Answer:
D. (-2,-5), (0, -7), (1, -4)
Step-by-step explanation:
From Function Theory we must remember that range of a function is the set of images related to elements of the domain. In this case, we must find the image of each of the three elements that forms the domain of [tex]f(x, y) = (y+2, -x-4)[/tex], which are: [tex]A(x,y) = (1, -4)[/tex], [tex]B(x,y) = (3,-2)[/tex] and [tex]C(x,y) = (0,-1)[/tex].
Then we proceed to find all elements of range:
[tex]A(x,y) = (1, -4)[/tex]
[tex]f(1,-4) = (-4+2,-1-4)[/tex]
[tex]f(1,-4) = (-2,-5)[/tex]
[tex]B(x,y) = (3,-2)[/tex]
[tex]f(3,-2) = (-2+2,-3-4)[/tex]
[tex]f(3,-2) = (0,-7)[/tex]
[tex]C(x,y) = (0,-1)[/tex]
[tex]f(0,-1) = (-1+2,0-4)[/tex]
[tex]f(0,-1) = (1,-4)[/tex]
Which corresponds to option D.
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviation of 0.65 F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 3 standard deviation of the mean, or between 96.23 F and100.3 F?
Answer:
99.7%
Step-by-step explanation:
Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we have mean of 98.18 F and a standard deviation of 0.65 F
The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is
μ - 3σ
= 98.18 - 3(0.65)
= 98.18 - 1.95
= 96.23 F
μ + 3σ.
98.18 + 3(0.65)
= 98.18 + 1.95
= 100.13 F
Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%
Customers arrive to a bank according to a Poisson process having a rate of 8.6 customers per hour. Suppose we begin observing the bank at some point in time. (a) What is the probability that 3 customers arrive in the first 30 minutes
Answer:
The value is [tex]P(X = 3) = 0.1798[/tex]
Step-by-step explanation:
From the question we are told that
The rate is [tex]\lambda = 8.6 \ hr ^{-1}[/tex]
General probability distribution for Poisson distribution is mathematically represented
[tex]P(X = x) = \frac{(\lambda * t)^{x} }{x!} * e^{-\lambda * t}[/tex]
Given that is in per hour then the unit of t is in hours
Generally 30 minutes = [tex]0.5 \ hours[/tex]
Generally the probability that 3 customers arrive in the first 30 minutes is mathematically represented
[tex]P(X = 3) = \frac{( 8.6 * 0.5 )^{3} }{3!} * e^{-8.6 * 0.5 }[/tex]
=> [tex]P(X = 3) = 0.1798[/tex]
These triangles are scaled copies of each other. Four right triangles labeled F, B, G, and H. Triangle F has the vertical side labeled 8, the horizontal side labeled 6, and the longest side labeled 10. Triangle B has the vertical side labeled 2, the horizontal side labeled 3 halves, and the longest side labeled 5 halves. Triangle G has the vertical side labeled 4, the horizontal side labeled 3, and the longest side labeled 5. Triangle H has the vertical side labeled 8 thirds, the horizontal side labeled 2, and the longest side labeled 10 thirds. For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first? Remember that area is scale factor x scale factor. Use Triangle G and Triangle F
Answer:
The question is not complete, below is the completed question:
These triangles are scaled copies of each other. Four right triangles labeled F, B, G, and H. Triangle F has the vertical side labeled 8, the horizontal side labeled 6, and the longest side labeled 10. Triangle B has the vertical side labeled 2, the horizontal side labeled 3 halves, and the longest side labeled 5 halves. Triangle G has the vertical side labeled 4, the horizontal side labeled 3, and the longest side labeled 5. Triangle H has the vertical side labeled 8 thirds, the horizontal side labeled 2, and the longest side labeled 10 thirds. For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first? Remember that area is scale factor x scale factor.
1. Triangle G and Triangle F
2. Triangle G and Triangle B
3. Triangle B and Triangle F
4. Triangle F and Triangle H
5. Triangle G and Triangle H
6. Triangle H and Triangle B
Answer:
1. Triangle G and Triangle F = 4 times
2. Triangle G and Triangle B = 0.2 times
3. Triangle B and Triangle F = 16 times
4. Triangle F and Triangle H = 0.11 times
5. Triangle G and Triangle H = 0.44 times
6. Triangle H and Triangle B = 0.56 times
Step-by-step explanation:
using the image of the triangles attached to this solution, let us calculate the area of each pair of triangles
1. Area of Triangle = [tex]\frac{base\ \times\ height}{2}[/tex]
[tex]F = \frac{6 \times 8}{2} = \frac{48}{2} = 24\\B = \frac{\frac{3}{2} \times 2 }{2} = \frac{3}{2} = \frac{3}{2}\\ G = \frac{3 \times4}{2}= \frac{12}{2} = 6\\ H = \frac{2 \times \frac{8}{3} }{2} = \frac{16}{6} = \frac{8}{3}[/tex]
To find by how many times the second triangle is larger than the first, we will calculate the ratio of the areas of the second triangle to the first
1. Triangle G and Triangle F = 24:6 = 4
∴ The area of triangle F is 4 times larger than triangle G
2. Triangle G and Triangle B = 3/2 : 6 = [tex]\frac{1}{4}[/tex] = 0.2
∴ The area of triangle B is 0.2 times larger than triangle G
3. Triangle B and Triangle F = [tex]24 : \frac{3}{2} = 16[/tex]
∴ The area of triangle F is 16 times larger than triangle B
4. Triangle F and Triangle H = [tex]\frac{8}{3} : 24 = \frac{1}{9} = 0.11[/tex]
∴ The area of triangle H is 0.11 times larger than triangle F
5. Triangle G and Triangle H = [tex]\frac{8}{3} : 6 = \frac{4}{9} = 0.44[/tex]
∴ The area of triangle H is 0.44 times larger than triangle G
6. Triangle H and Triangle B = [tex]\frac{3}{2} : \frac{8}{3} = \frac{9}{16} = 0.56[/tex]
∴ The area of triangle B is 0.56 times larger than triangle H
A single card is drawn from a standard deck. Find the probability of the following event. (Enter your probability as a fraction.) Drawing a black card or a face card
Answer:
8/13
Step-by-step explanation:
In a standard deck there are 52 cards. Let A denote the event of drawing a black card and B denote the event of drawing face card. We have to find P(A or B) or P(A∪B).
P(A∪B)=P(A)+P(B)-P(A∩B)
There are 26 black cards in a standard deck so,
P(A)=26/52.
There are 12 face cards in a standard deck so,
P(B)=12/52.
There are 6 cards that are black face cards.
P(A∩B)=6/52.
P(A∪B)=P(A)+P(B)-P(A∩B)
P(A∪B)=26/52+12/52-6/52
P(A∪B)=38/52-6/52
P(A∪B)=32/52
P(A∪B)=8/13
Thus, probability of drawing a black card or a face card is 8/13.
If Merrida multiplies the first term, 7 by a factor of 6 what should she do to find the other term for the equivalent
ratio?
2 x + 3 = x − 4 solve for x
Please anyone?
Answer:
x=-7
Step-by-step explanation:
[tex]2x - x = - 4 - 3[/tex]
[tex]x = - 7[/tex]
i think this is the answer
Answer:
x = -7
Step-by-step explanation:
subtract 3 from both sides and subtract x from both sides
x = -7
Bailey had 35.78 Elena have 39.51 how many seconds bailey could have won by
Answer:
the answer would be 3.73
Step-by-step explanation:
all you gotta do is subtract 39.51 and 35.78 and you get your answer
Does anyone know this stuff? Im bad at it
Answer:
6
Step-by-step explanation:
A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. What is the Probability of two or more questions right? X 0 1 2 3 P(X) .1875 .4375 .3125 .0625
Answer:
[tex]P(X\geq 2) = 0.375[/tex]
Step-by-step explanation:
Given
X ------0 --------1 -------- 2--------- 3
P(X) --.1875 -.4375 ---.3125 --- .0625
Required
Determine [tex]P(X\geq 2)[/tex]
This is calculated as:
[tex]P(X\geq 2) = P(X = 2) + P(X = 3)[/tex]
[tex]P(X\geq 2) = 0.3125 + 0.0625[/tex]
[tex]P(X\geq 2) = 0.375[/tex]
Use the measurements of the original figure and the scale drawing to calculate the scale factor and missing measures.
What is the scale factor?
What is the length of A?
What is the length of B?
Answer:
Step-by-step explanation: scale factor is 1/10 the length of a is 1 the length of b is 8.5
The scale factor is 1/10, the length of A is 1 cm and the length of B is 8.5 cm.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
From the given figure,
Scale factor = 6.2/62
= 1/10
The length of A = 1/10 ×10 cm
= 1 cm
The length of B = 1/10 ×85 cm
= 8.5 cm
Therefore, the scale factor is 1/10, the length of A is 1 cm and the length of B is 8.5 cm.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
#SPJ2
Joe Mathis works as a pianist in a local restaurant. He makes $8.50 an hour.
He was able to work 39 hours last week. How much money did he make that
week?
Answer:331.5
Step-by-step explanation:
Multiplication is the process of multiplying. The amount that is made by Joe last week is $331.5.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that Joe Mathis works as a pianist in a local restaurant. He makes $8.50 an hour. He was able to work 39 hours last week. Therefore, the amount that is made by Joe Mathis in the last week is,
Amount made by Joe = Amount paid per hour × Number of hours
= $8.50 per hour × 39 hours
= $331.5
Hence, the amount that is made by Joe last week is $331.5.
Learn more about Multiplication here:
https://brainly.com/question/14059007
#SPJ2
1. John and Sally each had a salad and two waters as well as a piece of
cheesecake for dessert, which came to $20.50. Their salads were
delicious, but their cheesecake was not as fresh and it should have
been. They decide to leave the standard 15% tip. How much of a tip will
they leave and how much is their total?
Can someone help me with number 1 and 2
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 117 chips. (a) Determine the 28th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 97% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate
Answer:
Using z score formula:
X = z ∂ + µ
= 157.833
Step-by-step explanation:
Solution:
Mean = µ = 1262
Standard deviation = ∂ = 117
(a) 28th percentile for the number of chocolate chip.
P( z < z) = 28%
= 0.28
P( z<- 0.58) = 0.28
Z = -0.58
By using z score formula:
Z = x - µ /∂
-0.58= x – 117 / 1262
X = (- 0.58)(117) + (1262)
= 1194.14
(b) Middle 97% of bag.
P(-z < z < z) = 97%
= 0.97
P( z < z) – p(z < -z) = 0.97
2p(z < z) -1 = 0.97
2p (z < z) = 1 + 0.97
P(z < z) = 1.97 / 2
= 0.99
P(z < 2.33) = 0.99
Z ± 2.33
By using z score formula:
Z = x - µ / ∂
X = z ∂ + µ
= - 2.33 x 117 + 1262
=989.39
Z = 2.33
X = z ∂ + µ
= 2.33 x 117 + 1262
=1533.61
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate.
By using standard normal table,
The z dist’n formula:
P(z < z ) = 25%
=0.25
P(z < -0.6745) = 0.25
Z = 0.6745
Using z score formula:
X = z∂ + µ
= - 0.6745 x 117 + 1262
= 1183.0835
First quartile = Q1 =1183.0835
The third quartile is:
P(z<z) = 75%
= 0.75
P(z < 0.6745) = 0.75
Z = 0.6745
Using z score formula:
X = z ∂ + µ
= 0.6745 x 117 + 1262
= 1340.9165
IQR = Q3 – Q1
= 1340.9165 – 1183.0835
= 157.833
Can you all help me ? Please this is my test grade
I only have 15 minutes to finish
Answer:
(x+2)+(x-6)=16
Step-by-step explanation:
the center of the circle is (h, k)
In this case it's (-2,6)
the radius is 4 which is known as r
the formula is: (x-h) + (x-k)= r^2
then you just plug it in
Find the value of each variable.
I need help only on 3 please
i have another one sry out fated meme but i need 1-1 is it 0? or is it -1
Answer:
It is 0
Step-by-step explanation:
Answer:
1-1 is 0 if it was 1-2 it would be -1
Step-by-step explanation:
A researcher wants to determine if birthweights of children born to U.S. mothers is affected in any way when large megadoses of caffeine are consumed routinely by the mother during pregnancy. It is known that the birthweights are normally distributed with mean 7.5 pounds and standard deviation 1 pound. When drawing a sample of size 40 from such a population, and computing the mean birthweight in the sample, use the Central Limit Theorem to find the 2.5-th percentile of the distribution of sample means.
Answer:
7.19
Step-by-step explanation:
Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by one-sixth. Is Sophia correct?
Answer:
Sophia is not correct
Step-by-step explanation:
The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values
Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]
Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6
Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]
Now it can be further reduced by a common factor i.e. 2
So now the fraction is [tex]\frac{5}{2}[/tex]
Thus, the ratio is 5:2
Hence, she is not correct
the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat
Answer:
450
Step-by-step explanation:
First we have to find the discount
20% of 1500 = 300
if you search up 20 x 1500/100, it would say 300
you can do that same equation in your maths book, and also by canceling out
10% vat tax
so 10% of 1500 = 150
since it is tax, we have to add it to our discount
300 + 150 = 450
450 is the answer
Write the expression as a monomial in standard form.
(−3xy^2)^3 · (-2/3x^2y^3)^4
Answer:
It would be -16/13x^11y^18.
The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is
-16 /3[tex]$ x^5y^6[/tex]
What is meant by standard form?A number in standard form in mathematics. Standard decimal numbers are the easiest to read and write. For example, the standard form of the decimal number 0.007 is 7 10-3. It can be difficult to read or write very large or very small numbers. As a result, we write them in standard format. Any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten is said to be in standard form.An equation is written in standard form as Ax + By = C, where A, B, and C are all integers. This form of the equation is especially useful for calculating the x- and y-intercepts.Given,
[tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(-3 x y^2\right)^3:-27 x^3 y^6 \\[/tex]
[tex]&=-27 x^3 y^6\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(\frac{-2}{3 x^2 y^3}\right)^4: \frac{16}{81 x^8 y^{12}} \\[/tex]
[tex]&=-27 x^3 y^6 \frac{16}{81 x^8 y^{12}}[/tex]
Apply the fraction rule:
[tex]$\quad a \cdot \frac{b}{c}=\frac{a \cdot b}{c}$[/tex]
∴ [tex]=-\frac{27 x^3 y^6 \cdot 16}{81 x^8 y^{12}}[/tex]
Factor the number: 81 = 27.3
[tex]=-\frac{27 x^3 y^6 \cdot 16}{27 \cdot 3 x^8 y^{12}}[/tex]
Cancel the common factor: 27
[tex]=-\frac{x^3 y^6 \cdot 16}{3 x^8 y^{12}}$$[/tex]
Simplify
[tex]$\frac{x^3}{x^8}: \frac{1}{x^5}$[/tex]
∴ [tex]=-\frac{y^6 \cdot 16}{3 x^5 y^{12}}[/tex]
Simplify the equation,
[tex]$\frac{y^6}{y^{12}}: \frac{1}{y^6}$[/tex]
then we get,
[tex]=-\frac{16}{3 x^5 y^6}[/tex]
Hence, The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is -16 /3[tex]$ x^5y^6[/tex]
To learn more about standard form, refer to:
https://brainly.com/question/187506
#SPJ2
Paul split an inheritance between two investments, one paying 7% annual interest and the other 10%. He invested twice as much in the 10% investment as he did in the 7% investment. If his combined annual income from the two investments was $4050, how much did he inherit?
Graph the linear function f(x) = 3 – 6x .
Answer:
put one point at (0,3)
put another point at (1,-3)
draw a line between them
Step-by-step explanation:
could u vote me brainliest plz? thx :)
The standard formula for calculating the equation of a line is expressed as
y = mx + b
m is the slope of the line
b is the y-intercept of the line
Given the equation to graph expressed as g(x) = 3 - 6x
First, we need to get the x and y-intercept of the line expressed as:
For the x-intercept, y = 0
0 = 3 - 6x
6x = 3
x = 0.5
The x-intercept is at (0.5, 0)
For the y-intercept, x = 0
y = 3 - 6(0)
y = 3
The y-intercept is at (0, 3)
Plot the graph of a line passing through the coordinate points (0.5, 0) and (0, 3) as shown below;
Learn more here: https://brainly.com/question/17003809
PLEASE HELP I CANT DO MATH
Answer:
c
Step-by-step explanation:
the number line says less than 4 so if you solce for all the equations c will be x<4
Can an opposite and an absolute value of an integer be the same?
Yes and opposite and an absolute value of an integer will be the same.
What is the measure of an exterior angle of a regular 14-sided polygon? Enter your answer as a decimal in the box. Round to the nearest tenth of a degree.
Answer:
21.715 degrees.
Step-by-step explanation:
There are 14 vertexes (vertices) for a 14-gon. It is 'regular' so all these angles are equal. So the exterior angle of each is 180-154.285 = 21.715 degrees.
Solve for n.
-53 + n = -28
-35
-25
25
35
Answer:
25
Step-by-step explanation:
-28+53
Hope this helps! :)
The Daily Info charges a fee of $650 plus $80 per week to run an add. The People's Paper charges $145 per week. For how many weeks must an ad run for the total cost at the Daily Info to be less expensive than the cost at the People's Paper?
Answer:
10 weeksStep-by-step explanation:
let the total cost be y
and let the number of weeks be x
Daily Info charges
y=650+80x---------1
People's Paper charges
y=145x---------------2
equating 1 and 2 to solve for x we have
650+80x=145x
650=145x-80x
650=65x
x=650/65
x=10
Therefore the answer is 10 weeks
Rewrite each of the following numbers
as a square or a cube of some other
number.
0.064
A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1664 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 206 149
Dorm 295 276
With Parent(s) 55 68
Sorority/Fraternity House 132 204
Other 180 99
What is the probability that a customer is female and lives in a dorm or is female and lives in 'Other'? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer: 0.2254
Step-by-step explanation:
Let E= Event of getting of female lives in a dorm.
F = Event of getting of female lives in a 'Other'.
From the table , n(E) = 276 and n(F) = 99
and n(E∩F) = 0 [E and F are Mutually exclusive]
Now, n(E∪F)= n(E) + n(F) - n(E∩F)
= 276+99-0
= 375
also, n(S) =1664 (Sample size)
Required probability : [tex]P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}[/tex]
[tex]=\dfrac{375}{1664}\approx0.2254[/tex]
Hence, the probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254
