If the number of papers is 56, the ratio of the total height in millimeters of 2 mm thick paper to the total height in millimeters of 23 mm thick paper is 2:23.
What is the ratio?The ratio is the relative size of two comparable quantities, values, or numbers.
Ratios are computed as the quotients of one value (the numerator) and another (the denominator).
We can depict ratios as decimals, fractions, percentages, or in their standard forms (:).
The total height in millimeters of 2 mm thick paper = 112 mm (56 x 2)
The total height in millimeters of 23 mm thick papers = 1,288 mm (56 x 23)
Ratio = 0.0869 (112 ÷ 1,288) or 2/23 or 8.69%.
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Luc is playing a trivia game with multiple choice questions. He runs out of time and needs to guess on the last 2 22 questions. Each question has 4 4
The requried probability that Luc gets both questions correct is 1/16 or approximately 0.0625.
The probability of guessing a single question correctly is 1/4, since there are 4 answer choices and only 1 is correct. Since the questions are independent, the probability of guessing both questions correctly is the product of the probability of guessing each question correctly.
Therefore, the probability that Luc gets both questions correct is:
P(both correct) = P(first correct) * P(second correct)
P(both correct) = (1/4) * (1/4)
P(both correct) = 1/16
Thus, the probability that Luc gets both questions correct is 1/16 or approximately 0.0625.
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Evaluate 5z - 3z for z = 3.
The value of the expression 5z - 3z, when z is equal to 3, is 6.
What is the value of the expression for z = 3?Given the expression in the question:
5z - 3zAlso, z = 3Evaluating an expression simply means substituting the given value of a variable into the expression and simplifying the result.
Given the expression 5z - 3z, we are given the value of z as 3.
Hence, we substitute z with 3 in the expression:
5z - 3z
Plug in z = 3
5(3) - 3(3)
Simplifying further using the order of operations (multiplication before subtraction), we get:
15 - 9
= 6
Therefore, the value of the expression is 6.
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Fill in the missing terms to complete the factorization. 15x^2 + x - 2 = (? -1) (? + 2)
a- 3x, 5x
b- x, 15x
c- 5x, 3x
d- 15x, x
Which experimental design will NOT result in a randomized sample?
A.
Selecting every 5th person from the class lists for each section of an algebra course
B.
Assigning a unique number to every medical study applicant and then using a random number generator to assign applicants to three different treatement goups
C.
Using all students from sections 1 and 2 of a statistics course to constitute two samples
D.
Dividing a list of voters into Democrats and Republicans and then selecting every 10th name from each of the two resulting lists
The experimental design that will not result in a randomized sample is C.Using all students from sections 1 and 2 of a statistics course to constitute two samples
What is Random sampling ?Random sampling can be regarded as the part of the sampling technique whereby each of the sample that is been involved in the population will have an equal probability of being chosen.
It should be noted that in this , the sample is chosen randomly which is unbiased representation , and in the third option, we can see that all the population was using.
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1000 randomly selected Americans were asked if they believed the minimum wage should be raised. 600 said “yes.” What is the 99% confidence interval for the proportion of Americans who believe that the minimum wage should be raised?
The 99% confidence interval for the proportion of Americans who believe that the minimum wage should be raised is: 0.56 < P < 0.64
How to find the confidence interval?We are given:
Sample size: n = 1000
Sample proportion: p = 600/1000 = 0.6
Formula for confidence interval for proportion is:
CI = p ± z√(p(1 - p)/n)
where:
p is sample proportion
n is sample size
z is z-score at confidence level
z at 99% CL = 2.576
Thus:
CI = 0.6 ± 2.576√(0.6(1 - 0.6)/1000)
CI = 0.6 ± 0.04
CI = (0.56, 0.64)
CI = 0.56 < P < 0.64
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The number of home runs a baseball player earned each season in his career are listed. 10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 Which of the following box plots best represents the data given? A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 20.5 to 38 on the number line. A line in the box is at 32. The lines outside the box end at 11 and 43. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 10 to 49 with tick marks every one unit. The box extends from 20.5 to 32 on the number line. A line in the box is at 30. The lines outside the box end at 12 and 46. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40. The graph is titled Career Home Runs and the line is labeled Number of Home Runs. A box plot uses a number line from 6 to 45 with tick marks every one unit. The box extends from 23.5 to 36 on the number line. A line in the box is at 30. The lines outside the box end at 9 and 39. The graph is titled Career Home Runs and the line is labeled Number of Home Runs.
The correct box plot is
A box plot uses a number line from 7 to 46 with tick marks every one unit. The box extends from 22.5 to 33.5 on the number line. A line in the box is at 30. The lines outside the box end at 10 and 40.
We have the data:
10, 14, 20, 25, 29, 30, 30, 31, 32, 35, 39, 40 .
So, First Quartile(Q1) = ((n + 1)/4)th Term.
= (12+1)/4
= 13/4
= 3.25 th term
= (20+25)/2
= 22.5
and, Second Quartile or median (Q2) = ((n + 1)/2)th Term.
Q₂ = ((12 + 1)/2)th term
= 6.5th term
= 30
and, Third Quartile(Q3) = (3(n + 1)/4)th Term.
Q₃ =3 (3.25)
= 9.75
= 33.5
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Select the correct answer. Which equation is a step in solving the equation |5 − 3x| + 2 = 19? A. |5 + 3x| = 17 B. 5 + 3x = -17 C. 5 − 3x = -17 D. |5 − 3x| = -17
Answer:B
Step-by-step explanation:i did the quiz
Simplify the expression: 4√12
Answer:
Step-by-step explanation:
It is
4
√
12
=
4
√
3
⋅
4
=
4
⋅
2
⋅
√
3
=
8
√
3
5(2x+2)-12x simplify
The simplified expression is 120x³ + 120x².
To simplify the expression 5x(2x+2)12x, we can use the distributive property of multiplication over addition and simplify the resulting terms.
First, we distribute 5x to the expression (2x+2), which gives us:
5x(2x+2) = 10x² + 10x
Next, we can multiply the result by 12x:
12x(10x² + 10x) = 120x³ + 120x²
Therefore, the simplified expression is 120x³ + 120x².
We can see that the original expression was a multiplication of three factors, and we used the distributive property to simplify it by expanding and multiplying the resulting terms. The final expression has a common factor of 120x², which we can factor out to get 120x²(x+1).
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Christina also plans on leaving her $10,000 invested for 20 years. Write an equation representing her investment’s value, y, after x years. What is the value of Christina’s investment after 20 years?
a) An equation representing Christina's investment's value, y, after x years is y = 10,000(1.05)^x.
b) Using the above equation, Christina's investment will be worth a future value of $26,532.98 after 20 years.
How the future value is determined:Equation Method:The principal = $10,000
Annual compound interest rate = 5%
The investment period = 20 years
Let the value of the investment after x years = y
Let the number of investment periods = x
y = 10,000(1.05)^20
= $26,532.98
Online finance calculator, the future value is determined as follows:
N (# of periods) = 20 years
I/Y (Interest per year) = 5%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
FV = $26,532.98
Total Interest = $16,532.98
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Question Completion:The investment compounds at a 5% interest rate yearly.
find the length of the missing side. round to the nearest tenth if nessasary. 9 and 6 are the length of the legs and c is the hypotenuse.
In the words that your describing it, I supposed we are talking about the pythagorean theorem
What is the formula for the theorem?
a^2+b^2= C^2
A being the height
B being the Bottom
C being the slant or hypotenuse
How to Solve?
Well supposed 9 is a and 6 is b
[tex]9^{2}[/tex]+[tex]6^{2}[/tex]=[tex]c^{2}[/tex]
9 squared is 81 and 6 squared is 36
81+36= 117
So, 117=[tex]c^{2}[/tex]
Which means [tex]\sqrt{117}[/tex] is the answer or 10.8
Hope this helped!
12. What is the value of the following expression when
a = -2 and b = -4?
5(4a3b)+ ab
A-108
B -92
C -12
D12
E 28
Answer:
1st one is b. 2nd one is A
Step-by-step explanation:
i did the quiz
If lina takes an assignment at 4:30 and it takes her 12 minutes to complete it at what time did she finished?
Answer: 4:42
Step-by-step explanation:
4:30 + 0:12 = 4:42
Each day, Charmaine earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of overtime (in hours) that she works.
The total at 0 id 100 hours and rate if increasing is 50 per hour.
From the given graph;
Let x represents the total hours
And y represents total pay
Then,
(a) When x = 0
Then from graph we have y = 100
So total pay is 100 dollars.
(b) When x = 1 then y = 150
Therefore,
Rate of increasing = (150-100)/(1-0) = 50
So it is increasing 50 per hour.
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The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written. The store manager then deposited $956.60. Find the checkbook balance
The checkbook balance is $5703.25.
To find the checkbook balance, we need to start with the original balance and then subtract the amounts of the checks written and add the amount of the deposit.
Original balance: $7349.44
Checks written: $1349.67 + $344.12 = $1693.79
Deposit: $956.60
To find the checkbook balance, we can subtract the total amount of the checks written from the original balance and then add the deposit:
Checkbook balance = Original balance - Checks written + Deposit
Checkbook balance = $7349.44 - $1693.79 + $956.60
Checkbook balance = $5703.25
Therefore, the checkbook balance after store manager deposited $956.60 is $5703.25.
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find the 81st term of the arithmetic sequence -2 -8 -14
Answer:
a₈₁ = - 482
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 2 and d = a₂ - a₁ = - 8 - (- 2) = - 8 + 2 = - 6 , then
a₈₁ = - 2 + (80 × - 6) = - 2 + (- 480) = - 2 - 480 = - 482
Phillip wants to find the width, QP, of his driveway. He walks along the edge of the driveway 45 ft and
marks point R. Then he walks 13 ft further and marks point N. He turns 90° and walks until his location,
point R, and point P are collinear. He marks point M at this location, as shown.
(a) Can Phillip conclude that ΔPQR and ΔMNR are similar? Why or why not?
(b) Suppose MN = 15 ft. Calculate the width of the driveway, QP. Show all your work and round
answer to nearest tenth.
ΔPQR and ΔMNR are similar and if MN = 15 ft then the side length of QP is 52.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
ΔPQR and ΔMNR are similar are similar because both have the corresponding angles are congruent and the corresponding sides are in proportion .
If MN=15 feet we have to find QP
As sides are proportional
45/13=QP/15
Apply cross multiplication
45×15=13QP
675=13QP
Divide both sides by 13
QP=52
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The entire graph of the function g is shown in the figure below. Write the domain and range of g using interval notation.
Answer:g=g(9)
Step-by-step explanation:
Find the volume of a rectangular prism with a length of 5cm and a height of 20cm, round to the nearest tenth of a cubic centimeter
A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?
Warm-Up Understanding Binomial Settings Ms. Lee gave out the homework passes as described previously, and it turns out that zero statistics students were selected. She plans to give out another homework pass tomorrow, but this time she will keep drawing names, still replacing and shuffling between each trial, until she gets a statistics student.
Is this a binomial setting?
O Yes, the conditions for a binomial setting are all met in this case.
O No, this time there is not a fixed number of trials,
O No, this time the trials are not independent.
O No, this time the outcomes are not binary.
The answer is : No, this time there is not a fixed number of trials,
How to get the solution of the binomial settingFixed Number of Trials (n): Established beforehand, the experiment consists of a specified set of trials or repetitions.
Binary Outcomes: Every trial possess just two feasible outcomes typically referred to as "success" and "failure."
Independent Trials: The result of a single trial will not affect the outcome of any subsequent trials.
Constant Success Probability (p): Per trial, the chances of success remain unchanging.
Taking into account the given circumstances, Ms. Lee intends on giving out another homework pass consequently, she will keep pulling names until concluding with a statistics student. She rearranges and shuffles the papers which contain the names in-between each trial.
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what concepts of algebra 2 would you use in real life explain your scenario and how the concepts apply and provide a worked example for each concept
There are numerous concepts in algebra 2 that can be applied in real life scenarios. Some of which are linear equations and quadratic functions. The linear equation, for instance, helps to estimate that the cost i.e. of gas for a trip.
What algebra 2 concepts have practical applications in real life?Linear equations can be used in real-life for calculating distances, rates and costs. For instance, during plan for a road trip, it can be used to estimate distance, time it takes to travel, estimated cost of gas etc.
An illustration is when one is planning a road trip from New York to Los Angeles. We can estimate that the distance between the two cities is 2,800 miles and car has average fuel efficiency of 25 miles per gallon.
If gas costs $3.50 per gallon, We can use the linear equation to get the cost of trip which is:
= Distance / Miles per gallon * Price per gallon
= 2,800 / 25 * 3.50
= $392.
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Christian owns a small business selling bagels. He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card.
In total, Christian had 62 customers in the last week.
What is the approximate value of the upper quartile
A 18
B 20
C 25
D 27
The approximate value of the median is 25
The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.
The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
To find the median, calculate the value mean by adding together the middle values and dividing them by two.
Hence, the approximate value of the median is Median
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What is the approximate value of the median?
A 18
B 20
C 25
D 27
Find the value of c that makes.....
The solution to the equation as it is given in (8) above is -21.
What is subtraction and multiplication properties of equality?According to the subtraction property of equality, If you subtract the same number from both sides of an equation, the equation remains true.
Also by the multiplication property of equality, If you multiply both sides of an equation by the same number (except zero), the equation remains true. These can be used to solve the question in (7) above
Given;
280 = -8(-14 + x)
280 = 112 - 8x
280 - 112 = -8x
x = -21
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The wingspan (in feet) of the actual airplane is equal to 87.5 feet.
A property of equality which you would use to solve the equation -15 = x/3 + 18 is: D. Subtraction property of equality and multiplication of equality.
The solution of the equation 280 = -8(-14 + x) is: B. x = -21.
How to determine the wingspan (in feet) of the actual airplane?Based on the scale model, we can logically deduce that the airplane has a length of 12.2 inches and a wingspan of 12.5 inches. This ultimately implies that, we would convert from inches to feet as follows;
1 inch = 1/12 feet
12.2 inches = 12.2 × 1/12 = 12.2/12 feet.
Therefore, the scaled factor is given by;
Scale factor = (85.4 × 12/12.2)
For the actual length of the wingspan with a scaled length of 12.5 inches, we have:
12.5 inches = 12.5/12 feet
Actual length of wingspan = 12.5/12 × (85.4 × 12/12.2)
Actual length of wingspan = 87.5 feet.
Question 7-15 = x/3 + 18
x/3 = -15 - 18 ⇒ (Subtraction property of equality)
x/3 = -33
x = 3(-33) ⇒ (Multiplication property of equality)
x = -99
Question 8280 = -8(-14 + x)
280 = 112 - 8x
8x = 112 - 280
x = -168/8
x = -21
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pls help! show work!
The student is correct because we can factorize x² - x - 56 to get (x - 8)(x + 7).
How to Factorize an Expression?
In order to determine if -56 is the integer that can replace the box in the expression, we can try to factorize the expression and see if it works.
Factorize x² - x - 56 using the sum-product pattern:
x² - x - 56
Take out the common factors from each pair:
(x² + 7x) - (8x - 56)
x(x + 7) -8(x + 7)
Rewrite in factored form:
(x - 8)(x + 7)
Thus, this shows that the student is correct.
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6. Solve for y ONLY *
Find the value of each variable.
The value of the angle y is 86 degrees
How to determine the valueTo determine the value of the variable, we need to take note of the properties of a parallelogram. They include;
Opposite sides of the shape are parallel and equal.The angles opposite to each other are equal.The consecutive angles are supplementary, that is sum to 180 degrees.Also, note that angles on a straight line is equal to 180 degrees.
From the information shown on the diagram, we have;
y + 94 = 180
collect the like terms
y = 180 - 94
Subtract the terms
y =86 degrees
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A survey asked people of different ages whether they get their news by
reading the paper. What is the probability that a person surveyed is under 40,
given that he or she gets the news by reading the paper? If necessary, round
Don't read
Read paper
Total
paper
36
your answer to the nearest percent.
Under 40
40 or older
Total
4
24
28
16
52
40
40
80
Answer:
To find the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper, we need to use Bayes' theorem:
P(Under 40 | Read paper) = P(Read paper | Under 40) * P(Under 40) / P(Read paper)
where
P(Under 40 | Read paper) is the probability that a person is under 40 given that he or she gets the news by reading the paper
P(Read paper | Under 40) is the probability that a person under 40 reads the paper (36/80)
P(Under 40) is the overall probability of selecting a person under 40 (40/80)
P(Read paper) is the overall probability of selecting a person who reads the paper, calculated as the sum of those who are under 40 and read the paper and those who are 40 or older and read the paper (36+24)/(80)
Plugging in the values, we get:
P(Under 40 | Read paper) = (36/80) * (40/80) / ((36+24)/80)
P(Under 40 | Read paper) = 0.6
So the probability that a person surveyed is under 40, given that he or she gets the news by reading the paper, is 60%.
HELPPP ASAPPP !!!
2. Point A on the graph below represents Nate's house, and Point B represents Nate's favorite restaurant. B A If each unit on the graph represents 3/4 of a mile, how many miles does Nate live from his favorite restaurant?
Answer:
10miles I think
Step-by-step explanation:
The required distance between, Nate's house and the restaurant is 7.5 miles.
From the graph,
Consider point C on the graph, which is 6 and 8 units apart from A and B respectively.
The distance between, Nate's house and the restaurant is given as,
AB = √[AC² + BC²]
AB = √[6² + 8²]
AB = 10 units
Now 1 unit = 3/4 miles
AB = 10 * 3/4
AB = 7.5 miles
Thus, the required distance between, Nate's house and the restaurant is 7.5 miles.
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Use a graphing calculator or other technology to answer the
question.
Which quadratic regression equation best fits the data set?
ŷ-1229.14x² - 379.14x + 32.86
ŷ 32.86x² - 379.14x + 1229.14
y= 32.86x² - 379.14x
y = 32.86x² + 379.14x1229.14
The quadratic regression equation that best fits the data-set is given as follows:
y = 32.86x² - 379.14x + 1229.14.
How to obtain the quadratic regression equation?To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.
Considering the table in this problem, the points on the data-set are given as follows:
(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).
Inserting these points into a calculator, the quadratic regression equation is given as follows:
y = 32.86x² - 379.14x + 1229.14.
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