Answer:
P(A) = 0.4 ; P(B) = 0.50 ; P(C) = 0.60 ; P(A u B) = 0.65 ; P(A n B) = 0.25 ;
A and C are mutually exclusive ;
0.5
Step-by-step explanation:
S = {E1, E2, E3, E4, E5, E6, E7}
P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05
Let:
A{E1,E4,E6}
B{E2,E4,E7}
C{E2,E3,E5,E7}
P(A) = 0.05 + 0.25 + 0.10 = 0.40
P(B) = 0.20 + 0.25 + 0.05 = 0.50
P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.60
AUB = {E1, E2, E4, E6, E7}
P(A u B) = 0.05 + 0.20 + 0.25 + 0.10 + 0.05 = 0.65
AnB = {E4}
P(A n B) = 0.25
A and C are mutually exclusive if AnC = ∅
A n C = ∅
Hence, A and C are mutually exclusive.
B complement = B' = {E1, E3, E5, E6}
P(B') = 0.05 + 0.20 + 0.15 + 0.10 = 0.5
a rectangular doorway has a temporary support beam across its diagonal. the height of the doorway is 2 times its width. if the beam across the diagonal is 14 feet, how wide is the door?
Answer:
The door has a width of 6.26 feet, with a height of 12.52 feet.
Step-by-step explanation:
You can solve this by taking two pieces of information we're given:
1) the diagonal size of the doorway is 14 feet
2) the height of the doorway twice its width
First lets describe the width and height using the diagonal length. We can do that with the Pythagorean theorem:
w² + h² = 14²
Now we can use the relationship between the width and height to eliminate one variable:
w² + (2w)² = 14²
w² + 4w² = 14²
5w² = 196
w² = 39.2
w ≈ 6.26
So the door has a width of 6.26 feet, with a height of double that, 12.52 feet.
Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The width of the door is 6.26 ft or √(196/5)ft.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the length of the rectangular door is two times its width, therefore, the length and width of the rectangular door are,
Width = x
Length = 2x
Since the measure of the diagonal of the rectangular door is 14 feet, therefore, using the Pythagorus theorem we can write,
x² + (2x)² = 14²
x² + 4x² = 196
5x² = 196
x² = 196/5
x = 6.26099 ≈ 6.26ft
Hence, the width of the door is 6.26 ft or √(196/5)ft.
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HELP ME PLEASE I HAVE 1 MINUTE LEFT TO TRUN THIS IN
Answer:
1jdjsbsjsnsisn Shane Jana aus she sue euw
Answer:
Number of walnut trees: 4n+15
Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of 7 1/2 inches.
Without calculating, predict which frame has the shorter width. Explain your reasoning.
Find the width that you predicted to be shorter.
Answer:
B, 6 inches
Step-by-step explanation:
The formula for area is width * height. If the area is the same in both times, increasing height means you must be decreasing width. B has a taller height so must have a shorter width.
7 and 1/2 = 15/2
45 / (15 / 2) = 45 * 2 / 15 = 6 inches
If an interest rate of 5% results in interest of $50,
what is the principal amount of the loan?
Answer:
Ñpswplmlpspapppapapa
Jimmy wants to calculate what 125% of 84 will be?
Answer:
105
Step-by-step explanation:
100% = 84
1% = 84 ÷ 100 = 0.84
125% = 0.84 x 125 = 105
Answer:
105
Step-by-step explanation:
Statements:
A lullaby is a song.
No song is prose.
Some proses are epics.
Conclusions:
1. Some proses are songs.
II. Some epics are lullabies.
III. Some songs are lullabies.
A)Only Il follows
B)Only I follows
C)Only III follows
D) Neither of I, II or III follows
Answer:
Answer:
C)Only III follows
Step-by-step explanation:
Let's review the conclusions;
I. Some proses are songs.
This is false because of the statement; No song is prose.
II. Some epics are lullabies.
This is false because of the following statements; A lullaby is a song. and No song is prose.
III. Some songs are lullabies.
This follows because of the statement; A lullaby is a song.
The correct option is;
C)Only III follows
The correct conclusion based on the logical statements is C) Only III follows.
Logical Statements:1. A lullaby is a song.
2. No song is prose.
3. Some proses are epics.
Possible Conclusions:I. Some proses are songs.
II. Some epics are lullabies.
III. Some songs are lullabies.
The first conclusion that some proses are songs is not sound because the earlier claim is that "no song is prose." In the same light, the second conclusion is incorrect because a lullaby is usually a song as asserted in statement 1. While epics can be prose or poem, a lullaby is not prose but a poem or a song.
Thus, the correct conclusion based on the logical statements is C) Only III follows.
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summarize what you have learned about this algebraic expressions
(giving brainiest)
tell how you solved the question
an example is
6 x 4 x 6 = 144
Answer:
144
Step-by-step explanation:
(6(2))(4)
aka (6*6)*4=144
Answer:
V = 144
Step-by-step explanation:
Volume is a measurement of space, or capacity.
V = h × w × l
V = 6 × 6 × 4
V = 144
good luck, i hope this helps :)
Graph the line with slope 3 passing through the point (5,-4).
Answer:
y = 3x-16
Step-by-step explanation:
two points where the line goes through is (5,-4) as mentioned and (0,-16)
An international company has 25,800 employees in one country. If this represents 31.1% of the companies employees, how many employees does it have in total?
Answer:
Rounded to the nearest integer, the company has a total of 82,958 employees.
Step-by-step explanation:
Given that an international company has 25,800 employees in one country, if this represents 31.1% of the companies employees, to determine how many employees does it have in total, the following calculation must be performed:
31.1 = 25,800
100 = X
100 x 25,800 / 31.1 = X
2,580,000 / 31.1 = X
82,958.1 = X
Thus, rounded to the nearest integer, the company has a total of 82,958 employees.
63% of US adults opposed to taxes on junk food and soda. You randomly select 10 US adults. Find the probability that the number of adults who oppose special tax on junk food and soda (a) exactly one, (b) at least four, and (c) less than eight
Answer:
a) 0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
b) 0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
c) 0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they are opposed to taxes on junk food and soda, or they are not. Each adult is independent of other adults, which means that the binomial probability distribution is used to solve the question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
63% of US adults opposed to taxes on junk food and soda.
This means that [tex]p = 0.63[/tex]
You randomly select 10 US adults.
This means that [tex]n = 10[/tex]
(a) exactly one
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
0.0008 = 0.08% probability that the number of adults who oppose special tax on junk food and soda is exactly one.
(b) at least four
This is
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.63)^{0}.(0.37)^{10} \approx 0[/tex]
[tex]P(X = 1) = C_{10,1}.(0.63)^{1}.(0.37)^{9} = 0.0008[/tex]
[tex]P(X = 2) = C_{10,2}.(0.63)^{2}.(0.37)^{8} = 0.0063[/tex]
[tex]P(X = 3) = C_{10,3}.(0.63)^{3}.(0.37)^{7} = 0.0285[/tex]
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0.0008 + 0.0063 + 0.0285 = 0.0356[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0356 = 0.9644[/tex]
0.9644 = 96.44% probability that the number of adults who oppose special tax on junk food and soda is at least four.
(c) less than eight
This is
[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]
In which
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.63)^{8}.(0.37)^{2} = 0.1529[/tex]
[tex]P(X = 9) = C_{10,1}.(0.63)^{9}.(0.37)^{1} = 0.0578[/tex]
[tex]P(X = 10) = C_{10,2}.(0.63)^{10}.(0.37)^{0} = 0.0098[/tex]
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1529 + 0.0578 + 0.0098 = 0.2205[/tex]
[tex]P(X < 8) = 1 - P(X \geq 8) = 1 - 0.2205 = 0.7795[/tex]
0.7795 = 77.95% probability that the number of adults who oppose special tax on junk food and soda is less than eight.
The number of people signed up for a bus trip increased from 32 to 45 what is the percent increase round to the nearest percent
Answer:
40.6%
Step-by-step explanation:
first find the increase (increase = 45 - 32) = 13
second divide increase by OG # (13 / 32) = 0.40625
then you multiply by 100
Answer:
41%
Step-by-step explanation:
Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. At that rate, how much would she pay in sales tax for an item that costs $40.00 before tax?
Answer:
She would pay $2.80 in sales tax.
Step-by-step explanation:
This question can be solved by proportions, using a rule of three.
Megan paid $2.52 in sales tax on an item that cost $36.00 before tax. How much in taxes for $40.00 before taxes?
$2.52 - $36.00
x - $40.00
Applying cross multiplication
[tex]36x = 40*2.52[/tex]
[tex]x = \frac{40*2.52}{36}[/tex]
[tex]x = 2.8[/tex]
She would pay $2.80 in sales tax.
Any help? I'm struggling.
Write an explicit equation for each of the following geometric sequences. Then use the equation to find the 15th term.
Answer:
Step-by-step explanation:
a=-7
r=21/-7=-3
[tex]a_{15}=a r^{n-1}=-7(-3)^{15-1}=-7(-3)^{14}=-33480783[/tex]
You've decided to give your best friend a
bag of marbles for his birthday.
Since you know that your friend likes
green marbles better than red ones, the
bag has twice as many green marbles as
red.
The label on the bag says it contains a
total of 84 marbles.
How many green marbles are in the bag?
Number of green marbles in the bag is equals to [tex]56.[/tex]
What is number?
" Number is defined as the count of any given quantity as per condition."
According to the question,
Given,
Total number of marbles [tex]= 84[/tex]
[tex]'x'[/tex] represents the number of red marbles
As per given condition,
[tex]'2x'[/tex] represents the number of green marbles
Required equation we have,
[tex]x + 2x = 84\\\\\implies 3x =84\\\\\implies x = \frac{84}{3} \\\\\implies x = 28[/tex]
Substitute the value of [tex]'x'[/tex] to get number of green marbles ,
Number of green marbles [tex]2x = 2\times 28[/tex]
[tex]= 56[/tex]
Hence, number of green marbles in the bag is equals to [tex]56.[/tex]
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3 bags of takis and 2 bags of doritos cost $17. 3 bags of dortios cost $12. How much does 1 bag of takis cost?
Answer:
$3.00
Step-by-step explanation:
3t + 2d = 17
3d = 12
d = 4
3t + 8 = 17
3t = 9
t 3
Answer:
A bag of takis is $3
Step-by-step explanation:
3 bags of doritos at $4 a piece
$17-$8=$9
$9/3=$3
a line can divide the figure into two identical four sided polygons each polygon has two bases and one one base is twice the length of the other base identify the polygon and give it's perimeter
Answer:
Step-by-step explanation:
I know know it that that girl is wrong
The polygon being described is a trapezoid, where one base is twice the length of the other base.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners
The polygon being described is a trapezoid, where one base is twice the length of the other base.
Let the shorter base be b and the longer base be 2b.
To divide the figure into two identical trapezoids, the line must pass through the midpoint of the longer base, creating two trapezoids that are mirror images of each other.
The perimeter of each trapezoid can be found as follows:
Perimeter = sum of lengths of all sides
Hence, the polygon being described is a trapezoid, where one base is twice the length of the other base.
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Elena is making greeting cards, which she will sell by the box at an arts fair. She paid $54 for
a booth at the fair, and the materials for each box of cards cost $9.50. She will sell the cards
for $11 per box.
At some point, she will sell enough cards so that her sales cover her expenses. How much will
the sales and expenses be? How many boxes of cards will that take?
Elena's sales and expenses will both be $
if she sells
boxes of cards.
Submit
Answer:
Elena's sales and expenses will both be $
396
if she sells
36
boxes of cards.
Step-by-step explanation:
The number of greeting cards are 36 and Elena's sales and expenses will both be $396.
Elena paid $54 for a booth at the fair, and the materials for each box of cards cost $9.50.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of cards be x.
At some point, she will sell enough cards so that her sales cover her expenses.
So, 54+9.50x=11x
⇒ 11x-9.50x=54
⇒ 1.50x=54
⇒ x=54/1.50
⇒ x=36
Thus, sales=expenses= 11x
= 11×36
= $396
Hence, the number of greeting cards are 36 and Elena's sales and expenses will both be $396.
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The first correct answer gets brainliest
Answer:
1.2 Cm.
Step-by-step explanation:
If you multiply these three fractions you get 1.2 Cm. Or in fraction from 6/5
Hope this helped. Please correct me if I am wrong
3. FIELD TRIP There is space for 120
students to go on a field trip. Currently
,
74 students have signed up. Write and
solve an inequality to find how many
more students can sign up for the
field trip.
i need help plz
well if
120-74=46
then 46 is the correct answer.
74+46= 120
46 more students can sign up for the field trip.
Answer:
74 + (x) = 120
Step-by-step explanation:
subtract 74 from 120
120 - 74 = 46
A can of tomato soup has a circular base with a diameter of 7 cm. If the surface area of the can is 104.3 cm. What is the height of the can?
Answer:
1.243 cm
Step-by-step explanation:
The surface area of a cylinder is the sum of the area of the two congruent circular bases and the rectangular lateral area.
[tex] SA = 2\pi r^2 + 2 \pi rh [/tex]
[tex] SA = 2\pi r(r + h) [/tex]
We are given the surface area and the diameter.
r = d/2 = 7 cm / 2 = 3.5 cm
We can solve for h, the height.
[tex] SA = 2\pi r(r + h) [/tex]
[tex] 2\pi r(r + h) = SA [/tex]
[tex] r + h = \dfrac{SA}{2\pi r} [/tex]
[tex] h = \dfrac{SA}{2\pi r} - r [/tex]
[tex] h = \dfrac{104.3~cm^2}{2(3.14159)(3.5~cm)} - 3.5~cm [/tex]
[tex] h = 1.243~cm [/tex]
Please help!?!??!??!
Answer:
1 1/4
Step-by-step explanation:
So basically the number is getting cut in half for example the 10 goes to a 5.
1 1/4 + 1 1/4 = 2 1/2
Please give me brainliest. Have a good day. :)
pls explain i dont get it
Answer:
C
Step-by-step explanation:
A: (0,__) (__ is the y-intercept)
In this case it is (0,3) so 3
B: y=mx+b (b is the y-intercept)
-4 is b so -4
C: y=2x+4
4 is b so 4
Let me know if you would like further explanation!!
The girls hockey team has 7 sixth grade and 9 seventh grade students on their team. What is the ratio of seventh grade students to sixth grade students?
Step-by-step explanation:
7:9 I'm pretty sure that's it
Willy the Wombat is 50 feet from a tree. The tree is 75 feet tall. At what angle of elevation should Willy look to see the top of the tree? Round to the nearest degree
find the value of x and y
Answer:
x= 9 y=5
Step-by-step explanation:
hello :
use phtagor-rul :
y² = 3²+4²
y² =25
so : y=5
same method :
15²=12²+x²
x² =15²-12²
x² =225-144
x² = 81
so : x= 9
there are 70 students in the school band. 40% of them are sixth graders, 20 % are seventh graders, and the rest are eight graders. How many band members are sixth graders? How many band members are Seventh graders? What percentage of the band members are eighth graders?
Answer:
28 are 6th
14 and 7th
40% are 8th
Step-by-step explanation:
Answer:
28= 6th grader
14= 7th grader
28= 8th grader
40% were 8th graders
Step-by-step explanation:
28= 6th grader
14= 7th grader
28= 8th grader
40% were 8th graders
a motion detector can detect movement up to 25 feet away through an angle of 105
Answer:
12. A motion detector can detect movement up to 25 feet away through an angle of 105 degree. What area can the motion detector monitor? Use your knowledge of area of sector of circle. Round your answer to the nearest tenth. (10 Points) O 1,145.4f12 572.7ft2 32812.5 ft2 8268.75 ft2
The area covered by the motion detector which having a radius of 25 feet and an angle of 105 degrees is 572.58 feet.
What is a circle?It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
A motion detector can detect movement up to 25 feet away through an angle of 105 degrees.
Then the area covered by the detector will be
[tex]\rm Area = \dfrac{\theta}{360} \times \pi r^2\\\\Area = \dfrac{105}{360} \times \pi \times 25^2\\\\Area = 572.58 \ ft^2[/tex]
The area covered by the detector is 572.58 square feet.
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The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer in simplest form.
The scale factor of the triangles will be 17 / 74 or 0.2297.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
There is no effect of dilation on the angle.
The triangle on the right is a scaled copy of the triangle on the left.
Then the scale factor of the triangles will be
⇒ 17 / 74
⇒ 0.2297
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Help me please quick.
Answer:
7 6/7
Step-by-step explanation:
To find the area, multiply 2 1/7 by 3 2/3. Then, simplify to get the answer of 7 6/7.
Answer:
7 and 6/7 in.²
Step-by-step explanation:
2 and 1/7 × 3 and 2/3
