Find the missing angle. Round your answer to the nearest degree.
37 FT
22 ft
f
x=
degrees
1
Answer:
53.52°
Step-by-step explanation:
cos x° = 22/37 = 0.59456
x = 53.52°
Given f(x)=14(5−x)2 what is the value of f(11)?
Answer:
I was unsure about the way your question was written so I solved for two equations: f(x)=14(5-x)*2 and f(x)=14(5-x)+2
Step-by-step explanation:
Given f(x) = 14(5−x)², the value of f(11) = 504
The given function is:
f(x) = 14(5 - x)²
To get the value of f(11), substitute x = 11 into the function f(x) = 14(5 - x)²
f(11) = 14(5 - 11)²
Simplify the expression
f(11) = 14(-6)²
f(11) = 14(36)
f(11) = 504
Therefore, given f(x) = 14(5−x)², the value of f(11) = 504
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Certain pieces made by an automatic lathe are subject to three kinds of defects X, Y, Z. A sample of 1000 pieces was inspected with the following results: 2.1% had type X defect. 24% had type Y defect. 2.8% had type Z defect. 0.3% had both type X and type Y defects. 04% had both type X and type Z defects. 0.6% had both type Y and type Z defects. 0.1% had type X, type Y, and type Z defects. Draw a Venn Diagram, then find:
(a) What percent had none of these defects?
(b) What percent had at least one of these defects?
(c) What percent were free of type X and/or type Y defects?
(d) What percent had not more than one of these defects?
Answer:
a) % age of samples containing none of these defects = 93.9%
b)% age of samples containing at least one of these defects = 6.1%
c) % age of samples free of type X and/or type Y defects = 95.8%
d) %age of samples with not more than 1 defect = 98.9%
Step-by-step explanation:
Data Given:
Number of Samples = 1000
Type X defect = 2.1% = 21 samples
Type Y defect = 2.4% = 24 samples
Type Z defect = 2.8% = 28 samples
Both Type X and Y defect = 0.3% = 3 samples
Both Type X and Z defect = 0.4% = 4 samples
Both Type Y and Z defect = 0.6% = 6 samples
Type X and Y and Z defect = 0.1% = 1 sample
Venn Diagram is attached in the attachment below. Please refer to attachment for the Venn Diagram.
a) % age of samples containing none of these defects.
Solution:
Number of samples containing none of these defects = Total - Samples with defects
Number of samples containing none of these defects = 1000 - { (Type X) + (Type Y) + (Type Z) - (Both X and Y) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
Number of samples containing none of these defects = 1000 - { (21) + (24) +(28) - (3) -(4) - (6) + (1) }
Number of samples containing none of these defects = 1000 - 61
Number of samples containing none of these defects = 939
% age of samples containing none of these defects = 939/1000 x 100
% age of samples containing none of these defects = 93.9%
b) % age of samples containing at least one of these defects:
We have already calculated this above, number of samples containing at least on of these defects:
number of samples containing at least on of these defects = { (Type X) + (Type Y) + (Type Z) - (Both X and Y) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
number of samples containing at least on of these defects = { (21) + (24) +(28) - (3) -(4) - (6) + (1) }
number of samples containing at least on of these defects = 61
% age of samples containing at least one of these defects = 61/1000 x 100
% age of samples containing at least one of these defects = 6.1%
c) % age of samples free of type X and/or type Y defects.
For this find, we need to find the samples with only Z Type defect.
Number of Samples with Only Z type defects = { (Type Z) - (Both X and Z) - (Both Y and Z) + (All defects X and Y and Z) }
Number of Samples with Only Z type defects = { (28) -(4) - (6) + (1) }
Number of Samples with Only Z type defects = 19
Now, we also know the number of samples without any defects = 939
Now,
The number of samples free of type X and/or type Y defect = Sum of Number of Samples with Only Z type defects and number of samples without any defects
The number of samples free of type X and/or type Y defect = 19+939
The number of samples free of type X and/or type Y defect = 958
% age of samples free of type X and/or type Y defects = 958/1000 x 100
% age of samples free of type X and/or type Y defects = 95.8%
d) %age of samples with not more than 1 defect:
For this find, we need to find number of samples with only X type and with only type Y and with only type Z.
We have already found the number of samples with only Z type defect = 19
Now,
number of samples with only X type defect = { (Type X) - (Both X and Z) - (Both X and Y) + (All defects X and Y and Z) }
number of samples with only X type defect = { (21) -(4) - (3) + (1) }
number of samples with only X type defect = 15
Similarly,
number of samples with only Y type defect = { (Type Y) - (Both Y and Z) - (Both X and Y) + (All defects X and Y and Z) }
number of samples with only Y type defect = { (24) -(6) - (3) + (1) }
number of samples with only Y type defect = 16
For,
samples with not more than 1 defect = number of samples with only Y type defect + number of samples with only X type defect + number of samples with only z type defect + number of samples without any defects
samples with not more than 1 defect = 939 + 16 + 15 + 19
samples with not more than 1 defect = 989
%age of samples with not more than 1 defect = 989/1000 x 100
%age of samples with not more than 1 defect = 98.9%
Which graph represents this system? 2x-5v=-5 y=-3x+1
Answer:
Please check the attached graph.
Step-by-step explanation:
The slope-intercept form of the line equation
[tex]y = mx+b[/tex]
where
m is the slopeb is the y-interceptGiven the system of equations
2x - 5y = -5 --- [Equation 1]
y = -3x + 1 --- [Equation 2]
converting the equation 1 in the slope-intercept form
2x - 5y = -5
5y = 2x+5
divide both sides by 5
y = 2/5x + 1
Thus, the y-intercept = 1
Now, please check the attached graph below.
The red line represents the equation 2x - 5y = -5
From the graph, it is clear that the red line has the y-intercept y = 1.
Now, considerng the equation 2
y = -3x + 1
comparing with the slope-intercept form of line equation
The y-intercept b = 1
Hence, the y-intercept of the line y = -3x + 1 is y = 1
The green line represents the equation y = -3x + 1
From the graph, it is clear that the green line has the y-intercept y = 1.
Point of Intersection:
It is clear from the graph:
The red line represents the equation 2x - 5y = -5.The green line represents the equation y = -3x + 1.As both lines meet or intersect at the point (0, 1).
Therefore, the point of intersection of both the lines is:
(x, y) = (0, 1)
As we know that the point of intersection of both the lines represents the solution to the system of equations.
Therefore, (0, 1) on the graph represents the solution to the system of equations.
The graph is attached below.
An event planner is reserving rooms for a company wide event. Each conference room can hold 22 people and 100 people are scheduled to stay in the ballroom, together they must hold 914 people who are attending, How many conference rooms will they need?
Answer:
37
Step-by-step explanation:
914-100=814
814/22=37
18
8
X
12
What is the value of x?
Mrs. Hart went to get her nails done at the salon. The cost was $35.00. What is the total amount if tax is 6% and she wants to leave a 18% tip?
A. $24.00
B. $43.40
C. $8.40
D. $59.00
Answer:
B) $43.40
Step-by-step explanation:
For the tax, 6% of 35 = 2.1
So with tax = $35 + 2.1 = $37.1
18% tip
So, 18% of 35 = 6.3
So we are gonna add all the costs together = 37.1 + 6.3 = $43.40
Answer:
Answer:
B) $43.40
Step-by-step explanation:
For the tax, 6% of 35 = 2.1
So with tax = $35 + 2.1 = $37.1
18% tip
So, 18% of 35 = 6.3
So we are gonna add all the costs together = 37.1 + 6.3 = $43.40
Step-by-step explanation:
HELP NOWWW!!
What is the quotient when 2 x 2 + 7 x – 15 is divided by 2 x – 3?
Answer:
yup 12
Step-by-step explanation:
The graph below represents a library fine, in dollars, for a book returned late after a number of days overdue.
A graph titled Library Fines. The horizontal axis shows days overdue and the vertical axis shows the fine (dollars). The line shows an increase to $10 at 19 days overdue, then constant.
Christen returned an overdue book to the library. Her fine was the same as the amount on the following day. Out of the fines show below, which one would be closet to the number of days overdue?
10
14
18
21
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
2+4x=2(2x+1)
Which statements are true?
Select each correct answer.
There is no value for x that will make the equation true.
The equation is an identity,
The solution is 2.
There are infinitely many solutions.
The equation is a contradiction.
There are no solutions.
The equation is true for all values of x.
10 points. Need answer fast!.
How many different arrangements can be made with the letters from the word MATH?
A. 24
B. 6
C. 256
D. 8
Answer:
b
Step-by-step explanation:
how much water must be added to a 9-liter solution that contains 3% extract on baneberry to get a solution that contains 2% extract of baneberry
Answer:
Amount water added = 4.5 L
Step-by-step explanation:
Given:
Amount of solution = 9 L
Amount of bane-berry = 3% of 9 L = 0.27 L
Computation:
Assume;
Amount water added = x L
Total solution = 9+x L
New percentage of bane-berry = 0.27x100/(9+x)
2 = 0.27*100/(9+x)
x = 4.5 L
Amount water added = 4.5 L
Gina can write 3 pages per hour. Emily can write 5 pages per hour. If they both write for x number of hours, how many pages will they write altogether? *
x (3 + 5)
x (4 + 4)
3 (x + 5)
5 (3 + x)
Answer:
3 (x+5)
Step-by-step explanation:
Write an expression to represent the perimeter of a rectangle with the length of x -4 and width of 2x +8.
Answer:
2(x-4) + 2(2x+8) OR long way (x-4) + (x-4) + (2x+8) + (2x+8)
Step-by-step explanation:
2(x-4) represents the (x-4) + (x-4) in the longer version since for perimeter you add the sides. Same thing for the other side, 2(2x+8) represents (2x+8) + (2x+8).
Not sure if you need the expression solved but here:
[tex]2(x-4) + 2(2x+8)\\(2x-8) + (4x+16)\\=6x+8[/tex]
To get from first line to second, use distributive property. To get from second to third line, combine like terms.
The perimeter of a rectangle with the length of (x - 4) and width of
(2x +8) will be (6x + 8).
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The length of rectangle = x - 4
The width of rectangle = 2x + 8
Now,
Since, The length of rectangle = x - 4
The width of rectangle = 2x + 8
We know that;
The perimeter of rectangle = 2 (Length + Width)
⇒ The perimeter of rectangle = 2 (x - 4 + 2x + 8)
⇒ The perimeter of rectangle = 2 (3x + 4)
⇒ The perimeter of rectangle = (6x + 8)
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Consider the original trapezoid and the reduction.
A trapezoid has corresponding side lengths of 13.5 centimeters and 9 centimeters. Side A corresponds to a side with length 3 centimeters.
Figures not drawn to scale.
What is the length of side A, in centimeters, on the reduced trapezoid?
1
1.5
2
4.5
Answer:
2
Step-by-step explanation:
yaw
Answer:
2
Step-by-step explanation
Got it correct in Edgen :D
When a number is increased by 35, the result is 38. What equation fits this statement
Answer:
3 + 35 = 38?
Step-by-step explanation:
Donna deposits $275 into her savings account. She leaves the money in her account,
untouched, for 6 years. If the account earns 4.5% simple interest each year, how much simple
interest will she have earned by the end of the sixth year?
$7,425.00
$74.24
$206.25
$12.38
The simple interest earned by Donna by the end of the sixth year is $74.24
What is simple interest?Simple interest is the interest charge on borrowing that's calculated using an original principal amount only and an interest rate that never changes.
Given that, Donna deposits $275 into her savings account for 6 years, the account earns 4.5% simple interest each year,
We need to find the interest earned by the end of the sixth year
Simple Interest = PRT / 100
Where,
P = Principal ($275)
R = rate (4.5%)
T = time (6 years)
SI = 275 × 6 × 4.5 / 100
= 7425 / 100
= 74.25
Hence, the simple interest earned by Donna by the end of the sixth year is $74.24
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The 2017 World Alma- nac and Book of Facts reported that the U.S. occupation projected to grow the most is personal care aide. By 2024 there will be a need for 160,328 personal care aides, a growth of about 26% over 2014 lev- els. How many personal care aides were there in 2014
Answer:
There were 118,637 personal care aides in 2014.
Step-by-step explanation:
By 2024, there will be a need for 160,328 personal care aides, a growth of about 26% over 2014 levels.
This means that the 2014 levels is 100% - 26% = 74% of the 2024 levels.
Number of personal care aides in 2014:
74% of 160,320. So
0.74*160320 = 118,637
There were 118,637 personal care aides in 2014.
What is the number based on the list of factors? 1,3,7, __
Please help
Answer:
21 I think, might be wrong.
At Mario's restaurant, 59% of his plates are dirty. If there are 118 dirty plates, how many plates are there total?
9514 1404 393
Answer:
200
Step-by-step explanation:
If P is the total number of plates, we have ...
0.59P = 118
P = 118/0.59 = 200
There are 200 plates total.
Express each ratio as a fraction in simplest form 16 feet out of 40 feet
Answer:
Step-by-step explanation:
Start by dividing top and bottom by 4
16 / 4 = 4
40/4 = 10
The result so far is 4/10
But 4/10 is not the answer. You can divide 4 and 10 by 2
4/2 = 2
10/2 = 5
Answer: 2/5
what is the answer of X
Answer: x = -5
Step-by-step explanation:
-3.4x - 9 = 8
+9 +9
-3.4x = 17
-3.4x ÷ -3.4 = x
17 ÷ -3.4 = -5
There are 20 chairs that are to be divided into different tables. Which expression shows how many chairs would be in each group if there are t tables
A
14t
B
14 + t
C
t ÷ 14
D
14 ÷ t
Answer:
D
Step-by-step explanation:
don't know why it says 14, but its the right formula for this question.
dividing 14 into how many tables there are (t)
A lion eats 462 pounds of food in a week.If the lion eats the same amount of food each day,how many pounds does a lion eat per day
Answer:
The lion eats 66 pounds of food per day
Step-by-step explanation:
Billy drove his car 290 miles in 5 hours. Sheila drove her car 132 miles in 2 hours. If each driver is traveling at a constant speed (in miles per hour), who is driving at a faster speed?
Answer:
Shelia is
Step-by-step explanation:
hope this helps plz mark brainlessly
Find the measure of the smaller angle formed by the hands of a clock at the following time.
5:25
Answer: 12°30’
Step-by-step explanation:
Raise b to the 7th power, then find the quotient of the result and 8
Answer:
b^7 / 8.
Step-by-step explanation:
I need help ASAP no rocky
Answer:
no rocky
Step-by-step explanation:
Answer:
The answer is C
Step-by-step explanation:
I think it's C and I am always right so it is C! You're welcome!
HELLO HELPPP PLEASE ASAPPP
Solve each problem by graphing
Y=-5x+3
Y=-5x-3
Answer:
I don't have graphing paper but this problem will have no solution. It will create two parallel lines going downwards.
Step-by-step explanation:
They both have the same slope and different y intercept so they will never intersect