start off by having two stores obviously. And we have the sales that they have. If the discount is 20% rhat means the new price will be 80% of 250. So we take 250 x .8 = 200
If the discount is 25%, that means the new price will be 75% of what it was before hand. So we take 280 x .75 = 210. So the better price is at Store a
Suppose the expected returns on equity of two firms, Macrosoft and Microsoft, that operate in the same business are 10.50% and 13.00%, respectively. What is the return on assets in this business if Macrosoft has no debt?
Answer:
The return on assets in this business for Macrosoft is
ROA = 10.50%
Step-by-step explanation:
Return on Equity:
ROE represents how much a firm is generating profits by using the shareholder's money.
ROE is calculated as
[tex]$ {ROE = \frac{Annual \:\: net\: \: income}{Average \:\: shareholder's \:\: equity} $[/tex]
Return on Assets:
ROA represents how much a firm is generating profits for every dollar of its assets.
ROA is calculated as
[tex]$ {ROA = \frac{Annual \:\: net\: \: income}{Total \:\: assests} $[/tex]
What is the return on assets in this business if Macrosoft has no debt?
Debt plays an important role in the calculations of return on assets.
We know that
Assets = Liabilities + Equity
Since the Macrosoft has no debt, its return on assets will be same as return on equity.
Assets = Equity
ROA = ROE
ROA = 10.50%
The amount of energy it takes to lift a box might be a function of which of the
following?
A. The weight of the objects inside the box
OB. The shape of the box
C. The time of day that you are lifting it
Answer:
A. The weight of the objects inside the box
Step-by-step explanation:
The energy required to lift a box is a function of the weight of it and of the distance it is lifted.
_____
In physics terms, the energy is the product of force and distance. The applicable force when lifting the box is the weight of the box (the box itself and any objects inside).
A rectangle or pyramid has a volume of 1296 in.³, a height of 24 inches, and a base length of 6 inches. What is the width of its base?
Answer: base width = 27 in
Step-by-step explanation:
Base width = 3 x (V / hl)
3 x (1296 / 24 x 6)
3 x (1296 / 144)
3 x 9 = 27
The access code for a garage door consists of three digits. Each digit can be any number from 1 through 5, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing.
Answer:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
Step-by-step explanation:
We are given that access code consists of 3 digits.
Each digit can be any digit through 1 to 5 and can be repeated.
Now, this problem is equivalent to the problem that we have to find:
The number of 3 digit numbers that can be formed using the digits 1 to 5 with repetition allowed.
(a) We have 3 places here, unit's, ten's and hundred's places respectively and each of the 3 places have 5 possibilities (any digit allowed with repetition).
So, total number of access codes possible:
[tex]5\times 5 \times 5 = 125[/tex]
(b) Suppose, an access code is randomly selected, what is the probability that it will be correct.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, only 1 code is correct, so
Number of favorable cases = 1
Total number of cases = 125
So, required probability:
[tex]P(E) = \dfrac{1}{125}[/tex]
(c) Probability of not selecting the correct access code on first time:
[tex]P(\overline E) = 1-P(E)\\\Rightarrow P(\overline E) = 1-\dfrac{1}{125}\\\Rightarrow P(\overline E) = \dfrac{125-1}{125}\\\Rightarrow P(\overline E) = \dfrac{124}{125}[/tex]
So, the answers are:
(a) 125
[tex](b) \dfrac{1}{125}[/tex]
[tex](c) \dfrac{124}{125}[/tex]
What is the greatest number that can be divided evenly into 78 and 104 without leaving a remainder?
Answer:
26 can be divides evenly into 78 and 104 without leaving a remainder
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
78= 2 × 3 × 13
104= 2 × 2 × 2 × 13
The required number is: 2 × 13= 26
Dylan paid a plumber $120 for 4 hours of labor. How much does the plumber charge per hour of labor? A. $15 per hour B. $30 per hour C. $116 per hour D. $480 per hour stay safe!
Answer:
Brainleist :)
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
B) 30 dollars for 1 hour of labor
answe:
B) 30 dollars for 1 hour of labor
Step-by-step explanation:
120 dollars for 4 hours of labor
120/4 dollars for 1 hour of labor
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What is the solution of √1-3x = x+3 ?
Answer:
{-1, -8}
Step-by-step explanation:
Please enclose "1 - 3x" inside parentheses so the reader will know that you want the square root of all of "1 - 3x".
Squaring both sides of the given equation, we get:
1 - 3x = x^2 + 6x + 9, or x^2 + 6x + 8 + 3x, or
x^2 + 9x + 8 = 0. Factoring, we get: (x + 8)(x + 1) = 0, so that the solutions are {-1, -8}.
Answer:
I hope the given equation is :
{-1, -8}
First step to solve this equation to remove square root from the left side. So, take square on each sides of the equation. Therefore,
1 - 3x = (x + 3)²
1 - 3x = (x + 3)*(x + 3) Since a² = a * a
1 - 3x = x² + 3x + 3x + 3² By multiplication.
1 - 3x = x² + 6x + 9 Combine the like terms.
x² + 6x + 9 - 1 + 3x = 0 Subtract 1 and add 3x from each sides of equation
x² + 9x + 8 = 0 Combine the like terms.
Next step is to factor the trinomial to solve the above equation for x.
For that break downn the constant 8 into two multiples so that the addition of the multiples will result the coefficient of x = 9.
So, 8 = 1 * 8
Addition of 1 and 8 will give 9. So, next step is to replace 9x with 1x + 8x. So,
x² + 1x + 8x + 8 = 0
(x² + 1x) + (8x + 8) = 0 Group the terms.
x ( x + 1) + 8 (x + 1 ) = 0 Take out the common factor from each group.
(x +1 ) ( x + 8 ) = 0 Take out the common factor (x + 1).
So, x + 1 = 0 and x + 8 = 0 Set up each factor equal to 0.
Hence, x = -1 and - 8.
Next step is to plug in -1 and -8 in the original equation to cross check the solutions.
For x = -1,
Simplify each sides separately.
2 = 2
2 = 2 is correct. So, x = -1 satisfy the equation.
Hence, x = -1 is the real solution of the given equation.
Similarly let's plug in x = -8 now. So,
Simplify each sides separately.
5 = 2
5 = 2 is not true. So, x = -8 is the extraneous solution.
Therefore, the only solution is x = -1.
Hence, the correct choice is C.
Hope this helps you!
Step-by-step explanation:
mark brainlies plssssssssss
Please help me....I need it
Answer:
Volume: 3x2x4=24 so the volume is 24 Meter3
Surface area:
52 Square meter
What is the equation of the graph below?
Answer:
y = csc(x - 3/4[tex]\pi[/tex])
Step-by-step explanation:
I forgot how to answer questions like these. I went ahead and tried re-learning this to answer this.
So, the first step is to recognize that this graph can only be the reciprocal function of sin or cosine. I will think of sine.
y = sin(x)
Look at where the x-coordinate of the sin is. (-3/4PI). This is going to be the c value. { y = asin(x-c) }
y = sin(x - 3/4[tex]\pi[/tex])
Now, what is the a value? or amplitude? Well, it's just 1.. and the simplest explanation is just to look at my picture.
Now, if we were to graph this, we would end up with the correct x and y values, but the shape is wrong, and the easiest way to fix this is to just take the recpriocal of the sine function.
y = csc(x - 3/4[tex]\pi[/tex])
Thank you for this question, I re-learned something I forgot back in pre-calc haha.
Answer:
The answer is B
Step-by-step explanation:
Emily worked only 4/5 of her normal 40-hr work week. If she makes $18 per hour, how much money did she earn for the week? Use the equation
Answer:
576 for the week
Step-by-step explanation:
First determine how many hours she worked
4/5 * 40 = 32 hours
32 hours times the hourly rate of 18
32*18 =576
The graphs below have the same shape. What is the equation of the blue
graph?
Answer: b
Explanation:
The -2 outside of the parentheses means it’s at y=-2 and the -4 inside the parentheses means it’s at x= 4 because it’s always the opposite
Randall invests $7200 in two different accounts. The first account paid 11 %, the second account paid 13 % in interest. At the end of the first year he had earned $832 in interest. How much was in each account?
Answer:
11% -- $520013% -- $2000Step-by-step explanation:
Let x represent the amount invested in the higher-earning account. Then the investment in the other account is (7200-x), and the total interest is ...
0.13x +0.11(7200 -x) = 832
0.02x = 832 -792 . . . . . . eliminate parentheses, collect terms, subtract 792
x = 40/0.02 = 2000 . . . . divide by the coefficient of x
$2000 was invested at 13%; $5200 was invested at 11%.
9-3x is greater than or equal to 2(x-3)
Answer:
x≤3
Step-by-step explanation:
9-3x≥2(x-3)
9-3x≥2x-6
-3x-2x≥-6-9
-5x≥-15
-5x/-5≥-15/-5
x≤3
After a 4% reduction, you purchase a new suit for $288. What was the original price of the suit?
Answer:
$300
Step-by-step explanation:
Let [tex]x[/tex] be the original price.
[tex]x \times (1-0.04)=288[/tex]
[tex]0.96x=288[/tex]
[tex]x=\frac{288}{0.96}[/tex]
[tex]x=300[/tex]
Answer:
$300
Step-by-step explanation:
If it was a 4% reduction then we get:
[tex]x*0.96=288\\[/tex]
Divide both sides by 0.96
[tex]x=300[/tex]
The original suit price was $300
A chemist mixes 175 millilters of solution that is 62% acid with 75 milliliters of pure acid. What percentage of the resulting Mixture is acid
Answer:
73.4%
Step-by-step explanation:
The ratio of acid to mixture volume is ...
(0.62·175 +1.00·75)/(175 +75) = 183.5/250 = 0.734 = 73.4%
73.4% of the resulting mixture is acid.
A marketing team is targeting people who might buy a hybrid car. In their city, with a population of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one. Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
Answer:
The population proportion is 0.1057.
For samples of size n: Mean = 0.1057, Standard deviation [tex]s = \frac{0.3075}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem for Proportions:
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]
Population proportion:
Of 30,000 people, 3,170 people either drive a hybrid car or have indicated on a recent survey that they would be interested in driving one.
This means that [tex]p = \frac{3170}{30000} = 0.1057[/tex]
The population proportion is 0.1057.
Mean and standard deviation of the sampling distribution for samples of size n
By the Central Limit Theorem, the mean is [tex]\mu = p = 0.1057[/tex]
Standard deviation:
[tex]s = \sqrt{\frac{0.1057*0.8943}{n}} = \frac{0.3075}{\sqrt{n}}[/tex]
The checking accounts of USF Credit Union are categorized by age of account and balance in account. We are going to select an account at random from this group of 2000 accounts.What is the conditional probability that the account has a balance at least $500, given that it is at least 3 years old, that is P(>=$500 | >=3 years)?
a. 1/2
b. 1/10
c. 1/4
d. None of these
Missing details to question is attached
Answer:
c) [tex] \frac{1}{4} [/tex]
Step-by-step explanation:
S
Required:
Find the probability that the account has a balance at least $500, given that it is at least 3 years old.
Which means: P(≥$500 | ≥3 years)
To find the probability, use the formula below:
P(≥$500 | ≥3 years) = (No. of accounts with balance≥ 500 and age ≥3 years) / (No. of accounts with age≥3 years)
Where from th given information:
Number of accounts with balance≥ 500 and age ≥3 years = 200
Number of accounts with age≥3 years = 600 + 200 = 800
Therefore,
P(≥$500 | ≥3 years) [tex] = \frac{200}{800} = \frac{1}{4} [/tex]
The probability that the account has a balance at least $500, given that it is at least 3 years old = [tex] \frac{1}{4} [/tex]
Which are true of the function f(x)=49(1/7)?select three options. A)The domain is the set of all real numbers. B) the range is the set of all real numbers. C) the domain is x >0. D)the range is y>0. E)as increases by 1, each y value is one -seventh of the previous y-value.
Answer:
A,D and E
Step-by-step explanation:
We are given that a function
[tex]f(x)=49(\frac{1}{7})^x[/tex]
The given function is exponential function .
The exponential function is defined for all real values of x.
Therefore, domain of f=Set of all real numbers
Substitute x=0
[tex]y=f(0)=49>0[/tex]
Range of f is greater than 0.
x=1
[tex]y(1)=\frac{49}{7}[/tex]
x=2
[tex]y=49(\frac{1}{7})^2=\frac{1}{7}y(1)[/tex]
As x increases by 1, each value of y is one-seventh of the previous y-value.
Therefore, option A,D and E are true.
Answer:
A D E
Step-by-step explanation:
Edge2020 quiz
Find the surface area of a sphere with a diameter 12 cm. Round your answer to the nearest whole number
Answer:
SA = 144π or 452 cm
Step-by-step explanation:
Surface area of a sphere: SA = 4πr²
To find r radius, we simply divide diameter by 2 to get r = 6. Now we simply plug in 6:
SA = 4π(6)²
SA = 4π36
SA = 144π or 452.389
Answer:
144pi
Step-by-step explanation:
calculator
Solve the following and
make sure to write your
answer in scientific
notation.
(1.5 x 105)(5 x 103)
Answer:
7.5* 10^8
Step-by-step explanation:
(1.5 x 10^5)(5 x 10^3)
Multiply the numbers
1.5*5=7.5
Add the exponents
10 ^(5+3) = 10^8
Put back together
7.5* 10^8
This is in scientific notation
Brian set a goal to horseback ride more than 6 miles. The horse he rode averaged a speed of 4.6 miles per hour. A 2-column table with 4 rows titled Brian's Activity time (hours). Column 1 has entries hiking, mountain biking, horseback riding, cross-country skiing. Column 2 has entries 3, 1.45, 1.2, 0.75. Brian rode miles. Did he reach his goal?
Answer:
BRIAN DID NOT REACH HIS GOAL! Brian rode 5.52 miles!
Step-by-step explanation:
Answer:
he didn't reach his goal. he rode 5.52 miles
Step-by-step explanation:
If 1 euro is 1.07 dollars and 1 pound is 1.25 dollars how many euro is to the pound
Step-by-step explanation:
1.07×1.25
=1.3375 euros
A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola yequals25minusxsquared. What are the dimensions of the rectangle with the maximum area? What is the area?
Answer:
The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"
Step-by-step explanation:
The rectangle should also be symmetrical to it because of the symmetry to the y-axis The pole of the y-axis. Its lower two vertices are (-x,0). it means that
and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:
The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).
The area of the rectangle:
[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]
The local extremes of this function are where the first derivative is 0:
[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]
Simply ignore the negative root because we need a positive length calculation
It wants a maximum, this we want to see if the second derivative's profit at the end is negative.
[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]
Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50 a plus 3.75 b equals 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold? Answer: 168 adult tickets
Answer:
Step-by-step explanation:
10.5a + 3.75b = 2071.50
b = 82 students
Substitute 'b' value in the equation
10.5a + 3.75 * 82 = 2071.50
10.5a + 307.5 = 2071.50
10.5a = 2071.50 - 307.5
10.5a = 1764
Divide both sides by 10.5
a = 1764/10.5
a =17640/105
a= 168
168 adult tickets were sold
If log 5 = p and log 2=q then log 200 can be written in terms of p and q as?
Work Shown:
log(200) = log(2^3*5^2)
log(200) = log(2^3) + log(5^2)
log(200) = 3*log(2) + 2*log(5)
log(200) = 3*q + 2*p
log(200) = 2p + 3q
The log rules I used were
log(A*B) = log(A)+log(B)
log(A^B) = B*log(A)
The equivalent expression of log(200) is 2p + 3q
The logarithmic expression is given as:
[tex]\mathbf{log 200}[/tex]
Rewrite as:
[tex]\mathbf{log(200) = log (25 \times 8)}[/tex]
Express as exponents
[tex]\mathbf{log(200) = log (5^2 \times 2^3)}[/tex]
Split
[tex]\mathbf{log(200) = log (5^2) +log(2^3)}[/tex]
Apply law of logarithms
[tex]\mathbf{log(200) = 2log (5) +3log(2)}[/tex]
From the question;
log(5) = p and log(2) = q
So, we have:
[tex]\mathbf{log(200) = 2p +3q}[/tex]
Hence, the equivalent expression of log(200) is 2p + 3q
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