Answer: Answer
Step-by-step-explanation: 4:2 plays a sport 13:9 does not
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 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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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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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
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.
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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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
The missing term of the factorization equation is A = ( -15x - 1 ) ( x + 2 )
Given data ,
Let the equation be represented as A
Now , the value of A is
A = -15x² - 31x - 2
On simplifying , we get
The expanded form of the expression ( -15x - 1 ) ( x + 2 ) can be calculated using the distributive property of multiplication over addition
So , on factorizing , we get
A = ( -15x - 1 ) ( x + 2 )
Hence , the factorized equation is A = ( -15x - 1 ) ( x + 2 )
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The complete question is attached below :
Fill in the missing terms to complete the factorization. 15x² + x - 2 = (? -1) (? + 2)
a- 3x, 5x
b- x, 15x
c- 5x, 3x
d- 15x, x
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
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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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.
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
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%.
if 5 is subtracted from the square of a number find the positive solution
If 5 is subtracted from the square of a number, the positive solution is √5.
How to determine the unknown number?In this exercise, you are required to determine or solve for an unknown number as follows. First of all, we would assign a variable to the unknown number and then translate the word problem into an algebraic expression as follows;
Assuming the unknown number is represented by the variable x.
Therefore, the required algebraic expression is given by;
x² - 5
In order to determine the positive solution, we would have to equate the algebraic expression to zero as follows;
x² - 5 = 0
x² = 5
x = ±√5
x = √5 (positive solution)
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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!
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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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:
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
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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the diagram shows a right angled triangle, find value of h
The value of the side length h is 19.1 cm.
What is the value of side h?The figure in the image is a right triangle:
Angle θ = 47 degrees
Opposite to angle θ = 14cm
Hypotenuse = h
To solve for side length h, we use trigonometric ratio.
Note that: sine = opposite / hypotenuse
Plug in the values and solve for h.
sin( 47° ) = 14 / h
h = 14 / sin( 47° )
h = 19.1 cm
Therefore, the value of h is 19.1 cm.
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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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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?
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
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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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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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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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
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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An engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car. The total trip took 6 h. Find the rate of the car.
The rate of car is 35 mph.
Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.
Let c be the rate of wind.
215 + c = rate of plane with wind
215 - c = rate of plane against wind
Therefore, the travel time =distance/rate
⇒ 750/(215+c) = 540/(215-c)
Cross multiplying we get,
540(215+c) = 750(215-c)
116100+540c = 161250-750c
1290c = 45150
c=35
Hence, the rate of car is 35 mph.
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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