Answer/Step-by-step explanation:
Given:
f(x) = 2x + 2
Domain = {-5, -1, 2, 3}
To write the range of f using set notation, substitute each domain value into f(x) = 2x + 2 to get each corresponding range value that will make up the set.
Thus:
✔️f(-5) = 2(-5) + 2
= -10 + 2
f(-5) = -8
✔️f(-1) = 2(-1) + 2
= -2 + 2
f(-1) = 0
✔️f(2) = 2(2) + 2
= 4 + 2
f(-1) = 6
✔️f(3) = 2(3) + 2
= 6 + 2
f(3) = 8
Range of f using set notation = {-8, 0, 6, 8}
✔️Graph f by plotting the domain values on the x-axis against the corresponding range values on the y-axis as shown in the attachment below:
*See attachment for the graph of f
On Halloween, a man presents a child with a bowl containing eight different pieces of candy. He tells her that she may have three pieces. How many choices does she have
Answer:
[tex]56[/tex] choices
Step-by-step explanation:
We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy does not matter.
To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.
Anyways, back to the solving! Remember that the combination formula is
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex], where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.
In this case, [tex]n=8[/tex] and [tex]r=3[/tex]. Substituting these values into the formula gives us:
[tex]_8C_3=\frac{8!}{3!5!}[/tex]
[tex]= \frac{8*7*6*5*4*3*2*1}{3*2*1*5*4*3*2*1}[/tex] (Expand the factorials)
[tex]=\frac{8*7*6}{3*2*1}[/tex] (Cancel out [tex]5*4*3*2*1[/tex])
[tex]=\frac{8*7*6}{6}[/tex] (Evaluate denominator)
[tex]=8*7[/tex] (Cancel out [tex]6[/tex])
[tex]=56[/tex]
Therefore, the child has [tex]\bf56[/tex] different ways to pick the candies. Hope this helps!
4) The measure of the linear density at a point of a rod varies directly as the third power of the measure of the distance of the point from one end. The length of the rod is 4 ft and the linear density is 2 slugs/ft at the center, find the total mass of the given rod and the center of the mass
Answer:
a. 16 slug b. 3.2 ft
Step-by-step explanation:
a. Total mass of the rod
Since the linear density at a point of the rod,λ varies directly as the third power of the measure of the distance of the point form the end, x
So, λ ∝ x³
λ = kx³
Since the linear density λ = 2 slug/ft at then center when x = L/2 where L is the length of the rod,
k = λ/x³ = λ/(L/2)³ = 8λ/L³
substituting the values of the variables into the equation, we have
k = 8λ/L³
k = 8 × 2/4³
k = 16/64
k = 1/4
So, λ = kx³ = x³/4
The mass of a small length element of the rod dx is dm = λdx
So, to find the total mass of the rod M = ∫dm = ∫λdx we integrate from x = 0 to x = L = 4 ft
M = ∫₀⁴dm
= ∫₀⁴λdx
= ∫₀⁴(x³/4)dx
= (1/4)∫₀⁴x³dx
= (1/4)[x⁴/4]₀⁴
= (1/16)[4⁴ - 0⁴]
= (256 - 0)/16
= 256/16
= 16 slug
b. The center of mass of the rod
Let x be the distance of the small mass element dm = λdx from the end of the rod. The moment of this mass element about the end of the rod is xdm = λxdx = (x³/4)xdx = (x⁴/4)dx.
We integrate this through the length of the rod. That is from x = 0 to x = L = 4 ft
The center of mass of the rod x' = ∫₀⁴(x⁴/4)dx/M where M = mass of rod
= (1/4)∫₀⁴x⁴dx/M
= (1/4)[x⁵/5]₀⁴/M
= (1/20)[x⁵]₀⁴/M
= (1/20)[4⁵ - 0⁵]/M
= (1/20)[1024 - 0]/M
= (1/20)[1024]/M
Since M = 16, we have
x' = (1/20)[1024]/16
x' = 64/20
x' = 3.2 ft
Which equation represents a circle whose center is left parenthesis negative 7 comma 4 right parenthesis with a radius of 5?
Answer:
last option
Step-by-step explanation:
(x-h)²+(y-k)²=r²
(x--7)²+(y-4)²=5²
(x+7)²+(y-4)²=25
The equation of the circle is (x + 7)² + (y - 4)² = 25.
Option D is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
The equation of a circle with center (h,k) and radius r.
(x - h)² + (y - k)² = r²
Substituting the given values, we get:
(x - (-7))² + (y - 4)² = 5²
Simplifying the equation:
(x + 7)² + (y - 4)² = 25
Therefore,
The equation of the circle is (x + 7)² + (y - 4)² = 25
Learn more about Circle here:
https://brainly.com/question/11833983
#SPJ3
The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 17 minutes.
What is the probability that washing dishes tonight will take me between 14 and 16 minutes?
Give your answer accurate to two decimal places.
The time it takes to wash has the probability density function,
[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]
The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,
[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]
If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.
Hannah's suitcase has the following dimensions.
length: 27 inches
width: 21 inches
depth: 14 inches
What is the volume of Hannah's suitcase in cubic inches?
Answer:7938 inches square
Step-by-step explanation:
multiply everything
Answer:
7938
Step-by-step explanation:
f(x)=2^x. show that f(x=3)=8 f(x)?
Step-by-step explanation:
[tex]f(x) = {2}^{x} [/tex]
x = 3
f(3) = 2³ = 2×2×2 = 4×2 = 8
A company wants to decrease their energy use by 17%. If their electric bill is currently $2500 a month, what will their bill be if they are successful
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. O c) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
Identify the slope and y intercept of the line with equation 2y = 5x + 4
Answer:
Slope is 5/2
y-intercept is 2
Step-by-step explanation:
Turn the equation into slope intercept form [ y = mx + b ].
2y = 5x + 4
~Divide everything by 2
y = 5/2x + 2
Remember that in slope intercept form, m = slope and b = y-intercept.
Best of Luck!
Answer:
slope: 2.5
y-intercept: 2
Step-by-step explanation:
First isolate the y variable which changes the equation to y=2.5x+2
The equation of a line is mx + b where m is the slope and b and the
y-intercept. Leading us to conclude that 2.5 is the slope and 2 is the y-intercept.
Find the diameter of a circle if the area is
153.86m2. Use 3.14 for pi.
Answer:
-Hello Fatema!
The formula to find out the area of a circle is πd so let's plug the known values and then solve for d [ diameter ] :[tex] \boxed{ \large{ \tt{✺ \: AREA \: OF \: A \: CIRCLE = \pi \: d }}}[/tex]
[tex] \large{ \tt{⟶ \: 153.86 = 3.14 \: d}}[/tex]
[tex] \large{ \tt{⟶ \: d = \frac{153.86}{3.14} }}[/tex]
[tex] \large{ \tt{⟶d = 49 \: m}}[/tex]
[tex] \large{ \boxed{ \boxed{ \tt{⤿ \: OUR \: FINAL \: ANSWER : \: 49 \: m}}}}[/tex]
Yayy! We're done! Let me know if you have any questions regarding my answer and also , notify me if you need any other help! :)Subsets and Sets HELP
Attached is the photo reference
Answer:
(a) (C U D) = {k, m, y, z}
(b) C ∩ D = {z}
please help!!!!!!!!!!
9514 1404 393
Answer:
-203.1875
Step-by-step explanation:
The ends of the interval are ...
(-4, g(-4)) = (-4, 1023 15/16)
(1, g(1)) = (1, 8)
The average rate of change is the slope of the line between these two points:
m = (y2 -y1)/(x2 -x1)
m = (8 -(1023 15/16))/(1 -(-4)) = (-1015 15/16)/5 = -203 3/16
The average rate of change on the interval is -203 3/16.
find the value of the trigonometric ratio
Answer:
15/17
Step-by-step explanation:
sinA = CB/CA =15/17
Answer:
15/17Step-by-step explanation:
sine = opposite / hypotenusesin A = BC/ACsin A = 15/1716.Brendan practiced soccer for 12 hours on Monday, 1 hours on
Tuesday, 14 hours on Wednesday, and hour on Thursday in
preparation for the game on Friday. How many total hours did
Brendan practice soccer in this week
Answer:
27
Step-by-step explanation:
If 8 bags of chips cost 10.32;how much will you pay for 20 bags?
Answer:
$25.80
Step-by-step explanation:
First, let's find the cost of one bag of chip:
10.32/8 = 1.29
If one bag costs $1.29, simply multiply the number of bags (20) by 1.29
1.29 x 20 = 25.80
= $25.80
Answer:
25.80
Step-by-step explanation:
We can use a ratio to solve
8 bags 20 bags
------------- = ----------------
10.32 x dollars
Using cross products
8x = 10.32 * 20
8x =206.40
Divide each side by 8
8x/7 = 206.40/8
x =25.80
Working at home: According to the U.S Census Bureau, 41% of men who worked at home were college graduates. In a sample of 506 women who worked at home, 166 were college graduates. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places. The point estimate for the proportion of college graduates among women who work at home is .
Solution :
a). The point estimate of proportion of college graduates among women who work at home,
[tex]$\hat p =\frac{166}{506}$[/tex]
= 0.3281
99.5% confidence interval
[tex]$=\left( \hat p \pm Z_{0.005/2} \sqrt{\frac{\hat p (1- \hat p)}{n}} \right)$[/tex]
[tex]$=\left( 0.3281 \pm 2.81 \sqrt{\frac{0.3281 \times (1- 0.3281)}{506}} \right)$[/tex]
[tex]$=(0.3281 \pm 0.0586)$[/tex]
[tex]$=(0.2695, 0.3867)$[/tex]
A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?
Answer:
384 cars
Step-by-step explanation:
To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:
34 ⋅ 40 = 1360
As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.
1360 - 976 = 384
Therefore, our answer is 384, specifically, 384 cars.
Answer:
384 cars.
Step-by-step explanation:
40 * 34 - 976
= 1360 - 976
= 384.
Graph x^2/49+y+1^2/4=1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Perhaps you want a graph of ...
x^2/49 +(y +1)^2/4 = 1
This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.
HURRY plSSSSSSSSSSSSSSSSSSSSSS
What is the measure of the unknown angle?
Image of a straight angle divided into two angles. One angle is eighty degrees and the other is unknown.
Answer:
The unknown is 100
Step-by-step explanation:
A straight line is 180 degrees
We have two angles x, and 80
x+80 = 180
x = 180-80
x= 100
The length of a rectangular field is 25 m more than its width. The perimeter of the field is 450 m. What is the actual width and length?
Answer:
length= 125
width= 100
Step-by-step explanation:
let width have a length of x m
therefore length= (x+25)m
perimeter=2(length +width)
p=2((x+25)+x)
p=4x+50
but we have perimeter to be 450,, we equate it to 4x+50 above,
450=4x+50
4x=400
x=100 m
length= 125
width= 100
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
Which function is best represented by the graph in the image?
Answer:
No image I cannot tell you
Step-by-step explanation:
Find m<1.
33°
47°
42°
28°
Answer:
<1 = 33
Step-by-step explanation:
The sum of the angle of a triangle is 180
31+116+x = 180
x+147=180
x = 180-147
x = 33
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Pls help me with this one:(
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
Answer:
Step-by-step explanation:
(-5,1) (2,0)
m=(y-y)/(x-x)
m = (0-1)/2- -5)
m = -1/7
(2,0)
y-0= -1/7 (x-2)
y = -1/7x + 2/7
Determine whether each relation is a function. Give the domain and range for each relation.
{(3, 4), (3, 5), (4, 4), (4, 5)}
Answer:
Not a function
Domain: {3,4}
Range: {4,5}
Step-by-step explanation:
A function is a relation where each input has its own output. In other words if the x value has multiple corresponding y values then the relation is not a function
For the relation given {(3, 4), (3, 5), (4, 4), (4, 5)} the x value 3 and 4 have more than one corresponding y value therefore the relation shown is not a function
Now let's find the domain and range.
Domain is the set of x values in a relation.
The x values of the given relation are 3 and 4 so the domain is {3,4}
The range is the set of y values in a relation
The y value of the given relation include 4 and 5
So the range would be {4,5}
Notes:
The values of x and y should be written from least to greatest when writing them out as domain and range.
They should be written inside of brackets
Do not repeat numbers when writing the domain and range
If 5000 is divided by 10 and 10 again what answer will be reached
Hey there!
First, divide 5,000 by 10. You will get 500.
Now, 500 ÷ 10, and you will get your answer, 50.
Hope this helps! Have a great day!
There is 2 questions here please help me! Thank you!
Answer:
3×(-4)×2
= -24
good day god bless you
Answer:
(−25)(5) = −125; he withdrew $125
-24
Step-by-step explanation:
Because he is withdrawing money, he is deducing money form his account, which makes the $25 negative in the equation. The weeks however, cannot be negative. so the correct answer is (−25)(5) = −125; he withdrew $125.
(3) x (-4) x (2)
(3 x -4) x (2)
(-12) x (2)
(-12 x 2)
-24
hope this helps! if you have any questions, let me know!
Find the surface area of a cube that has side length of 3.5 inches
Answer:
73.5
Step-by-step explanation:
Look at images below. : ]
Answer:
1) A
B) 5.818 stops
Step-by-step explanation:
Number One is less than or equal to 21 because the person only has 21 dollars, so she can't spend more than 21.
B can be solved through the equation by first subtracting $5, and then dividing 2.75 by 16.
Question 17 and 18 plz show ALL STEPS and HELP ME ASAP
Answer:
17) 750/9 and 18) 364
Step-by-step explanation:
17. Summation of 75*(0.1)^i from i=0 to infinity, that is equal to 75*(Summation of (0.1)^i). Summation of (0.1)^I is a geometric series with a sum of 1/(0.9)=10/9. Hence the series have a sum equal to 75*(10/9)=750/9
18) It's a series with sum=1+3+9+27+81+243=364