Answer:
A. Increase the level of confidence
Step-by-step explanation:
The margin of error is given by:
The margin of error is:
[tex]M = \frac{Ts}{\sqrt{n}}[/tex]
In which T is related to the level of confidence(the higher the level of confidence, the higher T is), s is the standard deviation of the sample and n is the size of the sample.
Increase the width:
That is, increasing the margin of error, as the width is twice the margin of error, the possible options are:
Increase T -> increase confidence level.
Increase s -> Increase the standard deviation of the sample.
Decrease n -> Decrease the sample size.
Thus, the correct answer is given by option A.
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
1 −4
2 20
3 −100
an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4
Given:
The geometric sequence is:
[tex]n[/tex] [tex]a_n[/tex]
1 -4
2 20
3 -100
To find:
The explicit formula and list any restrictions to the domain.
Solution:
The explicit formula of a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex] ...(i)
Where, a is the first term, r is the common ratio and [tex]n\geq 1[/tex].
In the given sequence the first term is -4 and the second term is 20, so the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{20}{-4}[/tex]
[tex]r=-5[/tex]
Putting [tex]a=-4,r=-5[/tex] in (i), we get
[tex]a_n=-4(-5)^{n-1}[/tex] where [tex]n\geq 1[/tex]
Therefore, the correct option is B.
(x²-9)(√x-2)=0 ??????????
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Help please, I attached the question. Is it a!?

Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
[tex]0=ax^2+bx+c[/tex]
The number of solutions it has can be determined using its discriminant:
[tex]\Delta = b^2-4ac[/tex]
Where:
If the discriminant is positive, we have two real solutions. If the discriminant is negative, we have no real solutions. And if the discriminant is zero, we have exactly one solution.We have the equation:
[tex]2x^2+5x-k=0[/tex]
Thus, a = 2, b = 5, and c = -k.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:
[tex]b^2-4ac=0[/tex]
Substitute:
[tex](5)^2-4(2)(-k)=0[/tex]
Solve for k. Simplify:
[tex]25+8k=0[/tex]
Solve:
[tex]\displaystyle k = -\frac{25}{8}[/tex]
Thus, our answer is indeed A.
Thorazine is available in a strength of 25 mg/mL. Express this strength as a percent.
Answer:
2.5%
Step-by-step explanation:
Thorazine is available in the strength of 25mg/mL.
To find out the percentage strength,
W/V = g/mL (weight in grams of solute/milliliters of solute.)
1mL of Thorazine contains 25mg.
Dissolve Thorazine with the 100mL solution.
Therefore, 25 x 100 = 2500mg
Which is equals to 2.5g
100mL solution contains 2.5g of Thorazine.
Percentage Strength (W/V) = 2.5 / 100 x 100 = 2.5%.
The percentage strength of Thorazine 25mg/mL has 2.5%
ABC ~ DEF. What sequence of transformations will move ABC ~ DEF
Answer:
D
Step-by-step explanation:
we first dilate it, making it the same size, then translate it to the right. I hope I have helped :)
Write the standard form of the equation of the circle with center (−7,10) that passes through the point (−7,7)
Answer:
(x+7)^2+(y-10)^2=9
Step-by-step explanation:
The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle
Dr. Burger rides his bike to work in the mornings. Usually, he leaves his house at 8:20 and gets to the office at 9:00 riding at a rate of 15 miles an hour. On this particular morning he has overslept and leaves at 8:45. How fast does he need to ride to avoid being late
Answer:
40 mph
Step-by-step explanation:
40 mins to bike usually, which means he bikes 10 miles. He needs to bike at a minimum of 10 miles in 15 mins, which translates to 40 miles in an hour.
P.S. He is going to surely be late.
khai niem hinh cat don gian ?
Answer:
khai niem hinh cat don gian?
By selling a radio for $8400 a dealer gained 12% .how much money did she gain
Answer:
Amount gained = $900
Step-by-step explanation:
Let the cost price be = x
Given selling price = 8400
And profit% = 12%
Profit = selling price - cost price
= 8400 - x
[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]
Therefore , cost price of the radio $7500
The amount she gained = 8400 - 7500 = $ 900
E. The ratio of monthly income to savings of a family is 7:2. If the savings is Rs. 500, find the monthly income and expenditure.
Step-by-step explanation:
Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t
Now, we are given that the savings is =Rs 500
So, According to our assumption, 2t=500
⇒t=250
Hence, the income of the family is =7×250=Rs 1750
And the expenditure is =Income−Savings
=Rs 1750−Rs 500
=Rs 1250
Which statement best compares the two functions?
A) Neither function A nor function B has an x-intercept.
B) Neither function A nor function B has a y-intercept.
C) The domain and range of both functions contain only
positive numbers.
D) The domain and range of both functions contain only
positive numbers and zero
Answer:
A) Neither function A nor function B has an x-intercept.
Step-by-step explanation:
Which one goes where?
"RS tangent to circle a..." is first statement Reason: Given
Second Reason: "Radius perpendicular to tangent"
Second Statement: "AR is parrallel to BS" Reason: "2 lines perpendicular..."
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2 gallons and the mean is 16 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
A sample of 784 is required to estimate the mean usage of water.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation is 2 gallons
This means that [tex]\sigma = 2[/tex]
They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?
This is n for which M = 0.14. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.14 = 1.96\frac{2}{\sqrt{n}}[/tex]
[tex]0.14\sqrt{n} = 1.96*2[/tex]
[tex]\sqrt{n} = \frac{1.96*2}{0.14}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*2}{0.14})^2[/tex]
[tex]n = 784[/tex]
A sample of 784 is required to estimate the mean usage of water.
Kevin has 17 trading cards. Billy has t more trading cards than Kevin. Choose the expression that shows how many trading cards
Billy has
Answer:
Step-by-step explanation:
Simplify to the extent possible: (
logx16)(log2 x)
Use the change-of-base property for logarithms to write
logₓ(16) log₂(x) = (ln(16) / ln(x)) (ln(x) / ln(2)) = ln(16)/ln(2) = log₂(16)
Then since 2⁴ = 16, we hvae
log₂(16) = log₂(2⁴) = 4 log₂(2) = 4
PLEASE HELP WILL MARK BRAINLIEST
9514 1404 393
Answer:
x = 10/3 = 3 1/3 ≈ 3.33
Step-by-step explanation:
Triangles ABC and ADE are similar, so corresponding sides are proportional.
DE/DA = BC/BA
x/(4+6) = 2/6
x = 10(2/6) = 10/3 = 3 1/3
Random samples of of outh bass and smallmouth bass were taken from a lake, and their lengths in millimeters) were deter mined. We wish to know if the mean standard length differs between the two species in this lake. The results were as follows:
Largemouth Bass Smallmouth Bass
x 164.8 272.8
s 96.4 40.0
n 97 125
Answer:
Hence , the means of Largemouth Bass and Smallmouth Bass are significantly different.
Step-by-step expl;anation:
From the question we are told that:
Largemouth Bass:
[tex]\=x_1 =164.8[/tex]
[tex]s_1=96.4[/tex]
[tex]n_1=125[/tex]
Smallmouth Bass:
[tex]\=x_2 =272.8[/tex]
[tex]s_2=40[/tex]
[tex]n_2=97[/tex]
Assume
[tex]\alpha =0.05[/tex]
Generally The hypothesis is given as
H_0: The Largemouth Bass and Smallmouth Bass are equal
H_1: The Largemouth Bass and Smallmouth Bass are not equal
Generally the equation for Test statistics is mathematically given by
[tex]T=frac{( \=x_2 - \=x_1 )}{\sqrt{\frac{s^{1}}{n_1} + \frac{s_1^{2}}{n_2}}}[/tex]
[tex]T =\frac{(272.8 - 164.8)}{\sqrt{\frac{96.4^{2}}{125} + \frac{40^{2}}{97}}}[/tex]
[tex]T=\frac{108}{9.530925}[/tex]
[tex]T=11.33[/tex]
Therefore
From table
Critical Value
[tex]T_{\alpha,n_2-1}[/tex]
[tex]T_{0.05,96}=1.661[/tex]
Conclude
Since 11.33 is greater that 1.661 we eject the null hypothesis that the means are the same.
Hence , the means of Largemouth Bass and Smallmouth Bass are significantly different.
What is the explicit formula for the sequence ? -1,0,1,2,3
Answer:
B
Step-by-step explanation:
substitute the values in the eq. Ot is also arithmetic progression.
The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.
Answer:
First term a = 3
Sum of first 20 term = 440
Step-by-step explanation:
Given:
8th term of AP = 17
12th term of AP = 25
Find:
First term a
Sum of first 20 term
Computation:
8th term of AP = 17
a + 7d = 17 ....... EQ1
12th term of AP = 25
a + 11d = 25 ...... EQ2
From EQ1 and EQ2
4d = 8
d = 2
a + 7d = 17
a + 7(2) = 17
First term a = 3
Sum of first 20 term
Sn = [n/2][2a + (n-1)d]
S20 = [20/2][(2)(3) + (20-1)2]
S20 = [10][(6) + 38]
S20 = [10][44]
S20 = 440
Sum of first 20 term = 440
6. Find average of the following
expressions (4-2x), (-7-3x), and
(11x+6)
Answer:
2x + 1.
Step-by-step explanation:
Average = sum of the expression / number of expressions
= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3
= (-2x - 3x + 11x + 4 - 7 + 6) / 3
= 6x + 3 / 3
= 2x + 1
Answer:
2x+1
Step-by-step explanation:
(4-2x), (-7-3x),(11x+6)
Add the three expressions
(4-2x)+ (-7-3x)+(11x+6)
Combine like terms
-2x-3x+11x+4-7+6
6x+3
Divide by the number of expressions which was 3
(6x+3)/3
2x+1
The average is 2x+1
Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
What is the value of x?
Enter your answer in the box.
units
Answer:
25
Step-by-step explanation:
40/24 = x/15
x = 15•40/24
x = 25
Answer:
25
Step-by-step explanation:
just use the facts that both triangles are similar
Using the digits 5, 6, 7, 8, 9 and repetition is allowed how many options are there to
Create a 4 digit even number?
[2]
Create a 4 digit odd number?
Answer:
250 options to create an even number
375 options to create an odd number
At which root does the graph of f(x) = (x + 4)^6(x + 7)^5 cross the x-axis?
O -7
O -4
O 4
Ο 7
Answer:
Step-by-step explanation:
to cross the x-axis you need to solve f(x)=0
x(x+4)(x+7)*5=0 which means you will have x=0 ,x+4=0 or x+7=0
so the final answer is
x=0 or x=-4 or x=-7
If $6^x = 5,$ find $6^{3x+2}$.
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!
A day trading firm closely monitors and evaluates the performance of its traders. For each $10,000 invested, the daily returns of traders at this company can be modeled by a Normal distribution with mean = $830 and standard deviation = $1,781.
(a) What is the probability of obtaining a negative daily return, on any given day? (Use 3 decimals.)
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row? (Use 3 decimals.)
(c) Give the boundaries of the interval containing the middle 80% of daily returns: (use 3 decimals) ( , )
(d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus? (Use 3 decimals.)
Answer:
a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.
c) (-$1449.68, $3109.68)
d) A bonus of $4,488.174 is needed.
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.
Normal distribution with mean = $830 and standard deviation = $1,781.
This means that [tex]\mu = 830, \sigma = 1781[/tex]
(a) What is the probability of obtaining a negative daily return, on any given day?
This is the p-value of Z when X = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 830}{1781}[/tex]
[tex]Z = -0.466[/tex]
[tex]Z = -0.466[/tex] has a p-value 0.321.
0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?
Each day, 0.3206 probability, so:
[tex](0.321)^2 = 0.103[/tex]
0.103 = 10.3% probability of having a negative daily return for two days in a row.
(c) Give the boundaries of the interval containing the middle 80% of daily returns
Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.
10th percentile:
X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = -1.28*1781[/tex]
[tex]X = -1449.68[/tex]
90th percentile:
X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 1.28*1781[/tex]
[tex]X = 3109.68[/tex]
So
(-$1449.68, $3109.68)
d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?
The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 2.054*1781[/tex]
[tex]X = 4488.174 [/tex]
A bonus of $4,488.174 is needed.
As one once said Another one
Answer:
f
Step-by-step explanation:
Answer:
S = 62.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan S = opp side / adj side
tan S = sqrt(42)/ sqrt (11)
tan S = sqrt(42/11)
Taking the inverse tan of each side
tan ^ -1( tan S) = tan ^-1(sqrt(42/11))
S=62.89816
Rounding to the nearest tenth
S = 62.9
