Answer:
D. 0.42
Step-by-step explanation:
First, convert 40 km to miles by dividing it by 1.6:
40/1.6
= 25
Create a proportion where x is the number of gallons the motorcycle will need to travel 40 km (25 miles):
[tex]\frac{60}{1}[/tex] = [tex]\frac{25}{x}[/tex]
60x = 25
x = 0.4166
Round this to the nearest hundredth:
x = 0.42
So, to travel 40 km, the motorcycle will need 0.42 gallons of fuel.
The correct answer is D. 0.42
A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles. Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles. Calculate a 99% confidence interval for the difference in the two proportions.
Answer:
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).
Step-by-step explanation:
Before building the confidence interval, 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]
A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles.
This means that:
[tex]p_S = \frac{82}{90} = 0.9111[/tex]
[tex]s_S = \sqrt{\frac{0.9111*0.0888}{90}} = 0.045[/tex]
Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles.
This means that:
[tex]p_N = \frac{86}{110} = 0.7818[/tex]
[tex]s_N = \sqrt{\frac{0.7818*0.2182}{110}} = 0.0394[/tex]
Distribution of the difference:
[tex]p = p_S - p_N = 0.9111 - 0.7818 = 0.1293[/tex]
[tex]s = \sqrt{s_S^2+s_N^2} = \sqrt{0.045^2+0.0394^2} = 0.0598[/tex]
Calculate a 99% confidence interval for the difference in the two proportions.
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/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 bound of the interval is:
[tex]p - zs = 0.1293 - 2.575*0.0598 = -0.0247[/tex]
[tex]p + zs = 0.1293 + 2.575*0.0598 = 0.2833[/tex]
The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).
If x and y are positive integers such that 5x+3y=100, what is the greatest possible value of xy? please include steps. Thank you!
Answer:
The greatest possible value of xy is 165.
Step-by-step explanation:
how many models does the following set have? 5,5,5,7,8,12,12,12,150,150,150
The three modes are 5, 12, and 150 since they occur the most times and they tie one another in being the most frequent (each occurring 3 times).
Only the 7 and 8 occur once each, and aren't modes. Everything else is a mode. It's possible to have more than one mode and often we represent this as a set. So we'd say the mode is {5, 12, 150} where the order doesn't matter.
Suppose you are conducting a study to determine if women are better drivers than men. You send your survey to over 1000 students on your campus and 5 students respond that women are better drivers and 4 students respond that women are not better drivers. What is the sample proportion for women as the better drivers using the large-sample method?
Answer:
555.56
Step-by-step explanation:
Purpose of the study: To determine if women are better drivers than men.
Survey or Opinion population: 1,000
You are experimenting on 9 out of a thousand opinions.
5 of these opinions are that women are better drivers
4 of these opinions are that women are not better drivers
You want to know the sample (full sample size is 9) proportion for women as better drivers; using the large sample method. This method is also called the asymptotic method.
This involves approximating the desired statistic, with just a small fraction of the population; in this case, 9/1000.
This approximation will get more and more accurate as sample size increases and you know that a larger sample size gives a better representation and interpretation of the population preference!
So using ratio, the sample proportion for women as the better drivers is given by:
5/9 x 1000 = 555.56 opinions
Find the product :
1) 6/10 × 10/6 × 5/9
2) 6/10 × 4/3 × 10/20
Hello!
1) 6/10 × 10/6 × 5/9 = 1/10 × 10 × 5/9 = 1 × 5/9 = 5/9 or 0,5
2) 6/10 × 4/3 × 10/20 = 6 × 4/3 × 1/20 = 2 × 4 × 1/20 = 2 × 1/5 = 2/5 or 0,4
Good luck! :)
Answer:
1) 5/9
2) 2/5
Explanation:
1) 6/10 × 10/6 × 5/9=
Multiply all the denominators and all the numerators then simplify= 300/540 = 5/9
2) 6/10 × 4/3 × 10/20=
Multiply all the denominators and all the numerators then simplify= 240/600 = 2/5
4. How much interest will you earn in 8 years if you invest $7500 at 4.25% compounded semi-annually?
Answer:
$10,499.64
Step-by-step explanation:
^ means to the power of or exponent
* means multiply
semi annually = 2
formula is A = P(1 + r/n)^nt
make 4.25% into a decimal = .0425 = r
then plug it in
A = 7500(1+.0425/2)^2*8
A = 7,500.00(1 + 0.02125)^16
A = $10,499.64
If a + b = s and a - b = t, then which of the following expresses the value of ab in terms of s and t?
Please help me out
Answer:
=(s^2 - t^2)/4
Step-by-step explanation:
a + b = s and a - b = t,
Add the two equations together
a + b = s
a - b = t
----------------
2a = s+t
a = (s+t)/2
Subtract the two equations
a + b = s
- a + b = -t
-------------------
2b =(s-t)
b = (s-t)/2
We want to find ab
ab = (s+t)/2 * (s-t)/2
FOIL
=(s^2 - t^2)/4
which choice are equivalent to the expression below? Check all that apply
I could not get the expressions to type correctly because I am new so I am sending a picture. I am having trouble working backwards to figure out which once to choose.
Answer:
A, B, and E apply
Step-by-step explanation:
One thing we can do is to make everything in the same format, under one square root, with no non-square roots.
First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108
For A, √3 * √36 = √108, so this applies
For B, √18 * √6 = √108, so this applies
For C, 108² = √something bigger than 108 = √11664, so this does not apply
For D, √54 ≠ √108, so this does not apply
For E, √108 = √108, so this applies
For F, √3 * √6 = √18, so this does not apply
What are the zeros of f(x) = (x - 2)(x + 7)? Select all that apply.
A. X= -7
B. X = -2
C. X = 2
D. X = 7
Answer:
2 = x -7 = x
Step-by-step explanation:
f(x) = (x - 2)(x + 7)
y = (x - 2)(x + 7)
Set y = 0
0 = (x - 2)(x + 7)
Using the zero product property
0 = x-2 0 = x+7
2 = x -7 = x
Answer:
Zeros happen when f(x) = 0. There are two zeros in the given function:
when (x - 2) = 0when (x + 7) = 0Therefore solve both equations above and you'll get:
Zero #1 = 2Zero #2 = -7th of
cm.
4 Mrs. Ayer is painting the outside of her son's toy
box, including the top and bottom. The toy box
measures 3 feet long, 1.5 feet wi de, and 2 feet high.
What is the total surface area she will paint?
1) 9.0 ft
2) 13.5 ft?
3) 22.5 ft?
4) 27.0 ft
Chau Took 5 3/8 hours to clean the bedroom. Then he took a 1/2 to clean the den. How much total time did he take to clean two rooms.
Answer:
It took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.
Step-by-step explanation:
Given that Chau took 5 3/8 hours to clean the bedroom, and then he took a 1/2 to clean the den, to determine how much total time did he take to clean two rooms the following calculation must be performed:
5 + 3/8 + 1/2 = X
5 + 0.375 + 0.5 = X
5.875 = X
0.875 = 7/8
60/8 x 7 = 52.5
Therefore, it took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.
Using Confidence Intervals
a. Assume that we want to use a 0.05 significance level to test the claim that P1
b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?
c. If we want to use a 0.05 significance level to test the claim that P1
d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: â0.000508
Because the confidence interval ________ does not contain contains _________ 0, the significance level, the critical value, the pooled sample proportion, there __________ does not appear to be appears to be a significant difference between the two proportions. Because the confidence interval consists __________ only of values greater than of values both less than and greater than only of values less than __________ the significance level, the critical value, the pooled sample proportion, 0, it appears that the first proportion is _________ not significantly different from less than greater than the second proportion. There is _______ insufficient sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
Answer:
There is no insufficient sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo.
Which of the following best describes the expression 4(y + 6)?
The product of a constant factor of four and a factor with the sum of two terms
The sum of a constant factor of six and a factor with the product of two terms
The product of two constant factors four and six plus a variable
The sum of two constant factors four and six plus a variable
Answer:
The product of a constant factor of four and a factor with the sum of two terms
Step-by-step explanation:
4(y + 6)
This is two terms, a constant 4 and a term with y+6
We a multiplying so we have a product
Answer:
A
Step-by-step explanation:
I believe A is the best answer because 4 is the constant factor with the sum of y + 6. I just think it best rrepresents the equation! :)
What procedure might one use to solve percent problems using proportions ?
Answer:
Proportions and percent
A five-year prospective cohort study has just been completed. The study was designed to assess the association between supplemental vitamin A exposure and mortality and morbidity for measles. The relative risk for incidence of measles was 0.75 and the relative risk for measles mortality was 0.5. Regarding the relative risk, which statement is correct?
a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.
b. Exposure to vitamin A appears to be a risk factor for morbidity and mortality for measles.
c. Exposure to vitamin A is not associated with morbidity and mortality for measles.
d. Exposure to vitamin A is a risk factor for morbidity and a protective factor for mortality for measles.
Answer:
Assessing the association between supplemental vitamin A exposure and mortality and morbidity for measles:
Regarding the relative risk, the correct statement is:
a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.
Step-by-step explanation:
Relative risk for incidence of measles = 0.75
Relative risk for measles mortality = 0.5
Relative risk for mortality and morbidity for measles = 0.375 (0.75 * 0.5)
The combined relative risk is less than 50%
The association is weak because RR is less than 1.
Therefore, there is no association between supplemental vitamin A exposure and mortality and morbidity for measles.
Last year Diana sold 800 necklaces. This year she sold 1080 necklaces. what is the percentage increase of necklaces she sold?
Answer:
the percentage increase is 35%
Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?
Answer: Choice B) [tex]\sqrt{2}[/tex]
Work Shown:
[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]
Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.
answers please formula
Answer:
-5
2
-125
-3
Step-by-step explanation:
5 + A = 0
Subtract 5 from both sides.
A = -5
-8/4 - B = -4
-2 - B = -4
B + 2 = 4
B = 2
C ÷ 25 = -5
C = -125
D × 13 = -39
D × 13/13 = -39/13
D = -3
BRAINLIESTT A spinner is divided into 8 equal-sized sections, and each section is labeled with a number 1 through 8.
if Kathryn spins the arrow on the spinner twice, what is the probability that the arrow will land on a section with an odd number the first time
and a number greater than 6 on the second spln?
Answer:
The probability would be 1/8.
Step-by-step explanation:
The probability of the spinner landing on an odd number is 1/2, and the probability of the spinner landing on a number greater than 8 is 1/4. So we multiply those two probabilites to get our answer 1/8.
(15 Points) Indicate the general rule for the arithmetic sequence with a3 = -4 and a8 = -29.
Step-by-step explanation:
[tex]a_3 [/tex] = - 4
[tex]a_3 [/tex] = a* + (3- 1) d*
- 4 = a + 2d . . . . . . . . .(i)
[tex]a_8 [/tex] = - 29
[tex]a_8 [/tex] = a + ( 8 - 1) d
- 29 = a + 7d . . . . . . . . (ii)
subtracting equations (i) and (ii)
25 = 5d
d = -5
placing d = -5 in equation (i)
a - 10 = -4
a = 6
For an arithmetic Progtession
[tex]a_n [/tex] = a + (n - 1)d
[tex]a_n [/tex] = 6 + (n- 1)-5
[tex]a_n [/tex] = 6 - 5n + 5
[tex] \underline {a_n = 11 - 5n }[/tex]
[tex]\\[/tex]
*[tex] \boxed{ \mathfrak { a \:stands\: for\: first\: term } } [/tex]
*[tex] \boxed{ \mathfrak { d \:stands\: for\: common \: difference } } [/tex]
Answer:
General rule » -5n+11
Step-by-step explanation:
a3 = a+2d = -4 .......(1)
a8=a+7d = -29..........(2)
(2)-(1) » 5d= -25
d = -25/5
. = -5
substitute d = -5 in ( 1)
» a-2×-5= -4
a-10 = -4
a = -4 +10
= 6
General rule » a +(n-1)d
» 6 +(n-1)×-5
» 6-5n+5
» -5n+11
Create a sample of 10 numbers that has a mean of 8.6.
Answer:
10 + 8 + 10 + 10 + 10 + 10 + 8 + 8 + 6 + 6
Many universities and colleges have instituted supplemental instruction (SI) programs, in which a student facilitator meets regularly with a small group of students enrolled in the course to promote discussion of course material and enhance subject mastery. Suppose that students in a large statistics course (what else?) are randomly divided into a control group that will not participate in SI and a treatment group that will participate. At the end of the term, each student’s total score in the course is determined.
a. Are the scores from the SI group a sample from an existing population? If so, what is it? If not, what is the relevant conceptual population?
b. What do you think is the advantage of randomly dividing the students into the two groups rather than letting each student choose which group to join?
c. Why didn’t the investigators put all students in the treatment group? Note: The article "Supplemental Instruction: An Effective Component of Student Affairs Programming" (J. of College Student Devel., 1997: 577–586) discusses the analysis of data from several SI programs.
Answer:
Step-by-step explanation:
Let many universities and colleges have conducted supplemental instruction(SI) programs. In that a student facilitator he meets the students group regularly who are enrolled in the course to promote discussion of course material and enhance subject mastery.
Here the students in a large statistics group are classified into two groups:
1). Control group: This group will not participate in SI and
2). Treatment group: This group will participate in SI.
a)Suppose they are samples from an existing population, Then it would be the population of students who are taking the course in question and who had supplemental instruction. And this would be same as the sample. Here we can guess that this is a conceptual population - The students who might take the class and get SI.
b)Some students might be more motivated, and they might spend the extra time in the SI sessions and do better. Here they have done better anyway because of their motivation. There is other possibility that some students have weak background and know it and take the exam, But still do not do as well as the others. Here we cannot separate out the effect of the SI from a lot of possibilities if you allow students to choose.
The random assignment guarantees ‘Unbiased’ results - good students and bad are just as likely to get the SI or control.
c)There wouldn't be any basis for comparison otherwise.
(07.05A)
Which statement best explains whether y = 4x + 8 is a linear function or a nonlinear function?
Answer:
Step-by-step explanation:
There are no statements provided, but since it is modeled after the linear function y = mx + b, it is a line. m is the slope or rate of change (which is constant; that's what makes this a line!), and b is the y-intercept (the value of y when x is equal to 0). Its slope is 4 (the function raises 4 units for every 1 unit it moves to the right). Its y-intercept is 8, having the coordinate (0, 8).
Answer:
y = 4x + 8 is a linear function.
Step-by-step explanation:
No statements are given, but here's why:
- It's in slope-intercept form, y = mx + b.
- It has a constant slope.
- A non-linear function does not have a constant slope, and this one does.
x^{2}-7x-25=0 to the nearest tenth
Answer:
x = 9.6
x = - 2.6
Step-by-step explanation:
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
Ignore the before the ± it wouldn't let me type it correctly.
x² - 7x - 25 = 0
a = 1
b = - 7
c = - 25
[tex]x=\frac{-(-7)±\sqrt{-7^{2}-4((1)(-25)) } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{49-4((1)(-25)) } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{49+100 } }{2(1)}[/tex]
[tex]x=\frac{7±\sqrt{149 } }{2}[/tex]
[tex]x=\frac{7±12.2}{2}[/tex]
Two separate equations
[tex]x=\frac{7+12.2}{2}[/tex]
[tex]x=\frac{7-12.2}{2}[/tex]
[tex]x=\frac{7+12.2}{2}[/tex]
[tex]x=\frac{19.2}{2}[/tex]
x = 9.6
[tex]x=\frac{7-12.2}{2}[/tex]
[tex]x=\frac{-5.2}{2}[/tex]
x = - 2.6
For this just use the quadratic formula to find the zeros. In this case, you get 7 +/- square root 149 over 2. Which gives you -2.6 and 9.6.
I need help with this
Answer:
below
Step-by-step explanation:
A AND C is the right option
congruent angles are angles with exactly the same measure
When ever you have time plz help me
Answer:
A is the correct answer!
solve the equation
r²-4s+s²=8r+2s=28
Answer:
[tex] {r}^{2} - 4s + {s}^{2} = 8r + 2s = 28 \\ \\ r = \frac{24}{5 } - i \frac{ \sqrt[4]{129} }{5} \\ \: s = \frac{58}{5} + i \frac{ \sqrt[2]{129} }{5 } \\ \\ r = \frac{24}{5} + i \frac{ \sqrt[4]{129} }{5} \\ s = \frac{58}{5} - i \frac{ \sqrt[2]{129} }{5} [/tex]
Please help
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
(4) y = (3 - 2x)³ + 24x
Use the power and chain rules:
dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24
dy/dx = 3 (3 - 2x)² (-2) + 24
dy/dx = -24x ² + 72x - 30
(5) y = 54x - (2x - 7)³
Same basic procedure:
dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]
dy/dx = 54 - 3 (2x - 7)² (2)
dy/dx = -24x ² + 168x - 240
1+4=5
2+3=10
10+5=25
4+1?
Answer:
8
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of: (-2,-2) and (2,8)
Answer:
(0 ; 3)
Step-by-step explanation:
hello :
the midpoint of the line segment is : ((-2+2)/2 ;(-2+8)/2 )
(0 ; 3)
