The inverse of the given function is, h^(-1)(x) = (x - 8)/6.
What is inverse of function?
What a function's inverse function is F is a function that reverses what F did. The inverse of f is represented by f-1 if it exists and only if f is a bijective function.
Consider, the given function
h(x) = 6x + 8
Let,
y = 6x + 8
Replace x with y,
x = 6y + 8
Solving the equation for y,
x - 8 = 6y
y = (x - 8)/6
Replace y with h^(-1)(x),
So,
h^(-1)(x) = (x - 8)/6.
Hence the inverse of the given function is, h^(-1)(x) = (x - 8)/6.
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Triangles acd and bcd are isosceles. Angle bac has a measure of 18 degrees and angle bdc has a measure of 48 degrees. Find the measure of angle abd.
The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees
What are isosceles triangles?
Isosceles triangles are triangles that have two sides equal in measurement.
Main Body:
From the given diagram;
∠BAC = 18 degrees
∠BDC = 48 degrees
Required angle : ∠ABD
From the diagram, ∠DAB = ∠BAC = 18 degrees
Also, ∠ADC + ∠ACD + ∠DAC = 180
Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes
∠ADC + ∠ADC + ∠DAC = 180
2∠ADC + ∠DAC = 180
2∠ADC = 180 - 36
2∠ADC = 144
∠ADC = 144/2
∠ADC = 72 degrees
This means that ∠ADB = 72 - ∠BDC
∠ADB = 72 - 48
∠ADB = 24 degrees
Get the required angle ABD
From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180
∠ABD + 24 + 18 = 180
∠ABD + 42 = 180
∠ABD = 180 - 42
∠ABD = 138 degrees
Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.
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a sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects. their mean score is 71.2 with a standard deviation of 10.5. construct the 99 percent confidence interval for the mean score of all subjects.
The 99 percent confidence interval for the mean score of all subjects lies greater than 63.464 and less than 78.936.
Given:
No. of samples (n)= 16
df = n-1 = 16 -1 = 15
The mean score is 71.2
The standard deviation = 10.5.
So, from the t-distribution of critical values table through the above-mentioned details. We get the values:
Alpha / 2 = 0.005
z = 99/100 + 0.005 = .99 + .005 = .995
Sample mean = xbar = 76.2
t = 2.947
The formula for standard error = E = value of t (at z, and df) / S.D./sqrt(n)
i.e. E = 2.947 x 10.5 / sqrt 16 = 7.736
I = 71.2 +/- E = 71.2 +/- 7.736
99 percent confidence interval - 71.2 +/- 7.736
Adding both sides 7.736 for range. We get,
63.464 < u < 78.936
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In a toy store the ratio of legos to board games is
9:6. If the store has 24 legos, how many board games
are in the store?
The store has 16 board games
What are equivalent ratios?
The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.
Let x = number of legos
Let y = number of board games
Given ratio: 9:6= 9/6
x/y = 9/6
substitute x=24
24/y=9/6
Do cross multiplication
(6*24)/9=y
16=y
or
y=16
So, the store has 16 board games
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Find the exact value of the trigonometric function given that in u = − 8 17 and co v = − 9 41. (Both u and v are in Quadrant III. ) ec(v − u)
Answer:
343
Step-by-step explanation:
find distance between (-5,6) and (8,-4) SHOW WORK PLEASE
Answer:
(3,2)
Step-by-step explanation:
-5+8=3
6-4=2
(3,2)
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $ each. She must deliver all the tee-shirts in days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
The equation to represent total amount of money that she receives for the tee shirts in terms of number of machines is 2800*n*(200 - n) .
In the question ,
it is given that
the cost of 1 tee - shirt = $14
total days required to deliver the tee shirt = 20
number of tee - shirts that a machine can produce = 200 per day
let the number of machines = n
so the number of days require to set up the machines = n
hence all the machine will work for = (20 - n) days
1 machines will produce 200(200 - n) tee shirts
n machines will produce = 200n(200 - n) tee shirts in the remaining (20 - n) days .
the selling price of 1 tee shirt is = $14
So, the total money M that she will receive is = 14*200*n*(200 - n)
= 2800*n*(200 - n)
Therefore , The equation to represent total amount of money that she receives for the shirts in terms of number of machines is 2800*n*(200 - n) .
The given question is incomplete , the complete question is
A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money( M ) she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).
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Dan is 12 4/5 years old. Karina is 1 1/6 years older than Dan and Jane is 1 1/3 years older than Karina. How old is Jane?
The age of Jane based on the information is 10 3/10 years.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.
In this case, Dan is 12 4/5 years old, Karina is 1 1/6 years younger than Sarah and Jane is 1 1/3 years younger than Greg
The age of Jane will be:
= 12 4/5 - 1 1/6 - 1 1/3
= 12 24/30 - 1 5/30 - 1 10/30
= 12 24/30 - 2 15/30
= 10 9/30
= 10 3/10
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What has the greater magnitude -41.5 47 -51 or 49
Answer:
The vector which has a greater magnitude.
Solution:
We know that, magnitude of a vector represents the length of it.
The first vector that is 2 meters long has a magnitude 2.
The second vector that is 4 meters long has a magnitude 4.
Clearly, 4 is greater that 2, i.e., 4 > 2. So, magnitude of second vector is greater.
Therefore, the vector that is 4 meters long has greater magnitude.
Step-by-step explanation:
Rajiv wihe to make a cube without a lid with cardboard. The amount of cardboard available i 245 q. Cm. What hould be the length of the ide chooen in order to make the cardboard box?
Rajiv chose to make a cardboard box of length 7 cm from the given cardboard available.
It is given that the amount of cardboard available is 245 cm. Therefore, the box's surface area will be less than or equal to 245 cm².
We are given that the box does not have any lid. Hence, the box is made up of 5 squares.
Let the length of one side of the box be x cm.
We know, that the surface of the area of a regular cube is
6a².
That means,
no. of squares X square of the length.
Hence, the surface area of the box is 5x².
Therefore from the given problem, we get that
5x² ≤ 245
or, x² ≤ 245/5
or, x² ≤ 49
49 is a perfect square of 7. Hence assuming Rajiv makes the largest possible box,
the length of the side he chose is 7 cm.
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Giving brainliest! answer quickly.
The expression on the left side of an equation is shown below.
3 (x + 1) + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
Group of answer choices
2 (x + 6) + x
4(x – 3) – x
3 (x + 4)
3 (x + 1) + 9 x
Answer:
The expression "2(x + 6) + x" would make the equation unsolvable (i.e., no solution),
Step-by-step explanation:
This initially appears to be an odd question, since one might imagine that there would always be a solution for x, no matter what is put into the "box." But lets take a look and see what the possible solutions look like when compared to the original equation. First, rearrange the reference equation so that we can better compared it to the answer options:
3 (x + 1) + 9 = box
3x + 3 + 9 = box
3x + 12 = box
3(x + 4) = box
Now look through the answer options and evaluate how, or if, they may be able to prevent us from finding an actual value or x::
-------------------------
Option[Box] Reformatted Complete Equation Unsolvable?
2(x + 6) + x 3x + 12 3(x + 4) = 3x + 123x + 12 = 3x +12
0 = 0 YES*
4(x – 3) – x 11x - 12 3(x + 4) = 11x - 123x + 12 = 11x - 12
-8x = -24
x = 3 NO
3(x + 4) 3(x + 4) = (x+4)2(x+4) = 0
2x = -8
x = -4 NO
(x + 1) + 9x 10x + 1 3(x + 4) = 10x+1 3x+12 = 10x + 1 -7x = -11 x = (11/7) NO
* The YES answer means that this expression would make the answer unsolvable. Note that the expressions on both sides of the equation are equal. So there is no one answer. Any choice of a value for x will always be a valid solution. A singkle value is not possible with this equation.
Evaluate.
(2/3)4
Enter your answer by filling in the boxes.
??$$
The value of the expression (2/3)4 is 8/3.
Expression:
An expression also known as algebraic expression consists of unknown variables, numbers and arithmetic operators. And it does not contain any equality or inequality symbols.
Given,
Here we have the expression (2/3)4
Now, we have to evaluate the expression to find the solution for this one.
In order to get the solution for this expression,
We have to rewrite the given expression like the following form,
=> (2/3) x 4
Now, we have to multiply 4 with the numerator, then we get,
=> 8/3
Therefore, the solution of this expression is 8/3.
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Bo fell asleep 84% if the total length was 600 miles how many miles had they travel when bo fell asleep
The total distance traveled when Bo fell asleep is 504 miles.
What is the distance traveled?
The path taken by an object to move from a starting point to an ending location in a specified amount of time with a specific velocity is known as the distance traveled.
Given, the total length of distance = 600 miles
Bo fell asleep = 84%
Let 'x' be the distance traveled.
Then, according to the question
x = 84% of 600 miles
or, x = [tex]\frac{84}{100} * 600[/tex]
or, x = 84*6
or, x = 504 miles
Hence, the total distance traveled when Bo fell asleep is 504 miles.
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consolidated builders has bid on two large construction projects. the company president believes that the probability of winning the first contract (event a) is 0.6, that the probability of winning the second (event b) is 0.5, and that the joint probability of winning both jobs (event {a and b}) is 0.4. what is the probability of the event {a or b} that consolidated will win at least one of the jobs?
The probability of an event {a or b} is 0.7
Probability: It is the branch of mathematics concerning numerical, descriptions of how likely an event is to occur or how likely it is that a proposition is true. the probability of an event is a number between
0 and 1.
if the two events a and b are mutually exclusive then the addition rule of probability is:
P( a or b) = P(a) + P(b) - P(a∩ b)
Given that,
P(a) = 0.6 P(b) = 0.5
P(a ∩ b)= 0.4
According to probability methods, if two events are mutually exclusive, then the probability of either occurring is denoted as P (a ∪ b).
Now, we know that,
P( a ∪ b) = P(a) + P(b) - P( a ∩ b)
= 0.6 + 0.5 - 0.4
= 0.7
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Use Product of Powers Property. Property. Do You Know How? 4. A bacteriologist estimates that there are 5.2 x 104 bacteria growing in each of 20 petri dishes. About how many bacteria in total are growing in the petri dishes? Express your answer in scientific notation.
There are in total 1.04 x 10^6 bacteria that are growing in the petri dish.
Given that, there are 5.2 x10^4 bacteria in each 20 petri dish, we have to multiply 5.3x10^4 by 20, get the total bacteria in all 20 petri dish.
5.2 x10^4x 20
= 1,040,000
We have to write this in scientific notation.
The goal of scientific notation is to make it simple for scientists to write extremely large or extremely small numbers.
Since it always follows this notation, calculating scientific notation for a positive integer is straightforward:
a x 10^b
1.040000
1 is a, there are 6 digits right to the decimal point.
a=1.04
b=6
The scientific notation for total bacteria in 20 petri dish is 1.04 x 10^6.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The compound interest compounded at a rate of 3% quarterly for 5 years is $15,095.39
Compound InterestThe compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The compound interest formula is given below:
A = P(1 + r/n)^nt
Compound InterestP = principalr = rate n = number of times compoundedt = timeSubstituting the values into the equation given;
A = 13000(1 + 0.03/4)^4 * 5
A = 13000(1.0075)^20
A = $15,095.39
The amount at the end of 5 years is $15,095.39
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3) What is the slope of the line from the following points (-3, -2) and (1, -7) ? (Please show your work for your full points)
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{1 +3} \implies \cfrac{ -5 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{5 }{ 4 } \end{array}}[/tex]
Find the points on the ellipse 5x2 + y2 = 5 that are farthest away from the point (1, 0).
The points on the ellipse 5x² + y² = 5 that are farthest away from (1, 0) are (-0.25, ±√4.6875).
The square of the distance from a point on the ellipse to the point (1, 0) is ...
d^2 = (x -1)^2 +y^2
Using the equation of the ellipse to write an expression for y^2, we have ...
d^2 = (x -1)^2 +5 -5x^2
d^2 = -4x^2 -2x +6
The expression on the right is that of a downward-opening parabola with ...
a = -4, b = -2, c = 6
The maximum is located at ...
x = -b/(2a) = -(-2)/(2(-4)) = -1/4
The value of y there is ...
y^2 = 5 -5(-1/4)^2 = 4 11/16
y = √4.6875
Hence the points on the ellipse farthest from (1, 0) are (-0.25,±√4.6875).
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Solve for the indicated letter.
b = 4c, for c
The solution is c = ____.
Answer:
1/4b
Step-by-step explanation:
after fitting a linear regression model to a dataset, the model's slope and intercept are -3 and 0 respectively. now, if we change our independent variable by adding 4.5 units to x, what is the absolute value of the change in the predicted value of dependent variable y?
The absolute value of change in the predicted value of dependent variable Y is 18.
Any variable whose value is influenced by an independent variable is said to be dependent. The thing that is measured or assessed in an experiment or mathematical equation is the dependent variable. The phrase "the outcome variable" is another name for the dependent variable.
Slope = b = -4
Intercept = a = -2.8
So, the equation of the regression line is
y = a + bx
y = -2.8 - 4x ...Equation 1
Now suppose the value of x is changed by adding 4.5
i.e. put x = x + 4.5
So,
y = -2.8 - 4(x + 4.5)
y = -2.8 -4x - 18 ...Equation 2
Comparing 1 and 2 ,
We get the predicted value of dependent variable Y as 18
Therefore The absolute value of change in the predicted value of dependent variable Y is 18
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-3.9 + v < -5.2 Solve the inequality for v.
Simplify your answer as much as possible.
Answer:
v<-1.3
Step-by-step explanation:
Add 3.9 to -5.2
v<-1.3
Hope this helped!
mr. patrick teaches math to 15 students. he was grading tests and found that when he graded everyone's test except payton's, the average grade for the class was 80. after he graded payton's test, the class average became 81. what was payton's score on the test?
Mr. Patrick instructs 15 students in math. He discovered that Payton had received a 95 on the test while grading them from average.
There are 15 kids in Mr. Patrick's class. The average score on his most recent exam was 80 for 14 candidates (not including Payton).
I'm going to use x to represent the unknowable sum of the 14 test scores. Average is computed by adding all the numbers in the set (whose average you're trying to get) together, then dividing by the total number of numbers in that set.
This was the total of their scores: x=1120.
Adding Payton's score now (I'll use the letter p to stand in for her score):
1120+p /15=81→ Her test score was included in the fifteen students' average, which was 81 1120+p=1215
P=95.
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the question is in the image
Answer:
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Step-by-step explanation:
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Three quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls?.
The ratio of boys to girls of the junior members of a tennis club is 1 : 3.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Three-quarters of the junior members of a tennis club are boys.
Assuming the total no. of boys and girls is 1.
∴ 3/4 members are boys and (1 - 3/4) = 1/4 are girls.
So, the ratio of boys to girls is 1/4 : 3/4 which is equal to 1 : 3.
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why would you want to transform a set of raw scores into a set of z-scores? check all that apply. to make all the transformed scores greater than 0 to make sure the z-scores are normally distributed to be able to describe the location of a raw score in the distribution of raw scores to make a distribution with a mean of 0 and a standard deviation of 1
When you transform row score into a set of z- score, you are able to compare the score of both distribution. When you compare the scores you can allow one to have a mean of 0 and standard deviation 01. A z- score let us see how many standard deviation away from the mean an element lies.
Z- score: It is a numerical measurement that describes a value's relationship to the mean of a group of values and is measured in terms of standard deviation from mean.
Raw score: A raw score is unaltered measured. For example:- if there is a test in a class and someone for 75 out of 100, 75 would be there raw score.
Transform a set a raw scores into a set of z score:
Lets understand the importance of transforming raw scores into a set of z score with the help of an example.
For admission in PG program students need to appear in the entrance exam which held in two batches. John appeared in both the exams and he scored 160 out of 200 in paper A and 145 out of 185 on paper B.
Solution: we needs to find the z score corresponding to each paper in order to compare them.
paper A: Score obtained : 160
Average score: 155
Standard Deviation: 10
Paper B: Score obtained: 145
Average obtained: 135
Standard deviation: 08
Using the Z- score formula:
Z = (x - μ) /α
Using the above Z score formula to calculate z score for given raw score values:
z score for Paper A = ( 160-155)÷ 10
Z score for paper B = ( 145 - 135 ) ÷ 1.25
While Evaluating based on z score, we can say that John performed relatively better in paper B as compared to paper A.
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Are the lines perpendicular? x=3 and y=5
A. Yes, their slopes are negative reciprocals
B. No, their slopes are not negative reciprocals
Answer: A. Yes, their slopes are negative reciprocals
Step-by-step explanation:
x=3 is a vertical line where every y value lands on x=3. (Undefined slope)
y=5 is a horizontal line where every x value lands on y=5 (Zero slope)
Even though the slopes are not numbers they can still be negative reciprocals. The lines are indeed perpendicular and thus the slopes are negative reciprocals. The relationship between undefined slopes and zero slopes is negative reciprocals because 0/1 cannot be inversed because anything divided by 0 is undefined.
1. If a circle is centered at (5, -7) and goes through the point (-3, -1), what is the radius?
2. Why do we prefer the standard form for the equation of a circle over the general form?
Answer: r = 11.3
Step-by-step explanation:
Standard form : (x-h)2 + (y-k)2 = r2
(h,k) = (5,7)
(x,y) = (-3,-1)
r2 = (-3-5)2 + (-1-7)2
r2 = [tex]-8^{2} + -8^{2} = 64 + 64 = 128\\r = \sqrt{128} = 11.3[/tex]
When coordinates of the center of the circle and a point on the circle are known, Standard form is the one to use.
Parking Lot Design. A rectangular parking
lot is 50 ft longer than it is wide. Determine the
dimensions of the parking lot if it measures 250 ft
diagonally.
The dimensions x and x+50 are 150 ft by 200 ft. When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them.
How to calculate the dimensions of the parking if it measures 250 ft diagonally?When two polygonal or polyhedral vertices are not on the same edge, a diagonal is a line segment connecting them. Any sloping line is known as a diagonal informally.
If you draw a diagonal, you have 2 right triangles, each with leg lengths of x and x + 50.
The diagonal is the hypotenuse, h = 250
Using Pythagorean theorem:
X² + (x+50)² = 250²
x² + x²+ 100x + 2500 = 62500
2x²+ 100x - 60000 = 0
All are even, so factor out a 2:
x² + 50x - 30000 = 0
From quadratic equation: x = [-50±√(50²-4(1)(-30000))]/(2(1))
x = (-50 ± 350)/2
We can disregard the negative so
x = (-50 + 350)/2 = 300/2 = 150 ft
The dimensions x and x+50 are 150 ft by 200 ft
The complete question is: A rectangular parking lot is 50ft longer than it is wide. Determine the dimensions of the parking lot if the diagonal distance from corner to corner of the lot is 250ft.
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According to the who monica project the mean blood pressure for people in china is 128 mmhg with a standard deviation of 23 mmhg. assume that blood pressure is normally distributed.
The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
What is standard deviation?
A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.
The mean blood pressure for people in china is 128 mmHg.
The standard deviation of 23 mmHg.
For blood pressure of 182.6 mmHg
=p(x> 182.6)
=p(z> 182.6-128/23)
=p(z> 2.37)
=0.0088
Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.
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What is the solution set for 5x−5=15, given the replacement set {0, 1, 2, 3, 4}?
Responses
A: x = 4
B: x = 3
C: x = 2
D: x = 1
E: x = 0
Answer: A: x=4
Step-by-step explanation:
5(4)-5=15
20-5=15
15=15
hank needs to pack 100 golf balls into 8 boxes. each box must contain an equal number of golf balls. how many golf balls does he have left over?
Answer: 4
Step-by-step explanation:
100/8 = 12 golf balls in each box
8*12 = 96 golf balls are used
100-96= 4 gold balls left
