Answer:
We conclude that the sample is from a population of songs with a mean greater than 210 seconds.
Step-by-step explanation:
We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.
Assume that the standard deviation of song lengths is 54.5 sec.
Let [tex]\mu[/tex] = population mean length of the songs
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}
The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean length of songs = 252.5 seconds
[tex]\sigma[/tex] = population standard deviation = 54.5 seconds
n = sample of current hit songs = 40
So, the test statistics = [tex]\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }[/tex]
= 4.932
The value of z-test statistics is 4.932.
Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the sample is from a population of songs with a mean greater than 210 seconds.
A line passes through the point (4, -4) and has a slope of -5/4
Write an equation in slope intercept form for this line.
Answer:
y= -5/4x + 1
Step-by-step explanation:
Slope-intercept form: y=mx+b
M is the slope
B is the y-intercept.
The slope is -5/4.
M = -5/4
y = -5/4 + b
We're looking for the y-intercept. Substitute point in.
(4,-4) x= 4 y= -4
-4 = -5/4(4) + b
-4 = -5+b
b= 1
y= -5/4x + 1
Use the formula A=P(1+r)" to solve the following problem.
Find the rate r at which $500,000 grows to $708,050 in 2 years.
Answer:
r= 0.19
Step-by-step explanation:
A= $708,050
P=$500,000
'' = 2
$708,050= $500,000(1+r)^2
-Divide $500,000 by both sides
1.4161= (1+r)^2
-Square Root on both sides
1.19= 1+r
-Subtract 1 on both sides
r= 0.19
Which inequality is represented by the graph?
HELP WILL NAME BRAINLIST
Answer:
y>= 2/3(x) - 2.5
Step-by-step explanation:
The sign should be "greater than or equal to" but my keyboard doesn't have that. Sorry.
The slope is "up two, over three" found by finding places where the line passes through the grid lines, and counting.
The y-intercept is -2.5. That tells you the "constant" to put in for "b" in the slope intercept form, y=mx+b
Which scenario can be modeled using the graph below? A temperature range is within 5 degrees of 60 degrees Fahrenheit. A scientist uses more than 55 and less than 65 mL of water in an experiment. A commuter train takes less than 55 minutes or more than 65 minutes to complete one route. A worker makes greater than $55 per day but less than $65 per day.
Answer:
A temperature range is within 5 degrees of 60 degrees Fahrenheit
Step-by-step explanation:
As per the number line which has been given, the circular marks at the ends of the shaded area are also seen to be shaded, not blank. This means that the values on which these marks fall, 55 and 65, have to go along with the list. A, a temperature range within 5 degrees of 60 degrees
Fahrenheit is the only choice that suits this as 5 degrees below 60 degrees is 55 while 5 degrees higher than the degrees of 60 is 65
Answer:
the answer is A
Step-by-step explanation:
i did the test
4. After paying 9 dollars for the pie, Alyssa has 50 dollars left. How much money did she have before buying the pie?
Answer:
Step-by-step explanation:
59 dollars
Answer:
59 dollarshere,
Left dollars+ paid dollars
= 50 dollars +9 dollars
=59 dollars
Hope this helps...
Good luck on your assignment..
HELP PLEASE!!!! I NEED HELP ASAP Which statement best describes the expression 3 + y ÷ 2? The quotient of 2 and the sum of 3 and y The quotient of the sum of 3 and y, and 2 The sum of 3 and the quotient of 2 and y The sum of 3 and the quotient of y and 2
Answer:
I believe it is D
Answer:
The sum of 3 and the quotient of y and 2.
Step-by-step explanation:
The order of operations requires that you evaluate the expression ...
3 + y ÷ 2
by first performing the division, then the addition. So, the addition gives you the sum of 3 and a quotient, because the quotient must be evaluated first.
The quotient is of y and 2 (not 2 and y), because the wording "the quotient of a and b" is always interpreted to mean a÷b.
So, the expression can be described as ...
the sum of 3 and the quotient of y and 2.
PLS I NEED HELP SIRR
Answer: you got this!
Step-by-step explanation:
Ms. Wilson draws a model of the factorization of a polynomial with integer factors. Her model is partially complete. A 2-column table with 2 rows. First column is labeled n with entries n squared, 5 n. Second column is not labeled with entries blank, 40. First row is not labeled with entries n squared, blank. Second row is labeled 5 with entries 5 n, 40. Which equation is represented by Ms. Wilson’s model? n2 + 3n + 40 = (n – 8)(n – 5) n2 + 13n + 40 = (n + 8)(n + 5) n2 + 40n + 13 = (n + 8)(n + 5) n2 + 40n + 3 = (n – 8)(n – 5)
Answer:
Second option
Step-by-step explanation:
Focus on the right side only. We have (n+8)(n+5).
Let's use FOIL to expand that out
F = first means we multiply the first terms n and n to get n^2
O = outer tells us to multiply the outer terms n and 5 to get n*5 or 5n
I = inner tells us to multiply the inner expressions 8 and n to get 8n
L = last meaning we multiply 8 and 5 to get 8*5 = 40
Add up those results: n^2+5n+8n+40 = n^2+13n+40
Notice how the like terms (5n and 8n) combine to have the expression simplify a bit.
This shows how (n+8)(n+5) turns into n^2+13n+40, which is why the second choice is the answer. The other choices aren't true equations for all values of n.
Answer:
its b
Step-by-step explanation:
I just took the test
Suppose E(X) = 5 and E[X(X-1)] = 27.5. What is E(X2)? V(X)? The general relationship among the quantities E(X), E[X(X-1)], and V(X)?
Answer:
[tex]E(X^2)=32.5\\V(X)=7.5\\E[X(X-1)]=E(X^2)-E(X)\\V(X)=E(X^2)-[E(X)]^2[/tex]
Step-by-step explanation:
We have the following properties:
[tex]E( X + Y ) = E(X) + E(Y)\\V(X) = E(X^2)-[E(X)]^2[/tex]
So, if we have that E[X(X-1)] = 27.5, we can write them using the first property as:
[tex]E(X(X-1))=27.5\\E(X^2-X)=27.5\\E(X^2)-E(X)=27.5[/tex]
Then, replacing E(X) by 5 and solving for [tex]E(X^2)[/tex], we get:
[tex]E(X^2)-5=27.5\\E(X^2)=27.5+5\\E(X^2)=32.5[/tex]
Finally, using the second property and replacing [tex]E(X)[/tex] by 5 and [tex]E(X^2)[/tex] by 32.5, we get that V(X) is equal to:
[tex]V(X) = 32.5 - 5^2\\V(X) =32.5 - 25\\V(X) = 7.5[/tex]
3
Select the correct answer.
What are the solutions to this equation?
16x² + 9 = 25
Answer:
Step-by-step explanation:
16x^2 + 9 = 25
16x^2 = 16
x^2 = 1
x = 1, -1
People counting calories have to be careful about the estimates placed on prepackaged food. Suppose testing shows that a certain brand of doughnut has a mean calorie count of 240, so that is the amount printed on the package. However, testing shows that the calories counts vary, following a normal distribution with a standard deviation of 15 calories.
A) Find the probability that an individual doughnut for this brand contains more than 275 calories.
B) Find the probability that a random sample of 12 of these doughnuts contains a mean number of calories between 230 and 260.
Answer:
A) P(X>275) = 0.01
B) P(230<M<260) = 0.99
Step-by-step explanation:
We have a normal distribution with mean: 240 calories and standard deviation: 15 calories.
To find the probability that an individual doughnut for this brand contains more than 275 calories, we calculate the z-score for X=275 in this normal distribution, and then calculate the probability for this z-score with the standard normal distribution:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{275-240}{15}=\dfrac{35}{15}=2.33\\\\\\P(X>275)=P(z>2.33)=0.01[/tex]
In the case we are talking about a sample mean, we use the standard deviation of the sample distribution.
The standard deviation for the sample means is equal to the standard deviation of the population divided by the square root of the sample size (in this case, n=12). The mean of the sampling distirbution is expected to be equal to the population mean.
[tex]\mu_s=\mu=240\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{15}{\sqrt{12}}=\dfrac{15}{3.4641}=4.33[/tex]
We have to calculate the probability that this sample mean is within 230 and 260.
[tex]z_1=\dfrac{M_1-\mu}{\sigma}=\dfrac{230-240}{4.33}=\dfrac{-10}{4.33}=-2.309\\\\\\z_2=\dfrac{M_2-\mu}{\sigma}=\dfrac{260-240}{4.33}=\dfrac{20}{4.33}=4.619\\\\\\P(230<M<260)=P(z<4.619)-P(z<-2.309)\\\\P(230<M<260)=1-0.01=0.99[/tex]
Which of the following fractions will convert to terminating decimals?
A.5/6
B. 5/2
C. 5/6
D. 5/3
E. 3/8
Answer:
B and E
Step-by-step explanation:
A terminating decimal is a decimal with a finite number of digits after the decimal point. If we input all of these fractions into a calculator, or solve them by hand, we find that B is equal to 2.5, and E is equal to 0.375, and all the others are repeating decimals.
Find the vector x determined by the given coordinate vector [x]B and the given basis B.
B = {[1 -3 1], [-3 8 3],[8 -2 3]}, [x]_B = [-3 -2 3]
a. [9 -13 0]
b. [0 -6 21]
c. [13 -24 -2]
d. [3 -13 16]
y=x2+3x+1 has how many real roots?
Answer:
2
Step-by-step explanation:
we will find the discriminant of the equation
d = b^2 - 4ac (here, a = 1 , b = 3 , c = 1. from the general formula: ax^2 + bx + c)
d = 9 - 4
d = 5
since d > 0, the roots are real and different
hence, the both the roots of this equation are equal
The freezing point of methanol is -97.6. What is the freezing point of methanol in Fahrenheit
Answer:
-143.68°F
Step-by-step explanation:
Celsius to Fahrenheit Conversion Formula: F = 1.8C + 32
Simply plug in c as -97.6:
F = 1.8(-97.6) + 32
F = -175.68 + 32
F = -143.68
Answer:
Fahrenheit= Celsius x 1.8 + 32
Step-by-step explanation:
-97.6 x 1.8 = -175.68
-175.68 + 32 = -143.68 / -143.7
logx - logx - 1^2 = x-4
Answer:
Look at the image below.
Find the critical value z Subscript alpha divided by 2 that corresponds to the confidence level 90%.
Answer:
,.........................................................
Find the increase in price of a single piece of design, when crafts design price is increased by 45% which makes a buyer to buy 8 design less, for $500?
Answer: Original price = $43.10, Increase = $19.40, Final price = $62.50
Step-by-step explanation:
Let x represent the original price, then
8x(1.45) < $500
[tex]x<\dfrac{500}{8(1.45)}[/tex]
x < $43.10
Increase is 0.45x
0.45($43.10)
= $19.40
Final price is Original + Increase
$43.10 + $19.40
= $62.50
The increase in price of a single piece of design is; Increase < $19.395
The new price can be represented as 145% the old price.
Let the initial price be x;
Therefore, the problem statement can be written as;
8x (1.45) < 500x < 500/11.6x < $43.1The former price is therefore 45% of $43.1;
Increase < 0.45($43.1)Increase < $19.395Read more:
https://brainly.com/question/24712879
Thirteen cards numbered 1,...,13 are shuffled and dealt one at a time. Say a match occurs on deal k if the kth card revealed is card number k. Let N be the total number of matches that occur in the thirteen cards. Determine E[N].
Answer:
E[N] = 1
Step-by-step explanation:
Here is the hint we are given on this problem - " Write N = [tex]1_{A_1}[/tex] + [tex]1_{A_2}[/tex] + · · · + [tex]1_{A_{ 13}[/tex]where [tex]A_k[/tex] is the event that a match occurs on deal k. "
_____
Now the standard thing is to do is let [tex]X_i[/tex] = 1, if there is a match on the [tex]i[/tex]-th pick and 0 otherwise. The number of matches is given to be [tex]X_1[/tex] + [tex]X_2[/tex] . . . + [tex]X_{13}[/tex]. Knowing that, we can use the linearity of expectation -
There are 13 cards and for [tex]i[/tex]-th pick, the probability of having a card with [tex]i[/tex] number is 1 / 13. Therefore, E[N] = E[[tex]X_1[/tex] + [tex]X_2[/tex] . . . + [tex]X_{13}[/tex]] = 1
_____
Solution: E[N] = 1
In January of 2002(group 1),700 out of the 1700 spots were bare ground (no vegetation). Find the sample proportion of bare ground spots.
Answer:
The sample proportion of bare ground spots is 0.4118
Step-by-step explanation:
The sample proportion of bareground spots is the number of bareground sports divided by the number of spots.
In this question
700 bareground spots
1700 spots
7/17 = 0.4118
The sample proportion of bare ground spots is 0.4118
Given data:
x = 700n = 1700The formula will be:
→ [tex]Sample \ proportion = \frac{x}{n}[/tex]
By substituting the given values, we get
[tex]= \frac{700}{1700}[/tex]
[tex]= 0.4118[/tex]
Thus the response above is correct.
Learn more about sample proportion here:
https://brainly.com/question/17037417
A company has developed a new type of light bulb, and wants to estimate its mean
lifetime. A simple random sample of 12 bulbs had a sample mean lifetime of 665
hours with a sample standard deviation of 59 hours. It is reasonable to believe that
the population is approximately normal. Find the lower bound of the 95% confidence
interval for the population mean lifetime of all bulbs manufactured by this new
process.
Round to the nearest integer. Write only a number as your answer. Do not write any
units.
Answer:
628
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 12 - 1 = 11
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.2\frac{59}{\sqrt{12}} = 37[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 665 - 37 = 628 hours.
The answer is 628
Put some air in your tires: Let represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of is as follows.
x 0 1 2 3 4
P (x) 0.1 0.2 0.3 0.3 0.1
A) Find P (1).
B) Find P(Greater than or equal to 3).
C) Find the probability that all four tires have low air pressure.
D) Find the probability that no tires have low air pressure.
E) Compute the mean uy.
F) Compute the standard deviationo Round the answer to at least three decimal places.
Answer:
A) P(1) = 0.2
B) P(greater than or equal 3) = 0.4
C) P(4) = 0.1
D) P(0) = 0.1
E) [tex]\mu_y = 0.2[/tex]
F) [tex]\sigma = 0.089[/tex]
Step-by-step explanation:
A)
to find P(1) we see in the table the value of P(x) when x is equal to 1.
when x=1, we have that P(x) = 0.2, therefore P(1) = 0.2
B)
To find P(greather than or equal 3), we just need to find P(3) and P(4), and sum their values. Seeing in the table, we have that P(3) = 0.3 and P(4) = 0.1, so:
P(greater than or equal 3) = P(3) + P(4) = 0.3 + 0.1 = 0.4
C)
All four tires having low air pressure is represented by the value of x equal 4, so we have to find P(4). Seeing in the table, we have that P(4) = 0.1
D)
No tires having low air pressure is represented by the value of x equal 0, so we have to find P(0). Seeing in the table, we have that P(0) = 0.1
E)
To find the mean of P(x) we just need to sum all the values and divide by the number of values:
[tex]\mu_y = (0.1 + 0.2 + 0.3 + 0.3 + 0.1)/5 = 1/5 = 0.2[/tex]
F)
The formula to calculate the standard deviation is:
[tex]\sigma = \sqrt{\frac{1}{N}\sum(x_i-\mu)^2}[/tex]
[tex]\sigma = \sqrt{\frac{1}{5}((0.1-0.2)^2+(0.2-0.2)^2+(0.3-0.2)^2+(0.3-0.2)^2+(0.1-0.2)^2)}[/tex]
[tex]\sigma = \sqrt{\frac{1}{5}(0.01+0+0.01+0.01+0.01)}[/tex]
[tex]\sigma = 0.089[/tex]
don't understand what is being asked
Answer:
theta = 60 degrees
Step-by-step explanation:
tan theta = sqrt(3)
Take the inverse tan of each side
tan ^-1 tan theta = tan ^-1 (sqrt(3))
theta = 60 degrees
I NEED HELP ASAP, THANKS! :)
Answer:
Last option
Step-by-step explanation:
Since it is asking for the limit of infinity, when we go to infinity, the graph also goes to infinity.
Answer:
Option D
Step-by-step explanation:
all lines are going from negative infinity to positive infinity
1. Which of these is a Pythagorean triple?
(a) (3, 4, 5)
(b) (5, 6, 7)
(c) (10, 11, 12)
(d) (15, 16, 17)
2. If y2 = 172 – 82. What is the value of y?
(a) 10
(b) 25
(c) 15
(d) 16
3. How many kilograms are there in 5 tonnes?
(a) 500 kg
(b) 50 000 kg
(c) 5, 000 kg
(d) 50 kg
4. If the probability that a girl win a race is 0.6. What is the probability that that the girl loses the race?
(a) 0.4
(b) 1
(c) 4
(d) 6
5. The distance from Lagos to Ibadan can be measured using which of the following units of measurement?
(a) centimeter
(b) Millimeter
(c) Kilograms
(d) Kilometer
6. The longest side of a right-angled triangle is called?
(a) right side
(b) Opposite
(c) Hypotenuse
(d) None of the above
7. The mass/weight of your pen can be measured using………
(a) Grams
(b) Kilometer
(c) Centimetre
(d) Tonne
8. There 5 blue balls, 8 red balls and 2 black balls in a basket. One ball is picked at random. Find the probability that the ball picked is red.
(a) 58
(b) 815
(c) 215
(d) 13
9. The mass of a lorry can be measured using which of the following?
(a) liter
(b) Kilometer
(c) Tonne
(d) Milligram
10. How many tonnes are there in 15 000 kg?
(a) 150 tonnes
(b) 15 tonnes
(c) 1500 tonnes
(d) 1.5 tonnes
11. What is 20% of #38 000?
(a) #7 600
(b) #3 800
(c) #2 800
(d) #760
12. Express 17:30 hours as a.m. or p.m. time.
(a) 7:30 pm
(b) 7:30 a.m.
(c) 5:30 p.m.
(d) 5:30 a.m.
13. Angle 900 is also called?
(a) left angle
(b) quarter angle
(c) right angle
(d) middle angle
14. “Kilo” is a Greek word from the word “khilioi” meaning what?
(a) Million
(b) Thousand
C) Billion
D) Hundred
15. Which is the most widely used system of measurement in the world?
(a) tape rule system
(b) counter system
(c) metric system
(d) none of the above
PART B
ANSWER ALL QUESTIONS
1. The largest unit of measurement for distance/length is kilometer. True or false …………………….
2. The probability that a student fails an examination is 0.2. What is the probability that the student passes the examination? .................
The members of a village cooperative agree to contribute time and money towards a one year village improvement programme (VIP). Below is the table of activities of the programme.
Activity
Time (hour)
Money(#)
Planting/ watering trees
300
20 000
Collecting/burning rubbish
200
0
Clearing storm ditches
80
5 000
Making speed bumps
20
5 000
3. How much is the total money pledged? …………..
4. Which activity takes more money? ………………..
5. Which activity cost no money? ……………………….
Answer
1. (a) (3,4,5)--3^2 +4^2=9+16=25=5^2
2. (b) 25--172-82=50/2=25
3. (c) 5,000 kg--1,000 kg in 1 tonne
4. (a) 0.4--1-0.6=0.4
5. (d) kilometer
6. (c) hypotenuse
7. (a) grams
8. i think it is (a) 58--5+8+2=15~~8/15 =0.53~closest answer is 58
9. (c) tonne
10. (b) 15 tonnes--1000 kg in 1 tonne
11. (a) #7,600--38000*20%, or 0.20, =7,600
12. (a) 7:30 pm
13. (c) right angle
(c) metric system
Part B
1. True
2. 0.8
3. 30,000 dollars--20,000 +0+5,000+5,000=30,000
4. Planting/watering trees--20 dollars
5. Collecting/burning rubbish--0 dollars
1. The graph shows the number of miles Peter's car traveled and the gallons of gas used.
MILEAGE OF PETER'S CAR
160
140
120
100
Milco Traveled
BO
(5, 1201
60
40
20
1 2 3 4 5 6 7 8 9 10
Gallons of Gas
slope =¥
Which equation can be used to find the distance in miles, d, that the car can travel on g
gallons of gas?
A. d = 169
B. d=209
cd=249
D. d = 309
Slzo
28
10
Answer:
C. d = 24g
Step-by-step explanation:
The problem boils down to determining the ratio between d and g. That is, for some equation ...
d = k·g
we want to determine the value of k. Solving the equation for that value, we find ...
k = d/g
So, we need only to read a point from the graph with sufficient accuracy to determine a good estimate for k.
(gallons, miles) = (g, d) = (5, 120) is a suitable point
Then ...
k = d/g = 120/5 = 24
The equation is d = 24g.
Determine if the given function can be extended to a continuous function at xequals0. If so, approximate the extended function's value at xequals0. If not, determine whether the function can be continuously extended from the left or from the right and provide the values of the extended functions at xequals0.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is A
Step-by-step explanation:
Now from the question we are given the function
[tex]f(x) = \frac{10^{2 x} -4}{x}[/tex]
Now as [tex]\lim_{x \to 0} [f(x) ] = \frac{10^{2*0} -4 }{0}[/tex]
=> [tex]\lim_{x \to 0} [f(x) ] = - \infty[/tex]
This implies that as [tex]x\to 0[/tex] the function [tex]f(x) \to -\infty[/tex] which means that at x = 0 the function is not continuous
A piece of paper graph y=-3x-2
Answer:
Use an xy chart and graph the equation.
Step-by-step explanation:
For the inverse variation equation xy = k, what is the value of x when y = 4 and k = 7? Four-sevenths Seven-fourths 3 28
Answer:
7/4
Step-by-step explanation:
Answer:
B,) 7/4
Step-by-step explanation:
What is the solution to this equation x/4=-12
Answer:
x = -48
Step-by-step explanation:
x/ 4 = -12
Multiply each side by 4
x/4 * 4 = -12 *4
x = -48
Answer:-48
Step-by-step explanation:x/4=-12
Cross multiply
X x 1 =-12 x 4
X=-48