Triangle ABC is the pre-image and triangle DFE is the image.
What is the scale factor of the dilation?
Please helppp!!!!!
Answers
Answer:
Scale factor = ½
Step-by-step explanation:
The original image is the preimage = ∆ACB
The new image is the image = ∆DFE
The scale of factor of dilation = image/preimage = DF/AC
DF = 6 cm (given)
AC = 12 cm (given)
Plug in the values into the equation to find the scale factor of dilation:
Scale factor = 6/12
Scale factor = ½
Related Questions
In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month. Find a 95% confidence interval for the proportion of customers whose service was interrupted one or more times in the past month.
Answers
Answer:
The correct answer is "0.3410, 0.4990".
Step-by-step explanation:
Given values are:
[tex]n=150[/tex]
[tex]p=\frac{63}{150}[/tex]
[tex]=0.42[/tex]
At 95% confidence interval,
C = 95%
z = 1.96
As we know,
⇒ [tex]E=z\sqrt{\frac{p(1-p)}{n} }[/tex]
By substituting the values, we get
[tex]=1.96\sqrt{\frac{0.42\times 0.58}{150} }[/tex]
[tex]=1.96\sqrt{\frac{0.2436}{150} }[/tex]
[tex]=0.0790[/tex]
hence,
The confidence interval will be:
= [tex]p \pm E[/tex]
= [tex]0.42 \pm 0.079[/tex]
= [tex](0.3410,0.4990)[/tex]
The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.
Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.
Write the equation that represents the volume of the storage container in terms of its width.
A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w
Answers
Answer:
A
Step-by-step explanation:
Step 1, setting variables:
We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).
Step 2, writing equations:
Great! We have everything now. Let us write the equation by substituting our variables in:
[tex]V=l*w*h\\V=6w(w+2)\\[/tex]
Ok! Let us expand the equation:
[tex]V=6w^2+12w[/tex]
[tex]\fbox{A}[/tex]
I hope this helps! Let me know if you have any questions :)
Farmer Jane would like to show a net profit of $1,000 per month. She is growing tomatoes and sells them for $3 per pound. Her variable costs per pound are $1, and she has $700 in fixed cost. How many pounds does she need to sell?
Answers
Answer:
850
Step-by-step explanation:
Each pound of tomatoes costs one dollar to produce, and sells for three dollars. That's a net profit of 2 dollars per pound of tomatoes.
We need a profit of 1000 dollars, and to pay the 700 dollars in operating costs, for a total of 1700 dollars needed.
So 1700 dollars divided by 2 dollars per pound of tomatoes comes out to 850 pounds of tomatoes.
A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F = the event of getting the white ball twice.
b. Let G = the event of getting two balls of different colors.
c. Let H = the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?
Answers
Answer:
See explanation
Step-by-step explanation:
Given
Represent the balls with the first letters
[tex]W =1[/tex]
[tex]R =1[/tex]
Solving (a): P(F) --- White balls twice
The event of F is:
[tex]F = \{(W,W)\}[/tex]
So:
[tex]P(F) = P(W) * P(W)[/tex]
[tex]P(F) = \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(F) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(F) = \frac{1}{4}[/tex]
Solving (b): P(G) --- two different colors
The event of G is:
[tex]G = \{(W,R),(R,W)\}[/tex]
So:
[tex]P(G) = P(W) * P(R) + P(R) * P(W)[/tex]
[tex]P(G) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(R)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(G) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(G) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(G) = \frac{1}{2}[/tex]
Solving (c): P(H) --- White picked first
The event of H is:
[tex]H = \{(W,R),(W,W)\}[/tex]
So:
[tex]P(H) = P(W) * P(R) + P(W) * P(W)[/tex]
[tex]P(H) = \frac{n(W)}{n} * \frac{n(R)}{n} + \frac{n(W)}{n} * \frac{n(W)}{n}[/tex]
[tex]P(H) = \frac{1}{2} * \frac{1}{2} + \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(H) = \frac{1}{4} + \frac{1}{4}[/tex]
[tex]P(H) = \frac{1}{2}[/tex]
Solving (d): F and G, mutually exclusive?
We have:
[tex]F = \{(W,W)\}[/tex]
[tex]G = \{(W,R),(R,W)\}[/tex]
Check for common elements
[tex]n(F\ n\ G) = 0[/tex]
Hence, F and G are mutually exclusive
Solving (e): G and G, mutually exclusive?
We have:
[tex]G = \{(W,R),(R,W)\}[/tex]
[tex]H = \{(W,R),(W,W)\}[/tex]
Check for common elements
[tex]n(G\ n\ H) = 1[/tex]
Hence, F and G are not mutually exclusive
Solve:
n = 8
4
O n = 2
0 n = 12
Ô n = 24
0 n = 32
Answers
Answer:
1/4 n = 8
n = 8 * 4
n = 32
so option 4 i.e.
n = 32. is the ans
Answer:
n=32
Step-by-step explanation:
Given :
[tex]\frac{1}{4} n=8[/tex]
Now,
Value of n can be calculated as :
[tex]\frac{1}{4} n=8[/tex]
n=8×4
n=32
Therefore, option (D) is correct.
Consider the expression 63+81 how can you use the distributive property and the gcf to find an equivalent expression?explain how you can check your answer
Answers
Step-by-step explanation:
63+81
gcf = 9
63÷9=7, 81÷9=9
so, 63+81 = (9×7)+(9×9)
= 9×(7+9)
63+81 = 144
9x(7+9) = 9×16 = 144
what is a bank statement
Answers
Step-by-step explanation:
a printed record of the balance in a bank account and the amounts that have been paid into it and withdrawn from it, issued periodically to the holder of the account.
Can you solve this problem
Answers
Answer:
x = 18
Step-by-step explanation:
8 x 18 - 3 = 141
Which is the graph of the parent function f(x) = x2?
Answers
Answer:
it should look like a U shape. Its called a parabola
(0,0) is the bottom center.
Step-by-step explanation:
Can :) mean happily taken on a bio? Alex got it on his?
Answer ASAPPPP
Someone
Answers
Answer:
Yes,
Step-by-step explanation:
When " :) " is used in a bio it means the person is happy
I have 8 carrots my Brother Ate 2
How Much I have left?
Answers
Answer:
6?Step-by-step explanation:
..........................
What are the values of A, B, C, and D?
A = 0; B = 1; C = -3; D = 3
A = 0; B = 1; C = 3; D = -3
A = 1; B = 0; C = -3; D = 3
A = 1; B = 0; C = 3; D = -3
Don’t know real answer
Answers
The values of A, B, C and D are (d) A = 1, B = 0, C = 3 and D = -3
How to solve for A, B, C and D?From the question, we have:
x^3 + 8x - 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D
Collect like terms
x^3 + 8x - 3 = Ax^3 + Bx^2 + 5Ax + Cx + 5B + D
By comparing the coefficients, we have:
Ax^3 = x^3
Bx^2 = 0
5Ax + Cx = 8x
5B + D = -3
Remove the x factors
A = 1
B = 0
5A + C = 8
5B + D = -3
Substitute A = 1 in 5A + C = 8
5(1) + C = 8
Solve for C
C = 3
Substitute B = 0 in 5B + D = -3
5(0) + D = -3
Solve for B
D = -3
Hence, the values of A, B, C and D are (d) A = 1, B = 0, C = 3 and D = -3
Read more about partial fractions at:https://brainly.com/question/18958301
#SPJ6
A bill originally amounting Rs 1550, now amounts to Rs 1736 after adding VAT. Find the VAT rate.kaabil original amounting
Answers
Answer: 12%
Step-by-step explanation:
Original amount = Rs 1550
VAT = Rs 1736 - Rs 1550 = Rs 186
VAT rate = VAT/Original amount × 100
= 186/1550 × 100
= 18600/1550
= 12%
Therefore, the VAT rate is 12%.
Check:
= Rs 1550 + (12% × Rs 1550)
= Rs 1550 + $186
= Rs 1736
Find two integers whose sum is -5 and product is -36
Answers
Answer:
-6 & 6
Step-by-step explanation:
-6 time 6 is -36
Answer:
-9+4= -5
Step-by-step explanation:
-9 times 4= -36
Negative Nine plus four equals negative five
negative Nine times four equals negative thirty six
The answer and how to find the answer
Answers
Answer:
x = 1.9
Step-by-step explanation:
Thanks to a theorem we can use this proportion
10.47 : 4.44 = 4.44 = x
x = (4.44^2)/10.47 = 1,882865 = 1.9
If Sarah turns 15 on august 27 and her graduation year is 2024 how old will she be when she graduates high school?
Answers
Answer:
She will be 17
Step-by-step explanation:
My sister is like that but she's graduating in 22'
It sort of depends where Sarah lives -.-
But if she starts high school when she's 15 (in 2021) and she graduates in 2024 it means high school is three years.
So 15 plus 3.
Sarah will be 18 when she graduates high school.
On a coordinate plane, a line goes through (negative 3, negative 3) and (negative 1, 5). What is the equation of the line parallel to the given line with an x-intercept of 4?
Answers
m = gradient
gradient of line:
[5 - (-3)]/[(-1) - (-3)]
= 8/2
= 4
y = mx + c
subsitute (4, 0)
0 = (4)(4) + c
0 = 16 + c
c = -16
equation of the line:
y = 4x - 16
hope this helped :)
Answer:
4, -16
Step-by-step explanation:
A fast-food chain claims one medium order of its onion rings weighs 114 grams. Patrice thinks she is getting less than what the restaurant advertises. She weighs the next 16 random orders of onion rings before she eats them and finds the sample mean is 112.4 grams and the standard deviation is 7.63 grams. What conclusion can be drawn α = 0.10?
Answers
Answer:
Patrice does not have sufficient evidence to reject the fast-food chain's claim.
Step-by-step explanation:
unless she already ate some fries, not enough evidence
Amanda, Bryan, and Carl are about to compete in 100
mixed IM swimming events. These are the only three
swimmers competing in this event. They are all working
hard to win first place.
How many different possible ways could the 3 swimmers
place?
2
Answers
9514 1404 393
Answer:
6
Step-by-step explanation:
Any of the three can be in first place.
Any of the remaining two can be in 2nd place.
The remaining swimmer will be in 3rd place.
There are 3 × 2 × 1 = 6 possible orderings of the swimmers.
Is 9/54 equivalent to 1/3
Answers
Answer: No.
Step-by-step explanation:
9/54 is equal to 1/6
Answer:
no, it is not
Step-by-step explanation:
9/54 can be simplified by dividing both sides by 3, getting 3/18. you can do this again and get 1/6. significantly smaller that l/3
2/5+3/7 is the same as?
Answers
Answer:
29/35
Step-by-step explanation:
Least common denominator of 5 and 7 is 35
[tex]\frac{2}{5}=\frac{2*7}{5*7}=\frac{14}{35}\\\\\frac{3}{7}=\frac{3*5}{7*5}=\frac{15}{35}\\\\\frac{2}{5}+\frac{3}{7}=\frac{14}{35}+\frac{15}{35}\\\\ \ = \frac{14+15}{35}\\\\ = \frac{29}{35}[/tex]
Kyle works at a donut factory, where a 10-oz cup of coffee costs 95¢, a 14-oz cup costs $1.15, and a 20-oz cup costs $1.50. During one busy period, Kyle served 14 cups of coffee, using 204 ounces of coffee, while collecting a total of $16.70. How many cups of each size did Kyle fill?
Kyle filled ___ 10-oz cup(s), ___ 14-oz cup(s), and ___ 20-oz cup(s).
Answers
Answer:
Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Step-by-step explanation:
Let 10-oz, 14-oz, and 20-oz coffees be represented by the variables a, b, and c, respectively.
Since a total of 14 cups of coffee was served:
[tex]a+b+c=14[/tex]
A total of 204 ounces of coffee was served. Therefore:
[tex]10a+14b+20c=204[/tex]
A total of $16.70 was collected. Hence:
[tex]0.95a+1.15b+1.5c=16.7[/tex]
This yields a triple system of equations. In order to solve a triple system, we should isolate the system to only two variables first.
From the first equation, let's subtract a and b from both sides:
[tex]c=14-a-b[/tex]
Substitute this into both the second and third equations:
[tex]10a+14b+20(14-a-b)=204[/tex]
And:
[tex]0.95a+1.15b+1.5(14-a-b)=16.7[/tex]
In this way, we've successfully created a system of two equations, which can be more easily solved. Distribute:
For the Second Equation:
[tex]\displaystyle \begin{aligned} 10a+14b+280-20a-20b&=204\\ -10a-6b&=-76\\5a+3b&=38\end{aligned}[/tex]
And for the Third:
[tex]\displaystyle \begin{aligned} 0.95a+1.15b+21-1.5a-1.5b&=16.7\\ -0.55a-0.35b&=-4.3\end{aligned}[/tex]
We can solve this using substitution. From the second equation, isolate a:
[tex]\displaystyle a=\frac{1}{5}(38-3b)=7.6-0.6b[/tex]
Substitute into the third:
[tex]-0.55(7.6-0.6b)-0.35b=-4.3[/tex]
Distribute and simplify:
[tex]-4.18+0.33b-0.35b=-4.3[/tex]
Therefore:
[tex]-0.02b=-0.12\Rightarrow b=6[/tex]
Using the equation for a:
[tex]a=7.6-0.6(6)=4[/tex]
And using the equation for c:
[tex]c=14-(4)-(6)=14-10=4[/tex]
Therefore, Kyle filled 4 10-oz cups, 6 14-oz cups, and 4 20-oz cups.
Joe told Mickey he got an hourly raise at work and his new rate will be $10.25 per hour. Mickey wants to know what Joe’s hourly rate was before his raise. If r represents the amount of the raise, which expression represents Joe’s hourly rate before his raise?
Answers
Answer:10.25-r= hourly rate
Step-by-step explanation:
what is the value of this expression
log2^8 + log3(1/3)
Answers
Answer:
2
Step-by-step explanation:
log2^8 + log3(1/3)
=>3 + (-1)
=>2
i need to see the steps for simplifying 3(m-5)+m
Answers
Answer:
4m - 15
Step-by-step explanation:
a( x + y) = ax + ay
[tex]3( m - 5 ) + m\\\\3m - 15 + m \\\\4m - 15[/tex]
Answer:
4m-15
Step-by-step explanation:
Distrubite 3 through the parentheisis
3m-15+m
Collect like terms
4m-15
What are the roots of the quadratic equation below?
2x2 + 8x + 7 = 0
ANSWER ASAP!
Answers
Answer:
x = 2 ± [tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
Natural logs can be written as _______.
Answers
Answer:
Step-by-step explanation:
The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
Answer:
Ln x as opposed to log x
Step-by-step explanation:
How many natural numbers are there between 8² and 9² ?
Answers
Answer:
19
Step-by-step explanation:
Answer:
i think the answer 17
81-64 =17Find the area of the composite figure.
Answers
Answer:
25m²
Step-by-step explanation:
it might be helpful for you
Consider the terms pyramid, line, square, and triangle. The term
is not defined in Euclidean geometry.
Answers
The term line is not defined in Euclidean geometry. ... These words are point, plane and line and are referred to as the "three undefined terms of geometry".
Answer:
LINE is not defined by Euclidian geometry
Step-by-step explanation:
In Euclidean geometry, there are 3 terms that are considered "undefined" they are; point, line and plane. I think it is because considered undefined because they are described, but not every formally defined.
As in a shape I mean I hope I am right,
