he two numbers that multiply to -35 and add to get -18 are -5 and 3.
To see why, you can use the factoring method. First, find two numbers that multiply to give you -35. The factors of -35 are -1, 1, -5, and 5. So, the two numbers that multiply to -35 are either -5 and 7 or 5 and -7.
Next, find which pair of numbers adds up to -18. It's clear that 5 and -7 add up to -2, so they don't work. However, if we choose -5 and 3, we get:
-5 + 3 = -2
So, -5 and 3 are the two numbers that multiply to -35 and add to -18.
PLEASE ANSWER THIS ILL GIVE BRAINLIEST
Answer:
Step-by-step explanation:
The equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.The price for t-shirts = $12 eachThe price for the sweatshirt = $15 eachLet's suppose x number of t-shirts and y number of sweatshirts bought.Then,12x + 15y = 120The equation represents the total number of t-shirts and sweatshirts bought if spend $120Thus, the equation 12x + 15y = 120 represents the total number of t-shirts and sweatshirts bought if spend $120
1. Find the Fourier series of the given function f (x), which is assumed to have the period
2π. Show the details of your work.
() = { , − < < 0
− , 0 < <
Answer:
The given function f(x) is:
f(x) = { 1, -π < x < 0
{ -1, 0 < x < π
Since the function is odd and has period 2π, the Fourier series will only have sine terms. The Fourier series of f(x) can be written as:
f(x) = Σ[b_n sin(n x)], where n >= 1
where b_n is the n-th Fourier coefficient, given by:
b_n = (1/π) ∫[0,π] f(x) sin(n x) dx
We can evaluate the integral to find the Fourier coefficients:
b_n = (1/π) ∫[0,π] f(x) sin(n x) dx
= (1/π) [ ∫[0,π/2] sin(n x) dx - ∫[π/2,π] sin(n x) dx ]
= (1/π) [ -cos(n x)/n |[0,π/2] + cos(n x)/n |[π/2,π] ]
= (1/π) [ (-cos(n π/2)/n + 1/n) - (cos(n π) - cos(n π/2))/n ]
= (1/π) [ (1 - (-1)^n) / n ]
Therefore, the Fourier series of f(x) is:
f(x) = Σ[(1 - (-1)^n)/(n π) sin(n x)]
Where the sum is taken over all odd integers n.
If a-1/a=7 what find the value of a4+1/a4
Question is below ⬇️.
Answer:
b.59
Step-by-step explanation:
this is the answer of whats you want
Line G passes through the point (7,11) and is parallel to the line given by y = 4(3x + 2). What is the equation of line G? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
Answer:
y = 12x - 73
Step-by-step explanation:
Pre-SolvingWe are given the line y=4(3x+2).
We want to find the equation of line G, which contains the point (7,11), and is parallel to y=4(3x+2) in the form y=mx+c. m is the slope, and c is the value of y at the y-intercept.
Parallel lines have the same slopes. So, we should start by finding the slope of y=4(3x+2).
SolvingWe can do the distributive property to distribute the 4 to both terms on the right side.
y=4(3x+2) => y=12x + 8
Notice how this equation is written in the form y=mx+c. As 12 is written in the place where m is, the slope of this line is 12.
It is also the slope of line G.
We can replace m in y=mx+c with 12 for line G. We'll get:
y=12x + c
Now, we need to find c.
We can use the point (7,11) to help us find c.
Substitute 7 for x and 11 for y.
11 = 12(7) + c
Multiply.
11 = 84 + c
Subtract 84 from both sides
-73 = c
Substitute -73 as c.
y = 12x - 73
Lou Barlow, a divisional manager for Sage Company, has an opportunity to manufacture and sell one of two new products for a five-year period. His annual pay raises are determined by his division’s return on investment (ROI), which has exceeded 22% each of the last three years. He has computed the cost and revenue estimates for each product as follows:
Product A Product B
Initial investment:
Cost of equipment (zero salvage value) $ 340,000 $ 540,000
Annual revenues and costs:
Sales revenues $ 380,000 $ 460,000
Variable expenses $ 170,000 $ 206,000
Depreciation expense $ 68,000 $ 108,000
Fixed out-of-pocket operating costs $ 86,000 $ 66,000
The company’s discount rate is 20%.
Required:
1. Calculate the payback period for each product.
2. Calculate the net present value for each product.
3. Calculate the internal rate of return for each product.
4. Calculate the profitability index for each product.
5. Calculate the simple rate of return for each product.
6a. For each measure, identify whether Product A or Product B is preferred.
6b. Based on the simple rate of return, which of the two products should Lou’s division accept?
The payback period for Product A is 2.21 years and the payback period for Product B is 1.85 years, NPV of A = $21,215 and NPV of B = -$50,256. Product A: IRR = 28.28%, Product B: IRR = 29.58%, A: PI = 1.00, B: PI = 0.91, A: SRR = 0.49 or 49%, B: SRR = 0.44 or 44%.
What is payback period?Payback period is a financial metric used to evaluate the time required to recover the initial investment made in a project or investment opportunity.
According to given information:To calculate the payback period, we need to find out how long it takes for the initial investment to be recovered by the annual cash inflows. We calculate the cumulative cash inflows for each year and determine in which year the cumulative cash inflows exceed the initial investment.
Product A:
Year 1: $380,000 - $170,000 - $68,000 - $86,000 = $56,000
Year 2: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $56,000 = $112,000
Year 3: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $112,000 = $168,000
Year 4: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $168,000 = $224,000
Year 5: $380,000 - $170,000 - $68,000 - $86,000 = $56,000 + $224,000 = $280,000
The payback period for Product A is 2.21 years (rounded to two decimal places).
Product B:
Year 1: $460,000 - $206,000 - $108,000 - $66,000 = $80,000
Year 2: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $80,000 = $160,000
Year 3: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $160,000 = $240,000
Year 4: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $240,000 = $320,000
Year 5: $460,000 - $206,000 - $108,000 - $66,000 = $80,000 + $320,000 = $400,000
The payback period for Product B is 1.85 years (rounded to two decimal places).
To calculate the net present value (NPV), we need to discount the cash inflows and outflows using the company’s discount rate of 20% and then subtract the initial investment.
Product A:
[tex]NPV = -$340,000 + ($56,000/(1+0.20)^1) + ($112,000/(1+0.20)^2) + ($168,000/(1+0.20)^3) + ($224,000/(1+0.20)^4) + ($280,000/(1+0.20)^5)[/tex]
NPV = -$340,000 + $38,611 + $64,357 + $79,396 + $81,193 + $77,658
NPV = $21,215
Product B:
[tex]NPV = -$540,000 + ($80,000/(1+0.20)^1) + ($160,000/(1+0.20)^2) + ($240,000/(1+0.20)^3) + ($320,000/(1+0.20)^4) + ($400,000/(1+0.20)^5)[/tex]
NPV = -$540,000 + $66,667 + $111,111 + $114,882 + $99,425 + $97,659
NPV = -$50,256
To calculate the internal rate of return (IRR), we need to find the discount rate that makes the NPV of the cash inflows and outflows equal to zero. We can use a financial calculator or spreadsheet software to solve for the IRR.
Product A: IRR = 28.28%
Product B: IRR = 29.58%
To calculate the profitability index (PI), we divide the present value of the future cash inflows by the initial investment.
Product A:
PV of future cash inflows = $38,611 + $64,357 + $79,396 + $81,193 + $77,658 = $341,215
PI = $341,215/$340,000
PI = 1.00
Product B:
PV of future cash inflows = $66,667 + $111,111 + $114,882 + $99,425 + $97,659 = $489,744
PI = $489,744/$540,000
PI = 0.91
To calculate the simple rate of return (SRR), we divide the average annual cash inflow by the initial investment.
Product A:
Average annual cash inflow = ($56,000 + $112,000 + $168,000 + $224,000 + $280,000)/5 = $168,000
SRR = $168,000/$340,000
SRR = 0.49 or 49%
Product B:
Average annual cash inflow = ($80,000 + $160,000 + $240,000 + $320,000 + $400,000)/5 = $240,000
SRR = $240,000/$540,000
SRR = 0.44 or 44%
6a.
Based on the payback period, Product B is preferred because it has a shorter payback period of 1.85 years compared to Product A’s payback period of 2.21 years.
Based on the net present value, Product A is preferred because it has a positive NPV of $21,215 compared to Product B’s negative NPV of -$50,256.
Based on the internal rate of return, Product B is preferred because it has a higher IRR of 29.58% compared to Product A’s IRR of 28.28%.
Based on the profitability index, Product A is preferred because it has a PI of 1.00, indicating that for every dollar invested, we receive one dollar in return. Product B has a PI of 0.91, indicating that for every dollar invested, we receive only $0.91 in return.
Based on the simple rate of return, Product A is preferred because it has a higher SRR of 49% compared to Product B’s SRR of 44%.
6b. Based on the simple rate of return, Lou’s division should accept Product A because it has a higher SRR of 49% compared to Product B’s SRR of 44%. However, other measures such as the net present value and internal rate of return suggest that Product A may not be the best choice.
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A rectangular prism shaped shipping container is 1014 inches wide, 1512 inches long, and 2012 inches tall.
What is the volume of the shipping container in cubic inches?
Responses
4614 in³
46 and 1 fourth, in³
15878 in³
158 and 7 eighths, in³
3000116 in³
3000 and 1 sixteenth, in³
32561516 in³
The volume of shipping container is calculated as:
c. 3000116 in³ 3000 and 1 sixteenth, in³
How to Find the Volume if Rectangular Prism Shipping Container?The shipping container in this problem has a shape of rectangular prism. To find it's volume, we will apply the formula for the volume of a rectangular prism which is given as:
Volume = length × width × height.
Given the parameters of the shipping container as:
Length = 1512 inches
Width = 1014 inches
height = 2012 inches
Plug in the values:
volume of shipping container = 1512 × 1014 × 2012
= 3.08473402e9 cubic inches.
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A boat traveled 189 miles downstream and back. The trip downstream took 9 hours. The trip back took 63 hours. Find the speed of the boat in still water and the speed of the current
The speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.
To find the speed of the boat in still water and the speed of the current, let's follow these steps:
Step 1: Let x represent the speed of the boat in still water, and y represent the speed of the current. The speed downstream is (x + y) and the speed upstream is (x - y).
Step 2: Use the formula distance = time × speed to write two equations based on the given information.
Downstream: 9(x + y) = 189
Upstream: 63(x - y) = 189
Step 3: Simplify both equations:
Downstream: x + y = 21 (divide both sides by 9)
Upstream: x - y = 3 (divide both sides by 63)
Step 4: Solve the system of equations by adding the two simplified equations:
2x = 24
x = 12
Step 5: Plug the value of x back into either equation to solve for y:
12 + y = 21
y = 9
So, the speed of the boat in still water (x) is 12 mph, and the speed of the current (y) is 9 mph.
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HELP PLEASE ILL GLADLY APPRECIATE IT.
The number line that shows the position of each country is added as an attachment
Completing the number lineFrom the question, we have the following parameters to create the number line
Panama = 4 * 10⁶Peru = 3.2 * 10⁷Thailand = 7 * 10⁷See attachment for the label of each tick as a multiple of the power of 10⁷
Next, we represent each country on the number line
See attachment for the completed number line
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Select the correct answer.
If f(x) = 2x²-x-6 and g(x) = x2 - 4, find f(x) + g(x).
Answer: The answer is C
Answer:
C. (2x+3)/(x+2)
Step-by-step explanation:
You want the expression representing f(x)/g(x) where f(x) = 2x² -x -6 and g(x) = x² -4.
SimplifyThe ratio of the functions can be simplified by canceling common factors.
[tex]\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}=\dfrac{(x-2)(2x+3)}{(x-2)(x+2)}=\boxed{\dfrac{2x+3}{x+2}}\qquad\text{matches choice C}[/tex]
<95141404393>
Calculate the product
20 (-15)
Answer:
Step-by-step explanation:
Product means multiply.
-300
Suppose we have a binomial random variable X with probability p. The probability of exactly 3 successes in 8 trials is {8}C{3}(p)^(3)(.45)^(5)
. What is the mean and standard deviation of X?
We may still infer something about their connection, though: the mean function and standard deviation both rise as p approaches 0.5, peaking at their highest levels at p = 0.5.
what is function?Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
A binomial distribution's mean or anticipated value is determined by the formula = np, where n is the number of trials and p is the success probability. The mean is = 8p in this instance since n = 8 and p is a parameter.
The formula for a binomial distribution's standard deviation is = sqrt(np(1-p)). We obtain = sqrt(8p(1-p)) using the same numbers as previously.
So, for this particular issue, we have:
Mean: μ = 8p
[tex]\Sqrt(8p(1-p))[/tex] is the standard deviation.
Since p is unknown, we are unable to determine the actual mean and standard deviation. We may still infer something about their connection, though: the mean and standard deviation both rise as p approaches 0.5, peaking at their highest levels at p = 0.5.
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1. A bag contains 10 red balls and 6 white balls, all with the same size. Randomly choose two balls one after the other without replacement. Find the probability that both are red balls.
2. Is the event likely or unlikely to occur? Explain why or why not?
Answer: 1. the probability of both balls being red is 3/8 or 0.375. 2.unlikely to occur
Step-by-step explanation:
Answer:
62.50
Step-by-step explanation:
The event is more likely to occur because there are 4 more red balls than white balls. The probability of 2 white balls selected are 37.50, which means that the probability of 2 red balls selected are 62.50.
Doug has 8 square pieces of wood. Each piece of wood has a side length of s centimeters. The total area of all eight pieces of wood is 200 square centimeters. Create a quadratic equation Dounfg can use to find the side length of each piece of wood.
Answer:
The area of a square is given by the formula A = s^2, where s is the side length. If Doug has 8 square pieces of wood, each with a side length of s centimeters, the total area of all the pieces can be expressed as:
8s^2 = 200
To solve for s, we can simplify the equation by dividing both sides by 8:
s^2 = 25
Now we can create a quadratic equation by subtracting 25 from both sides:
s^2 - 25 = 0
This is a quadratic equation in standard form, where the coefficient of the squared term is 1, the coefficient of the linear term is 0, and the constant term is -25. Doug can use this equation to find the side length of each piece of wood by solving for s using methods such as factoring, completing the square, or using the quadratic formula.
A new truck was purchased for $58,000. Each year after the truck was purchased, its value decreased by approximately seven-eighths. What is the value of the truck 12 years after
purchase?
Answer:
Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.
Step-by-step explanation:
To find the value of the truck after 12 years, we need to apply the seven-eighths decrease to the original value each year. Let's set up an equation:
Value after 12 years = $58,000 x (7/8)^12
Simplifying, we get:
Value after 12 years = $58,000 x 0.028
Value after 12 years = $1,624
Therefore, the value of the truck 12 years after it was purchased is approximately $1,624.
rechna notices her car driving at 40km/hr and knows that at that speed she will reach home in 2 hours if she wants to reach her home only in an half hour by what percentage does she need to increase her speed choose the correct answer 50%,100%,200%,400%
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.
What is speed?Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.
To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.
If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.
By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.
Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.
The time taken to reach her destination while travelling at her initial speed is 2 hours.
To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.
Therefore, the percentage increase in speed
= (30/120) x 100
= 25%.
Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.
To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.
Therefore, the correct answer is 200%.
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Tanner has a total of $2,250 to put into two different accounts.
He deposited $1,100 into one account that pays 3% compounded annually.
He deposited $1,150 into one account that pays 7.5% simple interest.
What will be the balance Tanner will have in the two accounts at the end of 7 years? (Round to the nearest cent)
At the end of 7 years, Tanner will have a total balance of approximately $3,101.29 in the two accounts.
For the first account with a principal of $1,100 and an annual interest rate of 3% compounded annually, we can use the compound interest formula:
Future Value (FV) = P * (1 + r)^n
where P is the principal, r is the annual interest rate (as a decimal), and n is the number of years.
FV1 = $1,100 * (1 + 0.03)^7
FV1 ≈ $1,100 * (1.03^7)
FV1 ≈ $1,100 * 1.22504
FV1 ≈ $1,347.54
For the second account with a principal of $1,150 and an annual interest rate of 7.5% simple interest, we can use the simple interest formula:
Future Value (FV) = P + P * r * n
where P is the principal, r is the annual interest rate (as a decimal), and n is the number of years.
FV2 = $1,150 + $1,150 * 0.075 * 7
FV2 = $1,150 + $1,150 * 0.525
FV2 = $1,150 + $603.75
FV2 ≈ $1,753.75
Now we add the future values of both accounts together:
Total Balance = FV1 + FV2
Total Balance ≈ $1,347.54 + $1,753.75
Total Balance ≈ $3,101.29
The functions f(x) = 500(1.015)* and g (x) =
500(1.021)* give the total amounts in two different savings accounts after x years. How do the graphs of f(x) and g(x) compare?
A. They have the same y-intercept, but the graph of f(x) rises more quickly over time.
B. They have the same y-intercept, but the graph of g(x) rises more quickly over time.
C. The function f(x) has a greater -intercept and rises more quickly over time.
D. The function g(x) has a greater -intercept and rises more quickly over time.
The graphs of functions f(x) and g(x) compare as -
Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The function f(x) is given as [tex]f(x)=500(1.015)^x[/tex].
The function f(x) is given as [tex]g(x)=500(1.021)^x[/tex].
The y-intercept of both functions is 500, which represents the initial amount in the savings accounts.
To compare the rates at which the functions rise over time, we need to compare their growth factors, which are 1.015 and 1.021 for f(x) and g(x), respectively.
Since 1.021 is greater than 1.015, the function g(x) grows at a faster rate than f(x).
Therefore, the correct answer is -
Option B: They have the same y-intercept, but the graph of g(x) rises more quickly over time.
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Real-life Problems Question 10
Answer :
a) It is given that
Everyday a machine makes 500000 staples and puts them into the boxes.
The machine need 170 staples to fill a box
One box contans = 170 staples.
Total number of staples = 500000
Number of box required to fill 500000 staples = Total number of staples/No. of staples 1 box contains.
[tex] \: :\implies [/tex] 500000 /170
[tex] :\implies \: [/tex] 2941 (approx)
Therefore, 2941 boxes are required to fill with 500000 staples.
b) It is given that,
Each staple is made of 0.21 g of metal .
Total weight of metal = 1 kg = 1000 g
1 staple = 0.21 g
Number of staples = weight of metal/ Weight of 1 staple.
[tex] \: :\implies [/tex] 1000/0.21
[tex] \: :\implies [/tex] 4761 (approximately)
Therefore, 4761 staples can be made from 1 kg of the metal.
on 9 of 20
Robert receives a salary of $60,000 per year, or $2,500 semi-monthly. How
much does his employer pay for his Medicare tax each pay period?
A. $46
B. $51
C. $36
D. $41
Answer:
Robert's semi-monthly salary is $2,500. This means he earns $5,000 per month. The Medicare tax rate is 1.45%, so his employer pays 1.45% of his salary for Medicare tax. This is equal to $72.50 per month. Since he is paid semi-monthly, his employer pays $36.25 for his Medicare tax each pay period. Therefore, the answer is C. $36.
¿Cuál es la tangente de la siguiente derivada:
f’(x) = 6x^2 - 6x - 12
Esta es la pendiente de la recta tangente a la curva f(x) en el punto x = a.
Que es derivado?La tangente de una derivada no es una operación matemática bien definida. Supongo que lo que se quiere encontrar es la pendiente de la recta tangente a la curva representada por la función f(x) cuya derivada es f'(x) = 6x^2 - 6x - 12 en algún punto x = a.
La pendiente de la recta tangente a la curva f(x) en el punto x = a está dada por la derivada de f(x) evaluada en ese punto, es decir:
m = f'(a)
Entonces, para encontrar la pendiente de la recta tangente a la curva de la función f(x) en el punto x = a, tenemos que evaluar f'(x) en x = a:
m = f'(a) = 6a^2 - 6a - 12
donde f(a) es el valor de la función en el punto x = a.
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Approximate the area of the circle segment bounded by DE and arc DE if r =20 and theta=47°. Photo Attached
Answer: 1256.63706
Step-by-step explanation: A=(π20)2
The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.
To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:
Area = (1/2) * r^2 * (θ - sinθ)
Where:
r is the radius of the circle (r = 20 in your case).
θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).
Let's calculate it:
θ = 47° * (π / 180) ≈ 0.8203 radians
Now, plug these values into the formula:
Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))
Area ≈ (1/2) * 400 * (0.8203 - 0.7317)
Area ≈ (1/2) * 400 * 0.0886
Area ≈ 17.72 square units
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Solve for g
3/16= (-5/4) + g
Answer:g=23/16
Step-by-step explanation: The negative number adds up.
How are quarts and gallons related?
Answer:A quart contains 4 cups or 2 pints while a gallon contains 16 cups or 8 pints. Hence, a liquid gallon is equal to 4 liquid quarts.
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What is the value of z in this triangle?
Enter your answer in the box.
z =
Answer:
z = 23
Step-by-step explanation:
62 + 95 = 157
180 - 157 = 23
If a binary logistic regression has a pseudo R-Square (L) of 60%, then a) the model is better than another logistic regression with a R-square (CS) of 50%. b) 60% of the variation in the data can be explained by the logistic regression c) Other types of pseudo R-squares may be greater or less than 60% with the same logistic regression model. d) the model is better than another multiple linear regression model with an R- square of 55%.
The correct answer is c) Other types of pseudo R-squares may be greater or less than 60% with the same logistic regression model.
Pseudo R-squares, such as the one used in logistic regression, are measures of how well the model fits the data, but they cannot be directly compared to R-squared values from other types of regression models. Therefore, we cannot conclude that the logistic regression model with a pseudo R-Square of 60% is better than another logistic regression with an R-square (CS) of 50% or a multiple linear regression model with an R-square of 55%. However, we can say that 60% of the variation in the data can be explained by the logistic regression model, based on its pseudo R-Square value.
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A car travels 220 miles in 4 hours. The car travels with constant speed.
Which table or equation represents the distance d, in miles, traveled in t hours?
Select TWO correct answers.
Answer:
110 in 2 hours
Step-by-step explanation:
by using division and knowledge of unit rates, we can divide 220 by 2 and get 110, we also have to divide 4 by 2 which results in 2. hope this helps
The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 1025 among its requirements, what PERCENTAGE of females do not satisfy that requirement? Write your answer as a percent! Use Excel to obtain more accuracy.
The percentage of females that do not satisfy the requirement is given as follows:
55.17%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 998, \sigma = 202[/tex]
The proportion that does not satisfy the requirement is the p-value of Z when X = 1025(proportion less than 1025), hence:
Z = (1025 - 998)/202
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
Hence the percentage is given as follows:
0.5517 x 100% = 55.17%.
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I need to know it please
Answer:
63 cm²
Concept used:
Area of a parallelogram = b · h
(b: base and h: height of the parallelogram)
Step-by-step explanation:
The given figure is a parallelogram.
Required Area = 9 * 7
= 63 cm²
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The solution of the logarithmic equation is v = 0.00137
How to solve the logarithmic equation?Here we want to solve the logarithmic equation:
log₃(v) = -6
Remember that:
logₐ(x) = ln(c)/ln(a)
Then we can rewrite the equation as follows:
log₃(v) = -6
ln(v)/ln(3) = -6
ln(v) = -6*ln(3)
Now we can apply the exponential equation in both sides, we will get.
exp(ln(v)) = exp(-6*ln(3))
v = exp(-6*ln(3))
v = 0.00137
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