Monthly sales of water heaters are normally distributed with a mean of 21 and a standard deviation of 5. What is the probability of selling 12 water heaters or
less?
a) 3.59%
Ob) 1.8096
O c) 96.41%
O d) 8.45%
Answer:
Option A: 3.59% is the correct answer
Step-by-step explanation:
Z-score is used to calculate the probabilities when mean and standard deviation is given.
Given
Mean = μ = 21
SD = σ = 5
We have to find the probability of selling 12 or less water heaters so our x value is 12
x = 12
The z-score of a value is calculated as:
z-score = (x-μ)/σ
Putting the values
[tex]z-score=\frac{12-21}{5} \\=\frac{-9}{5}\\=-1.8[/tex]
Now z-score table will be used to calculate the probability for z= -1.8
So we will go for the row with -1.8 and column 0, which gives us: 0.03593
As we have to calculate the probability in percentage
[tex]=0.03593*100\\= 3.593\%[/tex]
Hence,
Option A: 3.59% is the correct answer
PLEASE GUYS JUST HELPPP MEEE PLEASE
Answer:
Step-by-step explanation:
2. 27
3. 18
Answer:
s o w h a t y o u n e e d t o d o i s
Step-by-step explanation:
NEED HELP 45 POINTS PLZ
Is there enough information to prove that the triangles are congruent?
If yes, provide the correct Triangle Congruence Postulate or Theorem and a congruence statement.
If no, justify your answer.
put your answer in comments plz because it will be deleted
A bowl of raffle tickets contains the numbers 1 through 60. What is the probability that a randomly selected ticket will be a number that is not a multiple of 7
Answer:
[tex]Probability = \frac{13}{15}[/tex]
Step-by-step explanation:
Given
Ticket Numbers = 1 to 60
Required
Determine the probability of not selecting multiples of 7
First, we need to list out the multiples of 7 in this range:
[tex]Multiple = 7,14,21,28,35,42,49,56[/tex]
These are 8 in numbers. So, there are 8 multiples
Next, is that we determine the number of non multiples of 7. This s calculated as:
[tex]Non\ Multiples = 60 - 8[/tex]
[tex]Non\ Multiples = 52[/tex]
The required probability is then calculated as:
[tex]Probability = \frac{Non\ Multiples}{Total}[/tex]
[tex]Probability = \frac{52}{60}[/tex]
[tex]Probability = \frac{13}{15}[/tex]
Answer:
Step-by-step explanation:
There are 8 numbers between 24 and 31, inclusive. So the probability of getting a number in that range is 885. Therefore, by the complement rule, the probability of not getting one of these numbers is
[tex]1-(8/85)= 85- 8 /85=77/ 85[/tex]
After substituting, what is the first step when evaluating 7 when y = 8? Add 4 and 9. O Multiply 8 by 4. Divide 9 by 7. O Divide 4 by 7.
Note: you did not correctly enter the right expression. After a little research, I am able to find the correct expression which is as follows:
4y+9/7 when y = 8
Therefore, I am solving your query based on evaluating the expression
4y+9/7 when y = 8
Answer:
we conclude that after substituting, the first step is to 'Multiply 8 by 4'.
Step-by-step explanation:
Given the expression
4y+9/7
As we have to evaluate the given expression for the y=8
substituting y=8 in the expression
4y+9/7
= 4(8)+9/7
According to PEMDAS rule, we first need to do multiplication
Thus, the first step must have to be multiplying 4 and 8.
= 32 + 9/7
= 233/7
Therefore, we conclude that after substituting, the first step is to 'Multiply 8 by 4'.
Mrs. Culland is finding the center of a circle whose equation
is x2 + y2 + 6x - 4y – 3 = 0 by completing the square. Her
work is shown.
x2 + y2 + 6x + 4y - 3 = 0
x2 + 6x + y2 + 4y - 3 = 0
(x2 + 6x) + (12 + 4y) = 3
(x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4
Which completes the work correctly?
(x - 3)2 + ( - 2)= 42, so the center is (3,2).
(x + 3)2 + (y + 2)2 = 42, so the center is (3, 2).
(x - 3)2 + (x - 2)2 = 42, so the center is (-3,-2).
(x + 3)2 + (y + 2)2 = 42, so the center is (-3, -2).
Answer:
centre of circle (h,k) is (-3,-2)
Option D is Correct.
Step-by-step explanation:
The centre of circle can be found from the equation as:
[tex](x-h)^2+(y-k)^2=r^2 \ then \ (h,k) \ is \ center[/tex]
So, the steps then by Mrs Culland are:
[tex]x^2 + y^2 + 6x + 4y - 3 = 0\\x^2 + 6x + y^2 + 4y - 3 = 0\\(x^2 + 6x) + (y^2 + 4y) = 3\\(x^2 + 6x + 9) + (y^2 + 4y + 4) = 3 + 9 + 4[/tex]
The next step will be:
[tex](x + 3)^2 + (y + 2)^2 = 16[/tex]
I assume there is some calculating mistake in the given options. Instead of 42 there should be 16, according to solution shown above.
The general equation of circle is
[tex](x-h)^2+(y-k)^2=r^2 \ then \ (h,k) \ is \ center[/tex]
In our case: [tex](x + 3)^2 + (y + 2)^2 = 16[/tex]
h= -3 and k= -2, so the centre of circle (h,k) is (-3,-2)
Option D is Correct.
Answer:
D,,,, (x+3)²+(y+2)²=4², so the center is (-3, -2).
Step-by-step explanation:
Find the average rate of change of g(x)= -4x^3+1 from x= -4 to x = 1
Answer:
[tex]Rate = -52[/tex]
Step-by-step explanation:
Given
[tex]g(x) = -4x^3 + 1[/tex]
x = -4 to x = 1
Required
Determine the average rate of change
This is calculated using:
[tex]Rate = \frac{g(b) - g(a)}{b - a}[/tex]
Where
[tex]a = x = -4[/tex]
[tex]b = x = 1[/tex]
Calculating g(b):
g(b) = g(1)
If [tex]g(x) = -4x^3 + 1[/tex], then
[tex]g(1) = -4(1)^3 + 1[/tex]
[tex]g(1) = -4*1 + 1[/tex]
[tex]g(1) = -4 + 1[/tex]
[tex]g(1) = -3[/tex]
Calculating g(a):
g(a) = g(-4)
If [tex]g(x) = -4x^3 + 1[/tex], then
[tex]g(-4) = -4(-4)^3 + 1[/tex]
[tex]g(-4) = -4*-64 + 1[/tex]
[tex]g(-4) = 256 + 1[/tex]
[tex]g(-4) = 257[/tex]
So, the formula:
[tex]Rate = \frac{g(b) - g(a)}{b - a}[/tex]
becomes
[tex]Rate = \frac{g(1) - g(-4)}{1 - (-4)}[/tex]
[tex]Rate = \frac{g(1) - g(-4)}{1+4}[/tex]
[tex]Rate = \frac{g(1) - g(-4)}{5}[/tex]
[tex]Rate = \frac{-3 - 257}{5}[/tex]
[tex]Rate = \frac{-260}{5}[/tex]
[tex]Rate = -52[/tex]
Select all equations that have the solution x = 7.
a. 2(x + 7) = 28
b. 6(2x - 1) - 12 = -2(x + 10)
c. 60 = 4(x + 8)
d. 3(x - 5) = 1 + 5(x - 6)
Answer:
The correct answer is A.
Step-by-step explanation:
1. 2(x+7)
2. 2(7+7)
3. 2(14)
4. 28
Hope this helps!
Answer:
a, c and d
Step-by-step explanation:
Find the perimeter of quadrilateral ABCD with vertices A(-2,-2), B(-1,3),
C(5, 3), and D(4, -2).
Answer:
22.2Step-by-step explanation:
Step one
given the coordinates
ABCD with vertices A(-2,-2), B(-1,3), C(5, 3), and D(4, -2)
AB=(-2,-2),(-1,3)
BC=(-1,3), (5, 3)
CD=(5, 3),(4, -2)
DA=(4, -2),(-2,-2)
The distance between points AB=
[tex]AB= \sqrt (x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex]AB= \sqrt (-1+2)^2+(3+2)^2\\\\AB= \sqrt 1^2+(5)^2\\\\AB= \sqrt26\\\\AB=5.1[/tex]
The distance between points BC=
[tex]BC= \sqrt (5+1)^2+(3-3)^2\\\\BC= \sqrt 6^2+(0)^2\\\\BC= \sqrt36\\\\BC=6[/tex]
The distance between points CD
[tex]CD= \sqrt (4-5)^2+(-2-3)^2\\\\CD= \sqrt -1^2+(-5)^2\\\\CD= \sqrt26\\\\CD=5.1[/tex]
The distance between points DA
[tex]DA= \sqrt (4+2)^2+(-2+2)^2\\\\DA= \sqrt 6^2+(0)^2\\\\DA= \sqrt36\\\\DA=6[/tex]
Hence the perimeter = 5.1+6+5.1+6
= 22.2
I need help answering this question
Answer:
[tex] x = 7 [/tex]
Step-by-step explanation:
Given that AB and BC are perpendicular, it follows that:
m<ABC = right angle = 90°
Thus:
[tex] 75 + (x + 8) = 90 [/tex] (angle addition postulate)
Solve for x
[tex] 75 + x + 8 = 90 [/tex]
[tex] 83 + x = 90 [/tex]
Subtract 83 from each side
[tex] 83 + x - 83 = 90 - 83 [/tex]
[tex] x = 7 [/tex]
What is the derivative of this?
Dy/dx=x^2y+y^2x
Answer:
y^2+2xy/-x^2-2xy OR -y^2-2xy/x^2+2xy OR -y^2-2xy/(x)(x+2y)
Step-by-step explanation:
So, this is an implicit differentiation problem
x^2y+y^2x
so,
use product rule for both
x^2y'+2xy+y^2+2yy'x
collect all the y's
-x^2y'-2xyy'=y^2+2xy
y'(-x^2-2xy)=y^2+2xy
=y^2+2xy/-x^2-2xy
If DEF is congruent to JKL, DE = 18, EF =23, DF = 9x-23, JL = 7x-11, and JK = 3y-21, find the values of x and y
Answer:
x = 6, y = 13Step-by-step explanation:
if DEF is congruent to JKL, this means that the sides of JKL are all equal to that of DEF.
Hence we can say;
DE = JK
EF = KL
DF = JL
Given
DE = 18,
EF =23,
DF = 9x-23,
JL = 7x-11
JK = 3y-21,
Required
Values of x and y
Since DE = JK;
18 = 3y-21
18+21 = 3y
39 = 3y
y = 39/3
y = 13
Also, DF = JL
9x-23 = 7x-11
collect like terms
9x - 7x = -11+23
2x = 12
x = 12/2
x = 6
Hence the value of x is 6 and y is 13
Given: [tex]DE=18[/tex],[tex]EF=23,DF=9x-23,JL=7x-11,[/tex] and[tex]JK=3y-21.[/tex]
As [tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] [tex]\cong[/tex] [tex]\Delta JKL[/tex]
[tex]\Rightarrow DE=JK \ ; EF=KL \ and \ DF=JL[/tex]
[tex]\Rightarrow 18=3y-21 \ ; 23=KL \ and \ 9x-23=7x-11[/tex]
[tex]y=13[/tex] ; [tex]KL=23[/tex] and [tex]x=6[/tex]
Therefore, [tex]x=6[/tex] and [tex]y=13[/tex]
PLEASE HELP!! I’L MARK AS BRAINLIEST!!
The flow of water out of a bathtub would best be described as which type of data?
A. Discrete
B. Continuous
C. Linear
Answer:
Continuous
Step-by-step explanation:
given r,s, and p, which angle is not congruent to 4?
Answer:
Line R, S, and P are parallel lines meaning any lines that pass through them will form the same angles. Look at 4 and 2. One line is intersecting S and P to for the same angles. Corresponding angles in parallel lines which are formed by an intersecting line are equal. Therefore 4 and 2 are equal. That leaves B, C, and D left. 4 is also congruent to 5. This is because if 4 is congruent to 2 and 2 is congruent to 5 by vertical angles theorem, 5 must be equal to 4 (transitive property of equality: is a=b and b=c then a=c)
That leaves B and D left. Notice the angle made at the very top left. Across from that unlabeled angle is 6. By vertical angles theorem those 2 angles are congruent. The unmarked angle is equal to 2 and 4 because corresponding angles in parallels are congruent. Therefore lets mark that unmarked angle as 0. If the m< 6 = m< 0 and the m<0= the m<4 then m<6 must equal the m<4.
That leaves Just B remaining thus B is NOT congruent to 4
<3 is the answer
Step-by-step explanation:
The following data were reported by a corporation: Authorized shares 28,000 Issued shares 23,000 Treasury shares 7,500 The number of outstanding shares is:
Answer:
nnjvg Step-by-step explanation:
Please help
Multiple choice
Will appreciate it if u help!
Answer:
Linear
Step-by-step explanation:
It's constant. Each X is going up 1 while each Y is going up 80
write the percent as fraction: 8⅓%
Answer:
2700%
Step-by-step explanation:
8 1/3% expressed as a fraction is:
25/3
The given number is in mixed fraction 8 1/3 .
To write it in fraction follow the steps,
Step 1 - Multiply 8 by 3,
8x3=24
Step 2 - Add 24 and 1,
24+1=25
The required fraction became 8 1/3 = 25/3 .
Hopes this helps :)
given the area of a rectangle is 208 square inches, and given the length is 26 inches, find the width
Answer:
8
Step-by-step explanation:
208/26 = 8
CHECK
26x8=208
LxW=A
follow these steps to prove the given quadrilateral is a parallelogram 1. determine the slope of AB
Answer:
1.) 4/3
2.) 4/3
3.) 5
4.) 5
Step-by-step explanation:
I just took the test
Answer:
4/3
Step-by-step explanation:
i just did the assignment
Help me please I will give brainlist to whoever that does explaination
Answer:
1 and 7/30 minutes
Step-by-step explanation:
You know that the 3 commercials add up to 3 minutes of time. And that the first two are 1 1/6 minute and 3/5 minute. To add them you need a common denominator.
1 1/6=7/6. 7/6*5/5=35/30. 3/5*6/6=18/30. 35/30+18/30=53/30. 53/30 simplifies to 1 23/30 (don't need to simplify yet).Now, you need to subract that from 3. To write it over 30, multiply by 30/30. 3/1*30/30=90/30.90/30-53/30=37/30. 37/30 can be written as 1 7/30.intercept from the lines
Answer:
I mean tbh its pretty easy
The y intercept is: (0, 2.5)
The x-intercept is: (3.5,0)
just look at the graph lol but if im
wrong sorry
How do you multiply and divide rational expressions?
Step-by-step explanation:
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction.
Step 3: Simplify the rational expression.
Step 4: Multiply any remaining factors in the numerator and/or denominator.
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction
The product of two positive numbers is 48. Determine the two numbers if one number is triple the other
Step-by-step explanation:
x+x(3)=48
combine like terms
4x=48
Divide both sides by same term
4x/4=48/4
Simplify
x=12
Answer:
4
Step-by-step explanation:
(x * 3) * x = 48 ----> (4 * 3) * 4 = 48
The * are the multiplication signs. And hope this helps please choose my answer as the best so I can get brainliest pls.
Which calculation can be used to find 6% of 50?
Answer:
3
Step-by-step explanation:
We are required to find 6% of 50
To write it mathematically,
50 * 6%
Now, 6% can be rewritten as 6/100 because it tells us: '6 out of 100' and that is what percentage does
= 50 * [tex]\frac{6}{100}[/tex]
= [tex]\frac{300}{100}[/tex]
= 3
Hence, 6% of 50 is 3
Select the correct statement based on the relation shown above.
A)
The relation is a function because every element of the domain has exactly one corresponding element of the range.
B)
The relation is a function because every element of the range has been used.
C)
The relation isn't a function because not every element of the range has a corresponding element of the domain.
D)
The relation isn't a function because an element of the domain corresponds to two different elements of the range.
Answer:
The answer is D.
Step-by-step explanation:
hope that helps
x = 10 - y and y = x - 8
Answer:
x = 9 and y = 1
Step-by-step explanation:
Here,
x = 10 - y and y = x - 8 is given
then, name the equation
x = 10 - y ...(1)
y = x - 8 ...(2)
Now, put the value of x in equation (2) we get
y = x - 8
y = (10 - y) - 8
y = 10 - y - 8
y + y = 10 - 8
2y = 2
y = 2÷2
y = 1
Here, we get the value of y = 1
Now, we put the value of y in equation (1) we get
x = 10 - y
x = 10 - (1)
x = 10 - 1
x = 9
VERIFICATION:x = 10 - y
9 = 10 - 1
9 = 9
Hence, LHS = RHS
-TheUnknownScientist
Please answer see the image 30 points!
Answer:
37.7Step-by-step explanation:
perimeter of semicircle = 1/2 π d
= 1/2 π (6)
= 9.425 x 4 semicircles
= 37.7
Can Someone Evaluate This
Explanation:
Replace x with 4. Then use PEMDAS to simplify fully.
[tex]y = (14+x) \div 2\\\\y = (14+4) \div 2\\\\y = 18 \div 2\\\\y = 9\\\\[/tex]
When using PEMDAS, we evaluate the stuff in the parenthesis first. Afterward we divide.
this is an easy question so whoever is the first one who gets all of them I will make you the brainlist queen or King
Answer:
1. 3.87
2. 7.07
3. 69.89
4. 70.87
Step-by-step explanation:
Find the slope and Y-intercept for each table, and then write an equation.
Answer:
a. Slope = 2; y-intercept = 2
b. Slope = 2; y-intercept = 3
c. Slope = 2; y-intercept = -1
d. Slope = -2; y-intercept = 5
e. Slope = -3; y-intercept = -5
d. Slope = -2; y-intercept = 1
Step-by-step explanation:
I Hope That This Helps! :)