Answer:
When n is greater than 1/2 or always true
n > 1/2
Step-by-step explanation:
Rewrite.
0+0+6(n−1)=2(n+1)
Simplify by adding zeros.
6(n−1)=2(n+1)
Apply the distributive property.
6n+6⋅−1=2(n+1)
Multiply 6 by −1.6n−6=2(n+1)
Simplify 2(n+1).
6n−6=2n+2
Move all terms containing n to the left side of the equation.
4n−6=2
Move all terms not containing n to the right side of the equation.
4n=8
Divide each term in 4n=8 by 4 and simplify.
n=2
The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist entirely of boys?
0.2
0.04
0.33
0.02
The required experimental probability that a team will consist entirely of boys is 0.04. Option B is correct.
To find the experimental probability that a team will consist entirely of boys, we need to count the number of trials in which all three coin tosses resulted in tails (which represents a team consisting entirely of boys), and divide by the total number of trials (which is 50).
From the data, we can see that there are only 2 trials where all three coin tosses resulted in tails, so the experimental probability of a team consisting entirely of boys is:
2/50 = 0.04
Therefore, the experimental probability that a team will consist entirely of boys is 0.04.
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For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed that 52% of employers are likely to require higher employee contributions for health care coverage this year relative to last year. Suppose the survey was based on a sample of 900 companies likely to require higher employee contributions for health care coverage this year relative to last year.
1. At 95% confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answer to four decimal places.)
2. Compute a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answers to four decimal places.)
The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).
To compute the margin of error for the proportion, we use the formula:
Margin of error = z*√((P(1-P))/n)
where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have
P = 0.52 (sample proportion)
n = 900 (sample size)
z = 1.96 (for 95% confidence level)
Substituting these values into the formula, we get
Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344
Therefore, the margin of error is approximately 0.0344, or 3.44%.
To compute the confidence interval, we use the formula:
Confidence interval = P ± z*(√((P(1-P))/n))
where P, z, and n are the same as in part 1. Substituting these values into the formula, we get
Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)
Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.
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Find the 36th term.
5, 8, 11, 14, 17, ...
36th term = [?
Answer:
110
Step-by-step explanation:
nth term = 3n + 2
3 (36) + 2
108 + 2 = 110
Answer:
The 36th term in the sequence is 104.
Here's how to find it:
- Start with the first number in the sequence: 5.
- Add the common difference, which is 3, to get the second number in the sequence: 8.
- Add the common difference to the second number to get the third number: 11.
- Continue adding the common difference to each subsequent number to find the next term in the sequence.
- The 36th term is three less than 37 times the common difference added to the first term.
- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.
- Therefore, the 36th term in the sequence is 104.
6. The following are the costing records for the year 2020 of a manufacturer: Production 1,000 units, Cost of raw materials Rs,20,000, Labour cost Rs.12,000, Factory overheads Rs.8,000, Office overheads Rs.4,000, Selling expenses Rs.1,000, Rate of profit 25% on the selling price. The manufacturer decided to produce 1,500 units in 2021. It is estimated that the cost of raw materials will increase by 20%, the labour cost will increase by 10%, 50% of the overhead charges are fixed and the other 50% are variable. The selling expenses per unit will be reduced by 20%. The rate of profit will remain the same. Prepare a cost statement for the year 2021 showing the total profit and selling price per unit.
Answer:
Here's a cost statement for the year 2021:
Production of 1,500 units
Cost of raw materials = Rs. (20,000 x 1.2) = Rs. 24,000
Labour cost = Rs. (12,000 x 1.1) = Rs. 13,200
Fixed overheads = Rs. (8,000/2) = Rs. 4,000
Variable overheads = Rs. (8,000/2 x 1.5) = Rs. 6,000
Office overheads = Rs. 4,000
Selling expenses per unit = Rs. (1,000 x 0.8 / 1,500) = Rs. 0.53
Total cost per unit = Rs. (24,000 + 13,200 + 4,000 + 6,000 + 4,000) / 1,500 = Rs. 28.80
Profit = 25% of selling price
Selling price per unit = (28.80 / (1 - 0.25)) = Rs. 38.40
Total profit = (1,500 x 38.40 x 0.25) = Rs. 14,400
Therefore, the cost statement for the year 2021 shows a total profit of Rs. 14,400 and a selling price per unit of Rs. 38.40.
Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
complete the following table , what’s C, AC, BC
Answer:
C = 45
AC = 1
BC = 2
Step-by-step explanation:
C: 180 - (90 + 45) = 45
AC: Because the angles are the same, it is equal to the other leg, 1 cm
BC: a^2 + b^2 = c^2, so 1 + 1 = 2
x = 16 and y = 2, given that x is directly related to the square of y. If x = 100, what is one possible value of y?
Answer: 5
Step-by-step explanation:
Since x is directly related to the square of y, we can write the equation:
x = ky^2
where k is a constant of proportionality. We can solve for k using the given values of x and y:
16 = k(2^2) -> 16 = 4k -> k = 4
Now that we know k, we can use it to find y when x = 100:
100 = 4y^2 -> 25 = y^2 -> y = ±5
Since y cannot be negative, the only possible value of y is 5. Therefore, when x = 100, y could be 5.
Answer:
One possible value of y when x = 100 is y = 5.
Step-by-step explanation:
Using the direct variation formula, we know that x = ky^2, where k is a constant. Given that x = 16 and y = 2, we can solve for k:
16 = k(2)^2
k = 4
Now we can use this value of k to find y when x = 100:
100 = 4y^2
y^2 = 25
y = 5 or -5 (since the question only asks for one possible value, we can choose either solution)
Therefore, one possible value of y when x = 100 is y = 5.
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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CAN SOMEONE HELP WITH THIS QUESTION?
The number of cars that pass through the intersection between 6 am and 10 am is 4800.
To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].
Integrating r(t) with respect to t, we get:
∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C
where C is the constant of integration.
Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:
(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars
In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.
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Select the correct answer.
Credit cards and charge cards differ in two important ways. One is the method of payment. What is the other difference?
A. You can get a credit card from your bank but not a charge card.
в.
You have to pay interest on charge cards but not on credit cards.
C.
You have to pay interest on credit cards but not on charge cards.
A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
The volume of this rectangular prism is equal to: B. 8 in³.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;
Dimensions = 16 × (1/2)³ = 2inches.
By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 2 × 2 × 2
Volume of rectangular prism = 8 cubic inches.
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Complete Question:
A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
A. 2 in³
B. 8 in³
C. 16 in³
D. 32 in³
Question 3 of 5
What is the median of the data set?
7, 9, 11, 14, 18, 20, 30, 35
Answer:
16
Step-by-step explanation:
To find the median, we find the middle of the data set.
7, 9, 11, 14, 18, 20, 30, 35
There are 8 values
7, 9, 11, 14, 18, 20, 30, 35
The median is between the 4th and 5th numbers
We need to find the mean of the middle two numbers
(14+18)/2 =32/2= 16
Answer:
16
Step-by-step explanation:
Median means the middle term in a data set.Remember that, you have to arrange the data points from smallest to largest to find the median of a data set.The formula to find the median of a data set is:[tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]
Here,
n ⇒ number of terms
Let us find it now.
7, 9, 11, 14, 18, 20, 30, 35
[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]
In this case, add 4th and 5th data and divide it by 2.
[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]
1/3 divided by 2/9 simplified?
Answer:3/2
Step-by-step explanation:
1/3 ÷ 2/9=
1/3 ×9/2=3/2
Answer:
3/2 u can also do 1 1/2 their equivalent fractions
Step-by-step explanation:
sorry about the handwriting :) not the best
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
What is the image point of (-7,-8)after the transformation D1/2oT-1,0?
The image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
First, we apply the translation T-1,0, which moves every point 1 unit to the right (since the x-coordinate is decreased by 1) and leaves the y-coordinate unchanged. Therefore, the image of (-7,-8) under T-1,0 is (-7-1,-8) = (-8,-8).
Next, we apply the dilation D1/2, which scales every distance from the origin by a factor of 1/2. Therefore, the image of (-8,-8) under D1/2 is (-8/2,-8/2) = (-4,-4).
Thus, the image point of (-7,-8) after the transformation D1/2oT-1,0 is (-4,4).
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The equation x2 + y² - 6x + 2y = b describes a circle.
If the radius of the circle is 4 units, what is the value of b in the equation above?
Answer:
Step-by-step explanation:
given equation of a circle : x^2+y^2-6x+2y=b.
BY comparing it with x^2+y^2+2gx+2fy+c=0, we get
centre as (-g,-f)=(3,-1)
Since we know that radius r=sqrt(g^2+f^2-c)
Here radius is given as 4 units.
So,
4=sqrt((3)^2+(-1)^2-c)
=>16=9+1-c
Therefore, c=-6
For which distribution is the mode the best measure of center?
A. Skewed
B. Normal
C. Biomodal
Answer:
The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.
For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.
Please help me I am stuck at this thanks so much
Answer:
34.83/.9 = 38.7 g mass (after one hour)
38.7/.9 = 43 g (starting mass)
The starting mass of the ice cube was 43 grams.
Help is appreciated!
Answer:
Snacks: $75
Alcohol: $200
Dairy: $300
Average delivery charge per week: $63.89 (rounded to two decimal places)
Step-by-step explanation:
To find the average delivery charge the store pays each week, first calculate the total delivery cost for each category and then find the total cost for all deliveries. Finally, divide the total cost by the total number of deliveries.
Snacks:
3 deliveries * $25 per delivery = $75
Alcohol:
2 deliveries * $100 per delivery = $200
Dairy:
4 deliveries * $75 per delivery = $300
Total cost for all deliveries:
$75 (Snacks) + $200 (Alcohol) + $300 (Dairy) = $575
Total number of deliveries:
3 (Snacks) + 2 (Alcohol) + 4 (Dairy) = 9
Average delivery charge per week:
$575 (total cost) / 9 (total number of deliveries) = $63.89 (rounded to two decimal places)
Write an equation for a parabola with vertex (1,8) and directrix y = 3.
i Got u Bro!
Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.
What is the domain of the function shown on the graph?
Answer:
A
Step-by-step explanation:
the domain is the values of x covered by the graph
on the left the graph → - ∞
on the right the graph tends to + ∞
there are no excluded values of x on the domain , so
domain is - ∞ < x < ∞
A man earns $65000. He pays 18% of that in tax. (a) Calculate how much he has left, after paying the tax. (b) He invests $4500 and earns 6% interest per annum. Calculate the interest after 2 years. (c) He takes out a loan to buy a car. The price of the car is $24750. He pays $25740 altogether. What is the percentage interest?
a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
We have,
a)
The amount of tax the man pays.
= $65000 x 0.18
= $11700
Therefore, he has left.
= $65000 - $11700
= $53300
(b)
The interest earned after 2 years.
= $4500 x 0.06 x 2
= $540
(c)
The total amount of interest paid on the loan.
= $25740 - $24750
= $990
The percentage interest.
= ($990 / $24750) x 100%
= 4%
Thus,
(a) The amount left after paying the tax is $53300.
(b) The interest after 2 years is $540.
(c) The percentage interest is 4%.
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what are the answers to these 4? thank you.
The area of the different types of polygon with given dimensions are,
Area of octagon= 391.07 cm²
Area of pentagon = 232m²
Area of triangle = 21.22in²
Area of hexagon = 11.24square units.
Polygon name = octagon,
Side length = 9cm
Degree of central angle = 360° /8
= 45°
To find Apothem ,
draw right triangle .
base is half of the side length = 4.5
Top angle of the right triangle = (1/2) × 45°
= 22.5°
Using tangent ratio considering top angle as α
tanα = 4.5/ Apothem length
⇒Apothem length = 4.5 / tan22.5°
⇒Apothem length = 4.5 / (√2 - 1 )
⇒Apothem length = 4.5 / 0.414
⇒Apothem length = 10.86cm.
Area of octagon = 2 ( 1 + √2 ) × (side length)²
= 2 × 2.414 × 9²
= 391.07 cm²
Polygon name = Pentagon,
Apothem= 8m
Degree of central angle = 360° /5
= 72°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle = (1/2) × 72°
= 36°
Using tangent ratio considering top angle as α
tanα = half of side length /Apothem length
⇒(1/2) side length = 8 × tan36°
⇒ side length = 16 × (0.7265)
⇒ side length= 11.62m
Area of pentagon
= 5/2 × side length × distance from the center of sides to the center of pentagon
= 5/2 × 11.6 × 8
= 232m²
Polygon name = triangle,
Apothem= 2in
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =60°
Using tangent ratio considering top angle as α
tanα = half of side length / Apothem length
⇒(1/2) side length = 2 × tan60°
⇒ side length = 4 (√3)
⇒ side length= 6.928in
≈ 7 in
Area of triangle = √3/4 × 7²
= 21.22in²
Polygon name = hexagon,
Apothem= 5
Degree of central angle = 60°
To find Side length ,
Let 'x' be the side length
draw right triangle .
base is half of the side length = x/2
Top angle of the right triangle =30°
Using tangent ratio considering top angle as α
sinα = half of side length / Apothem length
⇒(1/2) side length = 5 × sin30°
⇒ side length = 10 (0.5)
⇒ side length= 5
distance from center of sides to the center of hexagon
= √5² - 2.5²
=4.33
Area = (3√3)/2 × distance from center of sides to the center of hexagon
= (3√3)/2 × 4.33
= 11.24square units.
Therefore, the area of the given polygon are octagon = 391.07 cm² , pentagon = 232m² , triangle = 21.22in² , and hexagon = 11.24square units.
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Find the length of each segment.
Answer:
1. 30; 2. 6.25.
Step-by-step explanation:
1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;
2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.
Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 24, 32, and 40 and a second triangle labeled D prime with side lengths of 6, 8, and 10 Determine the scale factor used. Scale factor of one half Scale factor of 4 Scale factor of 2 Scale factor of one fourth
The scale factor used is 1/4.
We have,
Length of sides of triangle D 24, 32, and 40.
Length of sides of triangle D' 6, 8, and 10.
So, scale factor
= length of corresponding side in D' / length of corresponding side in D
= 6/24
= 1/4
Thus, the scale factor used is 1/4.
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Determine the equation of the circle graphed below.
The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16
Determining the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (-4, -5)
Radius, r = 4 units
The equation of the circle graphed is represented as
(x - a)^2 + (y - b)^2 = r^2
So, we have
(x + 4)^2 + (y + 5)^2 = 4^2
Evaluate
(x + 4)^2 + (y + 5)^2 = 16
Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16
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The cost of 2 footballs and 3 tennis balls is £21.73.
The cost of 5 footballs and 7 tennis balls is £53.20.
Work out the cost of
a) a football.
b) a tennis ball.
Answer: A) £7.49
B) £2.25
Step-by-step explanation:
Step 1:
Let the cost of a football be [tex]f[/tex]and the cost of a tennis ball be [tex]t[/tex].
Step 2:
Write the 2 equations we have from the given information:
[tex]2f + 3t = 21.73[/tex] [tex] \textsf{(from the cost of 2 footballs and 3 tennis balls)} [/tex]
[tex]5f + 7t = 53.20[/tex] [tex] \textsf{(from the cost of 5 footballs and 7 tennis balls)} [/tex]
Step 3:
Solve for one variable in one of the equations. For example, we can solve for [tex]f[/tex]in the first equation:
[tex]2f + 3t = 21.73[/tex][tex]2f = 21.73 - 3t[/tex][tex]f = \frac{(21.73 - 3t)}{2}[/tex]Step 4:
Substitute this expression for [tex]f[/tex] into the second equation and solve for [tex]t[/tex]:
[tex]5f + 7t = 53.20[/tex][tex]5[\frac{(21.73 - 3t)}{2}] + 7t = 53.20[/tex][tex]54.325 - 7.5t + 7t = 53.20[/tex][tex]0.5t = 1.125[/tex][tex]t = 2.25[/tex]So, the cost of a tennis ball is £2.25.
Step 5:
Substitute this value of [tex]t[/tex] into the expression for [tex]f[/tex] and solve for [tex]f[/tex]:
[tex]f = \frac{(21.73 - 3t)}{2}[/tex][tex]f = \frac{(21.73 - 3(2.25))}{2}[/tex][tex]f = 7.49[/tex]So, the cost of a football is £7.49
Step 6:
Therefore, the cost of a football is £7.49 and the cost of a tennis ball is £2.25.
What is the circumference of a circle (to the nearest whole number) whose diameter is 12?
Answer: 3.14 is all ways the circumference
Step-by-step explanation:
Find the sum of x+9 and 7x^- 2x+1.
The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.
To find the sum of two expressions, we simply add their like terms.
The given expressions are x+9 and 7x²-2x+1.
The first expression has two terms - x and 9.
The second expression has three terms - 7x², -2x, and 1.
We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.
First, we can simplify the second expression by combining the like terms -2x and 1.
7x² - 2x + 1 = 7x² - (2x - 1)
Now, we can add the like terms from both expressions.
(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9
= 7x² - x + 10
Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.
(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1
= 7x² - x + 10
In either case, the final answer is 7x² - x + 10.
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marcus deposits $500 in an account that pays 6.8% simple annual interest. if he keeps the money in the account for 5 years how much interest will he earn
Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.
To calculate the interest Marcus will earn, we can use the formula:
I = P * r * t
where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.
In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.
So we can plug in these values into the formula:
I = 500 * 0.068 * 5
I = $170
This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.
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