Answers
The solutions to the equation:
8. The value of the integral is 0.
9. The value of the integral is approximately -0.336.
10. The value of the integral is π(b - a)/4
11. The value of the integral is π/4 - (1/2)(1 - e^4).
12. The value of the integral is -8π.
13. The value of the integral is π/64 + π/(32√2).
How did we get these values?8. To evaluate the integral ∫∫R(2x-y) dA over the region R in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x, we can use polar coordinates.
First, we convert the equations of the circle and line into polar coordinates:
x² + y² = 4 becomes r² = 4
y = x becomes θ = π/4
The region R can be described in polar coordinates as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/4. The differential element dA can be expressed in polar coordinates as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R(2x-y) dA = ∫₀^(π/4) ∫₀² (2r²cosθ - rsinθ) r dr dθ
= ∫₀^(π/4) ∫₀² (2r³cosθ - r²sinθ) dr dθ
= ∫₀^(π/4) [r⁴cosθ/2 - r³sinθ/3]₀² dθ
= ∫₀^(π/4) 8cosθ/3 - 8sinθ/3 dθ
= [8/3(sinθ - cosθ)]₀^(π/4)
= 8/3(1/√2 - 1/√2 - (0 - 0))
= 0
Therefore, the value of the integral is 0.
9. To evaluate the integral ∫∫Rsin(x² + y²) dA over the region R in the first quadrant between the circles with center the origin and radii 1 and 3, we can again use polar coordinates.
In polar coordinates, the region R can be described as 1 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫Rsin(x² + y²) dA = ∫₀^(π/2) ∫₁³ r sin(r²) dr dθ
= ∫₀^(π/2) [-cos(r²)]₁³ dθ
= ∫₀^(π/2) cos(1) - cos(9) dθ
= sin(1) - sin(9)
≈ -0.336
Therefore, the value of the integral is approximately -0.336.
10. To evaluate the integral ∫∫R y²/x² + y²dA over the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b, we can use polar coordinates.
In polar coordinates, the region R can be described as a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R y²/x² + y²dA = ∫₀^(2π) ∫ₐᵇ (r⁴cos²θsin²θ)/(r⁴cos²θ) r dr dθ
= ∫₀^(2π) ∫ₐᵇ sin²θ cos²θ dr dθ
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) d
= ∫₀^(2π) [(b-a)/4](cos²θ - sin²θ) dθ
= [(b-a)/8] ∫₀^(2π) (1 - sin(2θ)) dθ
= [(b-a)/8] (2π - 0)
= π(b - a)/4
Therefore, the value of the integral is π(b - a)/4.
11. To evaluate the integral ∫∫D e^(-x²-y²) dA, where D is the region bounded by the semicircle x = √(4 - y²) and the y-axis, we can use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D e^(-x²-y²) dA = ∫₀^(π/2) ∫₀² e^(-r²) r dr dθ
= ∫₀^(π/2) [-1/2 e^(-r²)]₀² dθ
= ∫₀^(π/2) (1/2 - 1/2e^4) dθ
= π/4 - (1/2)(1 - e^4)
Therefore, the value of the integral is π/4 - (1/2)(1 - e^4).
12. To evaluate the integral ∫∫D cos(√(x²+y²)) dA, where D is the disk with center at the origin and radius 2, we can again use polar coordinates.
In polar coordinates, the region D can be described as 0 ≤ r ≤ 2 and 0 ≤ θ ≤ 2π. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫D cos(√(x²+y²)) dA = ∫₀^(2π) ∫₀² r cos(r) dr dθ
= ∫₀^(2π) [2 sin(r) - 2r cos(r)]₀² dθ
= ∫₀^(2π) (-4) dθ
= -8π
Therefore, the value of the integral is -8π.
13. To evaluate the integral ∫∫R arctan(y/x) dA, where R = {(x,y) | 1 ≤ x² + y² ≤ 4, 0 ≤ y ≤ x}, we can use polar coordinates.
In polar coordinates, the region R can be described as π/4 ≤ θ ≤ π/2 and 1/√2 ≤ r ≤ 2. The differential element dA can be expressed as dA = r dr dθ.
Now we can evaluate the integral:
∫∫R arctan(y/x) dA = ∫π/4^(π/2) ∫1/√2² r arctan(tan(θ)) dr dθ
= ∫π/4^(π/2) [(r²θ/2 - r²tan(θ)/4)]1/√2² dθ
= ∫π/4^(π/2) [(2θ - π/2)/8] dθ
= [θ²/16 - (θ - π/4)/8]π/4^(π/2
= [π/16 - (π/4 - π/4√2)/8] - [(π/16 - (π/8 - π/8√2)/8)]
= π/64 + π/(32√2)
Therefore, the value of the integral is π/64 + π/(32√2).
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The question in text format:
8. ∫∫R(2x-y) dA, where R is the region in the first quadrant enclosed by the circle x² + y² = 4 and the lines x= 0 and y=x
9. ∫∫Rsin(x² + y²) dA, where R is the region in the first quadrant between the circles with center the origin and radii 1 and 3
Answer
10. ∫∫R y²/x² + y²dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² with 0 < a < b
11. ∫∫D e⁻ˣ²⁻ʸ²dA, where D is the region bounded by the semi-circle x = √4 - y² and the y-axis
12. ∫∫D cos √x² + y² da, where D is the disk with center the origin and radius 2
13. ∫∫R arctan (y/x) dA, where R= {(x,y) | 1 ≤ x² + y² ≤ 4,0 ≤ y ≤ x}
Related Questions
Which measurement is not equal to one mile
Answers
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
On a 8 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Answers
On an 8-question multiple-choice test, where each question has 2 answers, the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]
Probability is a way to gauge how likely something is to happen1. It is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.
In an 8-item multiple-choice test with 2 possible answers for each, the likelihood of getting at least one question wrong can be computed as follows:
P(at least one mistake) = 1 - P (none wrong)
P(at least one wrong) [tex]=1-(\frac{1}{2})^{10[/tex]
P(at least one wrong) [tex]=1-\frac{1}{1024}\\\\=\frac{1023}{1024}[/tex]
On an 8-question multiple-choice test, where each question has 2 answers, the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]
The complete question is-
On an 8-question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
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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?
Answers
-10p+560 = 7200
Subtracting 560 from both sides:
-10p = 6640
Dividing both sides by -10:
p = -664
This answer does not make sense as a price for a T-shirt. The negative value suggests that the expression does not apply for such a low price. Therefore, we can assume that the athletics department cannot sell T-shirts at such a low price.
To find the lowest possible price for a T-shirt that will raise exactly $7,200, we need to find the value of p that makes the expression equal to 7,200.
-10p+560 = 7200
Subtracting 560 from both sides:
-10p = 6640
Dividing both sides by -10:
p = -664
Again, this answer does not make sense.
Therefore, we need to try a higher price for the T-shirt. Let's try a price of $20 per shirt:
-10(20)+560 = 360
This means that for every T-shirt sold at $20, the revenue generated will be $360.
To find out how many T-shirts need to be sold to raise $7,200, we can set up an equation:
360x = 7200
Dividing both sides by 360:
x = 20
This means that the athletics department will need to sell 20 T-shirts at $20 each to raise exactly $7,200 in revenue.
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
Answers
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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Consider the equation and the following ordered pairs: (−4,y) and (x,2) . y=−3x−4 Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answers
To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.
For the ordered pair (-4, y):
y = -3(-4) - 4
y = 12 - 4
y = 8
So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.
For the ordered pair (x, 2):
2 = -3x - 4
6 = -3x
x = -2
So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.
Charlie is playing a boardgame she is rolling two number cubes.
How many outcomes are possible?
Create an outcome chart to prove your answer
Answers
Suppose that 17 inches of wire costs 85 cents. At the same rate, how many inches of wire can be bought for 65 cents?
Answers
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
Equation in vertex form
Answers
Answer:
f(x) = -(x-3)+7
Step-by-step explanation:
Complete the proof that the point (3, 7) does or does not lie on the circle with center (-1, 4) and containing the point (-1, 9).
Answers
The point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).
Describe Distance Formula?The distance formula is a mathematical formula used to calculate the distance between two points in a two or three-dimensional space. It is derived from the Pythagorean theorem and is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Where d represents the distance between the two points, (x1, y1) and (x2, y2) represent the coordinates of the two points in a two-dimensional space.
To determine if the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9), we need to calculate the distance between the center of the circle and the point (3, 7), and compare it to the radius of the circle.
Let's first find the radius of the circle. Since the circle contains the point (-1, 9), the distance between the center of the circle and (-1, 9) is equal to the radius. Using the distance formula, we get:
radius = √[(9 - 4)² + (-1 - (-1))²] = √[25] = 5
Now let's find the distance between the center of the circle (-1, 4) and the point (3, 7):
distance = √[(7 - 4)² + (3 - (-1))²] = √[3² + 4²] = 5
We see that the distance between the center of the circle and the point (3, 7) is equal to the radius of the circle. Therefore, the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).
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2x = 7, 2Y = 5, then 2 x - y
Answers
The calculated value of the expression 2x - y for the given values of x and y is 9/2.
Evaluating the expression for x and yWe are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.
This means that
x = 7/2 and y = 5/2
We can start by substituting the given values into the expression:
2x - y = 2(7/2) - (5/2)
Notice that since 2x = 7, then x = 7/2.
Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:
2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2
Therefore, the value of 2x - y is 9/2.
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What does 2y plus 5 equal
Answers
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]
I need help with this ( Q7 to Q12 )
Answers
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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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
Answers
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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A blueprint used a scale of 1.5 cm = 2 m to
represent a grain silo. If the height of the silo in
the drawing was 33 cm, how tall is the actual grain
silo?
Answers
Answer: The Silo is 44 meters tall
Step-by-step explanation:
To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)
5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
Answers
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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A line with a slope of 1/3 passes through (-1,-2). Write the equation of the line in general form.
Answers
Answer:
I think it will be
y=1/3x+0
NEED BY 15 mins !!!! Identify the leading coefficient of the polynomial!!!!
Answers
Can i please get help
Answers
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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Anyone pls help me do this equation
Answers
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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I need the answer pls help
Answers
Answer:
The function is shifted 1 unit to the right and then flipped over the x-axis. So the correct result is:
[tex]y = - f(x - 1)[/tex]
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?
Answers
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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What is the smallest possible average of 200 distinct positive and odd integers?
Answers
201.5 is the smallest average of 200 different positive and odd integers.
Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.
The average of this set is (1+3+5+...+397+399+401)/200 = 201.
Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.
One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.
The new set is {1, 3, 5, ..., 397, 399, 403}.
The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.
Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.
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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?
Answers
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.
help?? would really appreciate it! (i highly dislike being bad at math)
Answers
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
Graph the piecewise-defined function
Answers
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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As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.
Here is the salary function used to represent this situation in terms of the amount of merchandise sold:
s(x) = 0.23x + 200
Find Alysse's salary when she sells $2,200 worth of merchandise.
Answers
Step-by-step explanation:
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.
Here is the salary function used to represent this situation in terms of the amount of merchandise sold:
s(x) = 0.23x + 200
Find Alysse's salary when she sells $2,200 worth of merchandise.
A rectangular paperboard measuring 20in long and 12in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.)
Answers
Answer:
the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.
Step-by-step explanation:
The perimeter of the paperboard that remains after the semicircle is removed is equal to the sum of the four sides of the rectangular portion of the paperboard plus half the circumference of the semicircle.
The rectangle has dimensions of length = 20 inches and width = 12 inches. Therefore, the sum of the four sides of the rectangular portion of the paperboard is:
2(20) + 2(12) = 64 inches
The semicircle has a diameter equal to the width of the rectangle, which is 12 inches. Therefore, the radius of the semicircle is half the diameter, or 6 inches. The circumference of a full circle with a radius of 6 inches is:
2 * 3.14 * 6 = 37.68 inches
Half of the circumference of the semicircle is:
(1/2) * 37.68 = 18.84 inches
Therefore, the perimeter of the paperboard that remains after the semicircle is removed is:
64 + 18.84 = 82.84 inches
Thus, the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.
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:
Answers
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
How are the points
(4, 5) and (-4, 5) related?
Answers
Answer:
The two points (4, 5) and (-4, 5) have the same y-coordinate, which means they lie on a horizontal line. This horizontal line is the x-axis. So, the points are related in that they both lie on the x-axis, with a distance of 8 units between them.
Two students are selected at random from a class of 13 males and 6 females. Find the probability that both students are males. (See Example 4. Round your answer to two decimal places.)
Answers
The probability that both students selected are males is 0.46.
Multiplication rule of probability:The multiplication rule of probability for independent events states that the probability of two or more independent events occurring together is the product of their individual probabilities.
If event A has probability P(A) and event B has probability P(B), and A and B are independent events, then the probability of both A and B occurring
P(A and B) = P(A) x P(B)
Here we have
There are 13 males and 6 females in the class, for a total of 19 students.
The probability of selecting a male on the first draw is 13/19.
After one male has been selected,
There are 12 males and 6 females left in the class.
The probability of selecting another male on the second draw = 12/18
[ Since there is one less student in the class and one less male]
The probability of selecting two males in a row is the product of the probabilities of each individual event:
P(male and male) = P(male on the first draw) x P(male on the second draw | male on the first draw)
= (13/19) x (12/18)
= 0.456 or approximately 0.46 (rounded to two decimal places).
Therefore,
The probability that both students selected are males is 0.46.
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