Answer:
When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value. The standard deviation is approximately equal to the range of the data divided by 4. That's it, simple.
How many liters each of a 35% acid solution in a 80% acid solution must be used to produce 60 L of a 65% acid solution?
Let x and y be the required amounts of the 35% and 60% acid solutions, respectively.
x liters of 35% acid solution contains 0.35x L of acid.
y liters of 80% acid solution contains 0.80y L of acid.
Together, a combined (x + y) L of mixed solutions contains (0.35x + 0.80y) L of acid.
You want to end up with 60 L of 65% acid solution, which means
x + y = 60
0.35x + 0.80y = 0.65 × 60 = 39
Solve for x and y :
y = 60 - x
0.35x + 0.80 (60 - x) = 39
0.35x + 48 - 0.80x = 39
0.45x = 9
x = 20
y = 40
Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 63%. Approximate the probability using the normal distribution. Round your answer to four decimal places
Answer:
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
153 voters:
This means that [tex]n = 153[/tex]
Assume the probability that a given registered voter will vote in the presidential election is 63%.
This means that [tex]p = 0.63[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 153(0.63) = 96.39[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97[/tex]
Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.
Using continuity correction, this is: [tex]P(X \geq 88 - 0.5) = P(X \geq 87.5)[/tex], which is 1 subtracted by the p-value of Z when X = 87.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{87.5 - 96.39}{5.97}[/tex]
[tex]Z = -1.49[/tex]
[tex]Z = -1.49[/tex] has a p-value of 0.0681.
1 - 0.0681 = 0.9319
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
Solve the triangle.
B = 67° 45', c= 37 m, a = 76 m
What is the length of side b?
b= m
(Round to the nearest whole number as needed.)
What is the measure of angle A?
A=0°
(Round to the nearest whole number as needed.)
What is the measure of angle C?
C=
(Round to the nearest whole number as needed.)
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Answer:
b = 71 m
A = 83°
C = 29°
Step-by-step explanation:
Many calculators can solve triangles. Apps are available for phone and tablet, or on the internet, like the one used here. In general, it takes less time to use one of these than to type your question into Brainly.
Given two sides and the angle between them, the Law of Cosines is the appropriate relation to use for finding the third side.
b = √(a² +c² -2ac·cos(B))
b = √(76² +37² -2·76·37·cos(67.75°)) ≈ √5015.48
b ≈ 70.82005 ≈ 71 . . . meters
__
One a side and its opposite angle are known, the remaining angles are found using the Law of Sines.
sin(A)/a = sin(B)/b
A = arcsin(a·sin(B)/b) = arcsin(76·sin(67.75°)/70.82005) ≈ 83.33°
A ≈ 83°
C = arcsin(37·sin(67.75°)/70.82005) ≈ 28.92°
C ≈ 29°
Or, you can find the remaining angle from 180° -68° -83° = 29°.
I need help answering this question thank guys
Answer:
b
Step-by-step explanation:
the square root of 8 is 2 and the square root of 18 is 4.5 and both simplified is 4/9.
Aslo did this last week.
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R = 1/R1 + 1/R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 60 Ω and R2 = 80 Ω? (Round your answer to three decimal places.)
The rate of change of R with time in the given equation is 0.004 ohm/s
Given parameters:
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]
To find:
The rate of change of R with time in the given equation.First determine the value of R from the given equation;
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]
Finally, to determine the rate of change of R, differentiate the given equation.
[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]
[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]
Thus, from the given equation the rate of change of R with time is 0.004 ohm/s
Learn more here: https://brainly.com/question/14796851
Answer:
the verified answer is wrong.
Step-by-step explanation:
OP forgot to square R (34.286)
Consider the probability that no more than 28 out of 304 students will not graduate on time. Choose the best description of the area under the normal curve that would be used to approximate binomial probability.
a. Area to the right of 27.5
b. Area to the right of 28.5
c. Area to the left of 27.5
d. Area to the left of 28.5
e. Area between 27.5 and 28.5
Solution :
Here the probability that exactly 28 out of 304 students will not graduate on time. That is
P (x = 28)
By using the normal approximation of binomial probability,
[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]
∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]
[tex]$=P(27.5 \leq x \leq 28.5)$[/tex]
That is the area between 27.5 and 28.5
Therefore, the correct option is (e). Area between 27.5 and 28.5
The triangles are similar, find y
Answer:
y=3.6
Step-by-step explanation:
The scale factor is 3/2.4. So 4.5/y=3/2.4. y=3.6
Diego Company manufactures one product that is sold for $75 per unit in two geographic regions—the East and West regions. The following information pertains to the company’s first year of operations in which it produced 57,000 units and sold 52,000 units. Variable costs per unit: Manufacturing: Direct materials $25 Direct labor $18 Variable manufacturing overhead $3 Variable selling and administrative $5 Fixed costs per year: Fixed manufacturing overhead $627,000 Fixed selling and administrative expenses $645,000 The company sold 36,000 units in the East region and 16,000 units in the West region. It determined that $310,000 of its fixed selling and administrative expense is traceable to the West region, $260,000 is traceable to the East region, and the remaining $75,000 is a common fixed expense. The company will continue to incur the total amount of its fixed manufacturing overhead costs as long as it continues to produce any amount of its only product. Required: What is the company’s net operating income (loss) under absorption costing?
Answer:
626949
Step-by-step explanation:
The sum of three numbers is 124
The first number is 10 more than the third.
The second number is 4 times the third. What are the numbers?
Answer:
182/3,3 8/3, 152/3
Step-by-step explanation:
a+b+c=124
a trừ c= 10
4b=c
Answer:
a=29,b=79,c=19
Step-by-step explanation:
a=c+10
b=4c
=> a+b+c=c+10+4c+c=124
=> c=19
=> a= 29, b=79
please help me with geometry
Answer:
∠ DBC = 60°
Step-by-step explanation:
BD is an angle bisector , so
∠ DBC = ∠ ABD = 60°
angel ABD =60°
BD line is bisector
angel DBC=60° because both the angel are similar
Complete the equation
[tex] \sqrt{20} = \: \: \sqrt{5} [/tex]
Step-by-step explanation:
I'm not sure about it
Try it find examples
Step-by-step explanation:
so at the end 2=1
not sure but hopefully you get the idea :)
Help please this is due today
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Answer:
the correct choice is marked
Step-by-step explanation:
The end behavior matches that of an odd-degree polynomial. The only function shown that has that behavior is the one marked:
[tex]f(x)=\dfrac{x^2-36}{x-6}=\dfrac{(x+6)(x-6)}{(x-6)}=x+6\qquad x\ne6[/tex]
__
Additional comment
The other functions have horizontal (not slant) asymptotes, so do not have the described end behavior.
B: y=0
C, D: y=1
Simplify the radical expression.
3^√0.125b^3
A. -5b
B. -0.5b
C. 0.5b
D. 5b
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form.
Slope= 1/3, passing through the origin
Answer:
[tex](y - 0) = \frac{1}{3} (x - 0)[/tex]
[tex]y = \frac{1}{3} x[/tex]
Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
Required:
a. Construct and interpret a 99% CI for the true proportion of voters who prefer the Republican candidate.
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
Answer:
a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
So 120 - 62 = 58 favored the Republican candidate, so:
[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]
The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
what is the prime product of 120
Answer:
[tex]2^{3} * 3 * 5[/tex]
Step-by-step explanation:
In the past, Alpha Corporation has not performed incoming quality control inspections but has taken the word of its vendors. However, Alpha has been having some unsatisfactory experience recently with the quality of purchased items and wants to set up sampling plans for the receiving department to use. For a particular component, X, Alpha has a lot tolerance percentage defective of 52 percent. Zenon Corporation, from which Alpha purchases this component, has an acceptable quality level in its production facility of 20 percent for component X. Alpha has a consumer's risk of 10 percent and Zenon has a producer's risk of 5 percent. a. When a shipment of Product X is received from Zenon Corporation, what sample size should the receiving department test
Answer:
The answer is "28"
Step-by-step explanation:
[tex](LTPD) = 52\%\\\\(AQL) = 20\%\\\\\to \frac{LTPD}{AQL} = \frac{52\%}{20\%}= 2.6\\\\[/tex]
The value of [tex]\frac{LTPD}{AQL} = 2.6[/tex] that value of [tex]\frac{LTPD}{AQL} = 2.618[/tex]
Acceptance number, [tex]c = 9[/tex]
Value of [tex]n\times AQL = 5.426[/tex]
Sample size [tex]n = n\times \frac{AQL}{AQL} =\frac{5.426}{20\%} = 27.13=28[/tex]
Which expression is equivalent to (3 squared) Superscript negative 2?
Answer:
–81
Step-by-step explanation:
Many individuals over the age of 40 develop intolerance for milk and milk-based products. A dairy has developed a line of lactose-free products that are more tolerable to such individuals. To assess the potential market for these products, the dairy commissioned a market research study of individuals over 40 years old in its sales area. A random sample of 250 individuals showed that 86 of them suffer from milk intolerance. Based on the sample results, calculate a 90% confidence interval for the population proportion that suffers milk intolerance. Interpret this confidence interval. a) First, show that it is okay to use the 1-proportion z-interval. b) Calculate by hand a 90% confidence interval. c) Provide an interpretation of your confidence interval. d) If the level of confidence was 95% instead of 90%, would the resulting interval be narrower or wider
Answer:
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
b) See step by step explanation
CI 90 % = ( 0,296 ; 0,392)
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392)
d) the CI 95 % will be wider
Step-by-step explanation:
Sample Information:
Sample size n = 250
number of people with milk intolerance x = 86
p₁ = 86 / 250 p₁ = 0.344 and q₁ = 1 - p₁ q₁ = 0,656
To calculate 90 % of Confidence Interval α = 10% α/2 = 5 %
α/2 = 0,05 z(c) from z-table is: z(c) = 1.6
Then:
CI 90 % = ( p₁ ± z(c) * SE )
SE = √ (p₁*q₁)/n = √ 0,225664/250
SE = 0,03
CI 90 % = ( 0,344 ± 1,6* 0,03 )
CI 90 % = ( 0,344 - 0,048 ; 0,344 + 0,048)
b) CI 90 % = ( 0,296 ; 0,392)
a) To show that we can use the 1 proportion z-interval, we know that 250 ( size sample) is big enough to approximate the binomial distribution ( tolerance-intolerance) to a normal distribution.
c) We can support that with 90 % of confidence we will find the random variable between this interval ( 0,296 ; 0,392) .
d) CI 95 % then significance level α = 5 % α/2 = 2.5 %
α/2 = 0,025 z(c) = 1.96 from z-table
SE = 0,03
And as 1.96 > 1.6 the CI 95 % will be wider
CI 95% = ( 0,344 ± 1.96*0,03 )
CI 95% = ( 0,344 ± 0,0588 )
CI 95% = ( 0,2852 ; 0,4028 )
Let f(x,y) =2x^3 y-xy find the domain
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Answer:
x, y ∈ all real numbers
Step-by-step explanation:
For your function ...
f(x, y) = 2x^3·y -xy
there appear to be no values of x or y for which the function is undefined. The domain for both x and y is "all real numbers."
Find the slope of the graphed line
Answer:
4
Step-by-step explanation:
Pick two points on the line
(0,-5) and (1,-1)
We can find the slope using
m = (y2-y1)/(x2-x1)
= ( -1 - -5)/(1 - 0)
(-1+5)/(1-0)
4/1
= 4
what is the formula to solve midpoint
Answer:
(x1 + x2) , (y1+y2)
2 2
Step-by-step explanation:
What else would need to be congruent to show that ABC= A DEF by the
AAS theorem?
B
E
Given:
ZA ZD
AB DE
A
F
A. AC = DF
B. ZCE ZF
C. BC = BC
D. BEZE
Answer:
[tex]\angle C \cong \angle F[/tex]
Step-by-step explanation:
Given
[tex]\angle A \cong \angle D[/tex]
[tex]AB \cong DE[/tex]
See attachment
Required
What proves [tex]\triangle ABC \cong \triangle DE F[/tex] by AAS
We have:
[tex]\angle A \cong \angle D[/tex] --- Angle
[tex]AB \cong DE[/tex] --- Side
We need to prove that one more angle are congruent
[tex]\angle B \cong \angle E[/tex]
The above angles are congruent; however, it will prove [tex]\triangle ABC \cong \triangle DE F[/tex] by ASA
So, we make use of:
[tex]\angle C \cong \angle F[/tex] because it completes the proof by AAS
Find the value of x.
x
9
9
7
x = [?]
Answer:
14
Step-by-step explanation:
Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
The amount of money invested in a retirement fund is an example of which of the following?
a.
investment asset
b.
liquid asset
c.
long term asset
d.
use asset
Please select the best answer from the choices provided
Answer:
the answer is A
okay that it have a nice day
Answer:
the answer above me is correct!
Step-by-step explanation:
Edge 2021
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L if one side of the rectangle lies on the base of the triangle.
base=
height=
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Answer:
base: L/2height: L√3/2Step-by-step explanation:
Let x represent the ratio of the rectangle base to the triangle side length. Then the height of the small triangle above the rectangle will be x times the height of the equilateral triangle. Then the height of the rectangle is (1-x) times the height of the equilateral triangle. The rectangle's area will be ...
A = bh
A = (xL)(1-x)(L·√3/2) = (L²√3/2)(x)(1-x)
This graphs as parabola opening downward with x-intercepts at x=0 and x=1. The vertex is on the line of symmetry, halfway between these zeros, at x = 1/2.
The base of the rectangle is L/2.
The height of the rectangle is L√3/2.
_____
The general solution to this sort of problem is that one side of the rectangle is the midsegment of the triangle.
Help please, thanks as always in advance.
Which correlation coefficient indicates the data set with the strongest linear correlation?
0.41
−0.25
0.66
−0.83
Step-by-step explanation:
Which correlation coefficient indicates the data set with the strongest linear correlation?
0.66
The correlation coefficient indicates the data set with the strongest linear correlation is -0.83
What is correlation coefficient?"It measures the strength of the relationship between two relative variables."
What is linear correlation?"When the rate of change is constant between two variables then it is said to be linear correlation."
For given example,
We have been given correlation coefficients.
We need to find the correlation coefficient that indicates the data set with the strongest linear correlation.
We know, the correlation coefficient lies between -1 to 1.
So, the strongest linear correlation is indicated by a correlation coefficient of -1 or 1.
From given correlation coefficients,
-0.83 is close to -1.
Therefore, the correlation coefficient indicates the data set with the strongest linear correlation is -0.83
Learn more about linear correlation coefficient here:
https://brainly.com/question/12400903
#SPJ2
Assume a significance level of α=0.05 and use the given information to complete parts (a) and (b) below. Original claim: More than 49% of adults would erase all of their personal information online if they could. The hypothesis test results in a P-value of 0.0281.
Required:
a. State a conclusion about the null hypothesis.
b. Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion?
1. The percentage of adults that would erase all of their personal information online if they could is more than or equal to 49%.
2. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 49%.
3. There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is less than 49%.
4. The percentage of adults that would erase all of their personal information online if they could is less than 49%.
Answer:
Part a: The correct answer is A, reject H0 because p value is less than . Part B: The correct answer is C, the percentage of adults that would erase their personal information online if they could is more than 51%.
Step-by-step explanation:
part a. The essential idea of hypothesis testing in statistics is to evaluate the probability p (p value) of some representative parameter, compared to a level of likelihood that is set before starting the test (). In this case, we are interested in a level of likelihood , which means that if the probability of the parameter is less than 5%, we will reject the hypothesis that this parameter is representing, since it's so unlikely. Of course, the significance level is arbitrary and must be payed attention, according to the particular situation. Therefore, the correct anser is A.
part b. Since we rejected the hypothesis to a 5% significance level, we reject the fact that less than 51% of adults would erase their personal information online if they could. This is equivalent to saying that a percentage of adults equal to or more than 51% would erase their personal information if they
Charlie has an annual salary of $75,000.00. He is paid every two weeks. What is the gross income amount for each paycheck?
Answer:
$2884.62
Step-by-step explanation:
A year has 52 weeks
The number of times Charlie will receive a paycheck will be 52w ÷ 2w = 26 times
Charlie's gross income each paycheck will be 7500÷26 = $2884.62 every two weeks
75000 ÷ (52 ÷2)
7500 ÷ 26
$2884.62
