Answer:
0.0479 = 4.79% probability that fewer than 11 of them will vote
Step-by-step explanation:
For each voter, there are only two possible outcomes. Either they will vote, or they will not. The probability of a voter voting is independent of any other voter, which means that the binomial probability distribution is used to solve this 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.
70% of all eligible voters will vote in the next presidential election.
This means that [tex]p = 0.7[/tex]
20 eligible voters were randomly selected from the population of all eligible voters.
This means that [tex]n = 20[/tex]
What is the probability that fewer than 11 of them will vote?
This is:
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{20,10}.(0.7)^{10}.(0.3)^{10} = 0.0308[/tex]
[tex]P(X = 9) = C_{20,9}.(0.7)^{9}.(0.3)^{11} = 0.0120[/tex]
[tex]P(X = 8) = C_{20,8}.(0.7)^{8}.(0.3)^{12} = 0.0039[/tex]
[tex]P(X = 7) = C_{20,7}.(0.7)^{7}.(0.3)^{13} = 0.0010[/tex]
[tex]P(X = 6) = C_{20,10}.(0.7)^{6}.(0.3)^{12} = 0.0002[/tex]
[tex]P(X = 5) = C_{20,5}.(0.7)^{5}.(0.3)^{15} \approx 0[/tex]
The probability of 5 or less voting is very close to 0, so they will not affect the outcome. Then
[tex]P(X < 11) = P(X = 10) + P(X = 9) + P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1) + P(X = 0) = 0.0308 + 0.0120 + 0.0039 + 0.0010 + 0.0002 = 0.0479[/tex]
0.0479 = 4.79% probability that fewer than 11 of them will vote
if you had to report on the salaries for different occupations, do you think it would be better to report the mean or the median value
The subjects of an experiment should be selected at random so that they
represent the population from which they come.
O
A. True
O
B. False
Answer: True
Step-by-step explanation:
The subjects of an experiment should be selected at random so that they
represent the population is true.
Once the sample size has been decided, a sample should be taken from the sample size which will represent the population. This gives everyone an equal chance of being selected as there's no bias.
Define the word term
Answer:
A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.
hope this helps
have a good day :)
Step-by-step explanation:
Which of the following statements is true?
A.
m is parallel to /.
B.
/ and m bisect each other.
C.
The distance from A to A' equals the distance from A to m.
D.
m bisects /.
5th grade math. correct answer will be marked brainliest
Answer: How are we going to point it?
Step-by-step explanation:
The sea ice area around the North Pole fluctuates between about 6 million square kilometers in September to 14 million square kilometers in March. Assuming sinusoidal fluctuation, during how many months are there less than 9 million square kilometers of sea ice?
Answer:
there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
Step-by-step explanation:
Given the data in the question;
Let S(t) represent the amount sea ice around the North Pole in millions of square meters at a given time t,
t is the number of months since January.
Now, we use a cosine curve to model this scenario
Vertical shift will be;
D = ( 6 + 14 ) / 2 = 20 / 2
D = 10
Next is the Amplitude;
|A| = ( 6 - 14 ) / 2
|A| = 4
Now, the horizontal stretch factor will be;
B = 2π / 12
B = π/6
Hence;
S(t) = 4cos( π/6 × t ) + 10 ----------- let this be equation 1
Now we find when there will be less than 9 million square meters of sea ice;
S(t) = 9
so we have
9 = 4cos( π/6 × (t-2) ) + 10
9 - 10 = 4cos( π/6 × (t-2) )
-1 = 4cos( π/6 × (t-2) )
-1/4 = cos( π/6 × (t-2) )
so we have;
cos⁻¹( -1/4 ) = π/6 × (t₁-2) -------- let this be equation 2
2π - cos⁻¹( -1/4 ) = π/6 × (t₂-2) -------- let this be equation 3
so we solve equation 2 and 3
we have'
t₁ - t₂ = 6/π × ( 2π - cos⁻¹( -1/4 ) - cos⁻¹( -1/4 ) )
t₁ - t₂ = 6/π × ( 2π - 2cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - cos⁻¹( -1/4 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 6/π × ( π - 104.4775 )
t₁ - t₂ = 5.035
therefore, there are approximately 5.035 months when there is less than 9 million square meters of sea ice around the North Pole in a year.
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
(-3, 1)
(0,0)
Answer:
y=-3x
Step-by-step explanation:
The y intercept is zero because it goes through (0,0)
The slope is -3 because the line goes through -3 at 1, so it goes down 3 on the y axis for every 1 right on the x axis.
Which equation models this relationship?
Answer:
The one you selected is correct! You can check it by using the four values of m and w given.
2 times the sum of a number and 9 equals 4
Answer
Step-by-step explanation:
Find the value of x
A. 20
B. 28
C. 10
D. 50/7
Answer:
x=28
Step-by-step explanation:
Step 1, comparing triangles:
Let us look at [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].
They both share [tex]\angle A[/tex] ([tex]\angle A=\angle A[/tex])[tex]\angle ABC = \angle BDE[/tex] (Corresponding Angle Theorem)[tex]\angle ACB = \angle CED[/tex] (Corresponding Angle Theorem)Therefore, because of AAA (Angle Angle Angle), [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] are similar.
Step 2:
Because the two triangles are similar, their sides should be proportional. Notice that [tex]\overline{AB}[/tex] and [tex]\overline {AD}[/tex] should be proportional.
Therefore, [tex]\overline{AB}[/tex]: [tex]\overline {AD}[/tex] =
[tex]12:30+12=\\12:42=\\2:7[/tex]
(Note, [tex]\overline {AD}[/tex] = [tex]\overline{AB}[/tex]+ [tex]\overline{BD}[/tex]=12+30)
Step 3:
We figured out that [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex] have proportional sides of 2:7. Therefore, [tex]\overline{BC}[/tex] and [tex]\overline{DE}[/tex] should also have a ratio of 2:7.
[tex]8: \overline{DE}=2:7\\8:\overline{DE}=8:28\\\overline{DE}=\fbox{28}[/tex]
x=28
I hope this helps! Let me know if you have any questions :)
Answer:
x = 20
Step-by-step explanation:
If we look at the given diagram, we will see that ΔABC and ΔADE are similar. Because they a similar we know that corresponding sides are in proportion. In order to solve this question, we need to know what the coefficient of similarity is.
AB and AD are corresponding sides, in order to get from 12 to 30 we need to multiple 12 by 2.5. That means that the coefficient of similarity between the two triangles is 2.5. To get x (length of DE) we need to multiply the length of BC by the coefficient of similarity. And so we get...
x = 2.5(BC)
x = 2.5(8)
x = 20
please help! (listing BRAINLIST and giving points) :D
Answer:
40°
Step-by-step explanation:
because angle In an isosceles triangle base angles are same and angle in a triangle add up to 180° and angle on a straight line add up to 180°
hope this helps:)
determine the value of a in the figure shown
Answer:
d
Step-by-step explanation:
180-149= 31.
31+ 122= 153
180-153= 27
a= 27
Use logarithmic differentiation to differentiate the question below
[tex]y = x \sqrt[3]{1 + {x}^{2} } [/tex]
Answer:
[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Step-by-step explanation:
[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval
Answer:
Average rate of change = 5
Step-by-step explanation:
Average rate of change of a function is defined by the expression over the interval a ≤ x ≤ b,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using this rule for the average rate of change of the function (defined by the table) over the interval 4 ≤ x ≤ 5,
Average rate of change = [tex]\frac{f(5)-f(4)}{5-4}[/tex]
From the table,
f(5) = 10
f(4) = 5
Therefore, average rate of change of the function = [tex]\frac{10-5}{5-4}[/tex]
= 5
Answer:
=5
Step-by-step explanation:
Please help!! This is timed!!
for the function g defined above, a is a constant and g(4) = 8 what is the value of g(-4)
Answer:
-8
Step-by-step explanation:
g(4)=8
8÷4=2
g=2
g(-4)=2(-4)
=(-8)
holp it can help you.
A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. The interest rate applicable is j2=5.5% p.a applicable for the first five years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
a) Calculate the half-yearly payment required for each five-year interval
Did you manage to solve it?
There are nine counters in a bag numbered from one to nine. If a counter is drawn at random from the bag what is the probability that the number on the counter is not a multiple of three?
Step-by-step explanation:
jajajsjhshhsejjddjidndjdjdjxndjdkhsjdjddjdkd
The probability is 1/3 that the number on the counter is not a multiple of three.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have to determine the probability that the number on the counter is not a multiple of three.
There are nine counters in a bag numbered from one to nine.
If a counter is drawn at random from the bag.
One to nine, there are three numbers are multiple of three that is (3, 6, 9)
Here favorable outcomes = 3
So the probability that the number on the counter is not a multiple of three as
⇒ 3/9
⇒ 1/3
Therefore, the probability is 1/3 that the number on the counter is not a multiple of three.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
You collect the following data for explanatory variable A and response variable B:
A(x) B(y)
1 14.2
2 14.9
3 15.5
4 16.8
5 17.8
6 18.9
7 20.1
8 20.9
9 21.5
10 22
You calculate the following summary statistics: x-bar = 5.5, s subscript x = 3.03, y-bar = 18.26, s subscript y = 2.85, and r = .995.
Required:
What's the critical t value you'd use for a 95% confidence interval for the slope of this regression line?
Answer:
v
Step-by-step explanation:
There are 2 people in the Hill family. Each person
reads the same number of books. They read 12 books
in all. How many books does each person read?
A
18 books
B
6 books
C
8 books
D
10 books
Answer:
6
Step-by-step explanation:
The total body surface area, or BSA, of a human is difficult to calculate. There are various models that estimate BSA based on a person's weight and height. One simpler model is BSA= wh 3600
where w = weight in kg and h = height in cm.
a. Using this model, estimate the height of a person who weighs 75 kg and whose BSA is 1.9.
Round your answer to the nearest cm.
h = _______ cm
b. Using this model, estimate the weight of a person who is 166 cm tall and whose BSA is 2.2.
Round your answer to the nearest kg.
w= _________kg
Answer:
173 cm
105 kg
Step-by-step explanation:
Given :
BSA= √wh /3600
where w = weight in kg and h = height in cm.
A.)
w = 75 kg ; BSA = 1.9 ; h =?
BSA= √wh /3600
1.9 = √75h /3600
Take the square of both sides
1.9² = 75h /3600
1.9² * 3600 = 75h
12996 = 75h
h = 12996 / 75
h = 173.28 cm
h = 173 cm
B.)
h = 166 ; BSA = 2.2
BSA= √wh /3600
2.2 = √w166 /3600
Take the square of both sides
2.2² = 166w /3600
2.2² * 3600 = 166w
17424 = 166w
w = 17424 / 166
w = 104.96 kg
w = 105 kg
Using the model given, we have that:
a) h = 173 cm.
b) w = 105 kg.
The BSA, for a person of weight w and height h, is given by:
[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]
Item a:
[tex]BSA = 1.9, w = 75[/tex], hence:
[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]
[tex]1.9 = \sqrt{\frac{75h}{3600}}[/tex]
[tex]\left(\sqrt{\frac{75h}{3600}}\right)^2 = 1.9^2[/tex]
[tex]\frac{75h}{3600} = 3.61[/tex]
[tex]h = \frac{3600(3.61)}{75}[/tex]
[tex]h = 173[/tex]
Hence:
h = 173 cm.
Item b:
[tex]BSA = 2.2, h = 166[/tex], hence:
[tex]BSA = \sqrt{\frac{wh}{3600}}[/tex]
[tex]2.2 = \sqrt{\frac{166w}{3600}}[/tex]
[tex]\left(\sqrt{\frac{166w}{3600}}\right)^2 = 2.2^2[/tex]
[tex]\frac{166w}{3600} = 4.84[/tex]
[tex]w = \frac{3600(4.84)}{166}[/tex]
[tex]w = 105[/tex]
Hence:
w = 105 kg.
A similar problem, in which there is also an application of a formula, is given at https://brainly.com/question/24348510
find the approximate value of the circumference of a circle with the given radius use part equals 3.14 runner results to one more decimal than the given results 6 ft
c =
18.8 ft
18.8 ft
37.6 ft
37.7 fr
When a number is decreased by 40% of itself the result is 96. What is the number?
Answer:
160
Step-by-step explanation:
96 / (100%-40%) = 96/ (60%)
= 96/0.6 = 160
Q) 96/(100% - 40%)
→ 96/ 60%
→ 96/ 0.6
→ 160 is the number.
I’ll need brainliest
Answer:
I think no B
if wrong correct me pls
I HOPE IT HELPS
HAVE A GREAT DAY
[tex]#Liliflim[/tex]
Answer:
B
Step-by-step explanation:
C=7s
I can't find the surface area lol
n=3.14
Answer:
216 square feet
Step-by-step explanation:
The formula for the surface area of a rectangular prism is:
2 (lw + hl + hw)
w= width
h= height
l= length
Use the formula with the given dimensions:
2 (6 • 2 + 12 • 6 + 12 • 2)
= 2 (12 + 72 + 24)
= 2 (108)
= 216
Surface area is measured in square feet
(feet in this case)
Hope this helps
What is an equation for the line that passes through the coordinates (2, 0) and (0, 3)?
A 25 foot ladder is leaning against a tree. If the base of the ladder is 6 feet
away from the base of the tree, how high, to the nearest tenth, does the
ladder reach up the tree?
9514 1404 393
Answer:
24.3 ft
Step-by-step explanation:
If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...
h² +6² = 25²
h² = 625 -36 = 589
h = √589 ≈ 24.3
The ladder reaches about 24.3 feet up the tree.
A factory manufactures motorcycles. One of its employees, working in the quality control department, checks the first 10 and the last 10 motorcycles manufactured in a day. This is what type of sampling?
Answer:
Convenience sampling
Step-by-step explanation:
When sampling is done based in degree of ease or samples picked from observations that are easily accessible rather than prioritizing randomness or selection which will most be representative of the population, then such sampling is called convenience sampling. In some texts, it is also referred to as grab sampling as researchers choose from close, easy to reach samples. In the scenario above, the quality control takes the easy procedure of checking the first and last 10 motorcycles as this is easier than having to take samples at random tune intervals which will be a better representation of the entire motorcycles.
You are paid $25 per hour.
You work 7 hours a day.
You work 5 days a week.
How much is your total pay each week? $=
Answer:
The total pay would be $50, But there would also be tax to consider in this situation.
Keiko brought $51.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1/6 as much as the sketchbook, and the sketchbook cost 3/4 the cost of the paint set. Keiko had $3.00 left over after buying these items.
What was the cost of each item?
Step-by-step explanation:
[(1/6 × 3/4) + (3/4) + 1] n = 51.75 -3
(⅛ + ¾ +1)n = 48.75
15/8 n = 48.75
1.875 n = 48.75
n = 48.75/1.875
n = 26
so, the cost of :
the brush = ⅛×26 = $ 3.25
the sketchbook = ¾×26 = $ 19.5
the pain set = $ 26
