Answer:
the flagpole is 16 feet tall.
Step-by-step explanation:
A right angle triangle is formed.
The distance of the point on the ground from the base of the flagpole represents the adjacent side of the right angle. The height of the flagpole from the ground represents the opposite side of the right angle.
To determine the height, h of the flagpole, we would apply the Tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan 53 = h/12
h = 12Tan53 = 12 × 1.327
h = 16 feet to the nearest whole number
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%
Maya's test score average decreased by 18 points this semester.
Write a signed number to represent this change in average.
Answer: -18
Step-by-step explanation:
It is decreasing so the now will become negative since it is same as losing some points.
On planet Umpt, there are 8 mimstoons to every 11 hoots. If farmer grapple has 60 hoots on his Kent farm, how many mimstoons are on the farm?
Answer:
480/11
Step-by-step explanation:
8:11 as x:60
480 = 11x
x= 480/11
Pls mark Brainiest :)
40 POINTSSS AND BRAINLIEST 40 POINTS
-4y + 6x = -48
The x-intercept is ______
The y-intercept is ______
Answer:
the x intercept is x=-8
the y intercept is y=12
Step-by-step explanation:
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
if f(x) = x^2 and g(x) = 2x + 1, WHICH EXPRESSION IS EQUIVALENT TO (F O G)(X),
Answer:
(2x+1)^2 or 4x^2+4x+1
Step-by-step explanation:
I'm going to assume you need to find f(g(x)) when f(x)=x^2 and g(x)=2x+1
You first need to find g(x) which is 2x+1
You then take the f(x) function and replace x with 2x+1
This means our new equation is
(2x+1)^2
Your teacher may or may not want you stop here, really only you know the answer to that
But if we expand this we'll find that (2x+1)^2=4x^2+4x+1
The equivalent expression of (f o g) is 4x² + 4x + 1.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Two functions are given.
f(x) = x²
g(x) - 2x + 1
Now,
(f o g)(x) = f(g(x))
g(x) - 2x + 1
So,
f(g(x)) = f(2x + 1)
Now,
f(2x + 1)
= (2x + 1)²
= 4x² + 4x + 1
Thus,
The expression of (f o g) is 4x² + 4x + 1.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ2
WILL MARK BRAINLIEST ONLY HAVE 10 MINUTES
Answer:
the answer is
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
it is A
Find the soluition of equation 2(2x+3)=-4+2(2x+5)
Answer:
x=0
Step-by-step explanation:
2(2x+3)=-4+2(2x+5)
4x+6=-4+4x+10
4x-4x=-4+10-6
x=0
Answer:
0
Step-by-step explanation:
4x+6=4x-4+104x+6=4x+6=0Consider 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
PLZ HELP I WILL GIVE YOU BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
worth 20% of my grade
Answer:
d
Step-by-step explanation:
yw can i have brainliest since this is prob the right answer
15 is 4.06% of what??
Answer:
369.458128
Step-by-step explanation:
[tex]x (0.0406) = 15 \\ x = \frac{15}{0.0406} \\ x = 369.458128[/tex]
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
lindsay sounds a spinner once and then flips a fair coin twice, the spinner is shown below. what is the probability of the spinner landing on an odd number and the coin landing on tails both times
Answer: The probability is that it has a 50/50 chance of landing on either side
Step-by-step explanation:
i’ll give brainliest!!!
14a. =
15b. 2/3 is less than 0.667
16c. 3 7/8 is greater than 3.375
17d. 3/8 is less than 1/2
( 2 5/8 + 1/6) + 1 3/8
Answer:
25/6
Step-by-step explanation:
Answer:
25/6 or 4 1/6
a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/
8 = 16/8
b) Add the answer from previous step 16 to the numerator 5. New numerator is 16 + 5 = 21
Write a previous answer (new numerator 21) over the denominator 8.
Two and five eighths is twenty-one eighths
Add: 21/8 + 1/6= 21 · 3/8 · 3 + 1 · 4/6 · 4= 63/24 + 4/24 = 63 + 4/24 = 67/24
Hope this helps!!
5×-18<--8 may I please get the right answers step by step
9514 1404 393
Answer:
x ≤ 2
Step-by-step explanation:
Maybe you're trying to solve ...
5x - 18 ≤ -8
As with any 2-step equation, add the opposite of the constant that is on the same sides as the variable term.
5x -18 +18 ≤ -8 +18
5x ≤ 10 . . . . . . . . . . . simplify
Now, divide both sides by the coefficient of the variable.
5x/5 ≤ 10/5
x ≤ 2 . . . . . . . . . . . . . simplify
_____
Additional comment
If your comparison was < instead of ≤, use that (<) for your final answer. The same symbol is used throughout, for this problem.
The value of A is? The value of B is?
Answer:
C+B
Step-by-step explanation:
you add A + B = C
Answer:
A=10
B=35
Step-by-step explanation:
1 A rectangular picture frame has perimeter
70 cm.
a The width of the frame is x cm. Find an
expression, in terms of x, for the height
of the frame.
b Find an equation for the area of the
frame, Acm?, in terms of x.
c Plot the graph which shows how A
varies with x. Use a suitable domain and
range. Hence sketch the graph on paper.
d Find the x-intercepts of the graph in part c.
e State what these two values of x represent.
f Hence find the equation of the graph's
line of symmetry, and state what this
tells you in the context of the problem.
PLEASE HELP which is the graph of y=^3√x+1-2
Answer:
I used desmos to make the graph.
The function d (t)=65t models the total distance (in miles) that a truck travels from aurora, where d (t) represents the total distance traveled and t represents the number of hours traveled.
a. What is the y-intercept? What does it represent?
b. What is the slope? What does it represent?
c. Is the function increasing or decreasing?
d. What is the distance traveled after 10 hours, d(10)?
Which do one we answer?
question 4/3 y=1 what is y?
Answer:
y= 3/4
Step-by-step explanation:
Answer:
y=3/4
Step-by-step explanation:
4/3y=1
divide both sides by 4/3
1 divided by 4/3 is 3/4 so:
y=3/4
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
I GIVEEE BRAINLISTTTTT
Answer:
the ones with 16 dollar jeans
PLEASE HELP ME
how do you identify
which side of your triangle is the hypotenuse,
the adjacent side and the opposite side.
Answer:
In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.
Carpeting costs $9.95 per yard. If Jamie buys 8 yards, how much will it cost him?
Answer:
$79.6
Step-by-step explanation:
9.95 x 8 = 79.6
Which of the following expressions is equivalent to 5 + 2(10 – 3)?
1. 7(10 – 3)
2. 70 – 3
3. 5 + 20 – 3
4. 5 + 2(7)
Answer:
4
Step-by-step explanation:
1. 7(10-3)
7×7
49
2. 70-3
67
3. 5+20-3
25-3
22
4.5+2(7)
5+14
24
5+2(10-3)
5+2×7
5+14
24
There are 40 children and 12 adults going on a trip to New York City by car. Each car can hold a maximum of 5 people. What is the least number of cars needed for the trip?
Answer:
Number of cars needed for the trip = 11
Step-by-step explanation:
Given that:
Number of children = 40
Number of adults = 12
Total number = 40 + 12 = 52 people
Each car can hold 5 people.
Number of cars = [tex]\frac{52}{5}[/tex]
Number of cars = 10.4
Rounding off to next whole number as one car can hold a maximum of 5 people.
Number of cars = 11
Hence,
Number of cars needed for the trip = 11
4x - 2 - 8x = 22
help
Answer:
x = -6
Step-by-step explanation:
4x - 2 - 8x = 22
-4x - 2 = 22
-4x = 24
4x = -24
x = -6
PLEASE HELP!!! ILL MARK BRAINLIEST IF CORRECT!!!
Answer:
Im pretty sure the answer is 3.2m
Step-by-step explanation:
Answer:
6.7 sqm
Step-by-step explanation:
I answered first
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.