The values of x, y and z in the given simultaneous equation is:
x = 4
y = 6
z = -3
What is the solution to the simultaneous equation?The 3 simultaneous equations are given as:
x + 7y - z = 49
2x - 5y + 2z = -28
x - 6y=-32
Rearranging the first equation gives:
x = 49 - 7y + z
2x - 5y + 2z = -28
x - 6y = -32
Substitute 49 - 7y + z into equations 2 and 3 to get:
2(49 - 7y + z) - 5y + 2z = -28
49 - 7y + z - 6y = -32
Convert the equation in terms of u and solving simultaneously gives:
y = 6 and z = -3
Thus:
x = 49 - 7(6) + (-3)
x = 4
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Suppose you decide to invest in an annuity that pays 5% interest, compounded annually. How much money do you need to invest semiannually to reach a savings goal of $300,000 at the end of 25 years.
If your objective is to save $300,000 over 25 years, you would need to put away around $3077.41 every six months.
To solve this problem, we can use the formula for the future value of an annuity:
[tex]FV = P *\frac{((1 + r/n)^{(n*t)} - 1)}{(r/n)}[/tex]
where FV is the future value, P is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.
Since the interest is compounded annually, we have n = 1 and r = 0.05. To find the periodic payment P, we can rearrange the formula:
P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)
Plugging in the given values, we have:
[tex]P = 300000 * (0.05/2) / ((1 + 0.05/2)^{(2*25)} - 1)[/tex]
P ≈ $3077.41
Therefore, you would need to invest approximately $3077.41 every six months to reach a savings goal of $300,000 at the end of 25 years.
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AYOde deposit 600 at the end of each quarter for 15 year in a bank whose annual interest rate is 12% and compounding is done at each deposit
Find the total with of the account 60th deposit
Find the accumulate interest
The account's total value is $498,174.72.
The total interest paid is $174,174.72.
To solve this problemWe can utilize the calculation for the future value of a compound interest annuity to resolve this issue:
FV = P*(((1 + r/n)(n*t))-1) / (r/n).
where
FV is the future value of the annuityP is the periodic payment deposit, which is 600 in this caser is the annual interest rate, which is 12%n is the number of times the interest is compounded per year, which is 4 since the deposits are made quarterlyt is the total number of periods, which is 60 since there are 15 years and 4 deposits per yearWhen we enter the values, we obtain:
FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72
After the 60th deposit, the account's total value is $498,174.72.
We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:
Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72
Therefore, the total interest paid is $174,174.72.
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Two fair dice are rolled. What is the probability that the sum of the two numbers on the dice will be greater than 9?
A)11/12. B)5/6. C)1/12. D)1/6
Answer:
There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.
The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.
Answer: C) 1/12.
The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1). Under a series of transformations, the resulting figure ΔUNA has the following coordinates: U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).
Which statement is not true?
RB has the same length as UA.
GB is congruent to AN.
The measure of ∠R is the same as ∠N.
The original triangle ΔRGB is congruent to ΔUNA.
The statement that is not true is (c) The measure of ∠R is the same as ∠N.
From the question, we have the following parameters that can be used in our computation:
The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1). The coordinates of ΔUNA are U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)
This is a rigid transformation
And so, the side lengths and the corresponding angle measures are equal
However, angles R and N are not corresponding angles
So, the false statement is (c) The measure of ∠R is the same as ∠N.
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The table shows the number of bikes sold by a company from January to June of last year.
The mean number of bikes sold by the company from January to June was 146.17.
What is the mean number of bikes sold?
The mean, also called average refers to data set found by adding all numbers in the data set and then dividing by the number of values in the set.
Given data: 110 158 112 176 119 202
The total number of bikes sold is:
= 110 + 158 + 112 + 176 + 119 + 202
= 877
The number of months (Jan - Jun) = 6
The mean number of bikes sold will be:
= Ef/x
= 877 / 6
= 146.166666667
= 146.17
Full question "The table shows the number of bikes sold by a company from January to June of last year.
Find the mean number of bikes sold by the company from January to June.
January February March April May June
110 158 112 176 119 202"
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How do you convert this equation to rectangular form? The answer given in the book is (x-1)^2+y^2=9, but I need steps to show how you arrive at this answer.
The equation r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8 to rectangular form is (x - 1)² + y² = 9
Converting the equation to rectangular form?From the question, we have the following parameters that can be used in our computation:
r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8
The above equation is in its polar form, where
r² = x² + y²
cos(θ) = x/r
sin(θ) = y/r
Rearrange the terms in r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8
So, we have
r²cos²(θ) + r²sin²(θ) - 2rcos(θ) = 8
Factorize
r²(cos²(θ) + sin²(θ)) - 2rcos(θ) = 8
In trigonometry
cos²(θ) + sin²(θ) = 1
So, we have
r² - 2rcos(θ) = 8
Recall that
r² = x² + y²
cos(θ) = x/r
So, we have
x² + y² - 2r * x/r = 8
Evaluate
x² + y² - 2x = 8
Rearrange
x² - 2x + y² = 8
Express as perfect squares
(x - 1)² + y² = 8 + 1
So, we have
(x - 1)² + y² = 9
Hence, the equation to rectangular form is (x - 1)² + y² = 9
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Find (v) x (w) if ||v||=8, ||w||=12, and the angle between v and w is 60 degrees
The product of two given vectors is 48.
Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.
We know that, |a|·|b|=|a|×|b|×cosθ.
Here, |v|·|w|=8×12×cos60°
= 96× 1/2
= 48
Therefore, the product of two given vectors is 48.
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The minivan depreciates $3,000 in the first year. Write either a linear or exponential function to represent the value of the car x years after it was sold.
Answer:
Step-by-step explanation: However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000, 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put it into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the number of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply by 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer form. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.
Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/7
The best reason why 2/5 is the exact quotient for 1/4 divided by 5/8 is: ²/₅ * ⁵/₈ = ¹/₄
How to divide fractions?To divide fractions, firstly, you need to turn the 2nd fraction upside down. For example, 3/8 divided by 3/4 would be 3/8 divided by 4/3. After you have flipped the second fraction, you multiply them - 3*4 = 12. 8*3 = 24 so the answer would be 12/24. Which then could be cancelled down to 1/2.
Now, from the given question, we can say that:
1/4 ÷ 5/8
Now, from the earlier step in dividing fractions, the next step is to turn the 2nd fraction upside down and multiply by the first to get:
¹/₄ * ⁸/₅ = ²/₅
Rearranging, we have:
²/₅ * ⁵/₈ = ¹/₄
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Complete question is:
Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/8
Two homebuilders are working to get the windows installed on their homes. Tom uses the formula 42 = 7x + 2 to model the number of windows he is installing on his home and Suzanne uses the formula 37 = 6x + 5 to model the number of windows she is installing on her home. In each formula, x represents the number of days that Tom and Suzanne work on installing windows.
Tom is installing 6 windows each day and Suzanne is installing 6 windows each day as well.
To find the number of days it takes for each homebuilder to install the windows, we need to solve for x in each equation.
Tom's equation: 42 = 7x + 2
Subtracting 2 from both sides:
40 = 7x
Dividing both sides by 7:
x = 5.71 ≈ 6
So it will take Tom approximately 6 days to install the windows on his home.
Suzanne's equation: 37 = 6x + 5
Subtracting 5 from both sides:
32 = 6x
Dividing both sides by 6:
x = 5.33 ≈ 6.
So it will take Suzanne approximately 6 days to install the windows on her home.
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write an exponential model given two points. (6,85) (7,92)
The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
We have,
To write an exponential model given two points (6,85) and (7,92), we can use the general exponential function form:
y = a[tex]b^x[/tex]
where y is the dependent variable, x is the independent variable, a is the initial value (when x = 0), and b is the base of the exponential function.
To find the values of a and b, we can use the two given points as follows:
When x = 6, y = 85:
85 = a b^6
When x = 7, y = 92:
92 = a b^7
We now have a system of two equations with two unknowns (a and b).
We can solve for a by dividing the second equation by the first equation:
92/85 = (ab^7) / (ab^6)
1.0824 = b
Substitute this value of b into one of the equations to solve for a:
85 = a (1.0824)^6
a = 41.62
Therefore,
The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]
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20x+4y=8 in slope-intercept form, simplifying all fractions.
slope = -5, y intercept = 2
The graph is below.
======================================
Work Shown:
20x+4y = 8
4y = 8-20x
4y = -20x + 8
y = (-20x+8)/4
y = -20x/4 + 8/4
y = -5x + 2 is the final answer
slope = -5, y intercept = 2
Two points on this line are (0,2) and (1, -3)
The graph is below. I used GeoGebra to make it, but Desmos is another good choice.
Freemont run club surveyed a random sample of 30 of their members about their running habits
The reasonable estimate would be 25
How to solve for the estimateWe have to solve this using the rule of 3
9 out of 30 members said that they run more than 5 days a week.
We will form the equations
when 9 ran = 30 menbers
when n ran = 84 members
we will then cross multiply
84 x 9 = 30 x n
n = 25.2
When we round this, the reasonable estimate would be 25
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Complete question
Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.
There are 84 Freemont Run Club members.
Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?
Question 6
A square is placed within a rectangle. Find the area of the shaded region.
Select one:
O
✪
✪
O
559 ft²
640 ft²
721 ft²
604 ft²
32 ft
19A
9 ft
20 ft
The area of the shaded region is 559 ft².
How to find the area of the shaded region?In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:
area of the shaded region = area of rectangle - area of square
area of the shaded region = (32 * 20) - (9 * 9)
area of the shaded region = 640 - 81
area of the shaded region = 559 ft²
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Complete Question
See attached image
Jada is designing a study to determine whether mold grows faster in tap water or bottled water. To do this she compares growth rate of mold growing in a glass of tap water to the growth rate of mold growing in a glass of bottled water.
What type of study is Jada designing?
How could her design be improved to collect date that would be better for answering question of interest?
Jada is directing a comparative analysis to identify whether mold thrives faster in tap water or bottled water.
How to improve her designTo upgrade her design and procure data that would be more viable for addressing the question of interest, Jada might reflect on the following:
Randomized Controlled Trial (RCT): Preferably of just contrasting the rate of growth of mold in tap water versus bottled water in a glass, Jada could arbitrarily allote separate glasses to either tap water or bottled water categories.
Replicates and Sample Size: Jada may utilize several copies for each type of water to escalate the probabilistic force of her study.
Control Group: Jada should integrate a control group in her study, where no water is integrated into the glass.
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2. A 18 kg rock starting from rest free falls through a distance of 7.0 m with no air resistance. Find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earth’s velocity. Earth’s mass is 6.0 × 1024 kg. Show all your work, assuming the rock-earth system is closed.
The momentum change of the rock caused by its fall will be 35.49 x [tex]10{-24[/tex] m/sec and the magnitude of the earth velocity will be 212.94 kgm/s
We have,
Mass of the rock = 18 kg
Distance traveled = 7 m
Mass of earth = 6 x [tex]10^{24[/tex] Kg
Using second equation of motion
S= ut + 1/2 at²
If the body freely falls initial velocity will be zero.
u = initial velocity = 0
Then, S = 1/2 at²
7 = 1/2 x 10 x t²
14/ 10= t²
t= 1.183 sec
Now, Change in the momentum of the rock will be,
ΔP= FΔT
ΔP = (mg ) ΔT
ΔP= (18) x 10 x 1.183
ΔP=212.94 kg-m/s²
Now, Earth will also have same momentum change
ΔP(earth)= ΔP(rock)
6 x [tex]10^{24[/tex] Kg x Δv = 212.94
Δv = 35.49 x [tex]10{-24[/tex] m /sec
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Anna ordered a large pizza with 2 toppings. What was the total cost of her pizza? Write an equation and solve it to find the total cost.
Answer: The cost of a large pizza with 2 toppings depends on the pizza place. Let's say the cost is $15 per pizza, and each additional topping costs $2.
Let t be the number of toppings Anna has on her pizza. Then, the total cost of her pizza can be expressed as:
Total cost = $15 + $2t
Since Anna has 2 toppings on her pizza, we can substitute t = 2:
Total cost = $15 + $2(2)
Total cost = $15 + $4
Total cost = $19
Therefore, the total cost of Anna's pizza with 2 toppings is $19.
Exercise: Determine if x = 64 is a solution to the logarithmic equation.
log4(x)=3-log4(x - 63)
Answer:
yes
Step-by-step explanation:
log4(64)=3－0,4*4*4=64
What is the volume of the resulting solid
Note that the volume (V) of the resulting solid which is revolved around it's axis is given as V = 37.699 cubic units.
How do you compute the above?If we used the distance formula, to computer the distance between the coordinates, we'd arrive at the following side lenghts:
3, 4, and 5.
Since we are looking at a right triangle, it is correct to infr that the hypotenuse is the longer side, which is 5.
We can assume the height to be four units and the radius to be 3 units.
Thus, using the formula fo rthe volume of a cone:
V = (1/3) * π * r² * h
Inputting values, we have
V = (1/3) * 3.14159 * 3² * 4
V = 1.0472 * 9 * 4
V = 37.6992
If we approximate to the nearest thousandth, we have:
V = 37.699 cubic units
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The sun is a even number
The probability that the sum would be an even number, can be found to be 1 / 2 .
How to find the probability ?There are six sides on each die so the total number of outcomes is:
= 6 x 6
= 36 outcomes
We will get an even number if we get two odd numbers, and two even numbers. We will not get even, with an even number and an odd number.
The number of two odd number outcomes is:
= 3 x 3
= 9 outcomes
The two even outcomes:
= 3 x 3
= 9 outcomes
The probability that the sum is even is:
= ( 9 + 9 ) / 36 total outcomes
= 18 / 36
= 1 / 2
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in how many ways can a student choose four questions from a question paper that contains six questions if
a. Question No. 1 is compulsory
b. Question No. 2 should not be chosen
c. There is no restriction on any of the questions
The student can choose four questions from a question paper that contains six questions as follow:
a. 10 ways.
b. 5 ways.
c. 15 ways.
How to choose how many ways can a student choose four questions?Combination is a way of selecting items from a collection where the order of selection does not matter.
a. If Question No. 1 is compulsory, then the student can choose three more questions from the remaining five. That is:
5C3 (i.e. 5 combination 3) ways = 10 ways.
b. If Question No. 2 should not be chosen, then the student can choose four questions from the remaining five. That is:
5C4 ways = 5 ways.
c. If there is no restriction on any of the questions, the student can choose any four questions from the remaining six. That is:
6C4 ways = 15 ways
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if f(x)=-4x-2 is vertically tranfered up 6 units to g(x), what is the y intercept of g(x)
The y-intercept for the function g(x) is 4.
The y-intercept of a function is a point where the line crosses the y-axis. The linear function can be given as below.
f(x) = mx+n
Where m is the slope of the line and n is a real number and y-intercept of the line.
The given function is f(x)=-4x—2.
The function is vertically translated 6 units up to g(x).
The y-intercept of the function f(x) is -2. Then the y-intercept for the function g(x) can be given as below.
y-intercept g(x) = -2+6
y-intercept g(x) = 4
Hence, the y-intercept for the function g(x) is 4.
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ayer compre 3/4 kg de papas y hoy 1/2 kg cuantos kg tengo en total
Determine the Y intercept:
The y-intercept of the line is 2.
In the equation y = 9x + 2, x and y are variables that represent the coordinates of any point on the line.
To find the Y-intercept, we need to find the value of y when x equals 0.
When x equals 0, the equation becomes:
y = 9(0) + 2
Any number multiplied by 0 is 0, so the first term drops out and we are left with:
y = 0 + 2
Which simplifies to:
y = 2
Therefore, when x equals 0, y equals 2. This means that the point (0, 2) is on the line. In other words, the line intersects the y-axis at y = 2, which is the Y-intercept of the line.
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Dr. Suarez, a veterinarian, wants to estimate the average number of
calories a chihuahua typically eats in a day. She'll take a sample of n
chihuahuas and create a 99% confidence interval for the mean daily caloric
intake. She wants the margin of error to be no more than 8 calories. A pilot
study suggests that the daily caloric intake of chihuahuas has a standard
deviation of 30 calories.
Which of these is the smallest approximate sample size required to obtain
the desired margin of error?
Choose 1 answer:
The smallest approximate sample size required to obtain the desired margin of error is b. 180 Chihuahuas
What is the sample size?The sample size is defined as the number of observations used for determining the estimations of a given population. It should be noted that the size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.
The sample size will be:
= (2.576 × 26 / 5)²
= 180
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Looking at the ping-pong ball toss board below, whats the probability of landing on a white square? (Note the board contains 5 rows of 5 squares.)
The probability of landing on a white square is 4/5.
We have toss board of measurement 5 x 5.
Total squares in board = 25
White square = 20
Black square= 5
So, the probability of landing on a white square
= 20 / 25
= 4/5
Thus, the required probability is 4/5.
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Let's say you wanted to make a flute from one-inch PVC pipe. If the lowest desired note is C5 on the Equal Temperament Scale (523.25 Hz), what length should it be cut?
The length the one-inch pipe should be cut to make a flute with a lowest desired note of 523.25 Hz, based on the acoustic length formula is 12.9 inches
What is the acoustic length?The acoustic length is the length obtained from the sum of the bore length and the corrections at the foot and the sound hole.
The frequency of the lowest note = 523.25 Hz
Whereby the frequency of the lowest note = The fundamental frequency
The acoustic length formula for finding the length of the pipe, L, can be presented as follows;
L = (v/(2·f)) × √(1 + 4·A²/v²)
Where;
L = The length of the pipe
f = The frequency = 523.25 Hz
A = The cross-sectional area of the pipe = π × 1.315²/4 ≈ 1.36 in²
v = The speed of sound ≈ 343 m/s ≈ 13503.9 in/s
L = (v/(2·f)) × √(1 + 4·A²/v²)
L = (13503.9/(2×523.25)) × √(1 + 4×1.26²/13503.9²) ≈ 12.9
The length of the pipe is about 12.9 inches
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The following data relate to a firm’s purchase of a machine used in the manufacture of its product:
Invoice price $299,000
Applicable sales tax 2,100
Cash discount taken for prompt payment 1,300
Freight paid 1,160
Cost of insurance coverage on machine while in transit 1,025
Installation costs 1,900
Testing and adjusting costs 1,375
Repair of damages to machine caused by the firm's employees 1,450
Prepaid maintenance contract for first year of machine's use 1,200
Determine the acquisition cost of the machine.
The machine's purchasing cost is $309,210.
The acquisition cost of the machine is the total cost incurred by the firm to purchase and put the machine into service.
To determine the acquisition cost of the machine, we need to add up all the costs listed in the question.
Invoice price = $299,000
Applicable sales tax = $2,100
Freight paid = $1,160
Cost of insurance coverage = $1,025
Installation costs = $1,900
Testing and adjusting costs = $1,375
Repair of damages caused by the firm's employees = $1,450
Prepaid maintenance contract = $1,200
Total acquisition cost = Invoice price + Sales tax + Freight paid + Cost of insurance coverage + Installation costs + Testing and adjusting costs + Repair of damages caused by the firm's employees + Prepaid maintenance contract
Total acquisition cost = $299,000 + $2,100 + $1,160 + $1,025 + $1,900 + $1,375 + $1,450 + $1,200
Total acquisition cost = $309,210
Therefore, the acquisition cost of the machine is $309,210.
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Team People on Each Team A 7 B 3 C 7 D 5 E 6 F 7 G 8 H 5 I 3 J 5 K 7 Think about a line plot using the data from the table. Which statement is true?
Think about a line plot using the data from the table. Which statement is true?
A. The greatest value with a dot above it is 11.
B. There will be 11 dots in total.
C. There will be 4 more dots above 7 than above 8.
D. There will be 5 dots above 7.
Statement " There will be 5 dots above 7" is true. Therefore, option D is the correct answer.
A line plot is an effective way to visualize and compare data in a table. In this case, the line plot would show the total number of people on each team, with dots representing the values.
The greatest value in the table is 11, but this would not be represented with a dot in the line plot. There will be 11 dots in total, representing the 11 teams listed in the table.
There will be 4 more dots above 7 than above 8, since there are 4 teams with 7 people on each team and only 3 teams with 8 people on each team.
Finally, there will be 5 dots above 7, since there are 5 teams with 7 or more people on each team.
Therefore, option D is the correct answer.
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Use the equation of the line of best fit, =y+−0.76x8.76, to answer the questions below. Give exact answers, not rounded approximations. (a) For an increase of one hour in the time spent texting, what is the predicted decrease in the time spent exercising? hours (b) What is the predicted time spent exercising for a student who doesn't spend any time texting? hours (c) What is the predicted time spent exercising for a student who spends 5 hours texting?
For an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment will be; 1.86 units.
To Determine the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we need to find the slope of the line, which is the coefficient of x in the equation.
We are given that the equation of the line of best fit, y = −0.76x8.76
The slope is 1.86, that means that for every one unit increase in x (which in this case is one hour worked), y (in this case is the amount of money spent on entertainment) is predicted to increase by 1.86 units.
This is the change in the dependent variable (y) for a unit increase in the independent variable (x),
Based on the linear relationship described by the equation of the line fit.
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