Answers
To solve this problem, we will use the following expression:
[tex]\frac{favorable\text{ outcomes}}{total\text{ outcomes}}.[/tex]In this case:
[tex]\begin{gathered} Total\text{ outcomes}=21+6+6=33, \\ favorable\text{ outcomes}=6. \end{gathered}[/tex]Substituting the above values in the expression, we get:
[tex]\frac{6}{33}.[/tex]Finally, simplifying the above result, we get that the probability that his shirt number is from 67 to99 given that he weighs at most 210 pounds is:
[tex]\frac{2}{11}.[/tex]Answer:
[tex]\frac{2}{11}.[/tex]Related Questions
use the product to sum formula to help me solve this problem in trig
Answers
Explanation
The product-to-sum formula can be seen below.
[tex]cosAsinB=\frac{1}{2}(sin(A+B)-sin(A-B))[/tex]Therefore, we can insert the values of the angles into the formula
[tex]\begin{gathered} Cos37.5sin7.5=\frac{1}{2}(sin(37.5+7.5)-sin(37.5-7.5)) \\ =\frac{1}{2}(sin45-sin30) \\ =\frac{1}{2}(\frac{\sqrt{2}}{2}-\frac{1}{2}) \\ =(\frac{\sqrt{2}}{4}-\frac{1}{4}) \\ =\frac{\sqrt{2}-1}{4} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} A=2 \\ B=1 \end{gathered}[/tex]What’s the correct answer answer asap for brainlist I really need help
Answers
Answer:
A. clouds
Step-by-step explanation:
hope it helps :)
Use the given information to find the unknown value:y varies inversely with a. When x = 4, then y= 4. Find y when I = 2.Iyy =help (numbers)
Answers
Inverse variation:
[tex]y=\frac{k}{x}[/tex]k is a constant
Use the given information (when x=4 y=4) to find the value of the constant:
[tex]\begin{gathered} 4=\frac{k}{4} \\ \\ \text{Multiply both sides of the equation by 4:} \\ 4\times4=4\times\frac{k}{4} \\ \\ 16=k \\ \\ \\ k=16 \end{gathered}[/tex]Then, the given relationship has the next equation:
[tex]y=\frac{16}{x}[/tex]Use the equation above to find y when x=2:
[tex]\begin{gathered} y=\frac{16}{2} \\ \\ y=8 \end{gathered}[/tex]Then, when x=2, y=8Let p(x)=3x – 2 and q(x) = 2x + 5. Finda. p(x) – Q(x) =b. p(x) + q(x) =c. p(x)q(x) =
Answers
We are given the following functions;
[tex]\begin{gathered} p(x)=3x-2 \\ q(x)=2x+5 \end{gathered}[/tex]We shall find the values of the following;
[tex]p(x)-q(x)[/tex]We substitute for the values of each function and we'll have;
[tex]\begin{gathered} p(x)-q(x)=(3x-2)-(2x+5) \\ p(x)-q(x)=3x-2-2x-5_{} \end{gathered}[/tex]Take note that the negative sign in front of the parenthesis affects both values. Hence negative +5 becomes -5. We now have;
[tex]\begin{gathered} p(x)-q(x)=3x-2-2x-5 \\ p(x)-q(x)=3x-2x-5-2 \\ p(x)-q(x)=x-7 \end{gathered}[/tex](B):
[tex]p(x)+q(x)[/tex]Just like in part (a), we shall substitute for the value of each of the functions, as follows;
[tex]\begin{gathered} p(x)+q(x)=(3x-2)+(2x+5) \\ p(x)+q(x)=3x-2+2x+5 \\ p(x)+q(x)=3x+2x+5-2 \\ p(x)+q(x)=5x+3 \end{gathered}[/tex](C):
[tex]p(x)q(x)[/tex]In this case, we calculate the product of both functions, and we start by substituting for the value of each;
[tex]\begin{gathered} p(x)q(x)=(3x-2)(2x+5) \\ p(x)q(x)=3x\cdot2x+3x\cdot5-2\cdot(+2x)-2\cdot(+5) \end{gathered}[/tex]We can now simplify the above and we'll have;
[tex]\begin{gathered} p(x)q(x)=6x^2+15x-4x-10 \\ p(x)q(x)=6x^2+11x-10 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} (a)=x-7 \\ (b)=5x+3 \\ (c)=6x^2+11x-10 \end{gathered}[/tex]DIRECTIONS: Use this information to answer Parts A and B.
Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
Part A
How much interest will Marisol earn for a period of 5 years?
Part B
Marisol receives 8,450 when she close her savings account if she made no changes to the account, for how many years did Marisol keep the account open?
Answers
Answer: 287.&. Multiply 365 x 10 Great, you get 3650 . . . Multiply 287 by 3650 which then equals 1049375 . . . Wow! The interest will then be a total of 60929$ with the 8450 that she recieved that should equal 3 years total keeping it open . . .
Step-by-step explanation: Hope This Helps! Pls mark Branliest!
1....
1) 3х = 27
2) 5х-2 = 25
3) (1/7)х = 49
4) 2х+8 = 1/32
5) 6х-4 = 36
6) 3х+2+3х = 90
2...
1) 2х = 32
2) 6х-3 = 36
3) (2/3)х = 1,5
4) 52х-1 = 0,2
5) 9х-1 = 81
6) 2х+1+2х = 96
Answers
Answer:
Step-by-step explanation:
3x=27
compare the y-intercepts and the rates of change of the following items. y = -5x + 5 and a line which passes through the points (5, 0) and (-5, 5)
Answers
y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Here the points are (5, 0) and (-5, 5) and it is to find the equation of line passing through these points :
Now using slope formula to find the slope of line m :
m = (y₂-y₁)/ (x₂-x₁)
m = (5-0)/(-5-5)
m = 5/-10
m = -1/2
Let us first find the equation of the line using point-slope equation of line :
(y-y₁) = m(x-x₁)
Substituting all the values in above equation to get the equation of line :
(y-0) = -1/2(x-5)
2y = -x+5
2y = -x + 5
2y = -x +5
y = -x/2 + 5/2
Therefore, the equation of line passing through the points (5, 0) and (-5, 5) is y = -x/2 + 5/2 and its y-intercepts is 5/2
Now, the y-intercepts of line y = -5x + 5 is 5
That is, y-intercepts of line y = -5x + 5 is greater then a line which passes through the points (5, 0) and (-5, 5)
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please help me solve this please and thank you m8
Answers
We will hve the following:
[tex](5x+8)(x^3-x-4)=(5x^4-5x^2-20x)+(8x^3-8x-32)[/tex][tex]=5x^4+8x^3-5x^2-28x-32[/tex]What is the estimated probability that at least two of the puppies will befemale?A. 6/10 = 60 %B. 5/10 = 50 % C. 7/10 = 70 % D. 4/10 = 40 %
Answers
Answer:
C. 7/10 = 70 %
Explanation:
We are asked to find the total number of outcomes that give us at least 2 female puppies.
Now outcomes 1,2,4,5,7,9, and 10, which are 7 outcomes in total, give us at least two female puppies. Therefore, we can say 7 out of 10 times we get at least 2 female supplies and hence the probability is
[tex]\frac{7}{10}=70\%[/tex](Find the sum of the infinite geometric series 3 + 12 + 48 + 192 + ...
Answers
Given the Infinite Geometric Series:
[tex]3+12+48+192+...[/tex]You can find its sum by using this formula:
[tex]S=\frac{a_1}{1-r}[/tex]Where "r" is the common ratio and the first term is:
[tex]a_1[/tex]In this case, you can identify that each term is obtained by multiplying the previous term by 4. Therefore:
[tex]r=4[/tex]You can identify that:
[tex]a_1=3[/tex]Therefore, you can substitute values into the formula and evaluate:
[tex]S=\frac{3}{1-4}[/tex][tex]\begin{gathered} S=\frac{3}{-3} \\ \\ S=-1 \end{gathered}[/tex]Hence, the answer is: Option B.
Hello! Can you help with part A & B? Thank you!
Answers
we have the functions
[tex]\begin{gathered} g(x)=-2x^2+13x+7 \\ h(x)=-x^2+4x+21 \end{gathered}[/tex]Part A
Equate both equations
[tex]-2x^2+13x+7=-x^2+4x+21[/tex]Solve for x
[tex]\begin{gathered} -2x^2+13x+7+x^2-4x-21=0 \\ -x^2+9x-14=0 \end{gathered}[/tex]Solve the quadratic equation
using the formula
a=-1
b=9
c=-14
substitute
[tex]x=\frac{-9\pm\sqrt{9^2-4(-1)(-14)}}{2(-1)}[/tex][tex]x=\frac{-9\pm5}{-2}[/tex]The values of are
x=2 and x=7
The answer Part A
The distances are x=2 units and x=7 units
Part B
f(x)=g(x)/h(x)
so
[tex]f(x)=\frac{-2x^2+13x+7}{-x^2+4x+21}[/tex]Rewrite in factored form
[tex]\begin{gathered} f(x)=\frac{-2(x+\frac{1}{2})(x-7)}{-(x+3)(x-7)} \\ \\ f(x)=\frac{(2x+1)}{(x+3)} \end{gathered}[/tex]The given function has a discontinuity at x=7 (hole), a vertical asymptote at x=-3
and horizontal asymptote at y=2
The next model of a sports car will cost 3.1% less than the current model. The current model cost $54,000. How much will the price decrease in dollars? What will be the price of the next model?
Answers
Answer:
The price decrease will be $1,674
The price of the next model will be $52,326
Explanation:
Given the cost of the current model as $54,000.
We're told that the next model of the car will cost 3.1% less than the current model, let's go ahead determine the price decrease as seen below;
[tex]54000\times\frac{3.1}{100}=54000\times0.031=\text{ \$1,674}[/tex]We can see from the above that the price decrease is $1,674.
Let's go ahead and determine the price of the next model as seen below;
[tex]54000-1674=\text{ \$52,326}[/tex]Therefore, the price of the next model will be $52,326
(sorry the picture is sideways, i couldn’t type in the problem directly hopefully this will do)
Answers
The angle can be expressed as,
[tex]\begin{gathered} \frac{13\pi}{6}=(2\pi+\frac{\pi}{6}_{}) \\ \end{gathered}[/tex]So, the angle can be drawn as,
To find the reference angle if the angles is greeter than 2π, we first subtract 2π from the angle(here 13π/6) until it is below 2π.
[tex]\frac{13\pi}{6}-2\pi=\frac{\pi}{6}[/tex]So, the reference angle is π/6.
Find the radius of the given circle with the given central angle and arc length. Round your answer to the nearest tenth.
Answers
The arc length, when the central angle is measure in degrees, is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]In this case the arc length is 19.6 cm and the angle is 130°, plugging these values we have that:
[tex]\begin{gathered} 19.6=2\pi r(\frac{130}{360}) \\ r=(\frac{19.6}{2\pi})(\frac{360}{130}) \\ r=8.6 \end{gathered}[/tex]Therefore, the radius is 8.6 cm
Answer to this question
Answers
Answer:
A
Y = -4|x+2|+3
Step-by-step explanation:
we can see the graph is heading downwards -> it must be negative coefficient
The graph is going up 3 -> must have a plus 3 in formula outside absolute value
the graph is going to the left 2 -> must have a plus 2 in formula inside absolute value
Amortize Premium by Interest Method
Shunda Corporation wholesales parts to appliance manufacturers. On January 1, Year 1, Shunda Corporation issued $22,000,000 of five-year, 9% bonds at a market (effective) interest rate of 7%, receiving cash of $23,829,684. Interest is payable semiannually. Shunda Corporation’s fiscal year begins on January 1. The company uses the interest method.
a. Journalize the entries to record the following:
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1. Sale of the bonds. Round amounts to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
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2. First semiannual interest payment, including amortization of premium. Round to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
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- Select -
- Select -
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3. Second semiannual interest payment, including amortization of premium. Round to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank.
blank
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b. Determine the bond interest expense for the first year. Enter amounts as positive numbers. Round amounts to the nearest dollar.
Annual interest paid $
fill in the blank 6502c1ff4fd7045_1
Premium amortized
fill in the blank 6502c1ff4fd7045_2
Interest expense for first year $
fill in the blank 6502c1ff4fd7045_3
Question Content Area
c. Explain why the company was able to issue the bonds for $23,829,684 rather than for the face amount of $22,000,000.
The bonds sell for more than their face amount because the market rate of interest is
the contract rate of interest. Investors
willing to pay more for bonds that pay a higher rate of interest (contract rate) than the rate they could earn on similar bonds (market rate).
Answers
The journal entries for the bonds transactions of Shunda Corporation are as follows:
Journal Entries:1. Debit Cash $23,829,684
Credit Bonds Payable $22,000,000
Credit Bonds Premium $1,829,684
2. Debit Interest Expense $834,039
Debit Bonds Premium $155,961
Credit Cash $990,000
3. Debit Interest Expense $828,580
Debit Bonds Premium $161,420
Credit Cash $990,000
b. Bond Interest Expense for the first year is as follows:
Annual interest paid = $1,980,000
Premium amortized = $317,381
Interest Expense = $1,662,619
c. The bonds sell for more than their face amount because the market rate of interest is less than the contract interest rate. Investors are willing to pay more for bonds that pay a higher rate of interest (contract rate) than the rate they could earn on similar bonds (market rate).
Transaction Analysis:Face value of bonds = $22,000,000
Bonds Proceeds = $23,829,684
Bonds Premium = $1,829,684 ($23,829,684 - $22,000,000)
Coupon interest rate = 9%
Semi-annual interest payment = $990,000 ($22,000,000 x 9% x 1/2)
Effective market interest rate = 7%
1. Cash $23,829,684 Bonds Payable $22,000,000 Bonds Premium $1,829,684
2. Interest Expense $834,039 Bonds Premium $155,961 Cash $990,000
3. Interest Expense $828,580 Bonds Premium $161,420 Cash $990,000
1st Semiannual Interest Payment:Interest Payment at 4.5% $990,000
Interest Expense = $834,039 ($23,829,684 x 3.5%)
Amortized Premium = $155,961
Bond's carrying value = $23,673,723 ($23,829,684 - $155,961)
2nd Semiannual Interest Payment:Interest Payment at 4.5% $990,000
Interest Expense = $828,580 ($23,673,723 x 3.5%)
Amortized Premium = $161,420
Bond's carrying value = $23,512,303 ($23,673,723 - $161,420)
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You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing texts should be purchased from students for resale. Due to budget limitations, you cannot purchase more than 1050 of these textbooks each semester. There are also shelf-space limitations: Calculus texts occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 5 units each, and you can spare at most 1,700 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit?
calculus text(s):
history text(s):
marketing text(s):
What is the maximum profit the program can make in a semester?
Answers
Using linear programming, the amounts of each book that you should purchase are given as follows:
Calculus: 850.History: 0.Marketing: 0.The maximum profit will be of $850.
How to maximize a function given it's constraints?To maximize the function, we have to find the numeric values at the intercepts of the most restrictive constraints, as the maximum value is the highest numeric value. This strategy is called linear programming.
In the context of this problem, the variables are given as follows:
Variable x: number of calculus books purchased.Variable y: number of history books purchased.Variable z: number of marketing books purchased.The used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, hence the profit function is defined as follows:
P(x,y,z) = 10x + 4y + 8z.
The constraint related to budget limitations, as an equality, is given by:
x + y + z = 1050.
The most restrictive constraint is from shelf-space limitations, and is given as follows:
2x + y + 5z = 1700.
Hence the intercepts are given as follows:
(850, 0, 0) as 2x = 1700 -> x = 850.(0, 1700, 0), as y = 1700.(0, 0, 340), as 5z = 1700 -> z = 340.The numeric value of the profit function at each of these intercepts is:
P(850,0,0) = 10(850) = 8500.P(0, 1700, 0) = 4(1700) = 6800.P(0, 0, 340) = 8(340) = 2720.Hence, due to the maximum numeric value, the maximum profit will be of $850, when 850 calculus books are purchased.
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what’s the correct answer answer asap for brainlist
Answers
Answer:
A. 12
Step-by-step explanation:
PLEASE HELP ME!!!
How would I find the perimeter of this shape?
Explain your process and all steps
required.
Answers
Answer:
6x+8
Step-by-step explanation:
2 x 2x+3 = 4x+6
2 x x+1 = 2x+2
4x+6 + 2x+2 = 6x+8
how do I find the correct answer?Use deductive reasoning to show that angle A is congruent to angle E.
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We know that O is midpoint of BF, which means OF is equal to OB by definition of midpoint.
Also, angles FOE and BOA are congruent by vertical angles theorem. Angles B and F are congruent by given, both are right angles.
We can deduct that triangles EFO and ABO are congruent by ASA postulate of congruence.
From the congruence between triangles, we deduct that angles A and E are congruent.Determine whether the value is from a discrete or continuous data set.Number of members present at a meeting is 6Is the value from A) discrete B) continuous
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To answer this question we need to understand the difference between discrete and continous data:
• Discrete data can only take certain values along some interval.
,• Continuous data can take any value along some interval.
In this case we know that there will always be a integer number of people in the meeting, that is, we can only have certain values (we can't have 6.5 people in a meeting).
Therefore, this is a discrete data set.
x-y=3, 2x-y=5 what’s the solution
Answers
Answer:
x = 2, y = -1
Solve the following system:
{-y + x = 3 | (equation 1)
-y + 2 x = 5 | (equation 2)
Swap equation 1 with equation 2:
{2 x - y = 5 | (equation 1)
x - y = 3 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{2 x - y = 5 | (equation 1)
0 x - y/2 = 1/2 | (equation 2)
Multiply equation 2 by 2:
{2 x - y = 5 | (equation 1)
0 x - y = 1 | (equation 2)
Multiply equation 2 by -1:
{2 x - y = 5 | (equation 1)
0 x + y = -1 | (equation 2)
Add equation 2 to equation 1:
{2 x + 0 y = 4 | (equation 1)
0 x + y = -1 | (equation 2)
Divide equation 1 by 2:
{x + 0 y = 2 | (equation 1)
0 x + y = -1 | (equation 2)
Collect results:
Answer: |
| {x = 2
y = -1
I believe that this is truly the answer.
Cathan and Jakove went out to eat, and the bill for their food was $24.50. If theyleft their server a 20% tip, what was the total cost of their dining experience? *
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And the cost is $29,40
Help please I’m kinda confused
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If the original price of suitcase is $62 and sale price is 51.99 amount of
markdown is $ 10.01 and markdown % is 16.14.
Mark down = original price - sale price
= 62 -51.99
= $ 10.01
Mark down % = [tex]\frac{mark down}{original selling price} \times 100[/tex]
= [tex]\frac{ 10.01}{62} \times 100[/tex]
= 16.14%
What is markdown?markdown is the amount by which you reduce the selling price. The amount by which you reduce the price can be expressed as a percentage of the sale price, or the discount rate.
To calculate markdown percentage Divide the price difference by the actual selling price. Then multiply that result by 100. The result is a markdown percentage.
For example, suppose a broker sells XYZ stock to his clients at $20 per share. He originally bought the stock in the brokerage market at $0 per share. Therefore, the discount on the stock he sells is -$20 ($20 - $0)
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A sound receiving dish used at outdoor sporting events is constructed in the shape of a paraboloid, with its focus 5 inches from the vertex. Determine the exact width (in inches) of the dish if the depth is to be 2 feet.
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First, lets remember that a paraboloid is just a parabola that was rotated around the Y axis. So lets find the equation from our parabola that is been rotated. We know that the focus is in the point (0,5), so we can find our equation:
[tex]y=\frac{x^2}{4\times5}\rightarrow y=\frac{x^2}{20}[/tex]Just to remember, a parabola that has focus in (0,P) has equation as:
[tex]y=\frac{x^2}{4\times p}[/tex]We can draw our parabola:
So we want to find the width knowing that the depth is 2 feet our 24 inches. That means that he wants to know the X that make the Y be 24, so lets find it:
[tex]y=\frac{x^2}{20}\rightarrow x^2=24\times20\rightarrow x=\pm\sqrt[]{480}\rightarrow x^{\prime}\cong21.908\text{ and }x\~\~^{}\cong-21.908[/tex]The system of inequalities, r+ y > 10 * + y 2 Select the region that contains solutions to the system of inequalities modeled in the graph below O Region A Solutions to the system of inequalities lie in one ofthe regions shown on the coordinate plane. O Region B Region O Region D B A С Previous
Answers
we know that
inequality 1
The solution is the shaded area above the solid line x+y=10
Inequality 2
The solution is the shaded area below the solid line -x+y=-2
therefore
the solution of the system of inequalities is the region C
5.(A.3A) The table represents some points on the graphof a linear function. What is the slope of thisfunction?х у-6-70-106-1312-16
Answers
The slope of a linear function can be obtained as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1,y1) and (x2,y2) are points of the line.
For this problem we just have to pick 2 points from the table (they don't have to be consecutive). I'll pick:
• x1 = 0
,• y1 = 4
,• x2 = 2
,• y2 = 14
And now we compute the slope:
[tex]m=\frac{14-4}{2-0}=\frac{10}{2}=5[/tex]The slope is 5 (third option)
Erin receives a 20% employee discount at the camera store where she works. She alsoreceives a $10 off the price on Wednesdays.a. Write a function e(p) that calculates Erin's new price after the employee discount(hint: what percent of the original price does she have to pay?)ep) =B. Write a function a(p) that calculates Erin's new price using her Wednesday discountonlya (p) =C. Write the function e(a(p))e a(p)) =D. What would Erin's final price be for a $400 camera she purchases on a Wednesday?
Answers
ANSWERS
A. e(p) = 0.8p
B. a(p) = p - 10
C. e(a(p)) = 0.8p - 8
D. $312
EXPLANATION
A. The employee discount is 20%. To the total price, which is 100%, we have to subtract the 20% to find the final price of the product. If the price is p, then the price after the employee discount would be,
[tex]e(p)=(1-0.2)p=0.8p[/tex]Hence, the function is e(p) = 0.8p
B. On Wednesdays, Erin gets a $10 discount on the price p of a product in the store, so if she buys on a Wednesday, she would pay a(p) = p - 10.
C. Now we have to find the function e(a(p)). This is a composition, where we have to replace p with a(p) in function e(p),
[tex]e(a(p))=0.8a(p)=0.8(p-10)=0.8p-0.8\cdot10=0.8p-8[/tex]Hence, the function is e(a(p)) = 0.8p - 8
D. If Erin buys a $400 camera on a Wednesday she will get both discounts: the employee discount and the Wednesdays discount. To find the final price for a selling price of p = 400, we have to use the function found in part C,
[tex]e(a(400))=0.8\cdot400-8=320-8=312[/tex]Hence, the final price for the $400 camera is $312, after both discounts.
To indirectly measure the distance across a lake, Jeremiah makes use of a couplelandmarks at points O and P. He measures NR, RP, and Q R as marked. Find thedistance across the lake (OP), rounding your answer to the nearest hundredth of ameter.
Answers
Notice that triangles NPQ and NRQ are similar, then:
[tex]\frac{OP}{QR}=\frac{NP}{NR}.[/tex]Now, notice that:
[tex]PN=NR+RP.[/tex]Therefore:
[tex]\frac{OP}{QR}=\frac{NR+RP}{NR}.[/tex]Multiplying the above result by QR we get:
[tex]\begin{gathered} \frac{OP}{QR}\times QR=\frac{NR+RP}{NR}\times QR, \\ OP=\frac{NR+RP}{NR}\times QR. \end{gathered}[/tex]Substituting NR=125m, RP=65m, and QR=106.75m we get:
[tex]OP=\frac{125m+65m}{125m}\times106.75m.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} OP=\frac{190m}{125m}\times106.75m \\ =162.26m. \end{gathered}[/tex]Answer:
[tex]OP=162.26m.[/tex]
Let f be a differentiable function with f(2)=-3 and f'(2)=-4.
Answers
The value of differentiable function g(x)=x³ × f(x) if f(2)=-3 and f'(2)=-4 is -68.
If the derivative of a function exists at every point inside its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.
Given function
g(x)=x³ × f(x)
FInd out -
Value of g′(2) = ?
If f(2) = -3 and f'(2) = -4.
Let us apply the product rule of differentiation of a product of two functions. The product rule states that
d/dx (fg) = d/dx (f) × g + f × d/dx(g)
or
(fg)'(x) = f'(x) × g(x) + f(x) × g'(x).
Observe that if g(x) = x³ × f(x) then
g'(x) = 3x² × f(x) + x³ × f'(x).
Thus, g'(2) = 3 × 2² × f(2) + 2³ × f'(2)
Put the value of f(2) and f'(2)
= 3 × 4 × (-3) + 8 × (-4)
= -36 - 32
= - 68.
Therefore , If f(2)=-3 and f'(2)=-4, the value of the differentiable function g(x)=x³ × f(x) is -68.
To learn more about Differentiable function
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