Answer:
1 year, 3 months, 16 days.
Step-by-step explanation:
Adding one year would get you to December 24, 2005. Then, adding 3 months would take you to March 24, 2006. Then, because March has 31 days, adding 16 to 24 would get you to 40. Subtract 31 from 40 and you get the remaining 9 days.
A line has a slope of 9 and passes through the point (2, 8). What is its equation in slope-intercept form? Explain?
Answer:
y = 9x-10
Step-by-step explanation:
Slope-Intercept form is y = mx + b where m is the slope and b is the y intercept.
plug in what we are given
8 = 9(2) + b
solve for the y intercept (b)
8=18+b
8-18 = b
-10 = b
plug the slope (m) and y intercept (b) into our formula
y = 9x - 10
A rectangular room is 6 meters longer than it is wide, and its perimeter is 28
meters. Find the dimension of the room.
Answer: width = 4 and length = 10
Step-by-step explanation:
Width = w and length = w + 6
2(w) + 2 (w + 6) = 28
2w + 2w + 12 = 28
4w = 28 - 12
W = 16/4
W = 4 (width)
Length = w + 6
4 + 6 = 10
a rice cooker was sold for $60 after a discount of 60% waht was the usual price of the rice cooker plz simple for class 5 pleeease
Answer:
$150
Step-by-step explanation:
discount=60%
let the price=x
(100-60)% of x=$60
40% of x=60
x=60×(100/40)=150
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.Number of days Absent | Probability 0 0.60 1 0.20 2 0.12 3 0.04 4 0.04 5 0.001. What is the mean number of days absent? What are the variance and standard deviation?2. For the following probability distribution: a) x|10|11|12|13|14b) P(x)|.1|.25|.3|.25|.13. Find the mean, variance and standard deviation for the following probability distribution.
Answer:
(1)
[tex]E(x) = 0.72[/tex]
[tex]Var(x) = 1.1616[/tex]
[tex]\sigma = 1.078[/tex]
(2)
[tex]E(x) = 12[/tex]
[tex]Var(x) = 1.3[/tex]
[tex]\sigma = 1.14[/tex]
Step-by-step explanation:
Solving (1):
[tex]\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}[/tex]
(a): Mean
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00[/tex]
[tex]E(x) = 0.72[/tex]
Solving (b): The variance
This is calculated as:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Where:
[tex]E(x) = 0.72[/tex]
and [tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00[/tex]
[tex]E(x^2) = 1.68[/tex]
So, we have:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = 1.68 - 0.72^2[/tex]
[tex]Var(x) = 1.1616[/tex]
Solving (c): The standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{1.1616}[/tex]
[tex]\sigma = 1.078[/tex]
Solving (2):
[tex]\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}[/tex]
(a): Mean
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1[/tex]
[tex]E(x) = 12[/tex]
Solving (b): The variance
This is calculated as:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
Where:
[tex]E(x) = 12[/tex]
and [tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1[/tex]
[tex]E(x^2) = 145.3[/tex]
So, we have:
[tex]Var(x) = E(x^2) - (E(x))^2[/tex]
[tex]Var(x) = 145.3 - 12^2[/tex]
[tex]Var(x) = 1.3[/tex]
Solving (c): The standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{1.3}[/tex]
[tex]\sigma = 1.14[/tex]
If g(x) = x2 – 4, find g(5).
6
О
14
21
O
29
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]\sf \: g(x) = {x}^{2} - 4 \\ \\ \sf \: x = 5 \\ \\ \sf \: g(5) = {5}^{2} - 4 \\ \sf \: g(5) = 25 - 4 \\ \sf \: g(5) =\underline 2\underline1[/tex]
Answer ↦21 [Option C]
[tex]\tt \: g(x) = {x}^{2} - 4[/tex]
Substitute the value of x as 5 (given) in the above equation. The equation changes too..
[tex]\tt \: g(5) = {5}^{2} - 4[/tex]
Now you can easily solve the equation.
[tex]\tt \: g(5) = {5}^{2} - 4 \\\tt g(5) =( 5 \times 5) - 4 \\ \tt \: g(5) = 25 - 4 \\ \tt \: g(5) = 21[/tex]
Answer - [tex]\boxed{\sf{21}}[/tex]
Of 240 stamps that Harry and his sister collected, Harry collected 3 times as many as his sister. How many did each collected.
Answer:
Harry collected 180 stamps
Harry's sister collected 60 stamps
Step-by-step explanation:
Let X be the number of stamps that Harry's sister colleted.
The number of stamps Harry colleted is 3 time as many as his sister's
⇒ 3*X + X = 240
⇒ X = 60
⇒ 240 - 60= 180
Answer:
180 for harry and 60 for his sister
Step-by-step explanation:
Jack is a discus thrower and hopes to make it to the Olympics some day. He has researched the distance (in meters) of each men's gold medal discus throw from the Olympics from 1920 to 1964. Below is the equation of the line of best fit Jack found.
y = 0.34x + 44.63
When calculating his line of best fit, Jack let x represent the number of years since 1920 (so x=0 represents 1920 and x=4 represents 1924).
Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.
71.83 meters
65.03 meters
717.83 meters
44.63 meters
Answer:
65.03 meters
Step-by-step explanation:
The line of best fit, for the distance of the winning throw, in x years after 1980 is:
[tex]y = 0.34x + 44.63[/tex]
Using the line of best fit, estimate what the distance of the gold medal winning discus throw was in 1980.
1980 - 1920 = 60, so this is y(60).
[tex]y(60) = 0.34(60) + 44.63 = 65.03[/tex]
So the answer is 65.03 meters.
In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is
Answer:
(8.608, 9.392)
Step-by-step explanation:
We have the following information
Population standard deviation = 1.8
Sample mean = 9 hours
Sample n = 81
C I = 95%
So level of significance
Alpha = 1-0.95
= 0.05
Z critical at 0.05/2
Z(0.025) = 1.96
The 95% c.i =
9+-(1.96)(1.8/√81)
9+-(1.96)(0.2)
(9-0.392)(9+0.392)
(8.608, 9.392)
This is the confidence interval at 95%.
I hope you find my solution useful. Good luck!!!
What balance will be in an account that has an initial deposit of $4600 with an APR of
1.8%? The money is compounded quarterly for 30 years.
How much interest has been earned for the entire time period?
Answer:
100$or 20.4 that is the answer
The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 60
Answer:
The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.
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.
Standard deviation is 9.5 for a population.
This means that [tex]\sigma = 9.5[/tex]
Sample of 60:
This means that [tex]n = 60[/tex]
What is the standard deviation of the distribution of sample means for samples of size 60?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{9.5}{\sqrt{60}} = 1.2264[/tex]
The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=530x−9240 where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt. what is the slope of the line represent?
A. the GDP per capita of the country with the lowest corruption score
B. the corruption score needed for a GDP per capita of zero
C. the average GDP per capita for every point in the corruption score
D. the increase in GDP per capita for every increase of one in corruption score
Step-by-step explanation:
pandemic times: Potential ... - CAF
have shown evidence that the effect of corruption on real GDP per capita is more pronounced in countries with low levels of8
A can of soda is placed inside a cooler. As the soda cools, its temperature T(x) in degrees Celsius is given by the following exponential function, where is the number of minutes since the can was placed in the cooler.
T(x)=-22+44e^-0.03x
Find the initial temperature of the soda and its temperature after 18 minutes.
Answer:
Ans: -21.87 ≅ -22°C
Step-by-step explanation:
T(x)=-22+44e^-0.03x
Initial temperature (x = 0):
T(0) = = -22 + 44e-0.03(0) = -22 + 44(1) = 22°C
After 18 minutes (x = 18):
T(18) = -22 + 44e-0.03(18) = -21.87°C ≅ -22°C
Find the surface area of a sphere
with a radius of 9 cm.
Surface Area = [?] cm?
Answer:
[tex] 1,017.36 \: {cm}^{2} [/tex]
Step-by-step explanation:
Surface area of a sphere
[tex] = 4\pi {r}^{2} \\ = 4 \times 3.14 {(6)}^{2} \\ = 12.56 \times 81 \\ = 1,017.36 \: {cm}^{2} [/tex]
Answer:
1017.36 cm²
Step-by-step explanation:
Given :-
Radius = 9cm .We know ,
SA = 4π r²SA = 4* 3.14 * (9cm)² SA = 4 *3.14*81cm²SA = 1017.36 cm²Answer true or false and explain your answer. If it is important not to reject a true null hypothesis, the hypothesis test should be performed at a small significance level.
Answer: No, The goal when testing a hypothesis is to to guess a large significant level to possibly have the answer correct based upon evidence. False. It needs to be a large significant level
Step-by-step explanation:
A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.
This is the Written equation.
x+6x=56
Solve the equation.
Interpret the results and write the answer in words.
The smaller piece is x = _ in.
The longer piece is _x = _ ( ) = _ in.
The lengths of the two pieces are _ in
and _ in.
Part 1 of 2
_ in
Part 2 of 2
_ in
Answer:
8 inches
48 inches
total 56 inches
Step-by-step explanation:
x+6x = 56
7x = 56
Divide by 7
7x/7 = 56/7
x = 8
The smaller piece is x inches or 8 inches
The larger piece is 6x inches or 6*8 =48 inches
8+48 = 56 inches
The total length is 56 inches
Answer:
8 inches, and 48 inches
Step-by-step explanation:
x+6x=56
Solve the equation.
7x=56
x=8
Interpret the results and write the answer in words.
The smaller piece is x = 8 in.
The longer piece is 6x = 6 (8) = 48 in.
The lengths of the two pieces are 8 in
and 48 in.
Is there a difference in the number of people who have an Annual pass to Disney World comparing people who live in Florida to those who do not?
Answer:
Fail to reject the null hypothesis.
Step-by-step explanation:
People who live in Florida and also have annual pass to Disney world is 221, sample size selected for group 1 is 350.
People who do not live in Florida and have annual pass to Disney world is 365, sample size selected for Group 2 is 650.
Group 1 sample proportion is : 221 / 350 = 0.6314
Group 2 sample proportion is 365 / 650 = 0.5615
Test statistics is 0.8317
Since test stats value is greater than the sample proportion significance level, we fail to reject the null hypothesis.
The volume of a cone is given by the formula $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. The area of the base of a cone is 30 square units, and its height is 6.5 units. What is the number of cubic units in its volume?
9514 1404 393
Answer:
65 cubic units
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
V = 1/3Bh
V = 1/3(30)(6.5) = 65 . . . cubic units
Write a fraction for the portion of the grid that is NOT shaded.
15
8
15
7
7
15
8
15
7
15
because there are a total of 15 grid and the question asked to pick the grid that doesn't shaded
Answer:
7/15
Step-by-step explanation:
We can count the grids to see that there are 15. This is the total, and will become our denominator. From there, we can count the non blue squares to get to 7, our numerator. We put our numerator, 7, over pur denominator, 15. This gives us 7/15.
What is the circumference of the circle in terms of [tex]\pi[/tex]?
a. 900[tex]\pi[/tex] in.
b. 90[tex]\pi[/tex] in.
c. 60[tex]\pi[/tex] in.
d. 30[tex]\pi[/tex] in.
(duplicate, as I forgot the image)
[tex] \sf \: r \: = 30 \: in. \\ \sf \: C \: = 2\pi r \\ \\ \sf \: C \: = 2\pi(30) \\ \sf \: C = 2 \times 30\pi \\ \sf \: C = \boxed{\underline{ \bf c. \: 60\pi \: in.}}[/tex]
Which of the relations given by the following sets of ordered pairs is a function?
C_{(1,2), (2, 3), (3, 4), (5,6), (2, 1)}
C {( - 2,5), (7,5), ( – 4,0), (3,0), (1, - 6)}
Ċ {(2, – 8), (1, – 4), (0,0), (1, 4), (2,8)}
{(3, – 3), (3,
1), (3, 1), (3, 3), (3,5)}
Submit
Pass
elp
Don't know
answer
14
tv
va
The first or second one because a function can't have the x value repeating
James is applying for a new job at a game design company. Job A offers $40,000 starting salary with a $1000 raise each year. Job B offers $35,000 starting salary with a 8% raise each year. Which job should James take if he is working at this job for 5 years?
Job B because every year he gets a $2800 every year and if he continues for 5 years he will get a total of $14000 but if he works at job A he gets $5000 after 5 years
Step-by-step explanation:
A........a40,000 + b5000 WITH 5 YEARS
B........a35,000 + b14,000 with 5 years
answer B
Please help, will give brainliest!!!!!
Answer:
third option
Step-by-step explanation:
Brainliest please~
Help?? Please “Use a benchmark to compare 4/7 and 2/10”
Answer:
4/7 > 2/10
Step-by-step explanation:
4/7 is close to 1/2
2/10 is close to 0
4/7 > 2/10
The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 7 to 5. If there were 4115 no votes, what was the total number of votes?
Answer:
9876
Step-by-step explanation:
7:5
x:4115
To find x mulitply 7 by 823 (because this is what we multiplied 5 by in order to get 4115)
7*823= 5761
Take the sum to find the total number of votes
4115+5761= 9876
Suppose you just received a shipment of seven televisions. Four of the televisions are defective. If two televisions are randomly selected, compute the probability
that both televisions work. What is the probability at least oone of the two televisions does not work?
The probability that both televisions work is
(Round to three decimal places as needed.).
The probability that at least one of the two televisions does not work is
(Round to three decimal places as needed.)
e
Answer:
- What is the probability at least one of the two televisions does not work?
The probability at least one of the two televisions does not work is 0.8163
- The probability that both televisions work is?
The probability that both televisions work is 0.1837
Step-by-step explanation:
Total televisions are 7
Faulty televisions are 4
Number of televisions selected is 2
Solve for x. WILL GIVE BRAINIEST
Answer:
x≤16
Step-by-step explanation:
1/2x - 3 ≤5
Add 3 to each side
1/2x -3+3 ≤5+3
1/2x≤8
Multiply each side by 2
1/2x*2 ≤8*2
x≤16
Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest. compounded weekly. What is the value of the CD at the end of the 4 years?
Answer:
The value of the CD at the end of the 4 years is $5,808.86.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest.
This means that [tex]P = 5000, r = 0.0375[/tex]
Compounded weekly
An year has 52 weeks, so [tex]n = 52[/tex]
Then
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 5000(1 + \frac{0.0375}{52})^{52t}[/tex]
What is the value of the CD at the end of the 4 years?
This is A(4). So
[tex]A(4) = 5000(1 + \frac{0.0375}{52})^{52*4} = 5808.86[/tex]
The value of the CD at the end of the 4 years is $5,808.86.
Hey, I’m new to this app i download the app today, and i hope if is there people who can help me with this question in the picture above!!
Step-by-step explanation:
For a quadratic equation, the second differences will always be the same.
First, we must calculate the first differences between the output, or the y values. This can be calculated as shown, taking the first value and subtracting the second value from that (e.g. 34 - 17 = 17, and 1-2 = -1):
34 17 6 1 2 9 22
\ / \ / \ / \ / \ / \ /
17 11 5 -1 -7 -13
The second differences are the differences between the differences we just calculated. This can be calculated as shown:
17 11 5 -1 -7 - 13
\ / \ / \ / \ / \ /
6 6 6 6 6
The second differences are all 6, and as a result, we can verify that this is a quadratic relation
Find dy/dx given that y = sin x / 1 + cos x
Answer:
[tex] \frac{1}{1 + \cos(x) } [/tex]
Step-by-step explanation:
[tex]y = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
differentiating numerator wrt x :-
(sinx)' = cos x
differentiating denominator wrt x :-
(1 + cos x)' = (cosx)' = - sinx
Let's say the denominator was "v" and the numerator was "u"[tex] (\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} } [/tex]
here,
since u is the numerator u= sinx and u = cos x v(denominator) = 1 + cos x; v' = - sinx[tex] = \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} } [/tex]
[tex] = \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} } [/tex]
since cos²x + sin²x = 1
[tex] = \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} } [/tex]
diving numerator and denominator by 1 + cos x
[tex] = \frac{1}{1 + \cos(x) } [/tex]
14 ft
3 ft
6 ft
O 87
1313
252ft
0 262
52.31
Answer:
35
Step-by-step explanation:
