Answer:
The average would be 42 / 28 = $1.50 / day.
Answer:
$1.50 per day
Step-by-step explanation:
Take the dollar amount and divide by the number of days
42 dollars / 28 days
1.50 dollars per day
$1.50 per day
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x= 1.22 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)
1. What are we testing in this problem?
a. single proportion
b. single mean
2. What is the level of significance?
3. State the null and alternate hypotheses.
4. What sampling distribution will you use? What assumptions are you making?
a. The Student's t, since we assume that x has a normal distribution with known σ
b. The standard normal, since we assume that x has a normal distribution with known σ.
c. The standard normal, since we assume that x has a normal distribution with unknown σ.
d. The Student's t, since we assume that x has a normal distribution with unknown σ.
Answer:
1. B
Step-by-step explanation:
1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A
2. The level of significance is 1% (99% confidence interval)
3. The null hypothesis: u = 0.8
Alternative hypothesis: u =/ 0.8
4. a. The Student's t, since we assume that x has a normal distribution with known σ
5. Using the formula t = (x - u) / σ√n
Where x = 1.22 u = 0.8 σ = 0.44 n = 9
t = (1.22-0.8) / 0.44√9
t = 0.42/(0.44x3)
t = 0.42/1.32
t = 0.318
P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.
What is equivalent to
16x-12-24x+4
Answer:
-8x - 8
Step-by-step explanation:
You have to combine like term.
So you add 16x + -24x = -8x
And you add -12 + 4 = -8
Your answer would be -8x - 8
I hope this helps!
Sidney made $35 less than four times Casey’s weekly salary. If x represents Casey’s weekly salary, write an expression for Sidney’s weekly salary.
Answer: [tex]y=4x-35[/tex]
y = Sidney’s weekly salary
x = Casey’s weekly salary
Answer: y=4x-35
x is Casey's salary
Y is Sidney's salary
Step-by-step explanation:
Sidney makes a quarter of Casey,
y=4x,
Then it also states that he makes 35 less than the first equation.
Therefore,
Y=4x-35
Assume that SAT scores are normally distributed with mean mu equals 1518 and standard deviation sigma equals 325. If 1 SAT score is randomly selected, find the probability that it is greater than 1600. If 81 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.
Answer:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
Step-by-step explanation:
Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1518,325)[/tex]
Where [tex]\mu=1518[/tex] and [tex]\sigma=325[/tex]
We want to find this probability:
[tex]P(X>1600)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(X>1600)=P(\frac{X-\mu}{\sigma}>\frac{1600-\mu}{\sigma})=P(Z>\frac{1600-1518}{325})=P(z>0.252)[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>0.252)=1-P(z<0.252) =1-0.599= 0.401 [/tex]
For the other part we need to take in count that the distribution for the sampel mean if the sample size is large (n>30) is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\frac{sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{1600-1518}{\frac{325}{\sqrt{81}}}= 2.27[/tex]
And we can find this probability using the z score formula and the complement rule and we got:
[tex]P(z>2.27)=1-P(z<2.27) =1-0.988=0.012[/tex]
A car is driving at 75 kilometers per hour. How far, in meters, does it travel in 5 seconds?
75km convert to m 75x1000=75000m
converted I hour to seconds that is 3600seconds
If 75000m=3600seconds
? =5seconds
that id 75000x5=375000/3600
=104.26…metres
The distance will be 104.16 meters if the car is driving at 75 kilometers per hour.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
A car is driving at 75 kilometers per hour.
Let x be the distance.
As we know from the distance time relation:
Distance = speed×time
Speed = 75 km/h
Speed = 75 km/(3600)seconds
Speed = 0.0208 km/s
x = 0.0208×5
x = 0.10416 km
in meters
x = 0.104x1000
x = 104.16 meters
Thus, the distance will be 104.16 meters if the car is driving at 75 kilometers per hour.
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"The chance that a person selected at random has blue eyes is 16%. Two people are chosen at random (and are independent of each other). Find the probability at least one of them does not have blue eyes. Round your answer to 4 decimal places."
Answer:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=2, p=1-0.16=0.84)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we can find this probability:
[tex] P(X \geq 1)[/tex]
And we can solve this probability like this:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)[/tex]
And if we use the probability mass function we got:
[tex]P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256[/tex]
And replacing we got:
[tex] P(X \geq 1)=1 -P(X<1) = 1-P(X=0)=1-0.0256=0.9744[/tex]
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76
Answer:
The critical values of F at 95% confidence are 0.359 and 2.788.
Step-by-step explanation:
We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:
Store A Store B
nA = 21 nB = 16
SA = 28.284 SB = 20
And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.
AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.
The test statistics for F-test is = [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex] ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]
where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.
Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;
2.788 for right-part and 0.359 for the left-part.
A triangle has two sides of length 10 and 19. What is the smallest possible whole-number length for the third side?
Answer:
answer for the question is 130 length
Which of the following gives all of the sets that contain sqare root 9
1 the set of all irrational numbers
2.the set of all natural numbers, the set of all whole numbers, and the set of all integers
3. the set of all integers, the set of all rational numbers, and the set of all real numbers
4. the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers
Answer:
4. the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers
Step-by-step explanation:
√9 = 3
3 is every kind of number except irrational. It belongs to the sets of ...
natural numberswhole numbersintegersrational numbersreal numbers85 points!! | All of the following expressions have the same value, when x= -2 and y= 4, except
-2xy
0-4x2
0x²y
0 (-2) ²y
Answer:
They have two sets of equal answers...
Step-by-step explanation:
-2 * 2 * 4 = -16
0 - 4 * -2 * -2 = -16
0 * -2 * -2 * 4 = 0
0 * 4 * 4 = 0
{(1,3),(2,5)(3,-4),(4-3),(5,1)} a function or not a function
Answer:
yes the above is a function.
A meteorologist reports that the chance of snow is less
than 30%. The correct inequality to represent this
comparison is s < 30. The variable s represents the
likelihood of snow
Which numbers are solutions of the inequality?
Choose all that apply.
20%
35%
17%
30%
29
%
1.5%
Answer:
1, 3, 5, 6
Step-by-step explanation:
Your solution has to be less than the number they are giving you for example if you have -3 one solution could be -16
The numbers that are solutions to the inequality are as follows: 20%, 17%, 29.5%, 1.5%.
What are the solutions of the inequality?The solution of an inequality is the set of all possible values that could serve as the result of the expression. So, for the given problem, the set of values that would correspond to the likelihood of snow is 20%, 17%, 29.5%, and 1.5%.
In other words, these percentages are less than 30% and can be rightly represented by the variable s.
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Two competing gyms each offer childcare while parents work out Gym A charges $9.00 per hour of childcare. Gym B
charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answer:
They charge an equal amount of money each hour.
Answer:
Gym B and Gym A charge the same hourly rate for childcare.
Step-by-step explanation:
answer on edge
16 of 22
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Sample Space: Tutorial
Activity
In this exercise, you'll use the formula for the probability of the complement of an event.
Another game you've set up at casino night involves rolling a fair six-sided die followed by tossing a fair coin. In this game, players earn points
depending on the number they get on the die and which side of the coin turns up. For example, the player earns 5 points for getting (2, tails).
Question 1
Find the total number of possible outcomes in each trial of this game.
Answer:
The number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
Given
Rolling of a 6 sided die followed by tossing of a fair coin
Required
Number of possible outcomes
The first step is to list out the possible outcomes of rolling a die and tossing a coin
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {Head, Tail}
Let Head be represented by H and Tail be represented by T;
So,
Rolling a fair die = {1,2,3,4,5,6}
Tossing a coin = {H, T}
The question states that a roll of a 6 sided die is followed by a toss of a fair coin
This means that each trial is {A roll of die and A toss of coin}
So, the sample space is as follows
Sample Space = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
Number of outcomes in the sample space is 12.
Hence, the number of possible outcomes in each trial of this game is 12
Answer:
the total number of possible outcomes in each trial of this game is 12
Step-by-step explanation:
uhhhhhh none :) kk bye <3
Alex needs
80
cm
80 cm80, start text, space, c, m, end text of thread for a sewing project. The thread is on a spool with a circumference of
10
cm
10 cm10, start text, space, c, m, end text.
How many times must Alex unwind the spool to get the length of thread he needs?
Answer:
8 full turns
Step-by-step explanation:
80 cm is 8 times 10 cm, so is 8 times around the spool.
Alex must unwind 8 full turns of thread from the spool.
__
He must unwind it once.
Answer:
8 in total turns
Step-by-step explanation:
g It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products
Question:
It is known that 20% of products on a production line are defective. Products are inspected until first defective is encountered. a) What is the probability that the experimenter must inspect six products to find a defective product?
Answer:
P(x = 6) = 0.0655
P(x = 6) = 6.55%
Step-by-step explanation:
It is given that 20% of products on a production line are defective.
p = 0.20
Then
q = 1 - p = 1 - 0.20 = 0.80
Which means that 80% of products on the production line are not defective.
We want to find out the probability that the experimenter must inspect six products to find a defective product.
Let x is the number of inspections to get a defective product.
P(x = 6) = ?
If out of 6 inspections 1 is defective then it means 5 are not defective
so the probability is
P(x = 6) = p¹ × q⁵
P(x = 6) = 0.20¹ × 0.80⁵
P(x = 6) = 0.20 × 0.32768
P(x = 6) = 0.0655
P(x = 6) = 6.55%
Therefore, there is 6.55% chance that the experimenter finds a defetive product in 6 inspections.
Which geometric series converges?
Answer:
B
Step-by-step explanation:
Geometric series converge if |r| < 1.
A) r = 3
B) r = 1/2
C) r = -4
D) r = 2
Only B has |r| < 1.
The converging sequence of geometric progression is given by the relation A = 1 + 1/2 + 1/4 + 1/8 ... where the common ratio r = 1/2
What is Geometric Progression?A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
The general form of a GP is a, ar, ar2, ar3 and so on
Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
A = 1 + 1/2 + 1/4 + 1/8 ...
Now , the common ratio r of the GP is
r = second term / first term
On simplifying , we get
r = ( 1/2 ) / 1
r = 1/2
So , when | r | < 1 , the GP is a converging series
Hence , the GP is converging series
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Daniel deposits $300 into an account that earns 16% interest annually. Which equation can be used to model his account balance, y, after x years?
Answer:
[tex]y=300(1+0.16)^x[/tex]
Step-by-step explanation:
This account can be modeled using the compound interest formula.the compound interest formula is expressed as[tex]A= P(1+r )^t[/tex]
Where
A =final amount = y
P=initial principal balance = $300
r=interest rate = 16%= 0.16
t=number of time periods elapsed= x
Hence the equation to model his account balance/ final amount A (y) after time (x) years is
[tex]y=300(1+0.16)^x[/tex]
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
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Next
Submit
Mark this and return
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
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if this net were to be folded into a cube which number would be opposite of the number 1?
Answer:
6
Step-by-step explanation:
When the cube is folded, 6 is the opposite of 1.
2 is the opposite of 4 and 5 is the opposite of 3.
When the given net is folded into a cube, the number that we will find opposite 1 is 6.
What number will be opposite 1?When the net is folded, two will be folded left and up with 3 being the base. 4 will be folded right with 5 being the top of the cube.
We will then observe the following pairs opposite each other:
5 and 3.4 and 2.1 and 6.This means that the number that we will see opposite 1 will be the number 6.
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I don’t know this one
Answer:
C
Step-by-step explanation:
2/3x - 5>3
Add 5 to each side
2/3x - 5+5>3+5
2/3x > 8
Multiply each side by 3/2
3/2 *2/3x > 8*3/2
x > 12
There is an open circle at 12 and the lines goes to the right
Which of the following numbers are in setA? Check all that apply.
A = {x | x is a positive, odd integer less than 7}
0
1
2
5
3
Answer:
1, 3, 5.
Step-by-step explanation:
The members of the set are {1, 3, 5}.
Note 0 is an even integer so is not included in the set.
Also 0 is neither negative or positive.
Express each percent as a fraction in simplest form.
a. 85%
b. 5 72%
c. 12.55%
Answer:
(a) 17/20 b.5/18/25 c. 1.255
A 15-inch candle is lit and steadily burns until it is burned out. Let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches).
a. Write a formula that expresses r in terms of b.When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b. Graph the relationship between a and b
Answer:
(a)r=15-b
11.9 Inches
(b)See attached
Step-by-step explanation:
Length of the candle =15 inch
Let b represent the burned length of the candle (in inches)
Let r represent the remaining length of the candle (in inches).
Therefore:
(a) r+b=15
r=15-b
When b=3,1 Inches
Remaining Length, r=15-3.1=11.9 Inches
(b)The graph showing te relationship between r and b is shown below.
r is plotted on the y-axis while b is plotted on the x-axis as labelled.
Formula that express r in terms of b is
[tex]r=15-b[/tex]
Remaining length of candle is 11.9 inches
Given :
A 15-inch candle is lit and steadily burns until it is burned out
Let b represent the burned length and let r represent the remaining length
We need to write the formula
remaining length = initial length - burned length
[tex]r=15-b[/tex]
When 3.1 inches have burned from the candle, the remaining length of the candle is inches.
b is 3.1
remaining length [tex]r=15-3.1=11.9[/tex] inches
now we graph the relationship
Graph is attached below.
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Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
Answer:
1130
Step-by-step explanation:
since radius of the circle was given and the formula of the area is pie r square
Find the nth term and the 150th term of the following sequence 7,11,15,19,23,...
Answer:
for the 9th it is 39 for the 150th it is 607
Data on U.S, Work-Related fatalities by cause follow (The World Almanac,2012)Cause of Fatality Number of Fatalities Transportation Incidents 1795 Assaults and violent acts 837 Contacts with objects and equipment 741 Falls 645 Exposure to harmful substances 404 Fires and explosions 113 Assume that a fatality will be randomly chosen from this population. a. What is the probability the fatality resulted froma fall? b. What is the probability the fatality resulted from a transporation incident? c. What cause of fatality is least likely to occur? What is th probability the fatality resulted from this cause?
Answer:
a) Probability the fatality resulted from a fall = 0.1422
b) Probability the fatality resulted from a transportation incident = 0.3958
c(i) The cause of fatality that is least likely to occur is fatality due to fires and explosions with the lowest number of fatalities, 113.
c(ii) Probability that the fatality resulted from fires and explosions = 0.0249
Step-by-step explanation:
Data on U.S, Work-Related fatalities by cause follow (The World Almanac, 2012)
Cause of Fatality | Number of Fatalities Transportation Incidents | 1795
Assaults and violent acts | 837
Contacts with objects and equipment | 741
Falls | 645
Exposure to harmful substances | 404
Fires and explosions | 113
Total number of fatalities = 1795+837+741+645+404+113 = 4,535
Assume that a fatality will be randomly chosen from this population.
a. What is the probability the fatality resulted from a fall?
The probabilty of an event is given mathematically as the number of elements in that event divided by the Total number of elements in the sample space.
P(E) = n(E) ÷ n(S)
Probability the fatality resulted from a fall = (645/4535) = 0.14223 = 0.1422
b. What is the probability the fatality resulted from a transportation incident?
Probability the fatality resulted from a transportation incident = (1795/4535) = 0.39581 = 0.3958
c(i) What cause of fatality is least likely to occur?
The cause of fatality that is least likely to occur is the cause of fatality with the lowest frequency or number of fatalities. And this is fatality due to fires and explosions with the lowest fatalities of 113
c(ii). What is the probability the fatality resulted from this cause?
This is the probability that the fatality resulted from fires and explosions.
Probability that the fatality resulted from fires and explosions = (113/4535) = 0.02492 = 0.0249
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c. Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?
Answer:
A=12 feet²
Step-by-step explanation:
1/2*base*height=area
(1/2)*4*6=12
What is the value of log625^5 converted to a fraction
Answer:
1/4
Step-by-step explanation:
625^x = 5
x = 1/4
