Answer:
98% of confidence interval of Population proportion is determined by
(0.60683 ,0.67217)
Step-by-step explanation:
Given the sample size n = 1168
Given 747 out of 1168 female 12th graders said they always use a seatbelt when driving
The sample proportion 'p' = [tex]\frac{x}{n} = \frac{747}{1168} = 0.6395[/tex]
98% of confidence interval of Population proportion is determined by
[tex]p^{-} -Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^-)}{n} }, p^- +Z_{\frac{\alpha }{2} } \sqrt{\frac{p^-(1-p^-)}{n} } }[/tex]
The tabulated value Z₀.₀₂ score = 2.326
[tex](0.6395 -2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} }, 0.6395 +2.326 \sqrt{\frac{0.6395(1-0.6395)}{1168} } })[/tex]
on calculation , we get
(0.6395 -0.03267 , 0.6395 +0.03267)
(0.60683 ,0.67217)
6i4+6i3−2i2+−49−−−−√ rewritten in a+bi form
Answer:
[tex]8+i[/tex]
Step-by-step explanation:
We are given that an expression
[tex]6i^4+6i^3-2i^2+\sqrt{-49}[/tex]
We have to rewrite in the form of a+bi
[tex]6(i^2)^2+6i^3-2i^2+\sqrt{-49}[/tex]
We know that
[tex]i^2=-1[/tex]
[tex]i^3=-i[/tex]
[tex]\sqrt{-1}=i[/tex]
Using the identity
Then, we get
[tex]6-6i-2(-1)+7i[/tex]
[tex](6+2)+(7-6)i[/tex]
[tex]8+i[/tex]
This is required form of a+ib
Write the largest one digit,two digit,three digitnumbers and compare them with both signs< >
Answer:
[tex]9<99<999[/tex]
[tex]999>99>9[/tex]
Step-by-step explanation:
The largest one digit number=9The largest two digit number=99The largest three digit number=999We have that:
9<9999<999If a<b and b<c, then a<b<c.
Combining the two inequalities, we obtain: [tex]9<99<999[/tex]
In reverse, we can also write this as:
[tex]999>99>9[/tex]
A cylinder has a base diameter of 14m and a height of 15m. What is its volume in
cubic m, to the nearest tenths place?
Answer:
2310m^3
Step-by-step explanation:
base area which is the circle = πr^2
But diameter, d = 14, r = 14/2 = 7
area = π × (7)^2 = 22/7 × 49 = 22 × 7 = 154
Volume = base area × height
= 154 × 15 = 2310
Answer:
2309.1
Step-by-step explanation:
Deltamath
factoring area models x2 + 6x + 5
Answer:
factored is (x+1)(x+5)
Step-by-step explanation:
gradpoint
please help the Marshmello
So the value of X is 2.
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
[tex]x = 2[/tex]
First answer is correct
Step-by-step explanation:
[tex]9 = 1 + 8x - 8 \\ 9 - 1 + 8 = 8x \\ 16 = 8x \\ \frac{16}{8} = \frac{8x}{8} \\ x = 2[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
When solving a quadratic, how can x equal 2 different things? What is x?
Answer:
X = unknown
The highest degree of x is 2 .
Step-by-step explanation:
First of all x is the unknown variable to be determined by solving quadratically
Quadratic equation was chooses because of the degree of x.
The highest degree of x is 2 .
That's the the reason why the value of x will always be double.
If solving linear equation that has degree one, the value of x is one
If solving polynomial, the value of x will be 3 above.
Nancy hears a report that the current national average price of gasoline is $3.14. She averages the prices of stations near her home.she finds the average price of gas to be $2.95. Why are the averages different?
Answer:
Nancy's ambient locality might be having more suppliers, higher supply of Gasoline
Step-by-step explanation:
National average price of gasoline = $3.14
Stations near Nancy's home have an average price = $2.95
Gasoline price near Nancy's house is lesser than national average price level. Number of gasoline stations near her house might be more. It implies increase in its supply. This leads to competition among sellers & reduces the price level.
The mean age of 5 people in a room is 32 years.
A person enters the room.
The mean age is now 36.
What is the age of the person who entered the room?
Answer:
56
Step-by-step explanation:
If you could give me a thanks, that would be much appreciated.
The rate of growth of profit (in millions) from an invention is approximated by Upper P prime (x )equals x e Superscript negative x squared Baseline comma where x represents time in years. The total profit in year 2 that the invention is in operation is $ 25 comma 000. Find the total profit function Upper P (x ). Round to the nearest thousandth if necessary.
Answer:
The function is [tex]P(x) = \frac{1}{2} e^{-x^2} +0.016[/tex]
Step-by-step explanation:
From the question we are told that
The rate of growth is [tex]P'(x) = xe^{x} - x^2[/tex]
The total profit is [tex]P(2) =[/tex]$25,000
The time taken to make the profit is [tex]x = 2 \ years[/tex]
From the question
[tex]P'(x) = xe^{-x^2}[/tex] is the rate of growth
Now here x represent the time taken
Now the total profit is mathematically represented as
[tex]P(x) = \int\limits {P'(x)} \, = \int\limits {xe^{-x^2}} \,[/tex]
So using substitution method
We have that
[tex]u = - x^2[/tex]
[tex]du = 2xdx[/tex]
So
[tex]p(x) = \int\limits {\frac{1}{2} e^{-u}} \, du[/tex]
[tex]p(x) = {\frac{1}{2} [ e^{-u}} +c ][/tex]
[tex]p(x) = {\frac{1}{2} e^{-x^2}} + \frac{1}{2} c[/tex] recall [tex]u = - x^2[/tex] and let [tex]\frac{1}{2} c = Z[/tex]
At x = 2 years
[tex]P(x) =[/tex]$25,000
So
Since the profit rate is in million
[tex]P(x) =[/tex]$25,000 = [tex]\frac{25000}{1000000} =[/tex]$0.025 millon dollars
So
[tex]0.025 = {\frac{1}{2} e^{-2^2}} + Z[/tex]
=> [tex]Z = 0.025 - {\frac{1}{2} e^{-2^2}}[/tex]
[tex]Z = 0.016[/tex]
So the profit function becomes
[tex]P(x) = \frac{1}{2} e^{-x^2} +0.016[/tex]
Alex has 3 more quarters than dimes in his pocket, for a total of $5.25.
Which equation could be used to determine the number of dimes, x, in his.
pocket? *
Answer:
the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25
and the value of x = 7
Step-by-step explanation:
We are being told that:
Alex has 3 more quarters than dimes in his pocket, for a total of $5.25.
Let the value for the dimes in his pocket be x:
So he has 3 more quaters than x
We know that a quarter is 1/4
3 more quaters than x = (3/4) x
(3/4)x = 5.25
3x = 5.25 * 4
3x = 21
x = 21/3
x = 7
Thus, the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25
and the value of x = 7
Goofy's fast food center wishes to estimate the proportion of people in its city that will purchase its products. Suppose the true proportion is 0.06. If 280 are sampled, what is the probability that the sample proportion will be less than 0.09? Round your answer to four decimal places.
Answer:
[tex]\mu_{\hat p}= 0.06[/tex]
[tex] \sigma_{\hat p}= \sqrt{\frac{0.06*(1-0.06)}{280}}= 0.0142[/tex]
And we want to find this probability:
[tex] p(\hat p <0.09)[/tex]
[tex] z = \frac{p \mu_{\hat p}}{\sigma_{\hat p}}[/tex]
[tex] z = \frac{0.09-0.06}{0.0142}= 2.114[/tex]
And we can find this probability:
[tex] P(z<2.114)[/tex]
And using the normal table or excel we got:
[tex] P(z<2.114)= 0.9827[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 280[/tex] represent the sample size
[tex] p =0.06[/tex] represent the true proportion
The sample proportion can be approximated with this distribution:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}})[/tex]
The mean is given by:
[tex]\mu_{\hat p}= 0.06[/tex]
And the deviation is given by:
[tex] \sigma_{\hat p}= \sqrt{\frac{0.06*(1-0.06)}{280}}= 0.0142[/tex]
And we want to find this probability:
[tex] p(\hat p <0.09)[/tex]
And we can use the z score formula given by:
[tex] z = \frac{p \mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z = \frac{0.09-0.06}{0.0142}= 2.114[/tex]
And we can find this probability:
[tex] P(z<2.114)[/tex]
And using the normal table or excel we got:
[tex] P(z<2.114)= 0.9827[/tex]
Alonzo and Mitra wanted to share a pizza. Mitra ate of the pizza, and Alonzo ate of the pizza.
How much more pizza did Alonzo eat than Mitra?
Answer:
Alonzo ate 1/2 more than Mitra.
Step-by-step explanation:
In this question, you are supposed to find how much more Alonzo ate. We solve that like this:
Steps:
- Set up the Equation:
- 1/4 + ? = 3/4
- The question mark represents the answer.
- Inverse Operations:
- Change 1/4 + ? = 3/4 to 3/4 - 1/4 = ?
- Since Subtraction is the opposite of Addition, we flip the equation.
- Solve:
- [tex]\frac{3}4} -\frac{1}{4} =\frac{2}{4}[/tex]
- Then Simplify:
- [tex]\frac{2}{4} =\frac{1}{2}[/tex]
So, Alonzo ate 1/2 more than Mitra, or C.
Hope this helps! Good luck!
An electronics store offers students a discount
of 10% on purchases of computers. They
estimate that of computer sales are to
students. The average sale per customer is $498
and the store's profit is $80 before the discount.
What is the expected profit on the sale of a
computer?
show work
Answer:
83.9357% increase for the buyer
Step-by-step explanation:
a bag contains a mixture of almonds walnuts and cashews there's an equal quantity of each nut. If a nut is chosen randomly out of the bag what is the probability that an almond will be selected or that a cashew will be selected
Answer:
P(either almond or cashew) = ⅔
Step-by-step explanation:
We are told that the bag contains a mixture of almonds walnuts and cashews of equal number.
Since the 3 nuts are equal in number, they will have a ratio of 1:1:1.
So, when a nut is chosen randomly,
Probability of choosing almond = 1/3
Probability of choosing cashew = 1/3
Thus,
Probability of choosing either almond or cashew in a random selection will be the sum of their individual probability.
So,
P(either almond or cashew) = ⅓ + ⅓ = ⅔
Find the surface area of the rectangular prism.
6 yd
3 yd
1 yd
Answer:
54 yd²
Step-by-step explanation:
The surface area of the prism is the sum of the areas of its faces. Opposite faces have the same area, so we can write the formula as ...
SA = 2(LW +WH +LH) = 2(LW +H(L +W))
Filling in the numbers, we have ...
SA = 2(6·3 +1(6 +3)) = 2(18 +9) = 54 . . . . square yards
The area is 54 square yards.
1. A crash repair bill comes to $1380.00. How much is 10% of
the bill? What is the final bill once 10% is taken off?
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Answer:
1. 10% of the bill is $138. The final bill once 10% is taken off is $1242.
2. 20% of the total is $34.10. The final total once the 20% is taken off is $136.4
Step-by-step explanation:
1. A crash repair bill comes to $1380.00. How much is 10% of the bill? What is the final bill once 10% is taken off?
To find how much is 10% of the bill, we multiply the bill by 0.1
0.1*1380 = 138
10% of the bill is $138.
To find the final bill, we subtract the initial bill by 10%.
1380 - 138 = 1242
The final bill once 10% is taken off is $1242.
2. A person buys a new fan belt, a new alternator, and a new water pump for their car. The total comes to $170.50. What is 20% of the total? How much is the final total once the 20% is taken off?
Same logic as above.
0.2*170.50 = 34.1
20% of the total is $34.10.
170.50 - 34.1 = 136.4
The final total once the 20% is taken off is $136.4
Factor completely. 25+70x+49x^2
Answer:
(5+7x)^2
Step-by-step explanation:
25+70x+49x^2
This is a perfect square trinomial
a^2 +2ab + b^2 = (a+b)^2
5^2 *2*5*7x+ (7x)^2 = (5+7x)^2
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
No because the product of their slopes is not -1
In the attached file
c) A human resource analyst wants to know if the applicants this year score, on average, higher on their placement exam than the 52.5 points the candidates averaged last year. She samples 50 recent tests and finds the average to be 54.1 points. She fails to reject the null hypothesis that the mean is 52.5 points. At the end of the year, they find that the candidates this year had a mean of 55.3 points. Choose the correct answer below. A. The analyst did not make an error. The actual value was 55.3 points, which is close to 52.5. B. The analyst made a Type I error. The actual value was 55.3 points, which is greater than 52.5. C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5. D. The analyst made a Type II error. The actual value was 55.3 points, which is close to 52.5. E. The analyst made a Type I error. The actual value was 55.3 points, which is close to 52.5.
Answer:
Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
Step-by-step explanation:
Answer:
Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
Step-by-step explanation:
The null hypothesis was the applicants last year score, on average was 52.5 points.
Conclusion: She fails to reject the null hypothesis that the mean is 52.5 points.
At the end of the year, they find that the candidates this year had a mean of 55.3 points.
A type II error occurs when the researcher fails to reject the null hypothesis when it is false. Option C. The analyst made a Type II error. The actual value was 55.3 points, which is greater than 52.5
1. Nicole purchased new lawn furniture for $279.90. She used a coupon to
get a 15% discount. What was the final purchase price, excluding sales tax
of the lawn furniture?
Answer:
$237.92
Step-by-step explanation:
0.85 x 279.90 = 237.915 = ~237.92
pls help me with this and show any work
Answer: 9.5 (D.)
Step-by-step explanation:
SOCAHTOA
the sin of an angle is equal to the opposite side over the hypotenuse.
angle: 32
opposite side: x
hypotenuse: 18 m
1. sin32 = x/18
2. 18(sin32) = x
3. 9.5 = x
if you are confused with how it went from 18(sin32) to 9.5, you can plug 18(sin32) into your calculator.
What is the value of x in the equation
Answer:
It is b.
Step-by-step explanation:
0.7 x -3 = -2.1 and -2.1 - 1.4= -3.5
please branliest!!!!
A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1003 adults living in the United States by telephone. Of these, 462 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering.
A) Identify the sample size and the count.
B) Calculate the sample proportion.
C) Explain the relationship between the population proportion and the sample proportion.
Answer:
Given:
n = 1003
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
q = 1 - 0.4606 = 0.5394
a) The sample size and count.
Here the sample size is the number that took part in the poll. It is denoted as n = 1003.
The count is the number that answered yes. Count = 462
b) The sample proportion.
The formula for sample proportion is: [tex] p' = \frac{x}{n} [/tex]
Therefore, sample proportion =
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
c) The relationship between population proportion and sample proportion.
Since the sample size is greater than 30 (n>30), the sample size is large. Hence, for a large sample, the population proportion is approximately equal to the sample proportion.
This means the population proportion, p = 0.4606
Answer:
A) Sample size n=1003
Count x=462
B) Sample proportion p=0.46
C) The population proportion can be estimated with a confidence interval, with the information given by the sample proportion.
The 95% confidence interval for the population proportion is (0.429, 0.491).
Step-by-step explanation:
A) The sample size include all the adult that answer the poll. The sample size is then n=1003.
The count is the number of adults that answer Yes in this case. The count is x=462.
B) The sample proportion can be calculated dividing the count by the sample size:
[tex]p=\dfrac{x}{n}=\dfrac{462}{1003}=0.46[/tex]
C) The population proportion is not known. It can only be estimated with the information given by samples of that population. The statistical inference is the tool by which the sample information can be used to estimate the population characteristics.
With the sample proportion p we can estimate a confidence interval for the population proportion.
We can calculate a 95% confidence interval.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.46*0.54}{1003}}\\\\\\ \sigma_p=\sqrt{0.00025}=0.0157[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0157=0.031[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.46-0.031=0.429\\\\UL=p+z \cdot \sigma_p = 0.46+0.031=0.491[/tex]
The 95% confidence interval for the population proportion is (0.429, 0.491).
We have 95% that the population proportion is within this interval
An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.
The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2
h and k are the center point and r is the radius.
In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.
Center (-6,7)
Radius = 9
The required center is [tex](-6,7)[/tex] and the radius is 9 units.
Given equation is,
[tex](x + 6)^2 + (y-7)^2 = 81[/tex]....(1)
Equation of the circle: The general equation of the circle with the center (a,b) and the radius r is represented by,
[tex](x-a)^2+(y-b)^2=r^2[/tex]...(2)
We can write the given equation as,
[tex](x + 6)^2 + (y-7)^2 = (9)^2[/tex]
Comparing equations (1) and (2) we get,
The Centre of the given circle is [tex](-6,7)[/tex]
The radius of the given circle is 9 units.
Learn more about the equation of the circle:
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Answer:quadratic formula
Step-by-step explanation:
Answer:
Completing the square.
Step-by-step explanation:
x^2-8x+(-4)^2=22 can be rewritten as (x-4)^2=22. therefore, the best method would be completing the square.
the radius of a mini basketball is 4 inches. what is the volume rounded to the nearest tenth?
Answer:
268.08 inches3
Step-by-step explanation:
the volume rounded to the nearest tenth is 268.08 in³.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
given the radius of a basketball is 4 inches.
Since basketball has the shape of a sphere,
thus from the general formula of the volume of the Sphere:
Volume = 4/3 πr³
Where r is the radius
in our case
r = 4
Thus volume = 4/3 π 4³
The volume of basketball = 268.08 in³
therefore, the volume of the given basketball is 268.08 in³.
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a bag of sweets contains only two different flavours strawberry and orange. the probability that a sweet is strawberry is 0.8 what is the probability that a sweet is orange falvour
Answer:
0.2
Step-by-step explanation:
total = 1.0
strawberry = 0.8
1-0.8 =0.2
Answer:
0.2 is the probability of orange sweet.
XYZ Inc. produces two types of paper towels?regular and super-soaker. Regular uses 2 units of recycled paper per unit of production, and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. Let X1 be the number of units of regular produced per month and X2 the number of units of super-soaker produced per month. The appropriate constraint/s will be:_________
A) 2X1 + 3X2 = 10000
B) 180X1 + 80X2 geq 360
C) 2X1 + 3X2 geq 10000
D) 2X1 = 3X2
E) A, B, and C
Answer:
The appropiate constraint is:
[tex]2X_1+3X_2\leq10,000[/tex]
Step-by-step explanation:
There is only one restriction in this problem, and that is the available units of recycled paper per month.
There is a total of 10,000 units.
Regular paper (X1) uses 2 units per unit of production and Super-soaker (X2) uses 3 units per unit of production.
The total units used for both types of paper are:
[tex]2X_1+3X_2[/tex]
This amount has to be equal or smaller than the available (10,000 units):
[tex]2X_1+3X_2\leq10,000[/tex]
The appropriate constraint/s for the units of production being made by XYZ Inc is;
2X₁ + 3X₂ ≤ 10000
We are told that;
X₁ is the number of units of regular produced per month
X₂ the number of units of super-soaker produced per month.
we are told that;
Regular uses 2 units of recycled paper per unit of production. This is 2X₁
Also, we are told that super-soaker uses 3 units of recycled paper per unit of production. This is 3X₂.
We are now told that The total amount of recycled paper available per month is 10,000.
This means that;
2X₁ + 3X₂ ≤ 10000
The symbol less than or equal to is used because it is not possible for the 10000 to be exceeded as that is the amount available and also it's possible less than the 10000 may be used.
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Whats the point slope equation
Answer:
y-4 = 8/7(x-4)
Step-by-step explanation:
formula is y-y=m(x-x) just substitute the numbers in
Movie executives want to know if a movie watcher’s heart rate increases when they watch certain types of movies. Subjects in the experiment were given a free movie ticket and randomly assigned to watch one of four movies: an action-adventure film, a horror film, a romantic comedy, or an animated children’s film. They measured the average heart rate of all subjects while watching the assigned film.
Which of the following is the most appropriate statistical test to use to test if the average heart rate of the movie watchers was different for the four types of movies?
A. Matched pairs t-test
B. Chi-squared test for independence
C. ANOVA
D. Two-sample t-test
E. Inference for regression
Answer:
The correct option is C
Step-by-step explanation:
ANOVA is the correct option because it can be used to carry out comparison of average of more than two groups