Find the domain and range of the function y = √x-3 + 6
Answer:
Domain: [tex][3,\infty)[/tex]
Range: [tex][6,\infty)[/tex]
Step-by-step explanation:
I assume you mean [tex]y=\sqrt{x-3} +6[/tex]?
Take note of how x cannot be less than 3 because it would result in a negative number under the radical, which isn't real. However, x CAN be 3 because [tex]\sqrt{3-3}+6=\sqrt{0}+6=0+6=6[/tex] which is real.
Therefore, the domain of the function is [tex][3,\infty)[/tex]
As for the range of the function, we saw previously that the minimum of the domain resulted in the minimum of the range, which was 6.
Therefore, the range of the function is [tex][6,\infty)[/tex]
See attached graph below for a visual.
A local running group collected data on the number of miles its group members run each week, x, and their average mile time, y. The results are shown in the table below. Weekly Mileage, x 10 25 12 10 15 20 22 25 20 24 Avg. Mile Time, y 9.3 8.75 8.2 5.5 6.3 8.5 6.7 6.35 5.45 6.25 Calculate the correlation coefficient using technology and interpret what it represents. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, the average mile time decreases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, the average mile time increases. The correlation coefficient of the data is 0.87, which means as the weekly mileage increases, it has no affect on the average mile time. The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
Answer:
The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.Step-by-step explanation:
The correlation coefficient of a data set describes how closely related two variables are. Correlation coefficients close to positive 1 show a strong positive correlation, while correlation coefficients close to negative 1 show a strong negative correlation. When a correlation coefficient is close to 0, it shows no correlation between the data.
For the given data set, calculate the correlation coefficient using technology.
This r-value is closer to 0 then it is to -1. Thus, the correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
Answer:
The correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.Step-by-step explanation:
The correlation coefficient of a data set describes how closely related two variables are. Correlation coefficients close to positive 1 show a strong positive correlation, while correlation coefficients close to negative 1 show a strong negative correlation. When a correlation coefficient is close to 0, it shows no correlation between the data.
For the given data set, calculate the correlation coefficient using technology.
This r-value is closer to 0 then it is to -1. Thus, the correlation coefficient of the data is -0.13, which means as the weekly mileage increases, it has no effect on the average mile time.
During a sale, a store offered a 15% discount on a couch that originally sold
for $800. After the sale, the discounted price of the couch was marked up by
15%. What was the price of the couch after the markup? Round to the nearest
cent.
Answer:
t think the answer is 1040.
4 is a common factor of 28 and 32.
O A. True
O B. False
Answer:
True
Step-by-step explanation:
Answer:
Your answer is B
Step-by-step explanation:
Paul signs up for a new cell phone plan. He is offered a discount for the first five months. After this period, his rate increases by $8.50 per month. His total cost at the end of the year is $245.50. Paul wrote the following equation to represent his plan. 5x + 7(x + 8.50) = 245.50
Answer:
The first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
Step-by-step explanation:
Since Paul signs up for a new cell phone plan, and he is offered a discount for the first five months, and after this period, his rate increases by $ 8.50 per month, and his total cost at the end of the year is $ 245.50, and Paul wrote the following equation to represent his plan: 5x + 7 (x + 8.50) = 245.50; To determine the value of X, the following calculation must be performed:
5X + 7 x (X + 8.50) = 245.50
5X + 7X + 59.50 = 245.50
12X + 59.50 = 245.50
12X = 245.50 - 59.50
12X = 186
X = 186/12
X = 15.50
Therefore, the first 5 months Paul paid $ 15.50, and in the next 7 months he paid $ 24.
What is the product of the polynomials below?
(4x2 - 2x - 4)(2x + 4)
A. 8x? +12x-16-16
B. Bx+12x? - 16X-8
C. 8x +12x2 - 8x-16
O D. Bx° +12x2 - 8x-8
Help please I asp !!!
Answer:
Step-by-step explanation:
1
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
10 15 20
30
55
HI
Town B
5
20
30
40
55
H
0 5
10
15
20
45
50
55 60
25 30 35 40
Degrees (F)
Which statement is the most appropriate comparison of the centers?
O A. The median for town A, 30°, is less than the median for town B,
40°
B. The mean for town A, 20°, is less than the mean for town B, 30°
C. The median for town A, 20°, is less than the median for town B,
30°
O D. The median temperature for both towns is 30°.
Answer:
The answer is:
C. The median for town A, 20°, is less than the median for town B, 30°.
Step-by-step explanation:
Median is the middle (center) value.
Option (C) the median for town A, 20°, is less than the median for town B, 30°.
What is box plot?Box plot is a type of chart often used in explanatory data analysis. A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.
For the given situation,
The diagram shows the box plot of the daily low temperatures for a sample of days in two different towns.
From the box plot, the median of town A is 20° and the median of town B is 30°.
From the data,
⇒ [tex]20 < 30[/tex]
Hence we can conclude that option (C) the median for town A, 20°, is less than the median for town B, 30°.
Learn more about box plot here
https://brainly.com/question/12591498
#SPJ2
Find the slope of the line that passes through these two points. (0, -2): (5. 3)
Answer:
[tex]\displaystyle m = 1[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify
Point (0, -2)
Point (5, 3)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{3--2}{5-0}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{5}{5}[/tex][Fraction] Divide: [tex]\displaystyle m = 1[/tex]Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes. If 5 adult smartphone users are randomly selected, find the probability that exactly 3 of them use their smartphones in meetings or classes.
Answer:
Es el 60%
Step-by-step explanation:
Can y’all help me on question 18?!
Answer:
The answer is 220 cubic inches.
Step-by-step explanation:
To find the volume of the rectangular prism, use the formula for a rectangular prism, which is V= LWH. Next, plug in the information given from the question, and the formula will look like V= (10in) ([tex]5\frac{1}{2}[/tex] in) (4in).
Then, solve the equation for the answer, and the answer for the volume of the rectangular prism is 220 cubic inches.
PLZZZZZZZZZZZZZZZ HELP ME WITH THIS!!!
Elena and Diego each wrote an equation to represent the following diagrams. Decide which equation you agree with. And, you must provide your explanations in order to receive the points. You need to solve the equation you agree with. Finally, you need to describe, in words, the process you would use to find the missing values. You can assume that angles that look like right angles are indeed right angles.
1. Elean: w+148=180 , Diego: x+90=148.
We know that angle BKC=148 degrees.
I agree with : ( Elena / Diego /Both of them) .
Because:
Describe, in words, the process you would use to find the missing values:
Answer:
I agree with Elena. See explanation below.
Step-by-step explanation:
A right angle is equal to 90 degrees.
A straight line is equal to 180 degrees.
Elena: w + 148 = 180
Elena's equation is correct because 148 degrees is represented by variable k. When adding variable k and w together, they form a straight line which is equiavlent to 180 degrees. By using this equation, Elena can solve for w after isolating the variable:
w + 148 = 180
w + 148 - 148 = 180 - 148
w = 32 degrees
Diego: x + 90 = 148
Diego is incorrect. He added 90 degrees because of the right angle, but he failed to realize that x is within 90 degrees, meaning he would either have to subtract x from 90 degrees or add both x and w to get to 90 degrees. He cannot solve for x or w by using this equation.
To solve for x, add both w and x to get 90 degrees. Since Elena showed us w equals 32 degrees, we can set up an equation:
w + x = 90
32 + x = 90
32 - 32 + x = 90 - 32
x = 58 degrees
HELP ME PLEASEEEEEEEEEEEEEEEEE
Answer:
x
Step-by-step explanation:
f([tex]f^{-1}[/tex](x))
Lets work the brackets first!
[tex]f^{-1}[/tex](x)
To solve we are going to find the inverse of the function.
[tex]f^{-1}[/tex](x)
f ⇔ y
∴ y = x
Interchange x and y
x = y
Solve for y
y = x
∴ [tex]f^{-1}[/tex](x) = x
Now let's solve the rest of the equation.
f(x) = x
∴ f([tex]f^{-1}[/tex](x)) = x
Dwayne improved his score on Commander
Quest from 65,720 to 88,722. By what percent
did his score increase?
Answer:
35%
Step-by-step explanation:
What was the numerical difference?
88722 - 65720 = 23002
Which number is the denominator for the % increase?
It must be 65720.
23002/ 65720 * 100 = 35%
So if we take 35% of 65720 and add it on to 65720 what do we get.
35/100 * 65720 + 65720 = 88722 just as we should.
What is the probability that Omar will get to drive the car after the first roll?
Answer:
1/6
Step-by-step explanation:
For Omar to drive, he has to get a six when a die is rolled ;
The probability that Omar will get to drive his car is :
Required outcome = (6) = 1
Total possible outcomes = (1,2,3,4,5,6)
P(rolling a 6) = required outcome / Total possible outcomes
P(rolling a 6) = 1/6
Probability of Omar driving his car is 1/6
there are 6 glass bottles and eight plastic bottles on a rack. I f one is chosen at random, what is the probability of picking a glass bottle? Which simulation can be used to represent this situation
Answer:
6:8
Step-by-step explanation:
6 is the ratio of glass bottles and 8 is the plastic or you can put 3:4 because you divide the number b 2
A teacher offers 8 extra credit assignments.what is the domain of this graph
graph the line with intercept 6 and slope
[tex] - \frac{3}{2} [/tex]
Given:
The y-intercept of a line = 6
The slope of the line = [tex]-\dfrac{3}{2}[/tex]
To find:
The graph of the given line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
Putting [tex]m=-\dfrac{3}{2}[/tex] and [tex]b=6[/tex] in the above equation, we get
[tex]y=-\dfrac{3}{2}x+6[/tex]
At [tex]x=0[/tex],
[tex]y=-\dfrac{3}{2}(0)+6[/tex]
[tex]y=0+6[/tex]
[tex]y=6[/tex]
At [tex]x=2[/tex],
[tex]y=-\dfrac{3}{2}(2)+6[/tex]
[tex]y=-3+6[/tex]
[tex]y=3[/tex]
Plot these two points (0,6) and (2,3) on a coordinate plane and connect them by a straight line to get the graph of the required line.
The required graph is shown below.
What type of triangle has a circumcenter on the exterior of the triangle?
Answer:
acute triangle
if i m wrong please dont mind and
correct me
Please help !!!!!!!!!!!!!!!!!
Which pair of angles are vertical angles?
A)
B)
C)
D)
Answer:
Step-by-step explanation:
The angles opposite each other when two lines cross. They are always equal.
here,vertically opposite angles are
angle RQW and angle TQU
angle RQV ang angle SQU
angle SQR and angle UQV
angle WQV and angle SQT
Find a function whose graph is a parabola with vertex (1, −2) and that passes through the point (5, 14)
Answer:
[tex]f(x)=(x-1)^2-2[/tex]
Step-by-step explanation:
Equation of a parabola:
[tex]y=a(x-h)^2+k[/tex]
The vertex is given as [tex](h,k)[/tex] -> [tex](1, -2)[/tex]
Plug in both the given point and vertex to find the value of [tex]a[/tex]:
[tex]y=a(x-h)^2+k[/tex]
[tex]y=a(x-1)^2-2[/tex]
[tex]14=a(5-1)^2-2[/tex]
[tex]14=a(4)^2-2[/tex]
[tex]14=16a-2[/tex]
[tex]16=16a[/tex]
[tex]1=a[/tex]
[tex]a=1[/tex]
Therefore, the final function is [tex]f(x)=(x-1)^2-2[/tex]
See attached graph below for a visual of the function.
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below in years. Find the mean retirement age.56 65 62 53 68 58 65 52 56
Answer:
59.44
Step-by-step explanation:
Nine employees If an electronic company retired last year
The retirement ages are listed below
56, 65, 62, 53, 68, 58, 65, 52, 56
The mean retirement age can be calculated as follows
= 56+65+62+53+68+58+65+52+56/9
= 535/9
= 59.44
Hence the mean retirement age is 59.44
Find the center and radius of x^2 + y^2 +6x - 7=0
Answer:
The center (-3, 0)
9514 1404 393
Answer:
center: (-3, 0)radius: 4Step-by-step explanation:
The desired parameters can be found by putting the equation into the standard form for the equation of a circle:
(x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r
The values of h and k will be half the coefficients of the linear x- and y-terms, respectively.
x^2 +6x +9 +y^2 -7 = 9 . . . . . add 9 to complete the square
(x +3)^2 +y^2 = 16 . . . . . . . . . add 7 to get the desired form
This equation shows us (h, k) = (-3, 0) and r = 4.
The center is (-3, 0), and the radius is 4.
I NEED HELP PLZ, PLZ, I NEED HELP, I AM BEGGING YOU
Answer:
tn = 8n -7
Step-by-step explanation:
given : t2=9, t4=25
the formula is:
tn = t1 + (n-1) d
gonna find d first:
d = (25-9) /(4-2) = 16/2 = 8
and find tn1:
t1 = 9-8 = 1
so, tn = 1 + (n-1) (8) = 1 +8n -8
tn = 8n -7
Answer:
Solution given
n th term[tn]=?
1st term =a
difference =d
we have
t2=9
a+(n-1)d=9
a+(2-1)d=9
a+d=9
a=9-d..................[1]
again
t4=25
a+(n-1)d=25
a+(4-1)d=25
now
substituting value of a
9-d+3d=25
2d=25-9
d=16/2
d=8
substituting value of d in equation 1.
,a=9-8
a=1
we have
tn term =a+(n-1)d=1+(n-1)8=1+8n-8=8n-7
n th term =8n-7
Jill went on 8 hikes. The hikes were 6 miles, 4 miles, 2 miles, 3 miles, 7 miles, 5 miles, and 1 mile. What was the range of the lengths of Jill's hikes? :)
Answer:
range is 6
Step-by-step explanation:
The smallest number in this data set is 1 mile, the largest is 7 miles
the range is the difference between the biggest and smallest number so 7-1 = 6. The range is 6
PLEASE HELP ASAP !!! WILL MARK BRAINLIEST TO WHOEVER ANSWERS CORRECTLY
Answer:
See below.
Step-by-step explanation:
Alternate Interior Angles - 1
Alternate Exterior Angles - 2
Corresponding Angles - 4
Same-side Exterior Angles - 5
Same-side Interior Angles - 3
Answer:38292
A
Step-by-step explanation:w
jkwlw44444
Based on data from the U.S. Census Bureau, a Pew Research study showed that the percentage of employed individuals ages 25-29 who are college educated is at an all-time high. The study showed that the percentage of employed individuals aged 25-29 with at least a bachelor's degree in 2016 was 40%. In the year 2000, this percentage was 32%, in 1985 it was 25%, and in 1964 it was only 16%.+
What is the population being studied in each of the four years?
a. college educated individuals
b. college educated individuals aged 25-29
c. individuals aged 25-29
d. employed individuals aged 25-29
e. employed individuals
Answer:
d. employed individuals aged 25-29
Step-by-step explanation:
"Population" in a research study is the comprehensive group that the experimenter or the researcher is interested in.
It is given that US Census Bureau, showed that percentage of the employed individual who are of age group 25 years to 29 years are college educated and is at all time high.
The research study focuses on the specific age group of individuals those who graduated form college or at least have a bachelor degree.
Thus the population of the research study those who studied in each of the four years are the employed individuals aged from 25-29.
U.S. women aged 20 or over have a mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl. Assume that the distribution is Normal. What proportion of women have HDL below 45 mg/dl or less?
Answer:
0.2514 = 25.14% of women have HDL below 45 mg/dl or less.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl.
This means that [tex]\mu = 55, \sigma = 15[/tex]
What proportion of women have HDL below 45 mg/dl or less?
This is the p-value of Z when X = 45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 55}{15}[/tex]
[tex]Z = -0.67[/tex]
[tex]Z = -0.67[/tex] has a p-value of 0.2514
0.2514 = 25.14% of women have HDL below 45 mg/dl or less.
A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank 10 minutes after the leak develops if the water drains off at a rate that is proportional to the amount of water present.
Answer:
127.53 liters left after 10 minutes
Step-by-step explanation:
Let
[tex]A \to Amount[/tex]
[tex]t \to time[/tex]
Given
[tex]A(0) = 200[/tex] --- initial
[tex]A(5) = 200 * (1 - 20\%) = 160[/tex] --- the amount left, after 5 minutes
Required
[tex]A(10)[/tex] --- amount left after 5 minutes
To do this, we make use of:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(5) = 160[/tex] implies that:
[tex]160 = 200 * e^{k*5}[/tex]
Divide both sides by 200
[tex]0.80 = e^{k*5}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.80) = \ln(e^{k*5})[/tex]
[tex]\ln(0.80) = \ln(e^{5k})[/tex]
[tex]\ln(0.80) = 5k\ln(e)[/tex]
So, we have:
[tex]-0.223 = 5k[/tex]
Divide by 5
[tex]k = -0.045[/tex]
So, the function is:
[tex]A(t) = A(0) * e^{kt}[/tex]
[tex]A(t) = 200 * e^{-0.045t}[/tex]
The amount after 10 minutes is:
[tex]A(10) = 200 * e^{-0.045*10}[/tex]
[tex]A(10) = 200 * e^{-0.45}[/tex]
[tex]A(10) = 127.53[/tex]
