Answer: the probability that the number x of correct answers is fewer than 4 is 0.61
Step-by-step explanation:
Let x be a random variable representing the answers to the SAT questions. This is a binomial distribution since the outcomes are two ways. It is either the answer is correct or incorrect. Also, the probability of success or failure is constant for each trial. The probability of success, p = 0.35
The probability of failure, q would be 1 - p = 1 - 0.35 = 0.65
We want to determine P(x < 4)
n = number of trial = 9
x = 4
From the binomial distribution calculator,
P(x < 4) = 0.61
A random sample of 1285 residents from rural and urban areas were surveyed about their opinion about using daylight savings time. Below is the gathered data. Assuming there’s no relationship between residential area and opinion on daylight savings time, how many people who live in a rural area would you expect to be in favor of continuing to use daylight savings time? Please round up to a whole number.
Stop using Daylight Savings Time Continue using Daylight Savings Time Total
Rural 341 281 622
Urban 353 310 663
Total 694 591 1285
Pearson's Chi-square test
X-squared 0.32 df= 1 p-value ?
Answer:
The expected number of people that lives in rural areas and is in favor of continuing using daylight savings time is 287.
Step-by-step explanation:
Hello!
There were 1285 residents from rural and urban areas surveyed about their opinion about using savings time. There are two variables of interest:
X₁: Area where the resident lives, categorized: "Rural area", "Urban area".
X₂: Opinion about using daylight savings time, categorized: "Stop", "Continue".
To know how many people who live in a rural area would you expect to be in favor of continuing to use daylight savings time, you have to calculate the expected frequency for that cell (See table in attachment)
The formula to calculate the expected frequencies is:
[tex]E_{ij}= \frac{O_{i.}*O_{.j}}{n}[/tex]
i: categories in rows i=1, 2
j: categories in columns j= 1, 2
Oi.: total observations for the i-row
O.j: total observations for the j-row
The category "rural" is in the first row, so its marginal is symbolized O₁.
The category "Continue" is in the second column, so its marginal is symbolized O.₂
The expected frequency for the people that live n rural areas and is in favor of continuing using daylight savings time is:
[tex]E_{12}= \frac{O_{1.}*O.2}{n}= \frac{622*591}{1285} = 286.07= 287[/tex]
I hope this helps!
The length of a rectangle is 8 less than the width. The perimenter is 44 meters. Find the dimension of the rectangle
Answer:
Length = 7
Width = 15
Step-by-step explanation:
L= x
W= x-8
2x+2(x-8)=44
2. Is -1/3-4/5 positive,negative, or zero ?
The circle above has an area of 144 pi cm^2. What is the area of the blue sector? Use 3.14 for pi . A. 150.72 cm2 B. 25.12 cm2 C. 48 cm2 D. 113.04 cm2
Answer:
A. 150.72 cm2
Step-by-step explanation:
blue sector is 120 deg which is 1/3 of circle
so its area:
1/3*144 pi= 48 pi cm^2= 48*3.14 cm^2= 150.72 cm^2What’s the correct answer for this? Select all the apply
Answer:
B and C
Step-by-step explanation:
AP = BP
OC = OD
How many fluid ounces are there in 3 pints and 12 fluid ounces?
Answer:
60 fluid ounces
Mark my as brainliest please
Marco bought 5 gallons of gasoline for $17.70.
To find the unit price, the cost by the number of gallons.
The unit price is .
To find the unit price we need to all price divide by number of gallons, so
[tex]17.70\div5=3.54[/tex]
Answer: The unit price is $3.54
Answer:
Unit price = 3.54$
Step-by-step explanation:
By using criss-cross method:
5 gallons -> $17.70
1 gallon -> ?
Unit price = 1x17.70 / 5 = 3.54$
Hope this helps..
A truck was purchased for $120,000 and it was estimated to have a $24,000 salvage
value at the end of its useful life. Monthly depreciation expense of $2,000 was recorded
using the straight-line method. The annual depreciation rate is
Answer:
25
Step-by-step explanation:
64 less than y is no less than −128 Written in interval notation
Answer:
[tex]y\in [-64,\infty)[/tex] .
Step-by-step explanation:
The given statement is "64 less than y is no less than −128". It means 64 less than y is greater than or equal to −128.
[tex]y-64\geq -128[/tex]
Add 64 both sides.
[tex]y-64+64\geq -128+64[/tex]
[tex]y\geq -64[/tex]
It means possible value of y is greater than or equal to -64.
[tex]y\in [-64,\infty)[/tex]
Therefore, the required interval is [tex][-64,\infty)[/tex].
a village is 20 miles away from Belfast. Connor drives from the village to Belfast at an average speed of 40mph. Kelly drives from the village to Belfast at an average speed of 50mph. How much longer will the journey take Connor in minutes?.
Answer:
6 minutes
Step-by-step explanation:
Connor drives from the village to Belfast at an average speed of 40mph.
The distance covered is 20 miles.
Time = distance/ speed
Time = 20/40
Time = 0.5 hours
Time = 30 minutes.
Kelly drives from the village to Belfast at an average speed of 50mph.
Time = distance/speed
Time = 20/50
Time = 0.4 hours
Time = 24 minutes
It will take Conor 30 - 24 = 6 minutes longer than Kelly
which equation represents a circle with a radius of 8 centered at (-3,4)
Answer:
(x+3)^2 + (y-4)^2 = 64
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where ( h-k) is the center and r is the radius
(x--3)^2 + (y-4)^2 = 8^2
(x+3)^2 + (y-4)^2 = 64
Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Answer:
Step-by-step explanation:
Since x is a binomial random variable that counts the number of adults with at least a bachelor's degree, it means that there are only two outcome. It is either an adult has a bachelor's degree or not. The probability of success would be that the adult has a bachelor's degree. Therefore, probability of success, p = 20/100 = 0.2
Number of adults in the sample is 100
The number of success expected is x
We want to determine the probability of P(x ≥ 60)
Therefore, the most efficient way to calculate the probability that more than 60 adults have a bachelor's degree is
b. P(x<60)=binompdf(100.0.20.60)
This is because it is a discrete probability distribution function
Find the inequality represented by the graph
Answer:
There is no graph to find an inequality on...
Step-by-step explanation:
Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answer:
(r-s)/(r+s)
Step-by-step explanation:
Factor out the 5
Exactly one of the numbers 2,3 5 and 7 is placed in each of the 4 empty regions formed by circles A, B and C so that the sum of the numbers in each circle is the same. Each number is used. What is the sum of the numbers in each circle? *
Answer:
The sum of the numbers in each circle is 17
Step-by-step explanation:
The numbers to choose from are:
2, 3, 5, 7
By this alone the biggest number must be in the overlap of the three circles.
Then just fill in the numbers in such a way that they all are used.
The sum of the numbers in each circle is 17.
See picture for a solution.
In a recent survey, 70% of HR directors thought that it was very important for business students to take a course in business ethics. For a sample of 12 HR directors, what is the probability that at least one of them does not think it very important for business students to take a business ethics course
Answer:
0.9862
Step-by-step explanation:
Given: According to 70% of HR directors, business students should take a course in business ethics.
To find: the probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics course
Solution:
Probability refers to chances of occurrence of an event.
According to 70% of HR directors, business students should take a course in business ethics.
Therefore,
Probability that at least one of a sample of 12 HR directors does not think it very important for business students to take a business ethics
= 1 - Probability that everyone of a sample of 12 HR directors think that it very important for business students to take a business ethics
= [tex]1-\left ( \frac{70}{100} \right )^{12}[/tex]
[tex]=1-\left ( \frac{7}{10} \right )^{12}[/tex]
[tex]=1-(0.7)^{12}\\=1-0.0138\\=0.9862[/tex]
On a snow day, Brooklyn created two snowmen in her backyard. Snowman A was built to a height of 60 inches and Snowman B was built to a height of 44 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 5 inches per hour and Snowman B's height decreased by 3 inches per hour. Let A(t)A(t) represent the height of Snowman A tt hours after sunrise and let B(t)B(t) represent the height of Snowman B tt hours after sunrise. Write the equation for each function and determine the number of hours after sunrise when both snowmen have an equal height.
Answer: it will take 9 hours.
Step-by-step explanation:
The rate at which the height of each snowman decreased is linear. This means that it was decreasing in arithmetic progression. The formula for determining the nth term of an arithmetic progression is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference
n represents the number of terms(hours)
Considering snowman A,
Tn = A(t)
n = t
a = 60 inches
d = - 5 inches(since it is decreasing)
Therefore,
A(t) = 60 + (t - 1)-5
A(t) = 60 - 5t + 5
A(t) = 65 - 5t
Considering snowman B,
Tn = B(t)
n = t
a = 44 inches
d = - 3 inches(since it is decreasing)
Therefore,
B(t) = 44 + (t - 1)-3
B(t) = 44 - 3t + 3
B(t) = 47 - 3t
For both snowmen to have an equal height, it means that
65 - 5t = 47 - 3t
- 5t + 3t = 47 - 65
- 2t = - 18
t = - 18/- 2
t = 9 hours
Please answer this correctly I want helping hand people to answer this correctly
Answer:
q = 9
Step-by-step explanation:
Make a ratio equation:
36 : 54 = 6 : q
[tex]\frac{2}{3} =\frac{6}{q}[/tex]
2q = 18
q = 9
Answer:
q = 9
Step-by-step explanation:
These shapes are similar, so set up a proportion like so:
[tex]\frac{54}{36} =\frac{9}{q}[/tex]
→Cross multiply:
[tex]\frac{324}{36q}[/tex]
→Divide 324 by 36:
q = 9
Use properties of multiplication to show why 4 x 50 = 8 x 25.
Enter your answers in the boxes.
4 x 50 = 4 x
x 25) = (4 x
1) x 25 =
D) x 25
Answer: use the app: photomath
Step-by-step explanation:
How many school buses will be needed to take the children of Anderson school on a field trip ? Each bus can carry 60 people. 390 children and 30 adults are going on the trip
Answer:
7 school buses will be needed to take the children of Anderson school on a field trip
Step-by-step explanation:
number of children = 390
We are told that each bus carries 60 people
Therefore
60 people = 1 bus
1 person = (1 ÷ 60)
∴ 390 people = [tex]\frac{1}{60}[/tex] × [tex]\frac{390}{1}[/tex] = [tex]\frac{390}{60}[/tex] = 6.5 (approx. 7 buses)
Therefore, 7 school buses will be needed to take the children of Anderson school on a field trip, but the seventh bus will be half-filled with children.
The director of the IRS has been flooded with complaints that people must wait more than 40 minutes before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly selects 400 people entering IRS offices across the country and records the times which they must wait before seeing an IRS representative. The average waiting time for the sample is 60 minutes with a standard deviation of 22 minutes.
(a) Is there overwhelming evidence to support the claim that the wait time to see an IRS representative is more than 40 minutes at a 0.100 significance level?
Answer:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
Step-by-step explanation:
Information provided
[tex]\bar X=60[/tex] represent the sample mean
[tex]s=22[/tex] represent the sample standard deviation
[tex]n=400[/tex] sample size
[tex]\mu_o =40[/tex] represent the value to verify
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean for this case is higher than 40 minutes, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 40[/tex]
Alternative hypothesis:[tex]\mu > 40[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{60-40}{\frac{22}{\sqrt{400}}}=18.18[/tex]
The degrees of freedom are given by:
[tex]df=n-1=400-1=399[/tex]
The p value for this case would be given by:
[tex]p_v =P(t_{(399)}>18.18) \approx 0[/tex]
For this case since the p value is a very low value we can conclude that we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly higher than 40 minutes
Arguably, the top 5 race horses in U.S. history are Secretariat (S), Man O'War (M), Citation (C), War Admiral (W), and Seabiscuit (B).
Required:
a. Use this information to determine the number of possible samples (without replacement) of size 22 that can be obtained from the population of size 55.
b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________
Answer:
a) 10
b) 0.1 = 10%
Step-by-step explanation:
The combinations formula is used to solve this question, since the horses are chosen without replacement.
Combinations formula:
[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]
a. Use this information to determine the number of possible samples (without replacement) of size 2 that can be obtained from the population of size 5.
Combinations of 2 objects from a set of 5. So
[tex]C_{5,2} = \frac{5!}{2!(5-2)!} = 10[/tex]
b. If a simple random sampling procedure is to be employed, the chances that any particular sample will be the one selected are:________
In this procedure, the samples are all equally as likely to be chosen.
So
1/10 = 0.1 = 10%
which multiplication equation can be used to explain the solution to 15 divided by 1/3
1) 5 x 3 =15
2) 45 x 1/3
3) 1/3 x 15 =5
4) 1/5 x 15 =3
Answer:
Step-by-step explanation:
"15 divided by 1/3" comes out to:
15 15 3
------- = -----* ----- = 45
1/3 1 1
Recall that to divide 15 by 1/3 we invert 1/3, obtaining 3, and then multiply 15 by 3. The correct result is 45.
Multiplication equation B can be used to explain the solution to 15 divided by 1/3. Option 2 is correct.
What is the definition of arithmetic operation?Arithmetic is a branch of mathematics that studies numbers and the various operations that can be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.
The solution of the expression is;
[tex]x= \frac{15}{\frac{1}{3} } \\\\\ x= 15 \times 3\\\\ x=45[/tex]
The answer of the given equation resembles the option B. Multiplication equation B can be used to explain the solution to 15 divided by 1/3
Hence, option 2 is correct.
To learn more about the arithmetic operation, refer;
brainly.com/question/20595275
#SPJ2
A study conducted to assist the impact of caffeine consumption, smoking, alchohol consumption, and physical activity on cardiovascular disease. Suppose that 40% of participants consume caffeine and smoke. If 8 participants are evaluated what is the probability that: A. Exactly half of them consume caffene and they smoke?
Answer:
8.4
Step-by-step explanation:
tg105°-cotg105° = ?
Please help fast!!! Please
Using only the trig ratios of 45 and 60 degrees, we use angle-sum to compute [tex]\tan 105^\circ=\tan(60^\circ+45^\circ)=\frac{\tan 60^\circ+\tan 45^\circ}{1-\tan 60^\circ\tan 45^\circ}=\frac{\sqrt{3}+1}{1-\sqrt{3}}=-2-\sqrt{3},[/tex] so [tex]\cot 105^\circ=\frac{1}{\tan 105^\circ}=-2+\sqrt{3}[/tex] and [tex]\tan 105^\circ-\cot105^\circ=\boxed{-2\sqrt{3}}.[/tex]
6114 chocolate bars are to shared equally between 24 large cake mixes how many bars does each cake mix get
Answer:
146,736
Step-by-step explanation:
6114 divided by 24 is 146,736
A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 97 such fax machines, 5% are defective. Find the P-value for a test of the manufacturer's claim. Group of answer choices 0.3264 0.1736 0.3409 0.1591
Answer:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
Step-by-step explanation:
Information given
n=97 represent the random sample taken
[tex]\hat p=0.05[/tex] estimated proportion of defective
[tex]p_o=0.06[/tex] is the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to tests
We want to tet if the true proportion is less than 6%, the system of hypothesis are:
Null hypothesis:[tex]p\geq 0.06[/tex]
Alternative hypothesis:[tex]p < 0.06[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.05 -0.06}{\sqrt{\frac{0.06(1-0.06)}{97}}}=-0.415[/tex]
Now we can find the p value with the following probability:
[tex]p_v =P(z<-0.415)=0.3409[/tex]
A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent using substitution. The class has suggested four different methods. Which describes the correct method?
Answer:
Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
Answer:
The answer is:
B. Both expression should be evaluated with one value if the final values of the expressions are the same then the two expressions must be equivalent
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
JK = LM because they are equidistant from the centre and hence are equal in length
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:
question wrong
Step-by-step explanation:
2 same angles
[tex]\frac{13+5}{z} = \frac{z}{5} \\\\z^{2} = 5 * 18\\z^{2} = 90\\z = \sqrt{90} = 9,4[/tex]
