After answering the presented question, we can conclude that the probability of 30 or more seconds between vehicle arrivals is approximately 0.082.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.
exponential probability distribution
[tex]P(X ≤ 12) = ∫[0,12] f(x) dx = ∫[0,12] (1/12) * e^(-x/12) d\\P(X ≤ 12) = [-e^(-x/12)] [0,12] = -e^(-1) + 1 ≈ 0.632\\P(X ≤ 6) = ∫[0,6] f(x) dx = ∫[0,6] (1/12) * e^(-x/12) dx\\P(X ≤ 6) = [-e^(-x/12)] [0,6] = -e^(-1/2) + 1 ≈ 0.393\\[/tex]
Therefore, the probability that the arrival time between vehicles is 6 seconds or less is approximately 0.393.
P(X ≥ 30) = 1 - P(X < 30) = 1 - P(X ≤ 30) = 1 - ∫[0,30] f(x) dx
[tex]= 1 - ∫[0,30] (1/12) * e^(-x/12) dx[/tex]
[tex]P(X ≥ 30) = 1 - [-e^(-x/12)] [0,30] = e^(-2.5) ≈ 0.082[/tex]
Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.082.
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The diameter of a circle is 5in. Find the length of its radius.
Can i please get help
The expression is equivalent to -4x²-3x-5
Define equationAn equation is a statement of equality between two mathematical expressions that contain variables and mathematical operations. The goal of solving an equation is to determine the value of the variable that make the equation true. For example, in the equation 2x + 5 = 11, the variable x is being multiplied by 2, added to 5, and then compared to the number 11. To solve for x, one must isolate the variable on one side of the equation by performing the same operation on both sides of the equation until the variable is alone on one side. The resulting value of x will make the equation true.
Given expression is:
-4x²+2x-5(1+x)
Solving the expression
-4x²+2x-5-5x
-4x²-3x-5
Hence, the expression is equivalent to -4x²-3x-5.
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The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the shape 13 cm 5.7 cm 16 cm 7.3 cm 6.2 cm
Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.
Explain about the features of rectangle:Each vertex of a rectangle has a 90° internal angle.The total of a rectangle's internal angles is 360°.The diagonals cut each other in half.The diagonals are all the same length.A rectangle is also referred to as a parallelogram since its sides are parallel.While all parallelograms are rectangles, not all rectangles are parallelograms.Given data:
Length of rectangle ABCD 'l' = 16 cmWidth of rectangle ABCD 'w' = 13 cmRemoved length AE = 7.3 cmPerimeter = sum of all sides:
The shaded portion in the figure shows the left over rectangle:
Perimeter of EFCD = EF + FC + CD + DE
ED = FC = 16 - 7.3 = 8.7
P = 8.7 + 13 + 8.7 + 13
P = 43.4 cm.
Thus, the perimeter of the left shape when length of rectangle ABCD is reduced to 7.3 cm is found as: P = 43.4 cm.
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complete question:
The shape below is formed from a rectangle measuring 13 cm by 16 cm from which a rectangle of length 7.3 cm has been removed. Work out the perimeter of the left shape.
Which point on the number line represents ?
B
A
D
C
Answer:
B = 1/2
A = 1/3
D = 2/3
C = 5/6
Step-by-step explanation:
B = 3/6 = 1/2
A = 2/6 = 1/3
D = 4/6 = 2/3
C = 5/6
ind the x-intercept and y-intercept of the line.
=+−6x4y21
Write your answers as exact values. Do not write your answers as ordered pairs.
x-intercept:
y-intercept:
The x-intercept is 21/5 and the y-intercept is -7/2 of the given line.
What is the x and y-intercept of a line?
In a two-dimensional Cartesian coordinate system, the x-intercept of a line is the point where the line crosses the x-axis, which means the value of y is zero at that point. The x-intercept can be found by setting y = 0 in the equation of the line and solving for x.
Given that we have to find the y-intercept and x-intercept
The given equation is:
5x - 6y = 21
The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero
Finding x-intercept:
To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.
Substitute y = 0 in a given equation
5x - 6(0) = 21
x = 21/5
Thus x-intercept is 21/5.
Finding y-intercept:
To find the y-intercept, plug 0 in for 'x' and solve for 'y'
Substitute x = 0 in a given equation
5(0) - 6y = 21
-6y = 21
-2y = 7
y = -7/2
Thus y-intercept is -7/2
hence, the x-intercept is 21/5 and the y-intercept is -7/2 of the given line.
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Complete question:
Find the y-intercept and x-intercept of the line. 5x-6y=21
Round 473,615 to the nearest hundred. O A. 473,610 B. 473,000 O c. C. 473,700 D. 473,600 E. 473.100
473,615 rounded to the nearest hundred is D. 473,600.
What is number rounding?Number rounding or approximation is the adjustment of the digits (up or down) to make rough calculations easier.
The result of number rounding is an estimated value rather than a precise one.
Number rounding or approximation are useful when the precise information is not required for decision-making.
473,615 = 473,600
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What was the equation of the graph below before it was shifted to the right 1
unit?
GD)-(x-1.5)-(x-1.5)
OA. G(x) = (x)3
OB. G(x) = (x-0.5)³-(x-0.5)
C. G(x) = (x-2)3-(x-2)
D. G(x) = (x-.5)³
The equation of the graph before it was shifted to the right one unit is given as follows:
B. G(x) = (x - 0.5)³ - (x - 0.5).
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function in this problem is defined as follows:
G(x) = (x - 1.5)³ - (x - 1.5).
To remove the effect of a shift right one unit, we must shift the graph left one unit, hence the original rule is given as follows:
G(x) = (x - 1.5 + 1)³ - (x - 1.5 + 1).
G(x) = (x - 0.5)³ - (x - 0.5).
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5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
7) ∠1≅∠4 on the basis of opposite angles.
8) ∠1≅∠3 on the basis of opposite angles.
9) ∠5≅∠7 on the basis of opposite angles.
What are the rules guiding opposite angles in geometry?Opposite angles in geometry are equal in measure. This is known as the "vertical angles theorem." In other words, if two lines intersect, the opposite angles formed by those lines will have the same degree of measurement.
7) since ∠1 = ∠2
and ∠3 = ∠4, then by the rule of the congruence of opposite angles, ∠1≅∠4
8) In the above shape, we can see that ∠1 and ∠3 are a opposite angles, hence, they are both equal or congruent.
9) The logic is the same for ∠5 and ∠7. The are opposites hence they are equal.
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Question 10
According to a study on the effects of smoking by pregnant women on rates of asthma in their
children, for expectant mothers who smoke 20 cigarettes per day, 22.7% of their children
developed asthma by the age of two in the US. A biology professor at a university would like to
test if the percentage is lower in another country. She randomly selects 341 women who only
deliver one child and smoke 20 cigarettes per day during pregnancy in that country and finds that 71 of the children
developed asthma by the age of two. In this hypothesis test,
20 points
the test statistic, z =
and the p-value =
(Round your answers to four decimal places.)
Type numbers in the boxes.
aby Part 1: 10 points
aby Part 2: 10 points
part1)Rounding to four decimal places, the test statistic is z = -1.7918. part2) Rounding to four decimal places, the p-value is p = 0.0728.
what is decimal places ?
Decimal places refer to the number of digits to the right of the decimal point in a decimal number. For example, in the decimal number 3.14159, there are 5 decimal places, with the digit 1 being in the first decimal place, the digit 4 being in the second decimal place, and so on.
In the given question,
Part 1:
To calculate the test statistic, we use the formula:
z = (p - P) / √[(P(1-P))/n]
where p is the sample proportion (71/341 = 0.2082), P is the hypothesized proportion (0.227), n is the sample size (341).
z = (0.2082 - 0.227) / √[(0.227 * 0.773)/341]
z = -1.7918
Rounding to four decimal places, the test statistic is z = -1.7918.
Part 2:
To calculate the p-value, we use a standard normal distribution table or a calculator. Since this is a two-tailed test, we calculate the area in both tails of the distribution.
Using a calculator or a standard normal distribution table, we find that the area to the left of z = -1.7918 is 0.0364. Therefore, the area in the right tail is also 0.0364.
Thus, the p-value is 2*0.0364 = 0.0728.
Rounding to four decimal places, the p-value is p = 0.0728.
Therefore, we would fail to reject the null hypothesis at the 0.05 significance level since the p-value is greater than the level of significance. We do not have enough evidence to suggest that the percentage of children who develop asthma by age two for expectant mothers who smoke 20 cigarettes per day during pregnancy is lower in this other country compared to the US.
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Three distinct, five-sided dice are rolled, and the numbers showing are recorded. How many different outcomes are possible
Answer:
Step-by-step explanation:
Each die can show one of the five possible numbers. So, the number of possible outcomes for rolling one die is 5.
Since there are three dice being rolled, the total number of possible outcomes is the product of the number of possible outcomes for each die. That is:
Number of possible outcomes = 5 x 5 x 5 = 125
Therefore, there are 125 different outcomes possible when rolling three distinct, five-sided dice.
Suppose that 17 inches of wire costs 85 cents. At the same rate, how many inches of wire can be bought for 65 cents?
Answer:
13 inches
Step-by-step explanation:
17=85
1=85/17
1=5
Now
For 65 cents,
65=nx5
65/5=n
n=13 inches
Answer: 13 inches
Step-by-step explanation:
To solve this problem you would need to make a ratio.
A Ratio can be the symbol, : , / or the word to.
In this case you would need to do the problem as shown:
17/85 = x/65
First you would need to cross multiply, then flip the equation. And should end up with something like this:
85x =1105
Then Divide both sides by 85.
85x/85 = 1105/85
Answer:
X= 13
Se utilizan 3/5 de la capacidad de un camión para transportar sacos de papa. Un tercio de los sacos de papas son de papas chilotas y el resto es papas pukará. El resto del cargamento se divide en partes iguales entre lechugas y zapallos
¿Qué producto ocupa más capacidad?
Graph the piecewise-defined function
option D is correct answer As we can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0
what is exponential curve?
An exponential curve is a mathematical curve that rises or falls at an increasing rate as its values get larger. The curve is defined by an exponential function
In the given question,
To graph this function, we can start by plotting the points for different values of x. Since the function behaves differently for x <= 0 and x > 0, we will plot the points separately for each region.
For x <= 0:
x g(x)
-2 4
-1 1
0 0
For x > 0:
x g(x)
0.5 e⁰⁵ = 1.65
1 e = 2.72
2 e²= 7.39
x <= 0 x > 0
As you can see, the graph is a parabola for x <= 0 and an exponential curve for x > 0. The function is continuous, but not differentiable at x = 0 because the derivative from the left and the derivative from the right do not match.
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Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 8% interest for 30 years.
Your existing mortgage (the one you got 10 years ago)
How much money did you pay as your down payment?
$Correct
11,000
Correct Question 2. Points: 1 out of 1 possible.
How much money was your existing mortgage (loan) for?
$Correct
99,000
Partially correct Question 3. Points: 1 out of 3 possible.
What is your current monthly payment on your existing mortgage?
$Correct
724.96
Note: Carry at least 4 decimal places during calculations, but round your final answer to the nearest cent.
Untried Question 4 Points: 0 out of 2 possible. 2 available on this attempt.
How much total interest will you pay over the life of the existing loan?
Answer:
monthly payment: $726.43interest paid: $162,513.69Step-by-step explanation:
You want to know the monthly payment on a 30-year loan of $99,000 at 8%, and the total interest paid.
PaymentThe monthly payment is given by the amortization formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where P is the loan amount, r is the annual interest rate, and t is the loan period in years
A = $99000(0.08/12)/(1 -(1 +0.08/12)^(-12·30)) ≈ 726.42692814058
The monthly payment is $726.43.
Interest paidThe total of monthly payments is about 360 times the "exact" value of the monthly payment. There is always a slight adjustment made in the last payment to account for the fact that the payment value is always rounded. We can approximate that adjustment by using the "exact" monthly payment amount: $726.42693
The interest paid is the difference between the total of payments and the original loan amount:
I = 360×$726.42693 -99000 ≈ $162,513.69
The total interest paid is about $162,513.69.
__
Additional comment
If you use 360 times the monthly payment of $726.43, you will compute the interest paid as $162,514.80.
If you compute the future value of the loan after 360 payments of $726.43, you will find it is $4.58. This means the last payment will be $726.43 -4.58 = $721.85, and the total of payments will be $261,510.22, which includes $162,510.22 in interest.
If you make an amortization schedule, where interest is rounded every month (as in "real life"), the result will be different from any of these values. It is $162,510.63. (The last payment is $722.26.)
The upshot is that the amount you determine for total interest paid will depend on the method you use to determine it.
There is a card under 30% of the chairs at a booster meeting. Finn wants to find the probability that the first card he finds will be under the third chair that he checks. He generates 10 sets of random numbers from 1 to 10. The numbers 1-3 represent a chair with a card and 4-10 represent a chair without a card. Complete the table, and find the experimental probability of the event.
The experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%
How to find the experimental probability of the event?The experimental probability of finding a card is 30%. The complete table is given below:
Trial Numbers Generated Chairs Checked
1 6,5,1 No Card, No Card, Card
2 8,1 No Card, Card
3 10,1 No Card, Card
4 7,8,4,1 No Card, No Card, No Card, Card
5 9,3 No Card, Card
6 5,4,2 No Card, No Card, Card
7 3 Card
8 9,5,8,2 No Card, No Card, No Card, Card
9 7,3 No Card, Card
10 9,6,8,4,7,3 No Card, No Card, No Card, No Card, No Card, Card
The probability that the first card he finds will be under the third chair that he checks is calculated by taking the total number of trials in which the third chair had a card (3) and dividing it by the total number of trials (10).
The table can be completed by generating 10 sets of random numbers from 1 to 10 and checking the first three numbers in each set. If the first number is between 1 and 3, then the first chair has a card. If the second number is between 1 and 3, then the second chair has a card. If the third number is between 1 and 3, then the third chair has a card. If none of the first three numbers are between 1 and 3, then there are no cards in the first three chairs
Out of the 10 trials, 4 have a card under the third chair. Therefore, the experimental probability of finding a card under the third chair is 4/10 or 2/5, which is 0.4 or 40%.
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Anyone pls help me do this equation
Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.
What is polynomials?Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.
After Abby spent $37, she had A - 37 dollars left. After Nicky spent $61, she had N - 61 dollars left. We also know that after Abby spent $37, she had 3 times as much money as Nicky. So we can set up an equation:
A - 37 = 3(N - 61)
Substituting A = N from the earlier equation, we get:
N - 37 = 3(N - 61)
Expanding the brackets, we get:
N - 37 = 3N - 183
Simplifying and solving for N, we get:
2N = 146
N = 73
Therefore, Nicky had $73 initially. Since Abby had the same amount, Abby also had $73 initially.
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HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
The total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².
The shape described in the problem is a trapezoid. The formula to calculate the area of a trapezoid is:
[tex]Area = (base1 + base2) x height / 2[/tex]
We are given the following measurements:
Base1 = 21.3 yards
Height = 12.8 yards
A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards, which is a part of the base2.
A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards, which is the remaining part of the base2.
To calculate the missing part of base2, we subtract the known parts of base2 from the total length of the top, which is:
21.3 - 6.4 - 14.9 = 0
This means that the missing part of base2 is zero, and the trapezoid becomes a rectangle. Therefore, the area of the trapezoid is equal to the area of the rectangle, which is:
Area = base x height
Area = 21.3 x 12.8
Area = 272.64 square yards
Therefore, the total area of the figure is 272.64 yd². Hence the correct option is (a) 272.64 yd².
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The school athletics department is raising money for new gym equipment. To raise $7,200 by spring training, the department decides to sell T-shirts during the fall semester. Based on previous fundraising drives, the expression
–
10p+560 can be used to gauge how many shirts the department will sell depending on the price of a shirt, p.
What is the lowest shirt price the athletics department can use to raise exactly $7,200 in revenue?
Charlie is playing a boardgame she is rolling two number cubes.
How many outcomes are possible?
Create an outcome chart to prove your answer
In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.
Find the point estimate for the proportion parameter for this population. Write your answer as a decimal rounded to three decimal places.
O 0.305
O 0.695
O 0.272
O 0.50
4
The point estimate for the proportion parameter for this population is A)0.305.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
In a random sample of 892 college students in the United States, 272 say they skip at least one class per week.
From the given information then,
Sample size n = 892
No of favorable outcomes (i.e successes) x=272
We know ,
The point estimate for the population parameter [tex]\hat P[/tex]=x/n.
Where n=sample size , x=number of success.
Here x = 272 ,n=892 then
The point estimate for the proportion parameter for this population then,
=> [tex]\hat p[/tex] = 272/892 = 0.305.
Hence the point estimate for the proportion parameter for this population is A)0.305.
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What does 2y plus 5 equal
Answer:
[tex]-\frac{5}{2}[/tex] or -2.5
Step-by-step explanation:
1) [tex]2y + 5 = 0[/tex]
2) Move 5 over to the other side by subtracting
[tex]2y = -5[/tex]
3) Divide both sides by 2 so y is alone
[tex]y = -\frac{5}{2}[/tex]
help?? would really appreciate it! (i highly dislike being bad at math)
Step-by-step explanation:
Put both of the equations into y = mx + b form to compare them
m = slope if they have the same slope they are parallel and do not intersect
b = y axis intercept
if m and b are equal in each of the equations , they are the same line
2x+y = 0 ======> y = - 2x + 0
2y = -4x + 6 ====> y = - 2x + 3
The both have the same slope = -2 so they are parallel
but they have different b values so they are not the same lines
No intersection means no solution : parallel lines do not intersect
Use the 2020 Federal Tax Rates for Individuals to calculate the estimated taxes for a taxable income of $63,700.
Tax rate
10%
12%
22%
24 %
32%
35%
37%
2020 Federal Tax Rates for Individuals
Taxable Income Bracket
$0 to $9875
$9876 to $40,125
$40,126 to $85,525
$85,526 to $163,300
$163,301 to $207,350
$207,351 to $518,400
$518,401 or more
The estimated taxes for a taxable income of $63,700 using the 2020 Federal Tax Rates for Individuals is $9,804.00.
How the estimated taxes are determined:The estimated taxes for an individual with a taxable income of $63,700 for the fiscal year uses the progressive tax (graduated) system of the Federal Tax Rates for Individuals, as computed below.
Taxable Income for 2020 = $63,700
2020 Federal Tax Rates for Individuals:Tax rate Taxable Income Bracket Tax Payable
10% $0 to $9875 $987.50 ($9,875 x 10%)
12% $9876 to $40,125 $3,630.00 ($30,250 x 12%)
22% $40,126 to $85,525 $5,186.50 ($23,575 x 22%)
Estimated taxes $9,804.00
Thus, an individual whose taxable income is $63,700 in 2020 is expected to pay taxes amounting to $9,804.00.
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PLEASE HELP. company is going to make an oil container in the shape of a cylinder. As shown below, the container will have a height of 7m and a diameter of 8m. The container will be made from steel (including its top and bottom). If the steel costs 29$ for each square meter, how much will the steel cost in total? Use 3.14 for pi , and do not round your answer.
The container will be 7 meters high and 8 meters in diameter. Steel will be used to make the container (including its top and bottom). If a square meter of steel costs 29 dollars, the total cost of the steel will be $5,467.60.
The cylinder has a diameter of 8m and a height of 7m, which means the radius of the cylinder is 4m (half of the diameter).
The surface area of a cylinder is calculated as follows:
SA = 2πr² + 2πrh
where h is the cylinder's height and r is the radius.
Plugging in the values we get:
SA = 2 x 3.14 x 4² + 2 x 3.14 x 4 x 7
SA = 100.48 + 87.92
SA = 188.4 square meters
So, the surface area of the cylinder is 188.4 square meters.
If the steel costs $29 per square meter, then the cost of the steel for the cylinder would be:
Cost = 188.4 x $29
Cost = $5,467.60
Therefore, the cost of the steel for the cylinder would be $5,467.60.
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Allan needs to repay a $3000 loan. His bank offers personal loans at 9.5% per year, compounded monthly. Allan can afford to make monthly payments of $100. How long will it take him to repay the loan?
It will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.
What is interest rate?Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.
According to question:To calculate the time it takes for Allan to repay the loan, we can use the formula for the present value of an annuity:
PV = PMT x (1 - [tex](1 + r)^-n[/tex]) / r
where:
PV = present value
PMT = monthly payment
r = monthly interest rate (9.5% per year / 12 months = 0.00791667)
n = number of months
Plugging in the given values, we get:
3000 = 100 x (1 - (1 + 0.00791667)[tex]^-n[/tex]) / 0.00791667
Simplifying and solving for n, we get:
n = -ln(1 - (3000 x 0.00791667 / 100)) / ln(1 + 0.00791667)
n = 37.4 months
Therefore, it will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.
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Square
G
(x²-8)
meters
x meters
*.
...
What expression represents the total area of the
shaded figure. Simplify your expression.
The total area of the shaded portion is (x² - 16)(x²- 1) square meters.
What is a square?Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.
Equation:The area of the outer square is (x² - 8)², and the area of the inner square is x². Therefore, the area of the shaded region can be found by subtracting the area of the inner square from the area of the outer square:
Area of shaded region = Area of outer square - Area of inner square
= (x² - 8)² - x²
Expanding the first term using the formula for the square of a binomial, we get:
Area of shaded region = (x⁴ - 16x² + 64) - x²
= x⁴ - 17x² + 64
Therefore, the expression that represents the total area of the shaded figure is x⁴ - 17x² + 64, which can be simplified by factoring:
x⁴ - 17x² + 64 = (x² - 16)(x² - 1)
So the simplified expression for the total area of the shaded figure is (x² - 16)(x²- 1).
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I need help with this ( Q7 to Q12 )
The values of the composite function are (f + g)(x) = 2x² + 3x - 2, (f - g)(x) = -2x² + 3x - 8, (f . g)(x) = 6x³ + 4x² - 15x - 15, (f o g)(x) = 6x² + 4, (g o f)(x) = 18x² - 60x + 53, (f o g)(3) = 58
What are the values of the composite functionsTo determine the values of the composite functions, we have to evaluate or simplify each as
7. (f + g)(x) = f(x) + g(x) = (3x - 5) + (2x² + 3) = 2x² + 3x - 2
8. (f - g)(x) = f(x) - g(x) = (3x - 5) - (2x² + 3) = -2x² + 3x - 8
9. (f . g)(x) = f(x) * g(x) = (3x - 5) * (2x² + 3) = 6x³ + 4x² - 15x - 15
10. (f o g)(x) = f(g(x)) = f(2x² + 3) = 3(2x² + 3) - 5 = 6x² + 4
11. (g o f)(x) = g(f(x)) = g(3x - 5) = 2(3x - 5)² + 3 = 18x² - 60x + 53
12. (f o g)(3) = f(g(3)) = f(2(3)² + 3) = f(21) = 3(21) - 5 = 58
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If a town with a population of 8,380 doubles in size every 77 years, what will the population
be 462 years from now?
It might just be 536320
Which measurement is not equal to one mile
Answer:
B
Step-by-step explanation:
5280 yards does not equal one mile
Answer
B.5,280
Step-by-step explanation:
Im just smart like that
Madelyn is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop?
45 points
We can use the multiplication principle of counting to find the total number of possible outcomes.
Since there are 5 options on the first spinner, 6 options on the second die, and 3 options on the third spinner, there are a total of:
5 x 6 x 3 = 90
different possible outcomes.
Therefore, there are 90 different possible outcomes if Madelyn spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday, rolls a fair die in the shape of a cube that has six sides labeled 1 to 6, and spins a spinner with three equal-sized sections labeled Walk, Run, Stop.
Answer:
what is biology and types