Proof:
L.H.S. = A - (B - C)
= A - (B ∩ C'), since A - B = A ∩ B'
= A ∩ (B ∩ C')'
= A ∩ {B' U (C')'}, since (A ∩ B)' = A' U B'
= A ∩ (B' U C)
= (A ∩ B') U (A ∩ C)
= (A - B) U (A ∩ C) = R.H.S.
∴ A - (B - C) = (A - B) U (A ∩ C)
Hence, This completely the proof.
Some properties of set algebra:
1. A U Φ = A, A ∩ Φ = Φ
2. A U U = U, A ∩ U = A
3. A U A = A, A ∩ A = A
4. A U (B U C) = (A U B) U C
5. A ∩ (B ∩ C) = (A ∩ B) ∩ C
6. A U (B ∩ C) = (A U B) ∩ (A U C)
7. A ∩ (B U C) = (A ∩ B) U (A ∩ C)
8. A U A' = U
9. A ∩ A' = Φ
10. (A U B)' = A' ∩ B'
11. (A ∩ B)' = A' U B'
12. A - B = A ∩ B'
13. A - (B ∩ C) = (A - B) U (A - C)
14. A - (B U C) = (A - B) ∩ (A - C)
15. A Δ B = (A - B) U (B - A)
16. A Δ B = B Δ A
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26. Benson buys some pencils at $4 each and some pens at $6 each. The total number of pencils and pens bought is 37. The amount spent on buying pencils is $58 higher than that spent on buying pens. Find the amount of money spent on buying pens.
Solve the equation for y.
у - 5x = 3
y=
[tex]{ \boxed{ \red{ \sf{y = 3 + 5x}}}}[/tex]
Step-by-step explanation:
[tex]{ \blue{ \tt{y - 5x = 3}}}[/tex]
Shift -5x to right side then,
[tex]{ \boxed{ \blue{ \tt{y = 3 + 5x}}}}[/tex]
i need this answered
Considering the given sample, it is found that:
a) The confidence interval is: (71.43, 77.17).
b) The interval does not contain 78, hence the manufacturer's claim is not correct.
c) The sample size needed is: 55.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 12 - 1 = 11 df, is t = 2.201.
Using a calculator, the other parameters for the interval are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
Hence the lower bound of the interval is:
74.3 - 2.201 x 4.52/sqrt(12) = 71.43.
The upper bound is:
74.3 + 2.201 x 4.52/sqrt(12) = 77.17.
For item c, we have that:
The population standard deviation of [tex]\sigma = 3.91[/tex] is used.Since the population standard deviation is know, the z-distribution is used and the critical value is z = 1.95.The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Then the sample size is obtained when M = 1.04 as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up).
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The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answer:
step by step answer at least
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
The value of x is 66°.
What are parallel lines?
No matter how far they may extend in either direction, parallel lines are ones that are equally spaced apart from one another and never cross.
If line m is parallel to line n, the two angles given will be congruent because they will be alternate exterior angles (which are congruent).
Here, we have
m = 132°
n = 2x°
This means we will set both parallel lines equal to each other and solve for x.
132° = 2x°
x = 66°
Hence, the value of x is 66°.
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At a butcher shop, Hilda bought beef and pork. she left with 18,8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.
At a butcher shop, Hilda bought beef and pork. she left with 18.8/25 pounds of meat. Express the number of pounds of pork she bought using a decimal.
= 18.8/25
= 0.752
Which ordered pairs represent points on the graph of this equation? Select all that apply. 3x=y+4
(7,– 1)
(2,2)
(3,5)
(0,4)
(– 1,– 7)
(0,– 4)
The ordered pairs that are on the graph of the linear equation are:
{(2,2), (3,5), (– 1,– 7), (0, -4)}
Which ordered pairs represent points on the graph?Here we have a list of ordered pairs and we want to see which ones are solutions for the given linear equation:
3x = y + 4
To check that, we can just replace the values of each ordered pair in the equation and see if the equation is true or false. If it is true, then the ordered pair is a point on the graph.
1) (7,– 1)
3*7 = -1 + 4
21 = 3 this is false.
2) (2,2)
3*2 = 2 + 4
6 = 6 this is true.
3) (3,5)
3*3 = 5 + 4
9 = 9 this is true.
4) (0,4)
3*0 = 4 + 4
0 = 8 this is false.
5) (– 1,– 7)
3*-1 = -7 + 4
-3 = -3 this is true.
6) (0, -4)
3*0 = -4 + 4
0 = 0 this is true.
So the correct options are:
{(2,2), (3,5), (– 1,– 7), (0, -4)}
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Pls answer this is in khan academy pls answer fast rapidly
Answer
34.056 I'm pretty sure it's right. I took a test with the same question
Answer:
34.556
Step-by-step explanation:
= (3x10) + (4x1) + (5x1/10) + (5x1/100) + (6x1/1000)
= 30 + 4 + 0.5 + 0.05 + 0.006
12. How many quarters are there in 5 3/4
Answer: 23
Step-by-step explanation: Please give brianlist
-9 (1 + 6x) = 42 - 3x
Answer:
x = - 1
Step-by-step explanation:
- 9(1 + 6x) = 42 - 3x ← distribute parenthesis on left side by - 9
- 9 - 54x = 42 - 3x ( add 3x to both sides )
- 9 - 51x = 42 ( add 9 to both sides )
- 51x = 51 ( divide both sides by - 51 )
x = - 1
Answer:-1=x
Step-by-step explanation:
-9(1+6x)=42-3x
-9-54x=42-3x
+54x +54x
-9=42+51x
-42 -42
-51/51=51x/51
-1=x
By the end of the first week a movie had grossed $2.3million. By the end of is six week, it had grossed $6.8million. Graph the data with the week on the vertical axis, and draw a line through the points.Then find and interpret the slope of the line.
Answer:
The first step is to label the points being (1,2.3),(6,6.8) in which the first ordered pairs is the number of weeks, and the second one is the dollars in millions.
Hence, the slope is: m=(6.8-2.3)/(6-1) = 4.5/5 = 9/10 = 0.9
The slope represents the dollar rate in the millions per week. In this case, the movie grossed $0.9 million per week from week one to the sixth week.
The population of a certain town is approximately 158,000 and
increases exponentially at the rate of 7% every year. Which equation
best represents the population of the town after × years?
-y = 158,000 (.07) *
-y = 158,000 (1.7) *
-y=158,000(1.07) *
- y = 158,000 (. 93) *
The equation that best represents the population of the town after x years is C. y = 158,000(1.07)ˣ.
What is an exponential equation?An exponential equation is an equation with exponents.
Exponential equations have the exponents (or) parts of the exponent as variables.
Exponential equations are raised to the power of the indicated exponents or variables.
The population of a town = 158,000
Annual rate of increase = 7%
After x years, the population, y = 158,000 x 1.07ˣ
= 158,000(1.07)ˣ
Thus, in x years, the town's population will become the solution to equation C. 158,000(1.07)ˣ where x is the number of years after the approximation.
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¿cuales son los divisores del 27?
determine if the triangles can be proved similar
Answer:
no it can't be proved similar
A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the
Pythagorean Theorem. What are the measures of the other 2 angles?
Answer:
28.072°, 61.928°
Step-by-step explanation:
You want the measures of the acute angles in a right triangle with sides 8, 15, 17.
Trig functionsAny of the (inverse) trig functions can be used to find the angles. You know the acute angles are complementary, so finding one tells you the measure of the other.
Tan = Opposite/Adjacent
The smallest angle (A) is adjacent to side 15 and opposite side 8.
tan(A) = 8/15
A = arctan(8/15) ≈ 28.072°
The complement is angle B:
B = 90° -28.072° = 61.928°
__
Additional comment
We have taken sides {a, b, c} = {8, 15, 17}. The angles opposite those sides are A, B, C.
You can also use ...
A = arcsin(8/17)
B = arccos(8/17)
15 points please help
Evaluate the quantity one fourth squared times one fourth raised to the zero power end quantity all raised to the second power.
The value of one fourth squared times one fourth raised to the zero power end quantity all raised to the second power is 1/256.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
From the information, the exponent illustrated will be:
= (1/4^2 × 1/4^0)²
= (1/16 × 1)²
= (1/16)²
= 1/16 × 1/16
= 1/256
The value is 1 / 256.
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You deposit $300 each month into an account earning 4% interest compounded monthly.
A. How much will you have in the account in 20 years?
B. How much total money will you put into the account?
C. How much total interest will you earn?
You will have $1,09,545.455 in the account in 20 years. An you will put total $72,000 in the account. And you will earn $37,545.455 of total interest.
Here,
We deposit $300 each month earning 4% interest compounded monthly.
we will find the future value of this amount after 20 years.
for finding future value, The general formula is
FV=PV∙(((1+i)ⁿ-1))/i
Where,
FV= future value
PV=present value
i=interest
n=time period
now, our PV=300$ and we have 4% interest compounded monthly
i.e.
i=4/100∙1/12
i=0.0033
And, the period of time is
n=20×12
n=240
Now, we will calculate the future value
FV=300 (((1+0.0033)²⁴⁰-1))/0.0033
FV=300 (((1.0033)²⁴⁰-1))/0.0033
FV=300 (((2.205)-1))/0.0033
FV=300(365.15)
FV=1,09,545.455$
Now, The total money you put into account is
total amount=300×20×12
total amount=72,000$
Total interest,
total interest=109545.455-72000
total interest=37,545.455$
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A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t) = -16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ___ second(s) after launch.
(Simplify your answer.)
The time taken for the rocket to reach its maximum height is; 1.25 seconds.
The maximum height reached by the toy rocket is; 44.5 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 40t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 40 = 0
-32t = -40
t = -40/-32
t = 1.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 1.25 seconds.
Also, the maximum height reached by the rocket is at; h (1.25);
h(1.25) = -16(1.25)² + 40 (1.25) + 7
= -25 + 62.5 + 7
= 44.5
The maximum height reached is; 44.5 feet.
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Which number doesn't share the same pattern as: 2, 20, 4, 8, 300
Answer:
The number "2" does not follow the same pattern
Step-by-step explanation:
as the numbers "2, 20, 4, 8, 300." A pattern is given: 2,20, 4,8,300.
2 is the number which doesn't share the same pattern as 20, 4, 8, 300
What is Number system?A number system is defined as a system of writing to express numbers.
Given,
We need to find the number which doesn't share the same pattern as: 2, 20, 4, 8, 300
We can observe that in the given patterns 2,20, 4,8,300, all the numbers are divisible by 4 except 2.
Twenty by four equal to five
20/4=5
Four by four equal to one
4/4=1
Eight by four equal to two
8/4=2
Three hundred by four equal to Seventy five
300/4=75
2 is not divisible by 4.
Hence, 2 is the number which doesn't share the same pattern as 20, 4, 8, 300
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Rewrite 0.16 repeating a percent
Help please, can you explain and give answer
Answer:
IncreasingDecreasingDecreasingDecreasingStep-by-step explanation:
You can determine whether a function is increasing or decreasing by taking its derivative.
If the derivative is bigger than 0, then function is increasing.
If the derivative is less than 0, then the function is decreasing.
You can also graph the functions to determine whether they are increasing or decreasing.
Select the mapping that represents a function.
Then complete the table with the values from the mapping and press Submit.
The mapping that represents a function is Y.
And the table with the values from the mapping.
X Y
(-1, 4) (1, 4)
(-2, 5) (2, 4)
(-2, 6) (3, 5)
In this question we have been given two mappings i.e., we have been given two relations.
We need to select the mapping that represents a function.
We know that a relation is a function when for every input-value there should be associated with exactly one output-value.
From given table the mappings are:
X Y
(-1, 4) (1, 4)
(-2, 5) (2, 4)
(-2, 6) (3, 5)
We can observe that in mapping X, for input -2 there are two outputs.
This means, the mapping X is not a function.
Therefore, the mapping that represents a function is Y.
And the table with the values from the mapping.
X Y
(-1, 4) (1, 4)
(-2, 5) (2, 4)
(-2, 6) (3, 5)
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2+10+18+…+x=552=>x=?
The value of x is 90 if the 2+10+18+…+x=552 which is an arithmetic sequence.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
The given is:
2+10+18+…+x=552
The above is the arithmetic sequence:
a = 2
d = 10 - 2 = 8
a(n) = x
a + (n-1)d = x
2 + (n-1)8 = x ..(I)
s(n) = 552
(n/2)[a + x] = 552
(n/2)[2 + x] = 552 ..(II)
From equation (I) and (II)
The values of x and n:
[tex]\rm \begin{pmatrix}x=90,\:&n=12\\ x=-98,\:&n=-\frac{23}{2}\end{pmatrix}[/tex]
the value of n -23/2 is not possible
x = 90
Thus, the value of x is 90 if the 2+10+18+…+x=552 which is an arithmetic sequence.
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Use the table that shows popular sports cars colors in North America how many times more respondents to silver than red round to the nearest 10th if necessary(silver=0.2, red=0.09). Next question. How many times more respondents chose either silver or black than red? Round to the nearest tenth if necessary.
(a) The respondents who chose silver 2.3 times more than red , and
(b) the respondents who chose either silver or black are 3.8 times more than who chose red .
In the question ,
a table is given which shows popular sports cars colors in North America .
Part(a)
portion of respondents who chose silver = 0.20 ,
portion of respondents who chose red = 0.09 ,
the number of times more respondents chose silver than red = 0.20/0.09
= 20/9
= 2.22222
On rounding to the nearest tenth
≈ 2.3
Part(b)
portion of respondents who chose black = 0.14 ,
portion of respondents who chose either black or silver = 0.20 + 0.14
= 0.34
number of times more respondents chose either silver or black than red
= 0.34/0.09
= 3.7777777
rounding to the nearest tenth
≈ 3.8
Therefore , (a) The respondents who chose silver 2.3 times more than red , and
(b) the respondents who chose either silver or black are 3.8 times more than who chose red .
The given question is incomplete , the complete question is
Use the table that shows popular sports cars colors in North America
(a) how many times more respondents to silver than red round to the nearest 10th if necessary.
(b) How many times more respondents chose either silver or black than red? Round to the nearest tenth if necessary.
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Which of the following is the correct representation of permutation?
Answer:
Step-by-step explanation:
If is a permutation group of degree, then the permutation representation of is the linear representation of which maps to the corresponding permutation matrix (here is an arbitrary field). That is, acts on by permuting the standard basis vectors.
Draw a line through the points. Why does this line show a proportional relationship? Check all that are true. A. It is not curved B. It is a vertical line C. It connects all the dots D. It goes through the origin
Answer:
Without seeing the picture I would say that all are true
Step-by-step explanation:
A proportional relationship does go through the origin. It is a straight line. a straight line does not curve.
I am having trouble solving this.
Answer:
(f o g)(x) = 8x² + 10x + 3
Step-by-step explanation:
(f o g)(x) = f(g(x))
= 2 (4x² + 5x) + 3
= 8x² + 10x + 3
The capital letter Y is rotated 180°. Are there any other transformations that would result in the same image?
Explain your answer.
When the capital letter Y is rotated 180°, Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.
Define Transformations.A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given,
The capital letter Y is rotated 180°.
The coordinates shift from (x, y) to (x, z) when you reflect a figure across the x-axis (x, -y). The coordinates would change from (x, -y) to (x, y) if you then reflected it over the y-axis (-x, -y). As a result, reflecting over the x- and y-axes will be similar to turning 180 degrees counterclockwise. Our point A(x,y) rotates 180 degrees counterclockwise around the origin to become A' (-x,-y). transforming both x and y negative is all we do as a result.
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A carton can only contain 15 tins of biscuit. A wholesaler needs to re-pack 448 tins of biscuits into cartons. How many cartons does he need if he wants to pack all the biscuits?
