As per the sampling, an appropriate test value for a z test is 0.808
Sampling:
In math, sampling means selecting the group that you will actually collect data from in your research.
Given,
In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. the bookstore believes that the two groups spent the same amount.
Here we need to find the appropriate test value for a z test.
As per the given question, first we must know the definition of z test,
The term z-test means statistical test that can be used to determine whether two population means are different.
And it is used when the variances are known or the sample size is large.
And the formula of the z value, the test statistic for two population with large sample size is given by,
z = [x₂ - x₁] / √[(s₁²/n₁) + (s₂²/n₂)]
From the question we have, x1=$320, x2=$310, s1=$62, s2=$73, n1=60 and n2 = 60.
When we apply the value then we get the z value as
=> z = [310 - 320] / √[(62²/60) + (73²/60)]
=> 0.808
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It can sometimes get colder than 3 degrees in the north. Select all the
possible temperatures for the north.
A) -2 degrees
B) 0 degrees
C) 2 degrees
D) 4 degrees
E) 6 degrees
The possible temperatures for the north will be 4 degrees and 6 degrees. The correct option is D and E.
How to calculate the temperature?Mathematical statements with at least two terms connected by an operator and containing either numbers, variables, or both are referred to as expressions.
The direction that heat energy will spontaneously flow depends on temperature. Temperature is the degree to which a body is hot or cold. because it was mentioned that the north can occasionally experience temperatures below 3 degrees. D and E are the appropriate choices
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2 + 3 + 1 17/20 + 1/2 + 3/4
Answer:
Step-by-step explanation:
12.1
Answer:
8 [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]\frac{17}{20}[/tex] = [tex]\frac{34}{40}[/tex] Multiplied the numerator and denominator by 2
[tex]\frac{1}{2}[/tex] = [tex]\frac{20}{40}[/tex] Multiplied the numerator and denominator by 20
[tex]\frac{3}{4}[/tex] = [tex]\frac{30}{40}[/tex] Multiplied the numerator and denominator by 10
2 + 3 + 1 [tex]\frac{34}{40}[/tex] + [tex]\frac{20}{40}[/tex] + [tex]\frac{30}{40}[/tex]
6 [tex]\frac{84}{40}[/tex] This can be written
6 + [tex]\frac{40}{40}[/tex] + [tex]\frac{40}{40}[/tex] + [tex]\frac{4}{40}[/tex] another name for [tex]\frac{40}{40}[/tex] is 1
6 + 1 + 1 +[tex]\frac{4}{40}[/tex]
8[tex]\frac{4}{40}[/tex] Divide the numerator and denominator by 4 to simplify
8 [tex]\frac{1}{10}[/tex]
A line intersects the points (4, 3) and (11, -4). What is the slope of the line in simplest form? m = [?]
Answer: M=1
Step-by-step explanation:
hope this help!
PLEASE HELP ASAP
1. bisect an angle
2.copy an angle
3.construct a perpencicular line to a point not on the line
4. copy a segment
Answer:Bisect an angle :)
Step-by-step explanation:
An agent is paid a commission of 2% on the total sales in a year and a bonus of 0.5% on the excess of sales over Rs. 9,00,000. Find how much he receives as commission if the bonus amounts is Rs. 1500.
Ans:Rs.24000
3 letters are typed, with repetition allowed. what is the probability that all 3 will be vowels? write your answer as a percent. round to the nearest hundredth of a percent as needed.
The probability that all 3 will be vowels will be .01 to the nearest hundredth
Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.
There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.
First of all, we need to know the number of vowels in the 26 letters.
There are 5 vowels among the 26 letters,
probability (3 vowels of 3)
= (5/26)*(5/26)(5/26) multiplication of probability of each letters
=0.1923*0.1923*0.1923
≈0.0071
≈0.71%
or .01 to the nearest hundredth
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A boy who is 1.6 m tall casts a shadow when he stands 8.1 m from a base of an electric pole. how high above the ground is the light globe?
Answer:
The light globe is 1.6 meters above the ground.
Explanation:
height of light globe = height of boy x distance from light globe to base of electric pole / distance from boy to base of electric pole
Plugging in the values given in the problem, we get:
height of light globe = 1.6 m x 8.1 m / 8.1 m
This simplifies to:
height of light globe = 1.6 m
a club elects a president, vice-president, and secretary-treasurer. how many sets of officers are possible if there are 13 members and any member can be elected to each position? no person can hold more than one office.
The number of different sets of officers possible is 1716 sets.
The number of sets of officers possible is the number of ways people can be chosen for the given posts.
Since there are 13 people available for the post of president,
The choice can be made in
13 ways.
For the post of the Vice-President, there are 12 likely candidates. Hence, the choice can be made in
12 ways
Similarly for the post of treasurer, there are 11 likely candidates available. Hence, the choice can be made in 11 different ways.
Hence, the total number of sets of officers possible are
13 X 12 X 11
= 1716 sets.
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Tom is buying a home for $144,000. He will make a 10% down payment and borrow the remaining balance for 30 years at 4.5%. His monthly mortgage payments will be $985.24. What total amount of interest will he pay over the 30 year loan?
PLEASE SHOW WORK
Answer:
Tom will pay a total of $58,064 in interest over the 30 year loan.
Step-by-step explanation:
The purchase price of the home is $144,000, and Tom will make a down payment of 10%, or $144,000 * 10/100 = $14,400.
Therefore, Tom borrows $144,000 - $14,400 = $129,600.
Next, we need to calculate the total number of payments he will make over the 30 year loan. Since the loan is for 30 years and the payments are made monthly, there will be 30 years * 12 months/year = <<30*12=360>>360 payments.
Finally, we can use the mortgage formula to calculate the total amount of interest Tom will pay over the loan:
I = P * r * t
Where:
I is the total interest
P is the principal (the amount borrowed)
r is the annual interest rate (in decimal form)
t is the number of payments
Plugging in the values, we get:
I = $129,600 * 0.045 * 360 payments
= $58,064
A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 670 mi/h, how far is she from her starting position?
On solving the provided question, we got to know that - distance she covered from her starting position is 2731 miles
What is equation?If two things are equal, an equation declares it. A "=" equals sign will appear in the format: 7 + 2 = 10 − 1 What is on the left (7 + 2) equals what is on the right (10 1), according to that equation. The statement "this equals that" is analogous to an equation.
The flight's first leg is 1020 miles long and lasts (1.5 hours) at 680 mph. We'll refer to this as our triangle's side B.
The second leg of the journey is 1360 miles (2 hours x 680 mph) long. We'll refer to this as the triangle's side C.
The law of cosines allows us to determine the triangle's side a's length.A is a 170° angle between the two sides whose lengths we are aware of. (180° - 10° = 170°).
[tex]a^2 = b^2 + c^2 - (2)*(a)*(b)*cos(A)[/tex]
[tex]a^2 = (1020 miles)^2 + (1360 miles)^2 - (2)*(1020 miles)(1360 miles)*cos(170)\\ a^2 = 1040400 miles^2 + 1849600 miles^2 - (2774400 miles2)*cos(170)\\ cos(170) = -0.9848\\ a^2 = 2890000 miles^2 + 2732251 miles^2 = 5622250.6 miles^2\\ a = (5622250.6 miles^2)^{\frac{1}{2} } = 2371 miles[/tex]
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Hi can someone please help me with this!!!
Answer:
q = 50
r = 75
s = 115
t = 30
Step-by-step explanation:
determine weather the relationship between the two quantitates is porptional
The answer to the provided question is No, because the graph of the line connecting the ordered pairs does not pass through the origin.
what is proportionality?When two numbers or variables are linearly connected in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable declines in proportion to the other when it falls below 1/100th of its former value.
The relationship has the following form when two linear variables are directly proportional.
=> y = mx
where the constant ratio of change between the variables is denoted by m.
The graph of the direct proportion is a straight line that goes through the origin, which is one of its key characteristics.
You can see in the example image, though, that the line generated by those points won't cross the coordinate system's origin.
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Which equation represents a line
passing through the point (8, 16) with a slope of 3?
Please explain all of the steps
Answer: y = 3x - 8
Step-by-step explanation:
We will write a point-slope equation to help us write a slope-intercept equation.
y - 16 = 3(x - 8)
y = 3(x - 8) + 16
y = 3x - 8
The slope-intercept form equation that represents this line is;
y = 3x - 8
The shadow of the moon during a solar eclipse travels 2300 miles in 1 hour in the first 20 minutes the shadow traveled 7662/3 miles how long does it take for the shadow to travel 1150 miles
The time that it will take for the shadow to travel 1150 miles is; 30 minutes
How to solve linear equations?Let y represent the distance in miles
Let x represent the time in minutes
The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles
Thus, the coordinates are;
(60, 2300) and (20, 2300/3)
The slope is;
m = (2300 - 2300/3)/(60 - 20)
m = 115/3 mi/min
Thus, the linear equation in point slope form is;
y - 2300 = (115/3)(x - 60)
This gives;
y = (115/3)x
When y = 1150 miles, we have;
1150 = (115/3)x
x = 30 minutes
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in a local election, votes were cast for mr. dyer, ms. frau, and mr. borak in the ratio of 4:3:2. if there were no other candidates and none of the 2,700 voters cast more than one vote, how many votes did mr. dyer receive?
To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.
Ratio of votes = 4:3:2
Total votes = 4 + 3 + 2 = 9
Total votes cast = 2,700
Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes
The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).
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Sergio says the triangle DEF was dilated by a scale factor of 5/2. Simone says triangle DEF was dilated by a scale factor of 3/2.
The line at the top of the diagram is parallel to the base of the triangle.
What is the measure of angle x?
___ degrees
The value of the missing angle x in the given triangle is; x = 55°
What is the value of the missing angle?From the image attached, we are told that the line at the top is parallel to the line at the base of the triangle.
Now, alternate angles are defined as angles that occur on opposite sides of the transversal line and have the same size.
This means that the angle formed to the right of 50 degrees will be an alternate angle to 75° and as such they are congruent.
Now, we know that sum of angles on a straight line is equal to 180°. Thus;
x + 50 + 75 = 180
x + 125 = 180
x = 180 - 125
x = 55°
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if you have worked 52 % of the total 440 minutes, what percent of the 440 minutes do you have left to work?
The time that is needed to complete the pending work is 211.2 minutes.
To calculate the percentage, divide the value by the total value and then multiply the resultant by 100.
If the amount of work is 52%.
100% - 52% = 48%
The total minutes that are required is 440 minutes.
you have 48% of the 440 minutes left to work.
48% / 100 = .48 * 440 =211.2
Therefore, the time that is needed to complete the pending work is 211.2 minutes.
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If the cost function for a commodity is C(x) =1/90x3 + 8x2 + 8x + 18 dollars find the marginal cost MC at x = 9 units. (Round your answer to two decimal places.)
MC = $?
b.) Tell what the marginal cost predicts about the cost of producing 1 additional unit.The cost of producing 1 additional unit is $
c.) Tell what the marginal cost predicts about the cost of producing 2 additional units.The cost of producing 2 additional units is $
a) The marginal cost MC at x=9 units is $154.70.
b) The cost of producing 1 additional unit is $154.70.
c) The cost of producing 2 additional units is $309.40.
The Marginal Cost quantifies the incremental cost incurred from the production of each additional unit of a good or service. The marginal cost of production captures the additional cost of producing one more unit of a good/service.
The analysis of the marginal cost helps determine the “optimal” production quantity, where the cost of producing an additional unit is at its lowest point. The marginal cost of production must be lower than the price per unit for a company to be profitable – thus, the marginal cost pinpoints the output volume and pricing where incremental costs are reduced.
a) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)
C(x) = 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18
MC = dC/dx
MC = d( 1/90[tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 8[tex]x[/tex] +18) / dx
= 1/90 (3x²) + 8 (2x) + 8
= 1/30x² + 16x + 8
At x = 9 units, we get
MC(x=9) = 1/30 (9²) + 16 (9) + 8
= 154.7
Rounding off to two decimal places, we get 154.70.
Thus, the marginal cost MC at x=9 units is $154.70.
b) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)
154.70 = Change in costs/ 1
Change in costs = 154.70
So, the cost of producing 1 additional unit is $154.70.
c) Marginal Cost = (Change in Costs) ÷ (Change in Quantity)
154.70 = Change in costs/ 2
Change is costs = 309.40
So, the cost of producing 2 additional units is $309.40.
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You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
How many seconds does it take to reach the highest point (vertex)?
Options for what the answer could be that i was given are:
18 seconds
1 second
0.5 seconds
9 seconds
The time taken is 1 second to reach the highest point by using std equations of velocity, time and displacement .
What are 3 std equations of velocity, time and displacement ?
The three standard equations are given as :
1st std equation : v = u + at
2nd std equation : s = u*t + (1/2)at²
3rd equation : 2as = v²-u²
By using 1st std equation:
At highest point final velocity will be zero(0).
So, v = 0
u = 16
a = -16
0 = 16 + -16*t
t = 1sec
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How do you solve 16/48 = n/36?
Answer:
n = 12
Step-by-step explanation:
16/48 = n/36
cross multiply
16 × 36 = 48n
576 = 48n
n = 576/48
n = 12
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four standard six-sided dice are to be rolled. what is the probability that the product of the numbers on the top faces will be prime? express your answer as a common fraction.
The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.
As given in the question,
Number of six sided dice to be rolled = 4
Number of outcomes on one dice = 6
Total number of outcomes of 4 dice = 6⁴
= 1296
Conditions for the product of the numbers of top faces all four dice is prime:
Three dice should have 1 on the top face and fourth one should have prime number less than 6.prime number less than 6 are 2, 3, 5.Each prime number will comes on all the four dices top faces.Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),
( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)
Total number of favourable outcomes = 12
Required Probability = 12 / 1296
= 1 / 108
Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.
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Car A travels 702 miles on 12 gallons of gasoline. Car B travels 873 miles on 15 gallons of gasoline. Hugo wants to buy a car with lower fuel consumption. Find out the distance each car could travel per gallon of gasoline. Then, tell which of the two cars (A or B) Hugo should buy.
Answer: Hugo should buy car A
Step-by-step explanation:
Car A
Take 702 divided by 12 = 58.5 miles per gallon of gas
Car B
Take 873 divided by 15 = 58.2 miles per gallon of gas.
So Hugo should buy car A
The maker of an automobile advertises that it takes 11 seconds to accelerate from 25 kilometers per hour to 75 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 11 seconds. Round your answer to two decimal places. 168.06 m 152.78 m 305.56 m 76.39 m 32.73 m
The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
Explain the equation of motion?motion is shift in a body's orientation or position over time. Translation is defined as movement across a line or a curve. Rotation is a motion that modifies a body's orientation.Time t = 11 sec
Initial velocity u = 25 kmph
u = (25 × 1000)/(60 × 60) = 6.9 m/s
final velocity v = 75 kmph
v = (75 × 1000)/(60 × 60) = 20.83 m/s
From the first equation of motion;
v = u + at
Put the values;
20.83 = 6.9 + 11a
20.83 - 6.9 = 13a
11a = 13.93
a = 13.93 / 11
a = 1.26 m/s²
Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
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Find a unit normal to the surface cos(xy)=ez−2 at (1,π,0)
The Unit Normal to the Surface cos(x. y) = e. z - 2 at (1,π,0) is -2 ≤ z ≤ 2.
Let F(x, y, z) = cos(x.y) − e.z + 2 .
A given surface is the same as the set of planes F(x, y, z) = 0.
Since the gradient vector ∇F( 1 , π, 0) is normal to this surface at (1, π, 0) , find this vector and normalize it to get the unit vector normal to this surface.
Differentiate:
∇F(x, y, z) = (−y sin(x y), −x sin(x y), e(z)
or
∇F(1, π, 0) = (0 , 0 , 1).
This vector is already of length 1, so this is sufficient. Alternatively, you can use the vector opposite. Therefore, the two vectors that satisfy the problem are ±k. At problem point, the surface is flat horizontally.
We may want to see what this interface looks like. This is a computer-generated sketch corresponding to:
−4 ≤ x ≤ 4, −4 ≤ y ≤ 4, −2 ≤ z ≤ 2.
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antonio drive 26 miles north and then drives west at the end of his drive it is determined that he is 50 miles from where he started. how far did he drive west
Answer:Antonio drove 24 miles west
Step-by-step explanation: 50-26=24
A bag contains 6 red tiles, 8 blue tiles, and 6 green tiles. A tile is drawn , the color recorded, and then the tile placed back in the bag before a tile is drawn again. If this procedure is done 30 times, how many red tiles would you expect to draw?
Responses
Answer:
18 tiles
Step-by-step explanation:
There are 20 tiles in total. Red is 6 of the 20, or 6/20. That is 3/10 or 30%
Each draw has a 30% chance of being red. 30% or 20 tiles is 1.8 tiles. Over 30 draws, that would mean a total of 600 tiles are drawn, The overall chance of red is still 30%, so after 30 draws, the number of red tiles would be predicted to be 30% of 600:
(0.30)*(600) = 18 tiles will be red.
find the common ratio.
1\text{,}2\text{,}4\text{,}8\text{,}16\text{,}..1,2,4,8,16,...
48\text{,}12\text{,}4\text{, }2\text{,}..48,12,4, 2,...
The common ratios of the sequence are 4 and 1/4
How to calculate the common ratioFrom the question, we have the following parameters that can be used in our computation:
Sequence 1
1, 2, 4, 8, 16,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 2/1
Evaluate
Common ratio = 2
Sequence 2
Here, we have
48, 12, 4, 2,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 12/48
Evaluate
Common ratio = 1/4
Hence, the common ratio is 1/4
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there are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remaining 2 people are technicians. in how many ways they can be seated in a row so that no two software engineers are together?
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
What is combination?An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].
There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.
So the 3 software engineers =3! ways, 2 nurses =2! ways,
doctor =1! way , 2 technicians =2! ways.
We must determine how many different configurations are possible so that no two pieces of software may coexist.
In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.
[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]
Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.
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Jose can put together a transmission in 10 hours. Luis can build the same transmission in 8 hours. How long will it take them to build the transmission together?
The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total time required to finish building the transmission if Jose and Luis works together be = A
Now , the equation will be
The time required by Jose to build a transmission = 10 hours
The time required by Luis to build a transmission = 8 hours
If it takes one person 10 hours to build a transmission and another person 8 hours to build the same transmission , working together they could build the transmission even quicker
So ,
If Jose builds the transmission is 10 hours , he builds 1/10th of the transmission in one hour
If Luis builds the transmission in 8 hours , he builds 1/8th of the transmission in one hour
And ,
Together they build the transmission in
1/A = 1/10 + 1/8
where A is the total time required to finish building the transmission if Jose and Luis works together
So , the equation is
1/A = 1/10 + 1/8
1/A = 18/80
Taking reciprocals on both sides of the equation , we get
A = 80/18
A = 40/9
On simplifying the equation , we get
A = 4.44 hours
Therefore , the value of A is 4.44 hours
Hence , The total time taken to finish building the transmission if Jose and Luis worked together is 4.44 hours
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