The missing probability P(A∪B) will be 37/50.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given information;
P(A)= 7/20,
P(B)=3/5,
P(A∩B) =21/100 ,
We need to find the missing probability P(A∪B).
We know that
P(A∪B)= P(A) + P(B) + P(A∩B)
P(A∪B) = 7/20 + 3/5 + 21/100
P (A U B) = 37/50
Therefore, the missing probability P(A∪B) will be 37/50.
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ5
Simplify (a + b - c)(a + b + c)
Answer:
a^2 + b^2 - c^2 + 2ab
Step-by-step explanation:
(a + b - c)(a + b + c)
1. expand
(a^2 + ab + ac + ba + b^2 + bc - ca - cb - c^2)
2. rearrange,
(a^2 + b^2 - c^2 + ab + ba + ac - ca + bc - bc)
3. add and subtract
(a^2 + b^2 - c^2 + 2ab)
Type the correct answer in the box. Use numerals instead of words.
Find the area of this shape.
4 cm
2 cm
4 cm
4 cm
5.75 cm
The area of the shape is
square centimeters.
Answer:
35 cm squared
Step-by-step explanation:
Triangle area = bxh 2 = 5.75 x 8 / 2 = 23
Trapezium Area = a+b /2 x h = 8 + 4 /2 x 2 = 12
23 + 12 = 35
Hope that helped!!! k
please solve this equation using quadratic formula
Step-by-step explanation:
x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x
(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator
(x+3)4=4×+3
(1-x)(4x-8)
1(4x-8)-x(4x-8)
4x-8-4x^2-8x=4x
The tens digit is 2 less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
Answer:
68
Step-by-step explanation:
Hello, the number is 'ab' meaning that we can write it as 10a +b
For instance 42 = 10*4 + 2
So, a = b - 2
and 10a + b + 10b + a = 154
11(a+b)=154
a+b = 154/11 = 14
We replace a by b - 2
b+b-2 = 14
2b = 14 + 2 = 16
b = 8 and then a = 6
the original number is 68.
Thanks
Parabolic microphones are used for field audio during sports events. The microphones are manufactured such that the equation of their cross section is x=1/34y^2, in inches. The feedhorn part of the microphone is located at the focus
a. How far is the feedhorn from the edge of the parabolic surface of the microphone?
b. What is the diameter of the microphone? Explain your reasoning
c. If the diameter is increased by 5 inches, what is the new equation of the cross section of the microphone?
Answer:
a. 8.5 in.
b. 34 in
c. x = 1/39 x^2.
Step-by-step explanation:
Part a.
x = 1/34 y^2
y^2 = 34x
Comparing with y^2 = 4px where p is the focus:
4p = 34
p = 8.5 in.
Part b.
The diameter = 4p = 34 in.
Part c.
Diameter = 4p = 34 + 5 = 39 in
The new equation is x = 1/39 x^2.
Use the following prompt to answer the next 6 questions. Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131 Is there evidence to doubt the color distribution claimed by the website? Use ????=0.05
Answer:
The claim on the M&M’s website is not true.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 14.433.
The degrees of freedom is:
df = k - 1 = 6 - 1 = 5
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >14.433) =P(\chi^{2}_{5} >14.433) =0.013[/tex]
*Use a Chi-square table.
The significance level is, α = 0.05.
p-value = 0.013 < α = 0.05.
So, the null hypothesis will be rejected at 5% significance level.
Thus, concluding that the claim on the M&M’s website is not true.
Solve for x: -2x - 4 > 8
x<-6
X > -6
x<-2
x>-2
Answer:
x < -6
Step-by-step explanation:
-2x - 4 > 8
-2x > 12
x < -6, you have to flip the inequality when you multiply or divide by a negative
Answer:
a
Step-by-step explanation:
A. all real number
B. x>0
C. x>2
D. y>0
E. y>-1
F. y>2
Answer:
domain = E
range = (-&,&)
Step-by-step explanation: solved by graphing calculator
Alex has a block of wood that is in the shape of a prism with the dimensions shown. He cuts a 10-cm square hole through the center of the prism. What is the volume of the remaining solid?
Answer:
1,120
Step-by-step explanation:
Find the volume of the larger figure. This can be represented using the formula for volume.
V = lwh
V = 5*18*18
V = 1620
Now, find the volume of the cut out piece of the wood. We will subtract this from the larger block.
V = lwh
V = 5*10*10
V = 500
Subtract, and you will have your answer.
1620 - 500 = 1,120
PLEASE HELP ME !!!!!!!!!!!!!!!!!
Answer:
2
Step-by-step explanation:
The series is a geometric series with a common ratio (r) of 1/2 and a first term (a1) of 1/2^0 = 1. The sum of such a series is given by ...
S = a1/(1 -r) 1/(1 -1/2) = 2
The sum of the series is 2.
plz help asap i only have limited time i will give brainliest
Answer:
The answer is none.
Step-by-step explanation:
BecauseSide of the square is greater than breadth of rectangle. Answer: How can this be possible? Side of any square cannot be more than breadth of rectangle unless and until the square is bigger than the rectangle.Side of the square can be greater than length of triangle: Answer: Not at all possible. How can the length of a square be greater than the length of a rectangle? then the square would no longer have the same sides. And as i said before, squares cant be long unless and until they are bigger than the rectangle.Hope this helps....
Have a nice day!!!!
The perimeter of a square is numerically equals to its area. Find its side and area.
Answer:
4 and 16 units²
Step-by-step explanation:
The perimeter of a square of side s = 4s and area = s² , equating gives
s² = 4s ( subtract 4s from both sides )
s² - 4s = 0 ( factor out s from each term on the left )
s(s - 4) = 0
Equate each factor to zero and solve for s
s = 0
s - 4 = 0 ⇒ s = 4
However, s > 0, thus s= 4
That is side = 4 units and area = 4² = 16 units²
A box of 15 cookies cost nine dollars what is the cost of one cookie
Answer:
$1.67
Step-by-step explanation:
Divide 15 by 9 to find the price of one cookie:
15/9 = 1.67
= approximately $1.67
A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster loads removed. Assume that the reduction in the amount of waste each week is linear. Write an equation in function form to show the amount of trash removed each week. A f(x) = −2x + 40. B f(x) = 2x + 40 C f(x) = −2x + 50 D f(x) = 2x + 50
Answer:
The answer is A f(x) = -2x + 40
Step-by-step explanation:
it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.
Shelly and Terrence completed x tasks in a game. Terrence's total points were 20 less than Shelly's total. The expression below shows Terrence's total points in the game: 90x − 20
What does the first term of the expression represent?
A. The total points Shelly earned
B. The number of tasks Terrence completed
C.The sum of Shelly's and Terrence's total points
D. The number of tasks Shelly completed
Answer:
The correct option is;
A. The total points Shelly earned
Step-by-step explanation:
The given details are;
The number of tasks completed by Shelly and Terrence in the game = x
The total points scored by Terrence = 20 less than the total point scored by Shelly
The expression for Terrence's total point is 90·x - 20
Let the total points Shelly earned = Y
Therefore since the total points scored by Terrence = 20 less than the total point scored by Shelly, we have;
The total points scored by Terrence = Y - 20
Comparing the two expressions for the total points scored by Terrence which are;
90·x - 20 and Y - 20 we have;
90·x - 20 = Y - 20
Adding 20 to both sides of the equation gives;
90·x - 20 + 20= Y - 20 + 20
Which gives;
90·x = Y
Therefore, the first term of the expression 90·x - 20, which is 90·x is equal to Y, which is the total points Shelly earned
The correct option is therefore the total points Shelly earned.
Answer:
A. The total points Shelly earned
Step-by-step explanation:
Hope this helps!
Have a great day! :)
Can somebody please tell me if it’s right? i’ll mark u the brainliest
Answer:
Yes, you are correct.
Step-by-step explanation:
You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.
What is the value of the 6 in 13.76?
Answer:
0.06
Step-by-step explanation:
This is because the 6 is in the hundredths place.
━━━━━━━☆☆━━━━━━━
▹ Answer
0.06 (Hundreths)
▹ Step-by-Step Explanation
The '6' is in the hundreths place. This is written as 0.06. As a fraction, it is written as 6/100.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
solve for b in the mathematical formula A=1/2(a+b)h
Answer:
[tex]b = \frac{2A}{h} - a[/tex]Step-by-step explanation:
[tex]A = \frac{1}{2} (a + b)h[/tex]Multiply both sides by 2
We have
2A = (a + b)h
Divide both sides of the equation by h
That's
[tex] \frac{(a + b)h}{h} = \frac{2A}{h} [/tex]We have
[tex]a + b = \frac{2A}{h} [/tex]Move a to the right side of the equation to make b stand alone
We have the final answer as
[tex]b = \frac{2A}{h} - a[/tex]Hope this helps you
Please help! I have an answer but idk if it's right so please check and tell me if I made any mistakes! Thank you!
Answer:
p(1)=2-a+4-4
or,10=2-a
so,a=-8
Step-by-step explanation:
hope it helps you
Angles L and M are supplementary. What is the sum of
their measures?
The sum of the measures of angles L and M is
180 degree
Step-by-step explanation:
supplementary means anhke havinv sum of 180 degree
so sum to two supplemrntary angles is 180 drgree
Supplementary angles always add to 180.
One way I think of it is "supplementary angles form a straight angle", and both the words "supplementary" and "straight" start with the letter "S".
In contrast, complementary angles form a corner. Both "complementary" and "corner" start with "co". By "corner", I mean a 90 degree corner.
A man traveled to his country home, a distance of 150 miles and then back. His average rate of speed going was 50 miles an hour and his average return speed was 30 miles per hour. His average rate of speed for the entire trip was Need help will mark brainlist
Answer:
37.5 mi/h
Step-by-step explanation:
time = distance / speed
On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.
On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.
__
speed = distance / time
The average speed for the whole trip was ...
speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h
His average rate of speed was 37.5 miles per hour.
also being timed help!
Answer: 4
Step-by-step explanation:
A mural inspired by a photograph measures 108 inches by 180 inches. The scale of the photograph to the mural is 1.:12 in. What are the dimensions of the photograph
Answer:
108 inches and 2160 inches
Step-by-step explanation:
108 inches = 274.32 cm
180 inches = 457.2 cm
The area of the mural, A1 = 274.32 X 457.2 = 125419.1 cm²
Let the area of the photograph = A2
The scale A1 to A2,
1/12 = A1/A2
1/12 = 125419.1/A2
∴ A2 = 12 X 125419.1 = 1505029.2 cm²
For their lenghs
1/12 = L1/L2
1/12 = 457.2/L2
L2 = 12 X 457.2 = 5486.4 cm (or 2160 inches)
The width of the photograph
1505029.2/5486.4 = 274.3 cm ( 108 inches)
one day shahed was playing with numbers.He wrote 15 fractions using all natural numbers from 1 to 30 exactly once-either as numerator or as denominator.How many of these fractions are most is integers.
Answer:
15
Step-by-step explanation:
half of 30 is 15
he used all the numbers upto 30 once
all the numbers in between arent integers but decimals
SIMPLIFY (i)35 + 25 x 72 – 51 ÷(10 + 7) (ii)-6 x 9 + 7 – 12 ÷ 3 – 5 Pls give me the correct answer
Answer:
i.1832 ii.-56
Step-by-step explanation:
using BODMAS for the first question we solve for what's in the bracket after we go with the division and after multiplication next addition and subtract in doing all that we get
35+25*72-51/17
35+25*72-3
35+1800-3
1835-3
1832
you can also use your calculator to verify answer
ii.-6*9+7-4-5
-54+7-4-5
-47-4-5
-56
Find the distance between the two points (-4,4) and (1,0)
Answer:
The answer is
[tex] \sqrt{41} \: \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by
[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]
where
( x1 , y1) and ( x2 , y2) are the points
So the distance between (-4,4) and (1,0) is
[tex] \sqrt{( { - 4 - 1})^{2} + ( {4 - 0})^{2} } [/tex][tex] = \sqrt{ ({ - 5})^{2} + {4}^{2} } [/tex][tex] = \sqrt{25 + 16} [/tex]We have the final answer as
[tex] \sqrt{41} \: \: \: units[/tex]Hope this helps you
When writting a equation how do you know where to put the equal sign?
The lengths of the three sides of a triangle are 7, x+4 and 2x+1. The perimeter of the triangle is 36. What is the length of the longest side of the triangle?
Answer:
Length of the longest side = 17 units
Step-by-step explanation:
Given:
Three sides of triangle
A = 7
B = x+4
C = 2x + 1
Perimeter of the triangle = 36
Find:
Length of the longest side
Computation:
We know that
Perimeter of the triangle = A + B + C
Perimeter of the triangle = 7 + x + 4 + 2x + 1
36 = 12 + 3x
24 = 3x
x = 8
So
Side B = 8 + 4 = 12 unit
Side C = 2(8) + 1 = 17 units
Length of the longest side = 17 units
Answer:
17.
Explaination:
Dunno. I just put it on paper, and did the calculations there.
As a truck rounds a curve,a box in the bed of the truck slides to the side farthest from the center of the curve. This movement of the box is a result of
Answer: inertia
Step-by-step explanation:
Inertia is the resistance posed by any physical object to any change which may occur to its velocity. This changes includes the object's speed, direction of motion e.t.c. An important part of this property is the posibility of the objects to continue to move in a straight line at a constant speed, when no forces has acted upon them.
Answer:
B inertia
Step-by-step explanation:
Edg
Simplify the expression so there is only one positive power for each base. (5^-2 x 4^-4)^-2
Answer:
Step-by-step explanation:
[tex](5^{-2}[/tex] × [tex]4^{-4}[/tex] [tex])^{-2}[/tex]
=[tex](5^{-2}[/tex][tex])^{-2}[/tex] x [tex](4^{-4})^{-2}[/tex] ∴[tex](a.b)^{n} =a^{n} .b^{n}[/tex]
=[tex]5^{-2.-2}[/tex] x [tex]4^{-4 . -2}[/tex] ∴[tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex] // here m is an exponent of [tex]a^{n}[/tex].
=[tex]5^{4}[/tex] x [tex]4^{8}[/tex]
