Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f^-1 = x-1/3 , it is known as inverse function.
f(3)= 3*3 +1
=9+1
=10
To find inverse,
x=3x + 1
y=3x+1
Exchanging the position or x and y
x=3y+1
x-1=3y
.•. y=x-1/3
A restaurant was hiring for 6 positions, each with a different hourly wage. These wages were all between 15$ and 20$ per hour, v except for one position whose wage was 40$ per hour. The manager at the restaurant looked at the mean and median of the wages. Then, she decided to remove the 40$ per hour wage from the set and recalculate the mean and median.
How will removing this wage affect the mean and median?
Choose 1 answer:
(A) Both the mean and median will increase, but the mean will increase by more than the median.
(B) Both the mean and median will increase, but the median will increase by more than the mean.
(C)
Both the mean and median will decrease, but the mean will decrease by more than the median.
(D) Both the mean and median will decrease, but the median will decrease by more than the mean.
Help pls
Answer: its C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Please help
Find the area in square units of ABC△ plotted below.
Answer:
Use the distance formula on both points AC and AB.
Distance formula is this:
\begin{gathered}d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\end{gathered}d=(x2−x1)2+(y2−y1)2d=(1−−5)2+(8−−7)2d=(6)2+(15)2d=36+225d=261
Distance for AC is 16.16
Now do the same with the numbers for AB and get the distance of 5.39
2. To get the area, use the formula 1/2 x base x height
AB is the base and AC is the height.
1/2 x 16.16 x 5.39 = 43.55
the answer is 43.5
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Question 2(Multiple Choice Worth 2 points)
(Sample Spaces LC)
List the sample space for rolling a fair seven-sided die.
S = {1, 2, 3, 4, 5, 7}
S = {1, 2, 3, 4, 5, 6, 7, 8}
S = {1}
S = {7}
Question 3(Multiple Choice Worth 2 points)
(Sample Spaces LC)
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Question 4(Multiple Choice Worth 2 points)
(Theoretical Probability MC)
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 5(Multiple Choice Worth 2 points)
(Likelihood MC)
A spinner is given.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
Question 6(Multiple Choice Worth 2 points)
(Experimental Probability MC)
Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials..
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Compare the theoretical probability and experimental probability of pulling a brown marble from the bag.
The theoretical probability, P(brown), is 50%, and the experimental probability is 25%.
The theoretical probability, P(brown), is 50%, and the experimental probability is 22.5%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 13.0%.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
Question 8(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
The probability of not choosing red when choosing one marble from the bag is 90%.
S = {1, 2, 3, 4, 5, 7}
Flipping a fair, two-sided coin.
probability that a student studied for exactly 1 hour is 0.23.
The probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.
The experimental probability of drawing a spade is 0.15.
How to compute the probability?The probability of not choosing red when choosing one marble from the bag will be:
= (3 + 15 + 9)/30
= 27/30
= 90%
The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.
The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.
The probability that a student studied for exactly 1 hour will be:
= 8/(1+8+2+5+9+7+3)
= 8/35
= 0.23
The true statement is that the probability of landing on yellow is less than the probability of landing on blue.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.
The experimental probability of drawing a spade will be:
= 3/(7+3+6+4)
= 3/20
= 0.15.
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Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.
Step-by-step explanation:
The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.
Solve the right triangle. Round decimals to the nearest tenth
Answer:
j = 19.6
k = 25.9
J = 49°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.
AnalysisThe given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Tan = Opposite/Adjacent ⇒ Adjacent = Opposite/Tan
Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.
ApplicationHypotenuse = Opposite/Sin
IJ = 17/sin(41°) ≈ 25.9
Adjacent = Opposite/Tan
IK = 17/tan(41°) ≈ 19.6
Angle J = 90° -41° = 49°
In summary, ...
j = 19.6
k = 25.9
J = 49°
What is the volume of the box pictured below?
fractions 3 and 1 over 10 cubic feet
fraction 3 and 2 over 5 cubic feet
fraction 6 and 5 over 8 cubic feet
fraction 8 and 3 over 4 cubic feet
Graph h(x)=−|x+2|+4.
The graph is in the attached image.
Given below are lease terms at the local dealership. What is the total cash
due at signing?
Based on the various costs resulting from the lease terms at the local dealership, the total cash to pay at signing is $5,480
What is the total cash?This can be found by the formula:
= Down payment + Monthly payment + Security deposit + Acquisition fee
Solving gives:
= 4,100 + 475 + 415 + 490
= $5,480
In conclusion, option A is correct.
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Answer: B. $5005
Step-by-step explanation:
How fast must a 56. 5 g tennis ball travel to have a de broglie wavelength equal to that of a photon of green light (5400 angstroms)? (use scientific notation in your answer: 1. 0e39)
Answer:
Given:
Mass of the tennis ball=56.5 g
wavelength=5400 Angstroms
De-Broglie Wavelength = 5400 Angstrom.
= 5400 × 10⁻¹⁰ m.
Now, Using the Formula,
λ = h/mv
here,
h is the Planck's constant = 6.62 × 10⁻³⁴ J-s.
and v is the velocity of the tennis balls.
∴ 5400 × 10⁻¹⁰ = (6.62 × 10⁻³⁴)/ (0.054 × v)
⇒ 0.054v = (6.62 × 10⁻³⁴)/ (5400 × 10⁻¹⁰)
⇒ 0.054v = 0.0012 × 10⁻²⁴
⇒ v = 0.0012 × 10⁻²⁴/0.054
⇒ v = 0.023 × 10⁻²⁴ m/s.
Hence, the velocity of the tennis balls is 0.023 × 10⁻²⁴ m/s.
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A highway sign shows a speed limit of 65 miles per hour. Which of the following car speed measurements represent the same level of accuracy compared to the speed limit sign?
a. 66 ,ph
b. 56mph
c. 60mph
d.64mph
The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).
What is accuracy?Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.
Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.
According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.
64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.
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Find the term that must be added to the equation x2 4x=1 to make it into a perfect square.
The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.
What is Quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.
Why is it called a quadratic equation?This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.
According to the given information:x²+4x=1
as, the x has coefficient 4.
so,
half the coefficient of x and add and subtract the square of the remaining.
x²+4x + 2 ² - 2² =1
Now,
make the whole square term
x²+4x + 2 ² - 4 - 1=0
( x + 2)² -5= 0
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Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).
Which statement is true for the functions?It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².
On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.
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Given the functions f(x) = x3 x2 – 2x 3 and g(x) = log(x) 2, what type of functions are f(x) and g(x)? justify your answer. what key feature(s) do f(x) and g(x) have in common? (consider domain, range, x-intercepts, and y-intercepts.)
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
According to the statement
we have given that the some functions and we have to justify these functions.
The functions are given as:
f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2
This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common key features of the functions
To do this, we plot the graphs of both functions
From the attached graph, we have the following features:
Function f(x)
Domain: -∞ < x < ∞
Range: -∞ < y < ∞
y - intercept = 3
x - intercepts = -2.37
Function g(x)
Domain: x > 0
Range: -∞ < y < ∞
y - intercept = None
x - intercepts = 0.01
By comparing the key features above, we can conclude that the common features in both functions is their range.
The functions f(x) and g(x) are different functions
The function f(x) is a cubic function, while the function g(x) is a logarithmic function.
The common feature in both functions is their range
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2x + 4y = 12
y = A system of equations. 2 x plus 4 y equals 12. y equals StartFraction one-fourth EndFraction x minus 3.x – 3
What is the solution to the system of equations?
Answer:
x = 4, y = 1
Step-by-step explanation:
y = (1/4)x
2x + 4y = 12
replace y with something x
2x + 4(1/4)x = 12
3x = 12
x = 4
so y = 1
To make cream ice pops, nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. how much ice pop mixture can each mold hold when full? a. 30 pi cubic centimeters b. 10 pi cubic centimeters c. 20pi cubic centimeters d. 60pi cubic centimeters
Answer:
C
Step-by-step explanation:
Givens
r = 2 cm
h = 15 cm
pi = 3.14 The question does not expect a number for pi
Formula
V = (1/3) pi r^2 h Substitute givens into formula
Solution
V = 1/3 * pi * 2^2 * 15 Combine. Remember pi is left as it is
V = 1/3 * pi * 4 * 15
V = 1/3 pi * 60 Divide 60 by 3
V = 20 pi
A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
The weight of a 36-inch piece of PVC pipe is 0.20 pounds
How to determine the weight of a 36-inch piece of PVC pipe?The given parameters about the 36-inch piece of PVC pipe are
Height, h = 36 inches
Outside diameter, D = 0.82 inches
Inside diameter, d= 0.75 inches
The volume of the PVC pipe is then calculated as:
V = πh(D/2)^2 - πh(d/2)^2
Substitute the known parameters in the above equation
V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2
Evaluate the quotients
V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2
Evaluate the exponents
V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625
Evaluate the products
V = 19.002024 - 15.89625
Evaluate the difference
V = 3.105774 cubic inches
From the question, we have:
Weight = 0.063 pounds per cubic inch
So, the total weight is
Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch
Evaluate the product
Total weight = 0.195663762 pounds
Approximate
Total weight = 0.20 pounds
Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds
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what is Rational Number
Answer:
In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.
PLEASE HELP IM STUCK
Step-by-step explanation:
2 equations with 2 variables.
the most common approach is
1. use one equation to express one variable by the other.
2. use this expression in the second equation and solve for the second variable.
3. use that solution in the original first equation and solve for the first variable.
the end.
0.05N + 0.10D = 2.20
N + D = 23
1. N = 23 - D
2. 0.05(23 - D) + 0.10D = 2.20
1.15 - 0.05D + 0.10D = 2.20
0.05D = 1.05
D = 1.05/0.05 = 21
3. N = 23 - D = 23 - 21 = 2
2 Nickels, 21 Dimes
Qualitative data are made up of words rather than numbers. Because of this, analyzing the data is _____________. (Select all that apply)
Answer: 6328723894
Step-by-step explanation:
The points A(-3, 4), B(3, 2), C(1,4), and D(-5, -2) form quadrilateral ABCDin the coordinate plane. What condition verifies that the
diagonals are perpendicular?
PLEASED HELP
The diagonals of the qudrilateral will not be perpendicular to each other.
What is a quadrilateral?A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.
The slope of a coordinate pair is given by the change in y divided by the change in x, that is:
For the diagonal AD the slope will be:-
Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )
For the diagonal BC, the slope will be:-
Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1
The multiplication of the two slopes will be,
M = ( 1 / 3 ) x -1 = ( - 1 / 3 )
Therefore, the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.
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Answer:
The product of the slopes of the diagonals is -1.
Step-by-step explanation:
I had the question and got it right.
Find the surface area of the cylinder and round to the nearest tenth. (It is recommended that you use the π button on your calculator) (Note: Remember the radius is half of the diameter.)
If you are using a screen-reader, please consult your instructor for assistance.
The surface area of the cylinder is 18.84 square feet
How to determine the surface area?The given parameters are
Height, h = 2 ft
Diameter, d = 2 ft
The radius (r) is half of the diameter (d)
This is calculated as:
Radius = Diameter/2
So, we have:
r = d/2
Substitute 2 for d
r = 2/2
Evaluate the quotient i.e. divide 2 by 1
r = 1
The surface area is then calculated using the following formula
A = 2πr² + 2πrh
Substitute the given values in the above equation
So, we have:
A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2
Evaluate the exponents
A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2
Evaluate the products
A = 6.28 + 12.56
Evaluate the sum
A = 18.84
Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet
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The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 160t. match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
EachEach value of time elapsed (in seconds) corresponding instantaneous velocity (in feet/second) are:2s= 96, 3s = 64, 4s= 32, 5s = 0, 6s = -32, 7s = -64. 8s= -96, 9s= -128.
VelocityGiven equation:
f(t) = -16t² +160t
Velocity (v)=df(t)/dt
=-2×16t²+ 160t
=-32t+160
Hence:
-32t+160
1. -32×(1) + 160 = 128ft/s
2. -32×(2) + 160 = 96ft/s
3. -32×(3) + 160 = 64ft/s
4. -32×(4) + 160 = 32m/s
5. -32×(5) + 160 = 0m/s
6. -32×(6) + 160 = -32m/s
7. -32×(7) + 160 = -64m/s
8. -32×(8) + 160 = -96m/s
9. -32×(9) + 160 = -128m/s
The pairs are;
2s= 96
3s = 64
4s= 32
5s = 0
6s = -32
7s = -64
8s= -96
9s= -128
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The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for. b. The amount of variation in the dependent variable that is not explained by the regression function. c. The amount of variation in the independent variable that is not explained by the regression function. d. The amount of variation in the residuals that is explained by the regression function.
The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.
What is regression sum of squares?
The regression sum of squares serves as the sum of the differences that exist between the predicted value and the mean of the variable.
The Sum of Squared Error however states the difference between the observed and the predictive value.
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f(x)=4x^(3)+6x^(2 )-3x-4
g(x)=4x-3
Find (f - g) (x)
The value of (f - g)(x) is as follows:
(f - g)(x) = 4x³ + 6x² - 7x - 1
How to solve functions?f(x) = 4x³ + 6x² - 3x - 4
g(x) = 4x - 3
Let's find the function:
(f - g)(x)
Therefore,
(f - g)(x) = 4x³ + 6x² - 3x - 4 - ( 4x - 3)
Hence, let's open the bracket
(f - g)(x) = 4x³ + 6x² - 3x - 4 - 4x + 3
Let's combine like terms
(f - g)(x) = 4x³ + 6x² - 3x - 4x - 4 + 3
Therefore,
(f - g)(x) = 4x³ + 6x² - 7x - 1
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How is a circumference related to an arc
Answer:
An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.
Pls help
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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Which of the following BEST defines an output? please help me, I've been stuck on this one for a while!
A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined functionIn this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.
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Complete Question:
Which of the following best defines an output?
A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
D. An output is a set of ordered pairs in which no y-value repeats.
Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother had $15 more than the other. How much has each saved?
Answer:
20 and 35 dollars.
Step-by-step explanation:
x + x + 15 = 55
2x + 15 = 55
2x = 55 - 15
2x = 40
x = 40/2
x = 20
One of the brothers has saved 20 dollars, while the other has 35 dollars.
The total number of reds, yellows, and
greens on a scale is 9. The reds weighed
3 pounds each, the yellows weighed
6 pounds each, and the greens weighed
5 pounds each. The total weight is 44
pounds. If there are 2 more greens than reds,
how many of each color are there?
Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.
How to find each colour using total weight?The total number of reds, yellows, and greens on a scale is 9.
The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44
pounds. There are 2 more greens than reds.
Therefore,
let
x = number of reds
number of greens = x + 2
y = number of yellow
Therefore,
x + x + 2 + y = 9
2x + y = 7
3x + 6y + 5(x + 2) = 44
3x + 6y + 5x + 10 = 44
8x + 6y = 34
Hence,
2x + y = 7
8x + 6y = 34
8x + 4y = 28
8x + 6y = 34
2y = 6
y = 6 / 2
y = 3
2x + 3 = 7
2x = 7 - 3
2x = 4
x = 4 / 2
x = 2
Therefore,
the number red colour = 2
the number of green colour = 2 + 2 = 4
the number of yellow colour = 3
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Emily invests $x at a rate of 3% per year simple interest. After 5 years she has $20.10 interest. I Find the value of x.
The equation be 20.10 = X × 3 × 5/100 then, the value of X = 134.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
The formula for Simple Interest exists PTR/100,
where, P = Principal
T = Time period in years
R = Rate of interest per annum.
Simple interest = PTR / 100
20.10 = X × 3 × 5/100
simplifying the above equation, we get
20.10 = 15X / 100
15X = 20.10 × 100 = 2010
X = 2010/15 = 134
X = 134.
Therefore, the value of X exists at 134.
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The cost to produce a product is modeled by the function f(x) = 5x2 − 70x 258, where x is the number of products produced. complete the square to determine the minimum cost of producing this product. 5(x − 7)2 13; the minimum cost to produce the product is $13. 5(x − 7)2 13; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $7. 5(x − 7)2 258; the minimum cost to produce the product is $258.
The minimum cost to produce the product is $7.
What are functions?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.To determine the minimum cost:
We have to determine the minimum cost of producing this product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].
Dividing the above equation by 5, we get
[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]
Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.
Since the coefficient of 'x' is 14, and half of 14 is '7'.
So, adding and subtracting from the above equation.
[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]
Now, we have to determine the minimum cost to produce the product.
Since [tex]f(x) = 5x^{2} -70x+258[/tex].
[tex]f'(x) = 10x-70[/tex]
Now, let f'(x)=0
[tex]10x-70=0\\10x=70[/tex]
Therefore, x=7
Now, consider which is greater than 0.
Therefore, x= 7 is the minimum cost.
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Answer: The minimum cost to produce the product is $13.
I apologize for the late answer, hope this helps in the future!
Step-by-step explanation:
To complete the square, we need to rewrite the given function in the form:
f(x) = a(x - h)^2 + k
where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.
We start by factoring out the coefficient of x^2:
f(x) = 5(x^2 - 14x + 51.6)
To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:
f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)
= 5((x - 7)^2 + 13)
Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:
5(x − 7)2 + 13
