Answers
Answer:
y = 18
a = -2
Step-by-step explanation:
Hello There!
For the first one we need to create an equation to solve for y
23+7=y+12
30=y+12
isolate the variable using inverse operations
subtract 12 from each side
30-12=18
we're left with y = 18
for the second one we need to create an equation to solve for a
3+15+a=8+8+8
3+15=18
8+8+8=16
16=18+a
step 1 subtract each side by 18
16-18=-2
we're left with a = -2
Related Questions
An English professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 61% C: Scores below the top 39% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 72.8 and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
Answers
Solution :
The test is distributed normally with mean of 72.8 and the standard deviation of 7.3
Finding numerical limits for the D grade.
D grade : Scores below the top 80% and above the bottom 10%.
Let the bottom limit for D grade be [tex]$D_1$[/tex] and the top limit for D grade be [tex]$D_2$[/tex].
First find the bottom numerical limit for a D grade is :
[tex]$P(X<D_1)= 0.10$[/tex]
[tex]$P(X\leq D_1)= 0.10$[/tex]
[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_1-\mu}{\sigma}\right) = 0.10$[/tex]
[tex]$P\left(Z \leq \frac{D_1-72.8}{7.3}\right) = 0.10$[/tex] ..........(1)
From (1)
[tex]$\frac{D_1 - 72.8}{7.3} = -1.28$[/tex]
[tex]$D_1 = -1.28(7.3)+72.8$[/tex]
= 63.45
≈ 64
Now the top numerical limit for D grade :
[tex]$P(X>D_2)= 0.80$[/tex]
[tex]$1-P(X\leq D_2)= 0.80$[/tex]
[tex]$P(X\leq D_2)= 1-0.80$[/tex]
[tex]$P(X\leq D_2)= 0.20$[/tex]
[tex]$P\left(\frac{X-\mu}{\sigma} \leq \frac{D_2-\mu}{\sigma}\right) = 0.20$[/tex]
[tex]$P\left(Z \leq \frac{D_2-72.8}{7.3}\right) = 0.20$[/tex] ..........(2)
From (2)
[tex]$\frac{D_2- 72.8}{7.3} = -0.84$[/tex]
[tex]$D_12= -0.84(7.3)+72.8$[/tex]
= 66.668
≈ 67
Therefore, the numerical limit for a D grade is 64 to 67.
A circular garden has a diameter of 8 yards. What is the area of the garden?
Use 3.14 for TT.
O A. 12,56 yd
O B. 200.96 yd2
O c. 25.12 yd?
O D. 50.24 yd?
Answers
what fraction is 15 minutes of 1 hour explain also
Answers
Answer:
1/4
Step-by-step explanation:
15+15+15+15= 60
i hope this helps
Answer:
The answer is 1/4
Step-by-step explanation:
1 hour = 60 minutes
Therefore;
Fraction of 15 minutes with respect to 1 hour is;
15 minutes/ 1 hour
=15 minutes/60 minutes
=1/4
Therefore the answer is 1/4
Hope this helps.
How many solutions does this system have?
->
2x-3y = 10
-4x+6y=-20
one
two
an infinite number
no solution
Answers
Answer: I think there is only one
Step-by-step explanation:
Answer:
an infinite number
Step-by-step explanation:
Let's solve for y for both equations.
[tex]2x-3y=10\\-3y=10-2x\\y=\frac{2}{3}x-\frac{10}{3}[/tex]
[tex]-4x+6y=-20\\6y=4x-20\\y=\frac{4}{6} x-\frac{20}{6}[/tex]
By reducing fractions we get:
[tex]y=\frac{2}{3}x- \frac{10}{3}[/tex]
These two equations are EXACTLY the same.
Therefore, this system has an infinite number amount of solutions.
Using desmos graphing calculator, you can't see both lines because they're exactly the same line.
From the top of a lighthouse the angle of depression of a speed
boat is 35º. The boat is 134 meters from the base of the
lighthouse. Find the distance from the top of the lighthouse to the
boat.
Answers
Answer:
164m (to 3 s.f.)
Step-by-step explanation:
Please see the attached picture for the full solution.
Is 4/2 equivalent to 1
Answers
Answer:
False
Step-by-step explanation:
4/2 = 2/1 = 2
And 2 ≠ 1
Hence, 4/2 ≠ 1
Hope it helps :)
Answer:
no .
Step-by-step explanation:
4/2 is equivalent to 2 , if it were 2/2 then it would be yes .
An exponential distribution is formed by the waiting times for a patient in the emergency room. The average waiting time for this distribution is 38 minutes. Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes? Round your answer to three decimal places.
Answers
Answer:
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
Step-by-step explanation:
To solve this question, we should understand the exponential distribution and conditional probability.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
The average waiting time for this distribution is 38 minutes.
This means that [tex]m = 38, \mu = \frac{1}{38} = 0.0263[/tex]
Given that it has already taken 37 minutes, what is the probability that the wait time will be more than an additional 41 minutes?
Event A: Taking more than 37 minutes.
Event B: More than 37 + 41 = 78 minutes.
Probability of taking more than 37 minutes:
[tex]P(A) = P(X \leq 37) = 1 - e^{-0.0263*37} = 0.6221[/tex]
More than 37 minutes and more than 78 minutes:
The intersection is more than 78 minutes, so:
[tex]P(A \cap B) = P(X > 78) = e^{-0.0263*78} = 0.1286[/tex]
The probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1286}{0.6221} = 0.207[/tex]
0.207 = 20.7% probability that the wait time will be more than an additional 41 minutes
what is the greatest common factor of 10, 30 and 45
Answers
Answer:
5
Step-by-step explanation:
Two similar polygons are shown below.
Which transformation was performed on PORS to form POR'S?
O A dilation factor of 2
O A dilation factor of 4
O A dilation factor of
07 1 / 을
A dilation factor of
Answers
Answer:
??
Step-by-step explanation:
을("eul") ?????
A gardener can increase the number of dahlia plants in an annual garden by either buying new bulbs each year or dividing the existing to create new plants. The table below shows the expected number of bulbs for each method.
Answers
Answer:
May I please have the question or the table?
Step-by-step explanation:
Answer:here’s the table I don’t have the answer tho.
Step-by-step explanation:
Write the equation in standard form for the circle x^2 + y^2 + 16x + 28 = 0.
Answers
Answer:
( x + 8 ) ^2+ y^2= 36
Step-by-step explanation:
1. Use the triangle below to determine the values indicated:
Answers
Answer:
A. Sine Y = 20 / 29
B. Cos Y = 21 / 29
C. Tan Y = 20 / 21
D. Sine Z = 21 / 29
E. Cos Z = 20 / 29
F. Tan Z = 21 / 20
Step-by-step explanation:
A. Determination of Sine Y
Opposite = 20
Hypothenus = 29
Sine Y =?
Sine Y = Opposite / Hypothenus
Sine Y = 20 / 29
B. Determination of Cos Y
Adjacent = 21
Hypothenus = 29
Cos Y =?
Cos Y = Adjacent / Hypothenus
Cos Y = 21 / 29
C. Determination of Tan Y
Opposite = 20
Adjacent = 21
Tan Y =?
Tan Y = Opposite / Adjacent
Tan Y = 20 / 21
D. Determination of Sine Z
Opposite = 21
Hypothenus = 29
Sine Z =?
Sine Z = Opposite / Hypothenus
Sine Z = 21 / 29
E. Determination of Cos Z
Adjacent = 20
Hypothenus = 29
Cos Z =?
Cos Z = Adjacent / Hypothenus
Cos Z = 20 / 29
Determination of Tan Z
Opposite = 21
Adjacent = 20
Tan Z =?
Tan Z = Opposite / Adjacent
Tan Z = 21 / 20
if you need extra points (50 points) and brainiest answer this correctly plz
Answers
Answer:
D) 500 square feet
Step-by-step explanation:
20x40=800
30x10=300
800-300=500
Answer:
500 square feet
Step-by-step explanation:
Walk way A=bh
A=40 times 20
A=800
garden
A=30 times 10
A=300
Now subtract walkway from the garden. 800 - 300= 500
s + 10.7 = 7.2
s = ?
how do i solve
Answers
So -3.5 + 10.7 = 7.2
Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (−5)(50−2) to represent her profit based on the price per scarf,
Use the drop-down menus to complete the statements about Sofie's profit.
Answers
Answer:
The first part is 5
The maximum it can be is 200
Step-by-step explanation:
Because I said So
Sofie will not make a profit if she sells her scarves for $5 or less.
The maximum profit Sofie can make is $200.
What is a parabola?A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line.
According to the given problem,
y = (x - 5)(50 - 2x)
⇒ y + (-(x - 5)(50 - 2x) = (x - 5)(50 - 2x) + (-(x - 5)(50 - 2x)
⇒ y - (x - 5)(50 - 2x) = (x - 5)(50 - 2x) - (x - 5)(50 - 2x)
⇒ y - (x - 5)(-2x + 50) = 0
⇒ y - (-x *2x + x*50 + 5*2x -5*50) = 0
⇒ y - ( -2x² + 50x + 10x - 250) = 0
⇒ y - ( - 2x² + 60x - 250 ) = 0
⇒ y + 2x² - 60x + 250 = 0
⇒ 2x² -60x + y + 250 = 0
⇒ ( 2x² - 60x ) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{60}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - [tex]\frac{2^{2} *3*5}{2}[/tex]x) + y + 250 = 0
⇒ 2 ( x² - 30x ) + y + 250 = 0
⇒ 2( x² + 2(-15)x + 225 -225 +y + 250 = 0
⇒ 2( x - 15 )² + 2(-225) + y + 250 = 0
⇒ 2( x - 15 )² + y = -2(-225) - 250
⇒ 2( x - 15 )² + y = 450 - 250
⇒ 2( x - 15 )² + y = 200
⇒ y = -2( x - 15 )² + 200
This equation is in the form of y = a(x - h)² + k where the vertex of the parabola is (h , k).
Therefore the vertex of the parabola is at (15 , 200)
Hence, we can conclude that Sofie will maximum profit of $200 if she sells a scarf at 15$ and will make the least profit if she sells the scarf at $5 or less.
Learn more about parabola here:
https://brainly.com/question/5527217
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A group of friends were working on a student film that had a budget of $1200. They used $756 of their budget on props. What percentage of their total budget did they spend on props?
Answers
756/1200 = 0.63
In figure 5, what are the values of x and y?
(4x - 12)
(7y+12)°
(12x+8)°
Answers
Answer:
sorry
Step-by-step explanation:
Where is the figure?
Can someone please help!!!!!
Answers
A__ function is a function in the form f(x) = ax? + bx+c, where a, b, and care real
numbers and a 70, that will graph as a parabola.
is it
a) quadratic
b) first
c) parabolic
d) second
Answers
PLZ HELP!!! WILL MAKE BRAINLIEST!!!
Answers
what is the distributive property for 15x+25?
Answers
Answer:
5(3x+5)
Step-by-step explanation:
Answer:
5(3x + 5)
Step-by-step explanation:
Factor out 5 of 15x + 25 then you'll get your answer.
Hope this helps:)
URGENT
Explain:
Answer the following questions using 125 words or more:
1. Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What
would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do
differently?
2. What would happen if you reduced the comic's size rather than enlarged it? Would the process be the same? What
would you do differently?
Answers
The way in which the original comic would be similar to the enlargement is that they have the same proportion.
How is the original comic similar to the enlargement?Based on the fact that when a comic is enlarged, the original and enlargement would remain the same and the only difference would be a larger size.
Hence, we can see that because they have the same proportion, each individual pixel in the original is more visible and the enlargement displays the image in a small number of large pixels.
The use of a grid would likely reduce the effect of pixelation and if there is a reduction in the size of the comic, there would be the same effect, only that it would be smaller, but have the same proportion.
Read more about pixels here:
https://brainly.com/question/9017156
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Can someone help me plz
Answers
njjjwer:
jajajajaj
Step-by-step explanation:
yesHelp please I really need it
Answers
Answer:
40%
Step-by-step explanation:
it ads up to 90, so 50+x=90 x=40
Answer:
40° as it is a right angle
then 90 - 50= 40
A locker door is 13 inches wide by 27 inches tall. A company will use a scale factor of 2.5 to change the dimensions
of the door. What will be the new height of the locker door?
Answers
Answer:67.5
Step-by-step explanation:The question asked the HEIGHT. So multiply the scale factor (2.5) and the inches tall (27).
3. Given f(x)=-2(5)
Find f (4)
Answers
Answer:
f
(
x
)
=
2
, means, whatever be the value of
x
, f(x)=2#.
∴
f
(
−
4
)
=
2
.
22:4 :: x : 16, what is the value of x, if all the four numbers are in proportion.
Answers
Answer:
= 22:4 :: x : 16
22*16 = 4x
352 = 4x
x = 352/4
x = 88
Hope this helps you. Do mark me as brainliest.
What is the x-intercept of the graph of Y= 4x-36
Answers
y = 4x - 36
The y is your y-intercept.
The 4x is your slope. (4/1)
The -36 is your x-intercept.
The x - intercept of the line is at Point X(9, 0).
We have the following equation of a straight line -
y = 4x - 36
We have to find the x - intercept of the of this line.
What is the general equation of a straight line ?The general equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question, we have -
y = 4x - 36
Now, comparing this line with the general equation of line - y = mx + c, we get -
m = 4
c = - 36
for the x - intercept of the line, substitute y = 0. We get -
0 = 4x -36
4x = 36
x = 9
Hence, the x - intercept of the line is at Point X(9, 0).
Refer to the graph attached for more clarity.
To solve more questions on Graphs of straight line, visit the link below -
brainly.com/question/27757761
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I need help with this, pls put step by step
Answers
Cross multiply
24u = 27
U = 27/24
Simplify
U = 9/8 cm
Nick went canoeing on the river he traveled 1 mile in 17 minutes.at this rate,how far will he travel in an hour and 25 minutes
Answers
9514 1404 393
Answer:
5 miles
Step-by-step explanation:
An hour and 25 minutes is 85 minutes. Using the given information we can find the distance d with the proportion ...
[tex]\dfrac{\text{distance}}{\text{time}}=\dfrac{d}{85\text{ min}}=\dfrac{1\text{ mi}}{17\text{ min}}\\\\d=\dfrac{85\text{ min}}{17\text{ min}}(1\text{ mi)}\qquad\text{multiply by $85$ min}\\\\d=5(1\text{ mi})\qquad\text{simplify}\\\\d=\boxed{5\text{ mi}}[/tex]
In 1 hour and 25 minutes, Nick will travel 5 miles.