Answer:
{1, 2, 3}, {3, 4, 5}
Step-by-step explanation:
Write expressions for three consecutive integers: n, n + 1, n + 2.
Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).
(n + 1)(n + 2) = 7n - 1
Multiply (FOIL) the left side.
n^2 + 3n + 2 = 7n - 1
Subtract 7n and subtract 1 to make the right side 0.
n^2 - 4n + 3 = 0
Factor.
(n - 1)(n - 3) = 0
Set the two factors equal to 0
n - 1 = 0, n - 3 = 0
Solve for n.
n = 1, n = 3
One set of integers begins with 1, so it's {1, 2, 3}.
The other set begins with 3, so it's {3, 4, 5}
A nickel and a quarter are tossed once. What is the probability that both lands on tails? show work
Answer:
1/4
Step-by-step explanation:
1/2 x 1/2 = 1/4
What is the volume of the cube
Answer:
the answer should be V = a³=2³=8cm³
Answer:
8cm
Step-by-step explanation:
The volume of a cube is length x width x height. If it a equal cube, all sides should be the same. Meaning that 2 x 2 x 2, equaling 8 would be the answer.
Find the measurement of angle FRQ
Answer:
90 degrees
Step-by-step explanation:
What is the measure of angle SQR?
Answer:
All sides are the same length (congruent) and all interior angles are the same size (congruent). if Sqr refers to square
What is the equation of the graph below? y=1/2sinx y=1/2cosx y=1/2sin2x
Answer:
24
Step-by-step explanation:
I just did it in class. it was hard but you just have to think about the question
sum difference place value of 2 in 4242
Answer:
[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]
4242
2 = 200 ( 2 is in hundred's place )
4242
2 = 2 ( one's place )
Difference = ?
[tex] = 200 - 2 \\ = 198[/tex]
Sum = ?
[tex] = 200 + 2 \\ = 2[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
According to the 2000 U.S. Census, 80% of Americans over the age of 25 have earned a high school diploma. Suppose we take a random sample of 120 Americans and record the proportion, p, of individuals in our sample that have a high school diploma.
Answer:
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
80% of Americans over the age of 25 have earned a high school diploma.
This means that [tex]p = 0.8[/tex]
Suppose we take a random sample of 120 Americans
This means that [tex]n = 120[/tex].
Question a:
The mean is:
[tex]\mu = p = 0.8[/tex]
The mean is 0.8.
Question b:
The standard deviation is:
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.8*0.2}{120}} = 0.0365[/tex]
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
a) The mean is 0.8.
b) The standard deviation is 0.0365.
c) Normal
Here, we have,
we know that,
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean x and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean x and standard deviation s = σ/√n .
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean x=p and standard deviation s=√p(1-p)/n
80% of Americans over the age of 25 have earned a high school diploma.
This means that p=0.8
Suppose we take a random sample of 120 Americans
This means that n=120.
Question a:
The mean is:
x=p=0.8
The mean is 0.8.
Question b:
The standard deviation is:
s=0.0365
The standard deviation is 0.0365.
Question c:
By the Central Limit Theorem, approximately normal.
Learn more about standard deviation here:
brainly.com/question/23907081
#SPJ6
Help me plz what is the theme
Making new friends is too difficult, so you shouldn’t try.
You have to take risks in order to get rewards.
Jared felt lonely and sad because he was too afraid to take a chance.
Honesty is always the best policy.
Answer:
There is no passage/short story etc. to base this question off of, but if you copy and paste it I'll come back and edit my answer :)
3100 people attended a football game. If 5% of the people who attended were teenagers, how many teenagers attended the game?
Answer:
155 are teenagers
Step-by-step explanation:
3100 -5%= 2945
2945-3100=155
I really need help , someone please help :’( ... ill also make you brainlist.
Answer:
Step-by-step explanation:A)13 miles in feet = 68640 feet
we now need to get the number of cars, we use division to get groups
68640 / 15 = 4576.
we now see there are 4576 cars in the traffic jam.
B)Less, they are longer cars so the divosor would no longer be 15, it would be a higher number. 4576 cars would not be able to fit in a 13 mile stretch if those cars were any longer.
What is the probability that a person orders sandwich with cheddar cheese
Answer:
16.67%
Step-by-step explanation:
Please Help Me with this guys!! i need the answer to be typed please i cant see pics my school blocked them on my laptop oofie so please type it out
Answer:
Give me a sec and ill answer in this comments k
Step-by-step explanation:
3 less than the quotient of 18 and a number n
Answer:
(18÷n)-3
Step-by-step explanation:
The equation is above. There is no answer to the equation because we don't have a full equation to solve. Unless the question includes the answer to the equation, we can't fully solve it. But I believe that's the answer that you are looking for.
Angle Relationships
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.
The cosine of the complimentary angle to 38°
a. 0.68
b. -0.16
c. -0.22
d. 0.62
Please select the best answer from the choices provided
Answer:
D. 0.62
Step-by-step explanation:
I calculated it logically
please someone answer this question fast!
Answer:
100.05 in^2
Step-by-step explanation:
Area of parallelogram: base times height
=11.5 x 8.7=100.05 in^2
Plz help me well mark brainliest!!...
Answer:
B
Step-by-step explanation:
9+9+6+6=18+12=30
hope it helps :)
Simplify 150-(0.4 x 150 + 15)
Answer:
−60x + 135
Step-by-step explanation:
Answer:
150 - (0.4×150+15)
= 150-75
= 75
The area of a circle is pi square centimeters. What is the diameter? Please help!!!!
Answer:
Radius of the circle = 1 centimeter.
Step-by-step explanation:
Expression that represents the area of a circle,
Area = πr²
Here, r = Radius of the circle
Area of the circle given = π square centimeters
πr² = π
r² = 1
r = 1
Therefore, radius of the circle is 1 centimeter.
We have two urns. Urn 1 has 2 red balls and 3 yellow balls, while Urn 2 has 3 red balls and 7 yellow balls. We randomly select 75 balls form Urn 1, sampling with replacement. We independently randomly select 100 balls from Urn 2, sampling with replacement. Find the variance of the random variable defined as the number of red balls obtained from Urn 2 less the number of red balls obtained from Urn 1.
Answer:
[tex]\sigma (y_1-y_2)=39[/tex]
Step-by-step explanation:
From the question we are told that:
Urn 1 :2 Red, 3 Yellow
Urn 2:3 Red, 7 Yellow
Sample 1 [tex]n_1=75\ balls[/tex]
Sample 2 [tex]n_2=100\ balls[/tex]
Generally the Probability of Red ball drawn is mathematically given by
For Urn 1
[tex]P(R)_1=\frac{2}{5}[/tex]
[tex]P(R)_1=0.4[/tex]
For Urn 2
[tex]P(R)_1=\frac{3}{10}[/tex]
[tex]P(R)_1=0.3[/tex]
Generally the equation for Variance of two independent variables [tex]\sigma (y_1-y_2)[/tex] is mathematically given by
[tex]\sigma (y_1-y_2)=\sigma y_2 +(-1)^2 \sigma(x_1)[/tex]
Where red balls drawn from both Urn is Modeled
[tex]Urn_1\ is\ Modeled\ as (n_1=75,p_1=0.4)[/tex]
[tex]Urn_2\ is\ Modeled\ as\ (n_2=100,p_2=0.3)[/tex]
[tex]\sigma (y_1-y_2)=n_2 p_2(1_p_2)+n_1*p_1(1-p_1)[/tex]
[tex]\sigma (y_1-y_2)=100*0.3(1-0.3)+75*0.4(1-0.4)[/tex]
[tex]\sigma (y_1-y_2)=39[/tex]
Therefore the variance of the random variable defined as the number of red balls is
[tex]\sigma (y_1-y_2)=39[/tex]
The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
4
8
Оооо
32
64
Answer:
64
Step-by-step explanation:
Answer:
D 64
Step-by-step explanation:
The person above me is correct. Got it right on Edge 2021
A report from 2015 claims that the average salary of a server is $12 per hour. You collect data from a random sample of 30 servers in Atlanta and calculate the average salary for servers from your sample to be $11.00 with a standard deviation of $2.80. Conduct a hypothesis test to determine if the true average hourly wage of a server is different than the claim of $12.
Answer:
Since the calculated value z= -1.956 does not lie in the critical region z= ± 1.96 we conclude that true average hourly wage of a server is not different than the claim of $12.
Step-by-step explanation:
The null and alternate hypotheses are
H0: u= 12 against the claim Ha: u≠ 12
Taking significance level alpha = 0.05
The critical region is z= ± 1.96 for two tailed test
The sample size = n= 30
The sample mean = 11
Sample standard deviation= 2.80
Applying z- test
Z= x-u/s/√n
z= 11-12/2.8/√30
z= -1/0.5112
z= -1.956
Since the calculated value z= -1.956 does not lie in the critical region z= ± 1.96 we conclude that true average hourly wage of a server is not different than the claim of $12.
Greg made the dart board shown. It is divided into equal sections. A dart is randomly thrown and lands on the board.
5
1
2
3
3
2
4
1
5
What is the probability that a dart will land on a section marked with the number 1?
O A 5%
B. 10%
O C. 20%
OD. 25%
O E SOS
SRESET
Gianna Faith Russell, ID#***93
Question #22
Growth: Math 6+ MD 2011
A 407
1:24 PM
5/10/2021
Type here to search
RI
Answer:
Step-by-step explanation:
10
what is (20)+(475)? I need it now
What is the slope of y<-3/4x-1
Answer:
-3/4
Step-by-step explanation:
In slope-intercept form, the slope is the coefficient of x.
Which expressions are not equivalent
? Thanks!
Answer:
D
Step-by-step explanation:
There is no 2x in D answer
Suppose $3500 is invested at a rate of 5% per year compounded monthly.
Use the Law of Cosines to find the measure of ∠F. Round to the nearest degree.
f = 5, g = 6, h = 7
Use: f² = g² + h² – 2gh cos F
Answer:
Solution given.
f = 5, g = 6, h = 7
<F=?
we have;
f² = g² + h² – 2gh cos F
5²-6²-7²=-2×6×7 cos F
-60/-84=cos F
F=cos-¹(5/7)=44.41°
<F=44.4° is a required answer
The ___________ of a numerical set of data is the value that occurs most frequently.
A study was performed to determine the percentage of people who wear life vests while out on the water. A researcher believed that the percentage was different for those who rode jet skis compared to those who were in boats. Out of 500 randomly selected people who rode a jet ski, 85% wore life vests. Out of 250 randomly selected boaters, 90.4% wore life vests. Using a 0.05 level of significance, test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat. Let jet skiers be Population 1 and let boaters be Population 2. State the null and alternative hypotheses for the test.
Answer:
The null hypothesis is [tex]H_0: p_1 - p_2 = 0[/tex]
The alternate hypothesis is [tex]H_a: p_1 - p_2 \neq 0[/tex]
The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
Step-by-step explanation:
Before testing the null hypothesis, we need to understand the Central Limit Theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Out of 500 randomly selected people who rode a jet ski, 85% wore life vests.
This means that [tex]p_1 = 0.85, s_1 = \sqrt{\frac{0.85*0.15}{500}} = 0.016[/tex]
Out of 250 randomly selected boaters, 90.4% wore life vests.
This means that [tex]p_2 = 0.904, s_2 = \sqrt{\frac{{0.904*0.096}{250}} = 0.019[/tex]
Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
At the null hypothesis, we test that the proportions are the same, that is, the subtraction between them is zero. So
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternate hypothesis, we test that the proportions are different, that is, the subtraction between them is different of zero. So
[tex]H_a: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples, we have that:
[tex]X = p_1 - p_2 = 0.85 - 0.904 = -0.054[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.016^2 + 0.019^2} = 0.0248[/tex]
Test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.054 - 0}{0.0248}[/tex]
[tex]z = -2.17[/tex]
Pvalue of the test and decision:
The pvalue of the test is the probability that the difference differs from 0 by at least 0.054, which is P(|Z| > 2.17), which is 2 multiplied by the pvalue of z = -2.17
Looking at the z-table, z = -2.17 has a pvalue of 0.015
2*0.015 = 0.03
The pvalue of the test is 0.03 < 0.05, which means that we have enough evidence to accept the alternative hypothesis that he proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.
x + 2y = 4
4x + 8y = 64
find how many solutions there is
Answer:
No solutions
Step-by-step explanation:
Multiply the top equation by 4
4x + 8y = 16
now both equations have the same left hand side
4x + 8y
but one equals 16 the other 64
Therefor: no solutions
Answer:
Step-by-step explanation:
Multiply the top equation by 4
4x + 8y = 16
now both equations have the same left hand side
4x + 8y
but one equals 16 the other 64
( simultaneous equations )