Assuming that the company sells all that it produces, The profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.
Profit functionProfit = R-C = -(x-100)^2/2 +5000 - 50x -100 =
-(x^2 -200x +10000)/2 -50x +4900 =
-x^2/2 +100x -5000 +5000 -50x +4900
Collect like terms
-x^/2+50x -100
Hence,
Profit function = P(x)=-0.5x²+50x -100
Maximum profit generating output can be determine by taking the derivative and setting it equal to zero
R-C = -x^2/2 + 50x -100
R'-C' = -x + 50 =0
P(0)x = 50
Maximum profit can be determine by substituting x=50 into the original profit equation, R-C
P(50) =-(1/2)(50)^2 +50(50) -100
P(50)= -1250 + 2500 -100
P(50) = $1150 profit
P(120) =-(1/2)(120)^2 +50(120) -100
P(120)= -3600 + 6000 -100
P(120) = $2300 profit
Therefore the profit function is: P(x)=-x^/2+50x -100 or P(x)=-0.5x²+50x -100.
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What’s an Inequality?
Answer:
mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.
Answer:
The quality of being unequal or uneven is known as the inequality.FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
IF P(A OR B) = 0.9, P(A) = 0.5, AND P(B) = 0.6, FIND P(A AND B)
The value of the probability P(A and B) is 0.20
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.9
P(A) = 0.5
P(B) = 0.6
To calculate the probability P(A and B), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
P(A and B) = 0.5 + 0.6 - 0.9
Evaluate the expression
P(A and B) = 0.2
Hence, the value of the probability P(A and B) is 0.20
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Identify the slope and y-intercept of the line y = ×/2 -7
Answer:
Slope: [tex]-\frac{1}{5}[/tex] Y-intercept: (0,0)
Step-by-step explanation:
By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].
Solve the equation: (4x - 5)^4 = 81.
hope this helps
by
aman10we
The value of x after solving this equation is 2
What is a polynomial?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, the equation as : (4x - 5)^4 = 81.
(4x - 5)^4 = 3⁴.
4x - 5 = 3
x = 2
Hence, the value of x is equal to 2
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I need help please yall
use orders of operation and simplify
Answer: [tex]\large\boxed{12x^3-30x+3=0}[/tex]
Step-by-step explanation:
[tex]Solve:\\\ 6(2x^2-5)x=-3\\\\Use\ distributive\ property\ first\\\\(12x^2-30)x=-3\\\\Now\ multiply\ the\ terms\ in\ ()\ by\ 'x'\\\\12x^3-30x=-3\\\\\large\boxed{12x^3-30x+3=0}[/tex]
The width of a rectangle measures
(7h+3) centimeters, and its length measures
(8h−4) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter of the rectangle is 30h - 2
How to determine the perimeter expression?The dimensions of the rectangle are given as:
Length = 7h + 3
Width = 8h - 4
The perimeter of the rectangle is given as:
P = 2 * (Length + Width)
Substitute the known values in the above equation
P =2 * (7h + 3 + 8h - 4)
Evaluate the like terms
P = 2 * (15h - 1)
Evaluate the product
P = 30h - 2
Hence, the expression that represents the perimeter of the rectangle is 30h - 2
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What is the solution to 3/4 a>-16?
O a>-21/3
O a<-21
O a> 21-1/
O a <21/13
[tex] \frac{3a}{4} > - 16 \\ 3a > - 64 \\ a > \frac{ - 64}{3} \\ a > 21 \frac{1}{3} [/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\huge\textbf{Simplifying it:}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > -16}[/tex]
[tex]\mathsf{\dfrac{3}{4}a > - \dfrac{16}{1}}[/tex]
[tex]\huge\textbf{Divide \boxed{\dfrac{4}{3}} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4}{3}\times\dfrac{3}{4}a > -16\times\dfrac{4}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{a > \dfrac{4}{3}\times -16}[/tex]
[tex]\mathsf{a > - \dfrac{16}{1} \times\dfrac{4}{3}}[/tex]
[tex]\mathsf{a > \dfrac{-16\times4}{1\times3}}[/tex]
[tex]\mathsf{a > \dfrac{-64}{3}}[/tex]
[tex]\mathsf{a > -\dfrac{64}{3}}[/tex]
[tex]\mathsf{a > -21 \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{- \frak{21\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]In a flower garden of rose and sunflower, 40% of flowers are rose. if there are 120 sunflower in the garden, total of how many flowers are there in the garden?
Answer:
200
Step-by-step explanation:
If 40% are roses than 60% must be sunflowers (40% + 60% = 100%)
We are trying to find 60% of some number is 120.
Let n = the total number of flowers
.6n = 120 Divide both sides by .6
n = 200
Complete the square -3x^2+12x-7
Answer:
[tex]-3(x-2)^2+5[/tex]
Step-by-step explanation:
First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].
Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].
In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].
What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]
Finally, plugging [tex]b = -2[/tex] that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get [tex](x^2 - 4x + 4) = (x-2)^2[/tex].
So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].
In summary, the procedure is
[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]
Question 10 of 25
Which pair of functions are inverses of each other?
[tex]f(x) = \sqrt[3]{11x} \\ y = \sqrt[3]{11x} \\ x = \sqrt[3]{11y} \\ x {}^{3} = 11y \\ y = \frac{x {}^{3} }{11} [/tex]
Option A eliminated[tex]f(x) = \frac{x}{7} + 10 \\ y = \frac{x}{7} + 10 \\ x = \frac{y}{7} + 10 \\ x - 10 = \frac{y}{7} \\ y = \frac{x - 10}{7} [/tex]
Option B eliminated[tex]f(x) = \frac{7}{x} - 2 \\ y = \frac{7}{x} - 2 \\ x = \frac{7}{y} + 2 \\ x - 2 = \frac{7}{y} \\ y = \frac{7}{x - 2} [/tex]
Option C eliminatedBy elimination it's DConfirmation:[tex]f(x) = 9x - 6 \\ y = 9x - 6 \\ x = 9y - 6 \\ x + 6 = 9y \\ y = \frac{x + 6}{9} = g(x)[/tex]
The Tortoise and the Hare is a fable about a race with the
moral, “Slow and steady wins the race.” The Tortoise and the
Hare decide to “race” across the United States from
Washington D.C. to Los Angeles.
a. Charles Darwin studied the tortoises when he was on
the Galapagos in 1835. He thought they moved relatively quickly. “One large one, I found by pacing, walked at the rate of 60 yards in 10 minutes” he wrote in Zoology Notes.
i How many inches per minute does the Galapagos tortoise walk?
ii. How long would it take a Galapagos tortoise to walk across the U.S.? Use the most
appropriate unit for time.
b. The Hare can run up to 30mph.
i. How many inches per minute does the Hare run?
ii. How long would it take the Hare to complete the race across the U.S.? Use the
most appropriate unit for time.
c. In the fable, the Hare, confident that he is so far head, relaxes and takes a nap. How long would the Hare need to nap for the Tortoise to pass him and win the race?
a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).
a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).
b.i) The Hare runs 31,680 inches per minute (1,900,800/60).
b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).
c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).
What are the equivalent values for calculating distance?In this exercise, the following equivalent values are used for computing the distance and speed:
1 mile = 1,760 yards1 yard = 36 inches1 hour = 60 minutesDistance from Galapagos to the U.S. = 600 miles600 miles = 1,056,000 yards (600 x 1,760).Data and Calculations:Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)
Speed of Hare = 30mph
30 miles = 52,800 yards (30 x 1,760)
52,800 yards = 1,900,800 inches (52,800 x 36)
= 880 yards per minute (52,800/60)
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Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b. One-third d. Negative 3 Please select the best answer from the choices provided A B C D
The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.
What is the Slope of a Line?The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.
How to Find the Slope of a Line?If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).
Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:
(0, -6) = (x1, y1)
(2, 0) = (x2, y2)
Plug in the values into the slope formula to find the slope:
Slope (m) = (0 - (-6)) / (2 - 0)
Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]
Slope (m) = (6) / (2)
Slope (m) = 3
Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.
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Find the mean for the amounts: $17,484, $14,978, $13,521, $14,500, $18,540, $14,978
Answer:
$15666.83 (2dp)
Step-by-step explanation:
Mean = Total of all values / Number of Values
= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]
=[tex]\frac{94001}{6}[/tex]
= $15666.83 (2dp)
Consider the equation
x/x − 1 = 6x + 1/x − 1
What is the LCD?
Multiply both sides of the equation by the LCD and rewrite the resulting quadratic equation in general form. _____=0
Solve the equation and check the solutions in the original equation. (Enter your answers as a comma-separated list.) x=________
The solution to the original equation is 1, 1/6
Solving equationEquations are expressions separated by mathematical operations.
Given the equation below
x/x − 1 = 6x + 1/x − 1
From the given expression, the least common denominator is x -1
Multiply both sides by x-1 to have;
x = 6x(x-1) +1
Expand
x = 6x^2-6x + 1
Equate to zero
6x^2-6x-x + 1 = 0
6x^2-7x +1= 0
The resulting quadratic equation in general form is 6x^2-7x +1 = 0
Factorize
6x^2 -6x-x + 1 = 0
Group the result
6x(x-1)-1(x-1) = 0
(6x-1)(x-1) = 0
6x - 1 = 0 and x -1 = 0
x = 1 and 1/6
Hence the solution to the original equation is 1, 1/6
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PLATO Type the correct answer in each box. Use numerals instead of words. In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line A T at C, and R respectively such that the angle D C R is 77 degrees. Complete the given statement. The measure of ∠CRQ is °, and the measure of ∠CRS is °.
Answer:
c
Step-by-step explanation:
The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.
We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.
∠DCR = ∠SRT = 77°
∠CRQ = ∠CRS
We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have
∠CRQ + ∠SRT = 180°
∠CRQ + 77° = 180°
∠CRQ = 103°
Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
The diagram is given below.
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The entire graph of the function g is shown in the figure below.
Write the domain and range of g using interval notation.
The domain of the function is [-4, 4) and the range of the function is [-5, 2)
How to determine the domain and the range of the function?The domain
As a general rule, it should be noted that the domain of a function is the set of input values or independent values the function can take.
This means that the domain is the set of x values
From the graph, we have the following intervals on the x-axis
x = -4 (closed circle)
x =4 (open circle)
This means that the domain of the function is [-4, 4)
The range
As a general rule, it should be noted that the range of a function is the set of output values or dependent values the function can produce.
This means that the range is the set of y values
From the graph, we have the following intervals on the y-axis
y = -5 (closed circle)
y = 2 (open circle)
This means that the range of the function is [-5, 2)
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A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $29. For 5 pounds of trail mix and 2 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
the price of one pound of trail mix is $3
the price of one pound of jelly beans is $2.5
Step-by-step explanation :
let t be the price of one pound of trail mix.
and b be the price of one pound of jelly beans.
This statement:
“For 3 pounds of trail mix and 8 pounds of jelly beans,
the total cost is $29”
Can be translated mathematically like this :
3t + 8b = 29
This statement:
“For 5 pounds of trail mix and 2 pounds of jelly beans,
the total cost is $20”
Can be translated mathematically like this :
5t + 2b = 20
We obtain a system of two equations :
3t + 8b = 29
5t + 2b = 20
Solving the system:
3t + 8b = 29 (equation 1)
5t + 2b = 20. (equation 2)
3t + 8b = 29
20t + 8b = 80 [4×(equation 2)]
3t + 8b = 29
17t = 51 [4×(equation 2) - equation 1]
3t + 8b = 29
t = 51/17 = 3
9 + 8b = 29
t = 3
8b = 20
t = 3
b = 20/8 = 5/2
t = 3
b = 5/2
t = 3
Therefore ,the solution to our system is (3 , 2.5)
what is 4,928 will rounded to the nearest hundred
Answer:
4,928 rounded to the nearest hundred = 4,900
Step-by-step explanation:
Greetings!
Determine the two consecutive multiples of 100 that bracket 4,928.4,928 is between 4,900 and 5,000.4,950 is the midpoint between 4,900 and 5,000.As illustrated on the number line, 4,928 is less than the midpoint (4,950).Therefore, 4,928 rounded to the nearest hundred = 4,900.Hope it helps!
Answer:
The answer is 4900, because the next number is less than five, due to that we don't have to add a number (+1).
---
Thank you so much for participate in the community of Brainly.com
I hope help you :)
Kind regards, Antonio.
One fifth increase over 400
Answer:
480
Step-by-step explanation:
1/5 of 400 = 1/5 * 400 = 80
increase 400 by 80 = 480
Triangle Congruency Theorems: Edge High School Geometry
Answer is below:
DE ≅ CE given that side AD and side BC are equal and angle ∠BCD and angle ∠ADC are equal. This can be obtained by using triangle congruency theorems.
Prove that side DE and side CE is equal:Triangle congruency theorems required in the question,
SAS triangle congruency theorem - SAS means Side-angle-side. If two sides and the included angle of a triangle is equal to two sides and the included angle of another triangle then the triangles are congruent.AAS triangle congruency theorem - AAS means Angle-angle-side. If two angles and one side of a triangle is equal to two angles and one side of another triangle then the triangles are congruent.
In the question it is given that,
⇒ Side DE and side CE are equal ⇒ AD ≅ BC
⇒ angle ∠BCD and angle ∠ADC are equal ⇒ ∠BCD ≅ ∠ADC
AD ≅ BC (given in the question)∠BCD ≅ ∠ADC (given in the question)DC ≅ DC (since DC is a common side; reflexive property)Therefore we can say that,
ΔADC ≅ ΔBCD according to the SAS triangle congruency theorem
∠DAE ≅ ∠CBE (corresponding parts of congruent triangles are congruent (CPCTC))AD ≅ BC (given in the question)∠DEA ≅ ∠CEB (since they are vertically opposite angles - vertical angles theorem)ΔAED ≅ ΔBEC according to the AAS triangle congruency theorem
Thus DE ≅ CE since corresponding parts of congruent triangles are congruent (CPCTC).
Hence DE ≅ CE given that side AD and side BC are equal and angle ∠BCD and angle ∠ADC are equal.
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2. What is the length of the hypotenuse k?
Answer:
k ≈ 50.77
Step-by-step explanation:
using the cosine ratio in the right triangle
cos19° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{48}{k}[/tex] ( multiply both sides by k )
k × cos19° = 48 ( divide both sides by cos19° )
k = [tex]\frac{48}{cos19}[/tex] ≈ 50.77 ( to 2 dec. places )
Hi :)
————————————————We'll use sohcahtoa to solve this problem
[tex]\Large\boxed{\begin{tabular}{c|1} \sf{Sohcahtoa} ~&~~~~~Formula~~~~~~~ \\ \cline{1-2} \ \sf{Soh} & Opp~\div \text{hyp}\\\sf{Cah} & Adj \div \text{hyp}\\\sf{Toa} & Opp \div \text{adj} \end{tabular}}[/tex]
Looking at our triangle, we can clearly see that we have :
adj. side = 48 (adjacent to the angle)hyp. k (the one we need)Set up the ratio
[tex]\longrightarrow\darkblue\sf{cos(19)=\dfrac{48}{k}}[/tex]
solve for k
[tex]\longrightarrow\darkblue\sf{k\cos(19)=48}[/tex] > multiply both sides by k to clear the fraction
[tex]\longrightarrow\darkblue\sf{k=\dfrac{48}{\cos(19)}}[/tex] > divide both sides by cos (19)
[tex]\star\longrightarrow\darkblue\sf{k\approx50.77}\star[/tex]
[tex]\tt{Learn~More ; Work\ Harder}[/tex]
:)
Solve for x
Please write your work
Answer:
Step-by-step explanation:
12 + 2x + 24 = 27 + x
2x + 36 = 27 + x
x + 36 = 27
x = -9
2(-9) + 24 = -18 + 24 = 6
12 + 6 = 18
27 + (-9) = 18
Help me with this equation, please. (Image Attached)
So, the equation is sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
The question has to to with trigonometric identities?
What are trigonometric identities?Trigonometric identities are equations that show the relationship between the trigonometric ratios.
How to solve the equation?Given the equation sin(x + y)/sin(x - y)
Using the trigonometric identities.
sin(x + y) = sinxcosy + cosxsiny andsin(x - y) = sinxcosy - cosxsinySo, sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/(sinxcosy + cosxsiny)
Dividing the rnumerator and denominator of ight hand side by sinx, we have
sin(x + y)/sin(x - y) = (sinxcosy + cosxsiny)/sinx/(sinxcosy + cosxsiny)/sinx
sin(x + y)/sin(x - y) = (sinxcosy/sinx + cosxsiny/sinx)/(sinxcosy/sinx + cosxsiny/sinx)
= (cosy + cotxsiny)/(cosy + cotxsiny) (since cosx/sinx = cotx)
Dividing the numerator and denominator of the right hand side by cosy, we have
= (cosy + cotxsiny)/cosy/(cosy + cotxsiny)/cosy
= (cosy/cosy + cotxsiny/cosy)/(cosy/cosy + cotxsiny/cosy)
= (1 + cotxstany)/(1 + cotxtany) [since siny/cosy = tany]
So, sin(x + y)/sin(x - y) = (1 + cotxstany)/(1 + cotxtany)
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need heeeelp please
Answer:
376.99112cm²
Step-by-step explanation:
A=2 pi rh + 2 pi r²
A=(2 x pi x 5 x 7) + (2 x pi 5²)
pi 22/7
The mean of a normally distributed data set is 110, and the standard deviation is 15.
a) Use the standard normal table to find the probability that a randomly-selected data value is greater than 95.
b) Use the standard normal table to find the probability that a randomly-selected data value is greater than 125.
From the standard normal table, the respective probabilities are; 0.908 and 0.841
How to find the probability from z-score?
Formula for calculating the standard score or z score is:
z = (x - μ)/σ
where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
A) We are given;
x = 95
μ = 110
σ = 15
Thus;
z = (95 - 110)/15
z = 1.33
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.091759.
P(x > 95) = 0.908
B) We are given;
x = 125
μ = 110
σ = 15
Thus;
z = (125 - 110)/15
z = 1
From the normal standard distribution table we can find the probability from the z-score as;
P(x > 95) = 1 - 0.158655.
P(x > 95) = 0.841
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(pls help)
5. Write the rule for the linear function. Remember a function rule is written using using f(x).
The linear function whose points are given is f(x)=[tex]x/5 +1[/tex]
Given the points of the function f(-10)=-1,f(0)=1,f(10)=3.
We are required to find the function whose points are given.
Function is relationship between two or more variables that are expressed in equal to form. In function each value of x must have a corresponding y value.
x value is known as domain and y value if known as codomain of the function.
Take two points (-10,-1) and (0,1) and we can form one equation as under:
y+1=(1+1/0+10) * (x+10)
y+1=2/10 (x+10)
y+1=x/5 +10/5
y+1=x/5+2
y=x/5+2-1
y=x/5+1
Hence the linear function whose points are given is [tex]f(x) = x/5 +1[/tex]
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(02.03)
Figure ABCD is transformed to A′B′C′D′, as shown:
A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 comma 4, C at 5 comma 5 and D at 5 comma 3. Figure A prime B prime C prime D prime has vertices A prime at negative 5 comma 1, B prime at negative 5 comma 4, C prime at negative 7 comma 5 and D prime at negative 7 comma 3.
Which of the following sequences of transformations is used to obtain figure A′B′C′D′ from ABCD? (4 points)
Group of answer choices
Reflection about the x-axis followed by a translation right by 2 units
Reflection about the y-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units
What is the type of Transformation used?
As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.
Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).
Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)
Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).
Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).
This is the coordinates for A'.
Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.
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Which equation represents a parabola with a vertex at (7,-3)
Answer:
See Below
Step-by-step explanation:
y = a (x-7)^2 -3 where 'a' is any number except 0
Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately
a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is $11,949.50.
b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
How is the future value determined?The future value can be determined using an online finance calculator.
Data and Calculations:
a) Compounded Semiannually:Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Semi-Annually
Time (t in years): 8 years
Result:
A = $11,949.50
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,244.94
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 8,704.56(1 + 0.04/2)(2)(8)
A = 8,704.56(1 + 0.02)(16)
A = $11,949.50
b) Compounded Continuously:Using the formula A = Pert
Principal (P): $8,704.56
Annual Rate (R): 4%
Compound (n): Compounding Continuously
Time (t in years): 8 years
Result:
A = $11,987.29
A = P + I where
P (principal) = $8,704.56
I (interest) = $3,282.73
Calculation Steps:First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A, using the mathematical constant, e = 2.71828
A = Pert
A = 8,704.56(2.71828)(0.04)(8)
A = $11,987.29
Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is $11,949.50, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is $11,987.29.
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Suppose f(x) = x2. What is the graph of g(x) = f(4x)?
[tex]g(x)=f(4x)=(4x)^2 = 16x^2[/tex]
The graph is shown in the attached image.