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.
For every 2 hours, there are 7,200 seconds. Which equation best represents the number of seconds s na given
number of hours, h?
Answer:
[tex]s=60^{2} h[/tex]
While,
s seconds
h hours.
6x-3y=15 y=2x-5 help meeeeeeeeeeew
Hey there!!
Let me know if you need an explanation on how I reached my final answer:
As we solve for the first variable in one of the equations, we then substitute the result into the other equation.
Your answer:
Y=2x-5
Let me know if you have any questions or concerns!! Hope this helps!!
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
simplify the first expression 5(m+1)-1=
Answer:
-0.8/ -4/5
Step-by-step explanation:
5(m+1) -1 = 0
5m +5 -1 = 0
5m +4 =0
5m= -4
m= -4/5
can someone help with this plz:)
Answer:
XI and IX
Line above has arrow heads on both ends.
Step-by-step explanation:
XI and IX
Line above has arrow heads on both ends.
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
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.
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
the distributive property of 8(a+4)
Answer and Step-by-step explanation:
With the distributive property, the 8 will distribute itself to the a and the 4, resulting in 8a + 32.
#teamtrees #PAW (Plant And Water)
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
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.
More about the circle link is given below.
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If an interest rate of 5% results in interest of $50,
what is the principal amount of the loan?
Answer:
Ñpswplmlpspapppapapa
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
More about the dilation link is given below.
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Sara and Macki were doing a math activity together in class. They were told to review the two problem solutions shown below and determine which of the two cards is correctly solved.
Which of the two cards is correctly solved?
Answer:
I NEED THE ANSWER
Step-by-step explanation:
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
BRAINLIEST WILL GIVE
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:
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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How do you find the missing side
Answer:
just look
Step-by-step explanation:
two possible proper fractions such that their sum is 1 1/2
Answer:
2/2 + 1/2
Step-by-step explanation:
1 1/2 = 3 / 2
possible fractions = 2/2 + 1/2
Josh bought 5 pairs of $20 jeans. He also bought two shirts that were $13 each minus a $3 clearance
discount on each shirt. Finally he made a stop to get cookies for his party. The cookies cost $3 per dozen and
he needed 8 dozen. Which expression represents Josh's purchases? What was Josh's total money spent?
Answer:
5(20)+2(13-3)+3(8);$144
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.
Learn more about logical statements and conclusions at https://brainly.com/question/18575348
4.6.PS-14 Error Analysis On a math test a student, Sarah, has to identify all the coefficients an the expression 7n + 2 + m. Sarah says that 7 is a coefficient and 2 is a constant. Identi coefficients and constants of the expression. What error might Sarah have made? The coefficient(s) of the expression is/are (Use a comma to separate answers as needed.)
Answer:
7n is a coefficient
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]
el inverso de 13/25 es
Answer:
25/13
Step-by-step explanation:
you have one sheet of 18 stickers. If you put an equal amount of stickers on 3 sheets of paper, how many stickers will be on each page?
Answer
there will be 6 on all three pages
Step-by-step explanation:
divide 18 by 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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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!!
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
