1. Copy and complete: To multiply two powers with the same base, ? their exponents.
2. Give an example of an expression you could simplify using the quotient of powers property.
Find the product or quotient. Write your answer using exponents.
3. 4².4⁹ 4. 5³.5⁸ 5. 6₇.6 6. 7³.7⁴.7²
Answers
(1) To multiply two powers with the same base, add their exponents.
(2) An example of an expression you could simplify using the quotient of powers property is xᵃ / xᵇ
(3) The answer of following exponents are 4¹¹ , 5¹¹ , 6⁸ and 7⁹
A number's exponent indicates how many times the number has been multiplied by itself.
In general, xⁿ denotes that x has been multiplied by itself n times.
According to the question,
(1) Assuming two exponent having same base be xᵃ and xᵇ
Multiplying both the number => xᵃ . xᵇ
To Multiplying two exponent having same base , we add the power
=> x⁽ᵃ ⁺ᵇ⁾
Hence , To multiply two powers with the same base, add their exponents
(2) Simplifying using the quotient of powers property
Let xᵃ / xᵇ
Dividing exponent with same base , we subtract the powers
=> xᵃ⁻ᵇ
Simplifying the followings
3. 4².4⁹
=> 4⁽²⁺⁹⁾
=> 4¹¹
4. 5³.5⁸
=> 5 ⁽³⁺⁸⁾
=> 5¹¹
5. 6⁷.6
=> 6⁸
6. 7³.7⁴.7²
=> 7⁽³⁺⁴⁺²⁾
=> 7⁹
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Related Questions
If A flips n+1 and B flips n fair coins, show that theprobability that A gets more heads than B is ½.
.
(Hint: Condition on which player has more heads after each hasflipped n coins.)
Answers
If n is zero, Player A has one coin and Player B has none. B will always have 0 heads. There is a 50% chance that Player A has one head, and a 50% probability that Player A also has one head.
If they had the same number of coins, they would most likely obtain the same number of heads, and each person has an equal chance of getting more heads than the other player (the chance is less than 1/2).
If we give player A one more coin than player B, player A has a 50% probability of winning (if that extra coin comes out heads) which is the sample space.
There is a 50% probability that the coin will not provide an advantage (it come out tails). As a result, player A has a 50% probability of getting more heads than player B which is the required outcome.
Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.
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Regional Rent-A-Car is interested in studying how weight of a vehicle is related to the fuel efficiency for
several of its rental vehicles.
A random sample of 13 vehicles from Regional Rent-A-Car yielded the data in the table.
Weight (in pounds)
2000
3123
3775
2287
4000
2485
2114
2433
2525
2889
3186
3258
3622
Fuel Efficiency (in miles per gallon)
32.7
22.8
18.6
26.1
18.4
26.2
33.1
28.3
26.2
22.5
20.9
21.3
18.1
Answers
Answer:
Step-by-step explanation:
SolutionFinal answers are given below.
Back-up Theory and Details of calculations follow at the end.
Part (a)
Estimate of the slope for the least-squares regression line = - 0.0073 Answer 1
InterpretationFor every increase of 1 pound in car’s weight, the fuel efficiency would reduce by 0.0073 mpg. Answer 2
Part (b)
Correlation coefficient, r = - 0.9438 Answer 3
Interpretation An r-value of - 0.9438 indicates that there is a strong inverse linear relation between car’s weight and fuel efficiency.
Negative sign implies that as car’s weight increases, the fuel efficiency would come down.Answer 4
Part (c) The estimated regression equation is: Fuel efficiency = 45.4705 – 0.0073 x car’s weight. Substituting car’s weight = 2684 in the above equation, the estimated fuel efficiency = 25.83.So, residual = 24.5 – 25.84 = - 1.23.
Thus, Residual for a car weighing 2684 pounds and having an average fuel efficiency of 24.5 mpg= - 1.23 Answer 5
Part (d)
Substituting fuel efficiency = 20.2 in the above regression equation, the estimated car’s weight = 3461Estimate of the weight of a car whose fuel efficiency is 20.2 mpg = 3461 pounds Answer 6
The cost of a new home is $90,000 and the bank requires a 8.8% down payment.
What is the amount that will need to be borrowed from the bank after the down payment is paid?
The mortgage amount will be____.
Answers
To find the amount of the down payment, we need to multiply the cost of the home by the down payment percentage: $90,000 * 8.8% = $7,920.
This means that the total amount that will need to be borrowed from the bank is $90,000 - $7,920 = $82,080.
The mortgage amount will be $82,080. This is the amount that will need to be borrowed from the bank after the down payment of $7,920 is paid. The down payment is calculated by multiplying the cost of the home by the required down payment percentage: $90,000 * 8.8% = $7,920. The mortgage amount is then calculated by subtracting the down payment from the cost of the home: $90,000 - $7,920 = $82,080.
13. A contractor is building a new subdivision. A rectangular piece of land for a new
house and yard is 60 feet wide. The length of the land is longer than the width by a
distance of n feet. Which equation represents the area of the land?
Answers
Answer:
Area = (60 + n) * 60 = 3600 + 60n
Step-by-step explanation:
The length of the land is 60 + n feet. The area of the land is the product of the length and width, so the equation representing the area of the land is:
Area = (60 + n) * 60 = 3600 + 60n
This equation represents the area of the land in square feet.
the number that comes up when a die, loaded so that one comes up twice as often as each of the other five sides, is rolled
Answers
When a die is loaded so that the probability of one side appears twice as often as the other five, the number "1" will be the most frequent result when the die is rolled.
When a die is loaded so that one side appears twice as often as the other five, the number that comes up most often when the die is rolled is "1". This is because the loaded die has an unequal probability of rolling each number, with one side being twice as likely to come up as any of the other five sides. This means that the chances of rolling this particular number are twice as great as the chances of rolling any of the other five numbers. For this reason, the number "1" will be the most frequent result when the die is rolled.The probability of rolling the number "1" is 2/7, while the probability of rolling any of the other five numbers is 1/7. Therefore, the number "1" is twice as likely to come up as any of the other five numbers when the die is rolled.
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Find all relative extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]
Find all ABSOLUTE extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]
HELP!!!
Answers
a) The relative extrema of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:
Local minimum: (1.5, -1).Local maximum: (0,1).b) The absolute extremas of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:
Minimum: (1.5, -1).Maximum: (0,1).What are relative extrema and absolute extrema?Relative extrema are all the turning points on the graph of a function, which are the points in which the derivative of the function is zero, hence the function behavior's may change from increasing to decreasing or vice versa.
From the graph given by the image at the end of the answer, the extremas of the function are given as follows:
Local maximum: (0,1), as the function changes from increasing to decreasing.Local minimum: (1.5, -1), as the function changes from decreasing to increasing.These are also the absolute extremas, as there are only one minimum extrema and one maximum.
If there were multiple extremas, we would have that:
The absolute minimum is the local minimum with the lowest value of y.The absolute maximum is the local maximum with the highest value of y.More can be learned about relative and absolute extrema at https://brainly.com/question/13602432
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Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year. The employee was just promoted and received a 15% raise. What is the new yearly salary
Answers
The new yearly salary will be $31,694.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.
And, The employee was just promoted and received a 15% raise.
Now,
Since, Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.
And, The employee was just promoted and received a 15% raise.
Hence, The salary for 13.25 hours = 13.25 × 2080
= $27,560
And, The employee was just promoted and received a 15% raise.
Hence, The new salary = $27,560 + 15% of 27,560
= 27,560 + 4134
= $31,694
Thus, The new salary = $31,694
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This table represents a linear function?
X o 5
Y5 15
The greater unit of the two
Answers
The greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
From the given table, (0, 5) and (5, 15)
Here, slope(m)=(y2-y1)/(x2-x1) =(15-5)/(5-0)
= 10/5
= 2
Substitute m=2, (x, y)=(0, 5) in y=mx+c, we get
5=2(0)+c
c=5
Substitute m=2, c=5 in y=mx+c, we get
y=2x+5 --------(I)
From the graph, (-4, 0) and (0, 6)
Here, slope(m)=(6-0)/(0+4)
= 3/2
= 1.5
Substitute m=1.5, (x, y)=(0, 6) in y=mx+c, we get
6=1.5(0)+c
c=6
Substitute m=1.5, c=6 in y=mx+c, we get
y=1.5x+6 --------(II)
Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.
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Consider the equation a + b = c − d/2 when solved for each variable. Choose all that are correct.
A. d = 2a + 2b - 2c
B. b = 1/2(-2a + c - d)
C. c = a + b + d/2
D. a = 1/2(-2b + 2c - d)
Answers
The equations that are correct are a = 1/2(-2b + 2c -d) and c = a + b + d/2. The correct options are C. c = a + b + d/2 and D. a = 1/2(-2b + 2c -d)
Solving equationFrom the question, we are to solve the equation for each variable
The given equation is
a + b = c - d/2
Solving for a
a + b = c - d/2
a = -b + c -d/2
Multiply through by 2
2a = -2b + 2c -d
By multiplying both sides by 1/2, this can be written as
a = 1/2(-2b + 2c -d)
Solving for b
a + b = c - d/2
b = -a + c - d/2
Multiply through by 2
2b = -2a + 2c - d
By multiplying both sides by 1/2, this can be written as
b = 1/2(-2a + 2c - d)
Solving for c
a + b = c - d/2
a + b + d/2 = c
Therefore,
c = a + b + d/2
Solving for d
a + b = c - d/2
Multiply through by 2
2a + 2b = 2c - d
d = 2c - 2a - 2b
d = -2a - 2b + 2c
Hence, a = 1/2(-2b + 2c -d) and c = a + b + d/2 are correct
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Tim is building a brick wall that will be 4 feet
high and 57 feet long. It takes 7 bricks to build
1 square foot of wall.
(Area = length x width)
Answers
The approximate number of bricks he will use for the entire building is; 1596 bricks
How to find the area of the building?We are given that;
- Tim is building a brick wall that will be 4 feet high and 57 feet long.
- It takes 7 bricks to build 1 square foot of the wall.
The area of the building is gotten by applying the area of a rectangle which is;
Area of building = Length * Width
Thus;
Area = 4 * 57
Area = 228 square foot
Now, we are told that it takes 7 bricks to build one square foot of wall. Thus;
Number of bricks required here is;
N = 228 * 7
N = 1596 bricks
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The complete question is;
Tim is building a brick wall that will be 4 feet
high and 57 feet long. It takes 7 brick to build 1 square foot of wall
(Area = Length x Width)
Approximately how many bricks will he use for the entire building?
PLEASE ANS ASAP
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOKKKKKKKKKKKKKKKKKKKKKKKK
100 POINTS
BRAINLIEST IF POSSIBLE
Answers
a) The minimum number of hikers that could have walked between 6 miles and 17 miles is of: 9.
b) The maximum number of hikers that could have walked between 6 miles and 17 miles is of: 19.
How to obtain the amounts?The amounts are obtained by the frequency table given in the image, which shows the number of times that each range was observed.
The minimum number in the desired range will be obtained when:
The 2 hikers in the interval 5 < x < 10 walk less than 6 miles.The 8 hikers in the interval 15 < 20 < 20 walk more than 17 miles.Hence the minimum number is of 9, which is the number of people in the range 10-15.
The maximum number in the desired range will be obtained when:
The 2 hikers in the interval 5 < x < 10 walk more than 6 miles.The 8 hikers in the interval 15 < 20 < 20 walk less than 17 miles.Then the maximum number is calculate as follows:
2 + 9 + 8 = 19 hikers.
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In how may ways can the letters of the word 'SEMESTER' be arranged such that at least two vowels are together. Show ALL your work step by step to get credit. Final answers MUST be provided in decimal form
Answers
In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.
Arrangement in probability
A number of topics like statistics and probability are closely interrelated to the topic of permutation and combination. Permutation and combination is about making arrangements and making selections on the basic of certain formulas.Given that:
In SEMESTER there are 8 letters.
Which include 3 vowels (E) and 5 consonants (S, M, T , R )
Take 3 vowels as one letter, we have 6 letters
arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways
Number of words = 6! × 1!
= 6 × 5 × 4 × 3 × 2 × 1
= 720 ways
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Triangle Congruence: Question 1
In the accompanying proof, what is reason (5)?
Given: A B║DC
AB=DC
Prove: m ∠DAC= m ∠BCA
Select one:
SSS
SAS
SSA
ASA
Answers
In the accompanying proof, the reason (5) is SAS theorem.
In the given question,
Given: AB || DC
AB=DC
Prove: m∠DAC = m∠BCA
The statement used to prove this conditions are:
Statement Reason
AB || DC (1) Using the Quadrilateral Rule
AB=DC (2) Opposite sides are equal
m∠BAC = m∠DCA (3) Alternate interior angles Theorem
AC=AC (4) Common Side
∆ADC≅∆CBA (5) SAS Theorem
m∠DAC = m∠BCA (6) Alternate interior angles Theorem
We have to explain in the accompanying proof, what is reason (5).
So, in the accompanying proof, the reason (5) is SAS theorem.
In the proving we first prove one side equal, then angle equal and at last again one side equal.
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When graphing the line y = x - 1. how do you
move from one point to another on the line?
A. 2 units up. 1 unit to the right
B. 2 units up. 1 unit to the left
C. 1 unit down. 2 units to the right
D. 1 unit up. 2 units to the right
Answers
Answer: C. 1 unit down. 2 units to the right
Step-by-step explanation:
Please help will mark brainly
Answers
Answer: >
i might be wrong tho
Step-by-step explanation:
x=(-12,0)
y=(0,6)
m=6/-12
m=-1/2
slope is positive
m=1/2
y=1/2x+6
shade is to the right
y>1/2x+6
Propose a molecular formula that fits the following data: (a) A hydrocarbon \left(C_{x} H_{y}\right)(CxHy) with a molecular ion peak at m/z = 66. (b) A compound that absorbs IR radiation at 1720 \mathrm{cm}^{-1}1720cm −1 and exhibits a molecular ion peak at m/z = 70.
Answers
C₁₂H₁₂BrO₁N₁ is the molecular formula that fits the following data A hydrocarbon \left(C_{x} H_{y}\right)(CxHy) with a molecular ion peak at m/z = 66.
An analytical technique used to measure the mass to charge ratio of the ions is known as mass spectrometry. This is one of the best technique used to analyse the structure of a molecule. It is used in a a lot of applications such as carbon dating, food contamination detection, isotope detection, protein identification etc.
We have given that,
molecular ion at 265 m/z
another ion seen at 267 m/z
their ratio is 1:1
C₁₃H₉Cl₂ON₁ in this in here Cl have two isotopes that are
36 and 37 but m/z is not equal to 265
in here C₁₂H₁₂BrO₁N₁ Br have two isotopes
Br-79, Br-81 and m/z equals to 256 and 257
so the molecular formula is therefore C₁₂H₁₂BrO₁N₁
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Rosemary works two part-time jobs while attending college. During the day she works at the college bookstore and earns $8.25 per hour. In the evening she delivers pizza for Papa Gino's, earning $9.25 per hour. If Rosemary earned $247 last week from working a total of 28 hours, find how many hours she worked at Papa Gino's last week.
Answers
Answer: 16 hours
Step-by-step explanation:
We will write a system of equations to help us solve. Let x be equal to the number of hours worked at the college bookstore, and y be equal to the number of hours worked at Papa Gino's.
First, we will write an equation for the money earned. Then, we will write one for the hours worked.
8.25x + 9.25y = 247
x + y = 28
Now, we will will substitute the second equation into the first and solve for the hours worked at Papa Gino's last week, equal to y.
x + y = 28 ➜ x = -y + 28
8.25x + 9.25y = 247
8.25(-y + 28) + 9.25y = 247
-8.25y + 231 + 9.25y = 247
y + 231 = 247
y = 16
Rosemary worked 16 hours at Papa Gino's last week.
Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000, what is the interest rate on this loan?
Answers
The interest rate on this loan will be 5%.
How to calculate the interest?Given that Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000.
The interest on the loan will be:
= $22000 - $11000
= $11000
The interest rate on this loan will be:
Rate = Interest / Principal × Time
Rate = 11000 / (22000 × 10)
Rate = 11000 / 220000
Rate = 5%
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Kayla saves $110 to purchase a new outfit. She decides to buy a skirt for $29.65, a sweater for $38.32, and a purse for $31.00.
Question 1
Which choice is the total amount for the 3 items?
Responses
A $87.43$87.43
B $92.41$92.41
C $98.97$98.97
D $107.12$107.12
Question 2
Which amount of money will Kayla have left after the purchase?
Responses
A $11.03$11.03
B $9.74$9.74
C $6.92$6.92
D $7.15
Answers
The choice that is the total amount for the 3 items is C. $98.97.
The amount of money that Kayla have left after the purchase is A. $11.03.
How to calculate the amount?From the information, Kayla saves $110 to purchase a new outfit. She decides to buy a skirt for $29.65, a sweater for $38.32, and a purse for $31.00.
The cost of the items will be:
= Skirt + Sweater + Purse
= $29.65 - $38.32 + $31.00
= $98.97
The amount of money that Kayla have left after the purchase is:
= $110 - $98.97
= $11.03
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Answer:
c and a
Step-by-step explanation:
I don’t understand number 2
Answers
Answer:
They're asking you to plug in the x values for x. for example the first x in the table is "-6" so you will replace the x in 1/3(-6)^2 and the Y answer would be 12.
1/3 x (-6)^2 which is 36.
1/3 x 36= 12.
and you'll basically do that for each value. I hope that helps.
select each of the equations that represent a line segment between the points (1,5) and (3,13). a. x
Answers
On solving the provided question the equation of line segment is [tex]3y = x+11 OR y = 1/3x + 11/3[/tex]
What is equation?An equation in algebra is a condition on a variable. Only for a certain value of the variable does it satisfy. This indicates that the equation 2x - 5 = 13 can only be met when x = 9. Polynomial equations and linear equations are two significant kinds of equations that are taken into account in algebra. One-variable polynomial equations can be expressed as P(x) = 0, where P is a polynomial and ax + b = 0 is the standard form for linear equations. Here, the variables a and b are used.
Let y=m x + c be the slope intercept form of the equation.
Here, the slope m and the y-intercept c are unknown.
What is known is that this goes through (x 1, y 1) and (x 2, y 2), two coordinate pairs.
Consequently, we have three equations.
[tex]y=mx+c.........1\\ y1=mx1+c....2\\ y2=mx2+c ......3[/tex]
now let's delete m and c using these.
subtracting (2) from (1), we get [tex](y-y1)=m(x-x1) ......(4)[/tex]
and subtracting (2) from (3), we get[tex](y-2-y1)=m(x2-x1) ......(5)[/tex]
[tex]\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} \\\\\frac{y-3}{4-3} = \frac{x+2}{1+2} \\\\y-3 = \frac{x+2}{3}\\ 3y-9 = x+2\\3y = x+11\\OR\\y = 1/3x + 11/3[/tex]
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When a logistic regression coefficient is negative, the exponentiated coefficient, i.e. the EXP(B), will always be less than one.
True or False
Answers
Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level. Positive coefficients show that the event is more likely to occur at the reference level than at that level of the predictor.
What is Positive coefficients?Positive coefficients indicate that the event is more likely to occur at that predictor level than it is at the reference level for the factor.
Positive coefficients indicate that the event has a higher probability of happening at the reference level than at the predictor level.
The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.
To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.
However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.
Hence, Positive coefficients show that the event is more probable at that predictor level than it is at the factor's reference level.
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592x43 using standard algorithm showing answers
Answers
Answer:
25,456
Step-by-step explanation:
592 2 x 3 = 6 9 x 3 = 27 (You put the 7 in the tens place)
x 43 (And add 2 to the hundreds after multiplication)
______ 5 x 3 = 15 15 + 2= 17 (So you add 1 to the thousand place)
1776 Which would be 1776
2368
Now we do the same thing but with 4 this time, and we wont use the ones place because were putting the numbers in the tens place to start with since it's 40 2 x 4 = 8 (Goes in tens place)
9 x 4 = 36 (6 goes in hundreds place and 3 to thousands place)
5 x 4 = 20 (So 2 goes into the ten thousands place, and 3 to thousands place)
So it would be 2368
On the coordinate plane, point K is located at (3, -2) and point L is located at (x, 6). The
distance between points K and L is 10 units.
Graph one possible point L on the coordinate plane.
Answers
All of the points along the y-axis are located in the region of the coordinate plane that is equally distant from the coordinates a(-3 2) and b(3, 2).
Find the coordinate plane by what method?The x-axis, a horizontal number line, and the y-axis, a vertical number line, cross to create a coordinate plane. The coordinate plane's origin is where the two axes—plural for "axes"—vertically intersect.
What is an illustration of a coordinate plane?Each point on a coordinate plane will have an x coordinate and a y coordinate, which are stated as (x, y). For instance, the coordinate (3,2) has a y-coordinate of 2, an x-coordinate of 3, and a coordinate in between.
Here,
Given: K(3, -2) and (x, 6).
Thus ,distance between points K and L is 10 units.
Thus,
=> 10 = [tex]\sqrt{(3-x)^{2}-(-2-6)^{2} }[/tex]
=> 10 = [tex]\sqrt{9+x^{2} -6x+64\\[/tex]
=> 100 = 73 +[tex]x^{2}[/tex] -6x
=> 27 =[tex]x^{2}[/tex] -6x
=>[tex]x^{2}[/tex]-6x-27=0
=>x(x-9)+3(x-9)
=>x=-3 , x=9
Thus, x comes out to be x =-3.
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The quotient of 5 and a number, k ? Write the algebraic expression
Answers
Answer: [tex]\frac{5}{k}[/tex]
Step-by-step explanation:
To write an algebraic expression that represents this situation, we need to know that a quotient will involve division.
We will write the quotient of 5 and a number, k. also written as 5 divided by k, as;
[tex]\displaystyle \frac{5}{k}[/tex]
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The algebraic expression is - [tex]\frac{5}{k}[/tex]
If one number is divided by another number, the answer obtained is called the quotient.
In mathematics, a number that divides another number is called a divisor.
The number which is to be divided by the divisor is called a dividend.
In arithmetic, if we divide one integer by another, the 'leftover' portion is called the remainder.
In this case, 5 is the dividend, and k is the divisor, which is representing an unknown number.
We can not get an actual number, but we can use an algebraic equation to express the quotient as follows:
The quotient of 5 and k = [tex]\frac{5}{k}[/tex]
The algebraic expression is - [tex]\frac{5}{k}[/tex]
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*the data set `normtemp` (**usingr**) contains measurements of 130 healthy, randomly selected individuals. the variable `temperature` contains normal body temperature. does the data appear to come from a normal distribution? if so, perform a $t$-test to see if the commonly assumed value of 98.6 degrees fahrenheit is correct. (studies have suggested that 98.2 degrees fahrenheit is more accurate.)*
Answers
A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.
library(UsingR)
attach(normtemp)
print(normtemp)
hist(normtemp$temperature)
shapiro.test(normtemp$temperature)
qqnorm(normtemp$temperature)
qqline(normtemp$temperature)
We can observe that the data follows a normal distribution from the histogram and q plot.
The points in the q plot fall on a straight line and correspond to a normal distribution.
P-value = 0.2332, P>0.05, from the Shapiro test
hence, we fail to reject null htpothesis.
On accepting the null hypothesis we get to know that the data follows normal distribution.
The output for the given code will be ,
data: normtemp$temperature
t = 1527.9, df = 129, p-value < 2.2e-16
alternative hypothesis: true mean ≠0
90 percent confidence interval:
98.14269 98.35577
sample estimates:
mean of x
98.24923
Therefore , we can conclude that ,
The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.
98.6 is not included in the 90% confidence interval.
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Stock Market Worksheet 1
You need to show your work in order to receive full credit.
Business Organization
1. James invests $10,000 in a partnership with 3 other people. One of those people also invested
$10,000 and the other two invested $90,000 each. What percent of the business does James
own?
Answers
James owns on owns only 5 percent of the business capital.
How to calculate percentage?We should know that percentage deals with number of ratios as a fraction of 100
James = $10,000
One partner = $10,000
Other two partners = ($90,000+90,000)=$180,000
Total capital invested = $)10000+10000+90000+90000)
Total investment = $200,000
James proportion= [tex]\frac{10,000}{200,000} *\frac{100}{1}[/tex]
Simplifying this to have James percentage of investment as 5 percent
James =5%
In conclusion James has only 5% of the business investment
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You are running a special for the holiday season during the morning rush
hours. You have sold a total of 40 doughnuts and coffee in the morning rush
hours. You charged $4 per doughnut and $6 per coffee and the total sales were
$180. Determine the total number of coffee (c) and doughnuts (d) sold.
Answers
Answer:
40 donuts
10 Coffees
Step-by-step explanation:
d+c=40
4d+6c=180
-4d-4c=-160
+4d +6c +180
2C=20
C=10
d+10=40
d=30
you invested $20680 part of it in a stock that paid 12% annual interest. However the rest of the money suffered a 5% loss. if the total annual income from both investments was $2026 how much was invested at each rate?
Answers
The initial total investment is $8000.
x
+
y
=
8000
In a year, 0.12x was earned while 0.05 was lost. The net income for both is $620.
0.12
x
−
0.05
y
=
620
0.12
x
−
0.05
(
8000
−
x
)
=
620
[
Substitute y using the first equation
]
0.12
x
−
400
+
0.05
x
=
620
0.17
x
−
400
=
620
0.17
x
=
1020
[
Add 400 to both sides
]
x
=
6000
[
Divide both sides by 0.17
]
The remaining investment is:
y
=
8000
−
(
6000
)
[
Substitute x value
]
y
=
2000
$6000 was invested in a stock that paid 12% annual interest while $2000 was invested on another investment that suffered a loss.
research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers. (meaning, they help students understand the value of fractions and how the size of these numbers relates to the whole numbers that students already know.)
Answers
The pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers is number line.
What is meant by pedagogical tool?
In math, pedagogical tool refers designed to convey important lessons and allow people to improve their understanding of a problem or undertaking.
Here we need to find the research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers.
While we looking into the given question, here we need to find the tool that is used to find the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers that is none other than number line because it uses the visual representation of the number that gives better understanding of number.
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