The graph and inverse of a function are reflections of each other along the line y = x.
A relation made up of ordered pairs (x, y) has as its inverse the set of all ordered pairs (y, x).
When a point is mirrored over the line y = x, the x- and y-coordinates swap places. Similarly, when a point is mirrored over the line y = -x, the x- and y-coordinates swap places and become negated.
Therefore,
The point (x, y)'s reflection over the line y = x is (y, x).
The point (x, y)'s reflection over the line y = - x is (-y, -x).
Thus, the graph and inverse of a function are reflections of each other along the line y = x.
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In a sample of 16 employees randomly selected at a company, the average age is 25 years and the standard deviation is 2 years. We want to test if the average age of all employees is greater than 24. If ages are normally distributed in the population, using a significance level of 0.05, we can claim that the population mean is: Group of answer choices
If ages are normally distributed then using a significance level of 0.05 , we can claim that the population mean is greater than 24.
Given sample mean of 25 years , sample size of 16 ,standard deviation of 2 years.
We have to find whether the population average is greater than 24.
We have to use t test because n is less than 30. It is right tailed.
We have to first form Hypothesis.
[tex]H_{0}[/tex]:μ>24,
[tex]H_{1}[/tex]:μ<24.
t=X-μ/S/[tex]\sqrt{n}[/tex]
t critical at 5% significance level and degree of freedom=15 (16-1)=1.7531
t=24-25/2/[tex]\sqrt{16}[/tex]
=-1/0.5
=-2
Because 1.7531 is greater than -2 so we will accept the null hypothesis.
Hence we can say that the average of population is greater than 24.
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Note: Figure is not drawn to scale.
The object above is symmetrical through Z. If Y = 14 inches, Z = 14 inches, and H = 10 inches, what is the area of the object?
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of kite = (product of diagonals)/2
Area of kite = (10 * 14) / 2 = 70 in²
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
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The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 26 white-collar employees worked on average 42.08 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 40? Assume that the population standard deviation is 3.39 hours. Please use the exact value (from R) for all critical values. c) Is there any evidence to suggest the true mean number of hours worked per week by white-collar workers is greater than 40? Perform the hypothesis test at a 0.5% significance level. (0.5 pts.) Calculate the test statistic. 3.13 You are correct. Your receipt no. is 152-5185 Previous Tries (0.5 pts.) Calculate the p-value. Please write your answer in scientific notation using an E for the exponent and including at least 3 decimal places. For example, 1.234 x 10-5 would be written as 1.234E-5. 8.782x10-4 (0.5 pts.) d) Calculate the appropriate 99.5% bound that is consistent with what you did in parts b) and c).
The necessary assumptions are to get the sample for random sampling and ensure they are normal.
a. The required assumptions to form hypothesis are:Sample has to be drawn from random sampling.Sample has to be approximately normalThe samples have to be independentb. The standard deviation is known hence we have to make use of the z distribution.
c. test statistic42.08 - 40 / (3.39 /√26)
= 2.08 / 0.6648
= 3.129
≈3.13
p value
p(Z > 3.13)
= 0.0008770
8.7e-4
d. Z critical value = 2.81
42.08 +- 2.81 * 3.39/√26
= 42.08 +- 2.81*0.6648
= 42.08 - 1.868, 42.08 + 1.868
= 40.212 ,43.948
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Help me in this question please dont put wrong answers!
Step-by-step explanation:
Has greater balance = Heba
Has more debt = Nour
Read the "note" thing on there it says banks use Negative balances meaning the negative sign ( minus sign) to represent an account with debt which means an account that is owning money e.g -$11, -$15 etc.And they use positive balances meaning the positive sign to represent account that contains valuee.g $2, $7 etc( You might wonder why I didn't put a positive sign on it, the reason is because it's already a positive number so no need to add a positive sign (+) to it) ( BUT they can still add a positive sign to it but it isn't necessary )If you see any number or amount without a negative sign (-) then that number or amount is positive e.g 1, 2,3,4,5,6,11,14,17,20,100,8, $3, $15, $23 and so on..
Hope this helps.Good luck ✅.
Using the number line:
Heba has the greater account balance
Nour has the most debt.
What is a Number Line?A number line shows where a number lies according to the order. Values greater than 0 and are on the right side are greater than values and vice versa.
Given their balances, $29.17 is greater than -$11.99. Therefore, Heba has the greater account balance using the number line.
Since - indicates debt, Nour has the most debt.
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The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
Answer:
Step-by-step explanation:
Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38
Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....
Extra seats - 37,
So,
37 x 10 = 370
TOTAL SEATS = 370
Answer:
1083 seats
Step-by-step explanation:
The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.
SetupThe sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...
Sn = (2a1 +d(n -1))(n/2)
The sum of the series of interest is ...
S38 = (2(10) +1(38 -1))(38/2)
Total seatsThe total number of seats in the theater can be found by evaluating the expression for S38:
S38 = (20 +37)(19) = 57×19 = 1083
There are 1083 seats in the theater.
Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
Given: AD is parallel to BC
Prove: DC = 6 units
Which step is missing?
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
Option C is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
AD is parallel to BC
From the figure and the given information,
We have,
∠DAC ≅ ∠BCA
AC ≅ AC∠DCA ≅∠BACThis means,
Angle-Side-Angle (ASA) Congruence
ΔDAC ≅ ΔBCA
Thus,
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
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Calculating Volume of a Composite Figure 2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units. Which statements about the composite figure are true? Check all that apply. The composite figure consists of two rectangular pyramids. The composite figure can be broken down into rectangular prisms. The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5). The total volume is 45 units3. The total volume is 90 units3.
The answer which are true about the two rectangular pyramids are;
The composite figure consists of two rectangular pyramids.The composite figure can be broken down into rectangular prisms.The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5).Which statements about the composite figure are true?It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.
On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.
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The sales department has determined that the average purchase value for their catalog business is normally distributed with a mean of $30.44 and a standard deviation of $14.99. What is the purchase value at the 20th percentile
The purchase value at the 20th percentile is $17.85 for the distribution with a mean of $30.44 and a standard deviation of $14.99.
How to calculate Z-score to raw score X?The formula for the X is
X = μ + Z × σ
where,
Z- score, μ is the mean, and σ is the standard deviation
Calculation:It is given that,
μ = $30.44
σ = $14.99
x% is given as the 20th percentile
So, α = 0.20
then, the Z score from the normal distribution table is -0.84
On substituting,
X = μ + Z × σ
= 30.44 + (-0.84 × 14.99)
= 30.44 - 12.59
= 17.85
Therefore, the purchase value at the 20th percentile is $17.88.
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In London, the charge of a tour bus consists of a fixed rental price plus a per kilometre rate, that depends on the distance of the trip.
The per kilometre rate is $12/km. You decide to go on a 5 km trip, and it costs you $70.
a) What is the fixed rental cost? Show your work.
b) Determine the equation relating the cost, C, in dollars, and the distance, d, in km.
d) What is the cost of an 18 km trip?
e) What is the distance travelled if the total cost is $250?
PLEASEEEEEEEE
Using a linear function, we have that:
a) The fixed cost is of $10.
b) The equation is: C = 10 + 12d.
c) The cost of an 18 km trip is $226.
d) The distance traveled is of 20 km.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:
C(d) = 12d + b
70 = 60 + b
b = 10.
Hence the equation is:
C(d) = 12d + 10.
For a trip of 18 km, d = 18, hence the cost is:
C(12) = 12 x 18 + 10 = $226.
When the cost is of $250, the distance is found as follows:
250 = 12d + 10
12d = 240
d = 240/12
d = 20 km.
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What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
(–4, –3) and (–2, 1)
(–4, –3) and (2, 1)
(–4, 5) and (2, 1)
(–4, 5) and (–2, 1)
Answer:
(–4, 5) and (–2, 1)
Step-by-step explanation:
Answer: A: (-4,-3) (-2,1)
Step-by-step explanation:
I got this correct on the test. Using the substitution method give brainliest
what is 12(w-3) if w= 10
Hey there!
12(w - 3)
= 12(10 - 3)
= 12(10) + 12(-3)
= 120 - 36
= 84
OR
12(w - 3)
= 12(10 - 3)
= 12(7)
= 84
Therefore, your answer should be:
84
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
Mr. lee walks into the courtyard after school and wants to know the height of the tree. he measures an angle of 47* between a line of sight to the top of the tree and the ground and he is 22 feet away from the tree. how tall is the tree? *
The tree is 23.54 feet tall.
What is an angle?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. It is not necessary for the angle to be in Euclidean space if it lies in the plane. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean.
According to the question,
Height of tree= 22*tan [tex]47^{o}[/tex]
= 22* 1.07
= 23.54 ft.
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Quick algebra 1 assignment for 50 points!
Experts and Geniuses please help asap, TYSM!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
How to use inverse variation to represent a situation
Herein we should present a statement that represents a real life situation and solve that statement. Here is an example:
In accordance with the Coulomb's law, electric force is inversely proportional to the square of the distance between the two electrically charged particles. If you know that electric force is 20 N when the two particles are 10 cm apart, what is the electric force if the distance is doubled.
Based on the statement, we have the following relationship:
F ∝ 1/r²
Where:
F - Electric charge, in newtonsr - Distance between the two electrically charged particles, in centimeters.From such relation, we can determine the resulting force by the following equation:
F/20 = 10²/20²
F = 20 × 10²/20²
F = 5 N
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
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need answered asapp!!
Answer:b
Step-by-step explanation:goooooooo
Solve for x using
cross multiplication.
3x + 6
4
=
4x - 3
5
x = [?]
Enter
Answer:
x = 42
Step-by-step explanation:
Cross multiplying is done as follows:
the denominator of the second fraction is multiplied with the numerator of the first equation and denominator of the first fraction is multiplied with the numerator of the second equation
5(3x+6) = 4(4x-3) multiply inside the parenthesis
15x + 30 = 16x - 12 transfer like terms to same side of the equation
30 + 12 = 16x - 15x
42 = x
At birth, one puppy weighs 15/16 pounds. A second puppy weighs 1 and 1/8 pounds. How much more did the second puppy weigh?
Answer:
3/16 pounds more.
Step-by-step explanation:
It is 1 1/8 - 15/16
= 9/8 - 15/16
= 18/16 - 15/16
= 3/16.
It takes you two and a half hours to drive 175 miles. how fast were you driving? (mph)
If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .
Calculation of the speedDistance travels= 175 miles
time is taken to cover 175 miles = 2.5 hours
We have to find out the speed in mph.
We know that,
Distance = speed x time
⇒speed = distance / time
Putting the value of distance and time, we get:
speed = 175 / 2.5 = 70 mph
Hence the final answer is 70 mph.
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Which function could be a stretch of the exponential decay function shown on the graph?
f(x) = 2(6)x
f(x) = One-half(6)x
f(x) = 2(one-sixth) Superscript x
f(x) = One-half (one-sixth) Superscript x
The function that could be a stretch of the exponential decay function shown on the graph is B. f(x) = One-half(6)x.
How to illustrate the function?From the information given, it can be seen that function A is a monotonically increasing function.
Also, it can be seen that C and D don't pass through (0, 1).
Therefore, the function could be a stretch of the exponential decay function shown on the graph is B.
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Answer:
b
Step-by-step explanation:
A variable that can only take on specific numeric values is called a _____. Group of answer choices categorical variable discrete random variable continuous random variable categorical variable
A variable that can only take on specific numeric values is called A discrete random variable.
According to the statement
A variable which is used to select a specific numeric value and we have to find a those variable
A discrete random variable is one which may take on only a countable number of distinct values.
So, A variable that can only take on specific numeric values is called A discrete random variable.
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I really need help :(((
Answer:
B solving by factoringA the quadratic formulaStep-by-step explanation:
1.The "zero product principle" or "zero product rule" tells you a product will be zero if and only if one or more of the factors is zero. This fact is used to solve quadratic equations by factoring.
Factoring the equation y = ax² +bx +c to the form y = a(x -r)(x -s) allows you to immediately identify the solutions of y=0 as x=r and x=s. These are the values of x that make the factors zero, hence making the product zero.
Finding the values of x that satisfy ax² +bx +c = 0 by rearranging it to the form a(x -r)(x -s) = 0 is called "solving by factoring."
2.When the process of "completing the square" is applied to the standard-form quadratic y = ax² +bx +c, the result is a formula for the two solutions to y = 0:
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
This quadratic formula tells you the solutions based on the coefficients of the original equation, so does not require rearranging the equation in any way.
3x-6=15 what is the value of x?
Answer:
7
Step-by-step explanation:
frist simplfying
3x-6=15
addind six to both side
3x-6+6=15+6
3x=21 dividing by 3
x=7
Josie has 16 coins. Each of her coins is either a quarter or a dime. If she has 6 more dimes than quarters, and the total value is $2.35, how many quarters does Josie have?
Josie has a total of 5 quarters.
How to find the number of quarters using equation?Josie has 16 coins. Each of her coins is either a quarter or a dime.
Let
x = number of quarters
y = number of dime
she has 6 more dimes than quarters.
Therefore,
y = 6 + x
x + y = 16
-x + y = 6
2y = 22
y = 11
11 = 6 + x
x = 11 - 6
x = 5
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Which equation describes this graph?
A. y=−2x
B. y=−2x−3
C. y=−2x+3
D. y=−3x−3
Answer:
D
Step-by-step explanation:
if you look the point on the y axis is -3 which is your starting point
in y=mx+b m is the slope
Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3
The value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
How to simplify the expression?The expression is given as:
6 to the power of 5/6to the power of 2.
Rewrite properly as:
6^5/6^2
Apply the law of indices
6^(5-2)
Evaluate the difference
6^3
Hence, the value of 6 to the power of 5/6to the power of 2 is 6 to the power of 3
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What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis? Choose 1 answer: Choose 1 answer: (Choice A) A \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction (Choice B) B 333 (Choice C) C -\dfrac13− 3 1 minus, start fraction, 1, divided by, 3, end fraction (Choice D) D -3−3
The slope of the line through the points is -3
How to determine the slope?The points are given as:
(-1, 8) and (3, -4)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (-4 - 8)/(3 + 1)
Evaluate the expression
m = -3
Hence, the slope of the line through the points is -3
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The slope of the line that passes through (-1, 8) and (3, -4) is: -3.
How to Find the Slope of a Line?Slope of a line (m) = change in y / change in x.
Given the points, (-1, 8) and (3, -4):
Slope (m) = (-4 - 8)/(3 - (-1))
Slope (m) = (-12)/(4)
Slope (m) = -3
Thus, the slope that passes through the given points is: -3.
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15-point question. Pls help
Answer:
3/8
Step-by-step explanation:
There are 8 equal slices so each slice is 1/8th of the whole pizza
1/8+1/8=2/8 he ate right away
2/8+1/8 for what he ate before going to sleep
2/8+1/8=3/8
Raj measures the height of 70 plants calculate the estimate of the mean height of the plants
The mean height of plants is 44.07cm.
Given that a raj measures the height of 70 plants which is shown in the table in the image attached below.
The mean is defined as the mean value equal to the ratio of the total number of a given set of values to the total number of values contained in that set.
Firstly, we will find the midpoint of the height by using the formula
(upper limit +lower limit)/2
When h is 10<h<20 then the midpoint is
x₁=(10+20)/2
x₁=15
When h is 20<h<0 then the midpoint is
x₂=(20+40)/2
x₂=30
When h is 40<h<50 then the midpoint is
x₃(40+50)/2
x₃=45
When h is 50<h<60 then the midpoint is
x₄=(50+60)/2
x₄=55
When h is 60<h<90 then the midpoint is
x₅=(60+90)/2
x₅=75
Now, we will find the mean height by using the formula
x=(f₁x₁+f₂x₂+f₃x₃+f₄x₄+f₅x₅)/(Σfi)
Here, f₁=7,f₂=15,f₃=27,f₄=13,f₅=8
and Σfi=7+15+27+12+8=70
Substitute these values in the formula, we get
x=(7×15+15×30+27×45+12×55+8×75)/70
x=(105+450+1215+715+600)/70
x=(3085)/70
x=44.07
Hence, the estimate of the mean height of the plants when raj measures the height of 70 plants is 44.07cm.
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