Answer: the probability is 0.13
Step-by-step explanation:
First, each question has 5 options and only one is correct.
Then, selecting at random, the probability of getting a correct answer is equal to:
p = 1/5 = 0.20 (and the probability of getting it incorrect is p = 4/5 = 0.80)
Now, if out of 30 questions, we got 4 correct and 26 incorrect, the probability for a given combination is;
p = (0.20^4)*(0.80^26)
But we also need to multiply this by the total number of combinations.
This is we have 30 questions in total, and we can select 4 of them that will be the correct ones.
Now, if we have N objects in total, the number of different combinations of K elements out of those N elements is
[tex]C = \frac{N!}{(N-K)!*K!}[/tex]
In this case, N = 30 and K = 4.
[tex]C = \frac{30!}{(30 -4)!*4!} = \frac{30*29*28*27}{4*3*2} = 27,405[/tex]
Then the probability of getting exactly 4 correct answers is:
P = (0.20^4)*(0.80^26)*27,405 = 0.13
What is the product of 6 and one-half and 9 and one-fourth?
Answer:
60.125 or 60.13 when rounded to the nearest tenths.
Step-by-step explanation:
6 and one-half into a mixed number is 13/2
9 and one-forth into a mixed number is 37/4
13 x 37 = 481 divided by 8
2 4
When you divide 481 by 8 = 60.125 or 60.13 when rounded to the nearest tenths
I really hope this helps.
1. Find the value of x
37.5
17
52.5
a. 39.5
b. 75
c. 40
d. 42.5
Answer:
d
Step-by-step explanation:
The segment inside the triangle bisects the angle and divides the opposite sides into segments that are proportional to the other two sides, that is
[tex]\frac{x}{17}[/tex] = [tex]\frac{37.5}{52.5-37.5}[/tex] = [tex]\frac{37.5}{15}[/tex] ( cross- multiply )
15x = 637.5 ( divide both sides by 15 )
x = 42.5 → d
Evaluate the geometric series or state that it diverges.
[infinity]
Σ e^-5n
n=0
Answer:
sum = = 1 / ( 1-e^(-5) )
( 1.00678 to 5 decimals)
Step-by-step explanation:
Question: sum
[infinity]
Σ e^-5n
n=0
We note that this is a geometric series,
with n=0, e^(-5n) = e^0 = 1
with n=1, e^(-5n) = e^(-5)
with n=2, e^(-5n) = e^(-10)
...
Therefore the common ratio is r=e^(-5)
and the sum for a geometric series
a+ar+ar^2 + ... ar^N
=a(1-r^(N+1)) / (1-r)
=1(1-r^(infinity-1)) / (1-e^(-5))
= 1 / ( 1-e^(-5) )
Find the sum. Please
Answer:
[tex]\dfrac{2y^2 +12y -8}{y^3-3y+2}[/tex]
Step-by-step explanation:
It usually works to factor the denominators, so you can determine the least common denominator.
[tex]\dfrac{2y}{y^2-2y+1}+\dfrac{8}{y^2+y-2}=\dfrac{2y}{(y-1)^2}+\dfrac{8}{(y-1)(y+2)}\\\\=\dfrac{2y(y+2)}{(y-1)^2(y+2)}+\dfrac{8(y-1)}{(y-1)^2(y+2)}=\dfrac{2y^2+4y+8y-8}{(y-1)^2(y+2)}\\\\=\boxed{\dfrac{2y^2 +12y -8}{y^3-3y+2}}[/tex]
Which could be the side lengths of a triangle? (A) 2,2,4 (B) 3,4,7 (C) 4,5,8 (D) 5,5,10 (E) 7,3,10 PLEASE HELP
Answer:
(C) 4,5,8
Step-by-step explanation:
Since 4+5 = 9 and 9 is bigger than 8, that means that the side 8 can fit into the triangle without there being an open space.
Answer:
Option C { 4,5,8 }
Step-by-step explanation:
By the Triangle Inequality Theorem, the length of two sides together must be greater than the length of the remaining side. Respectively their difference must be less than the length of the another side.
* I like to memorize this concept by thinking about a door. The more you open the door, the greater the distance between the door and the wall - as they are proportional. That is how we concluded this theorem.
______
{ 2, 2, 4 } is our first option. The difference of 4 and 2 is equal to the remaining length, 2. { 3, 4, 7 } is not applicable as well, considering that the addition of 3 and 4 is equivalent to the length of the 3rd side, 7. However, the lengths { 4, 5,8 } have no such " errors. " It could be the side lengths of a possible triangle.
______
Solution = { 4,5,8 }
In which one of the figures is AB congruent to AC
A property is listed for $580,000. The listing agreement promises to
pay a 7% commission. A buyer makes an offer of $547,000 on May 4th
and gives a $2,000 deposit. The offer is accepted with no change on
May 8th and a closing date is set for June 5th. The day of closing goes
to the buyer. Taxes for the property are $5309 and are paid in arrears.
The buyer will pay for the inspection at closing $280.00 and the seller
will pay for a home warranty in the amount of $360.00. The mortgage
remaining is $480,000. Using the 365 day method, what will the seller
net?
$506,095
$544,386
$26,096
$26,085.00
Answer:
$26,096
Step-by-step explanation:
property taxes = 31 January + 28 February + 31 March + 30 April + 31 May + 4 June = 155 days
property taxes = (155 days/365 days) x $5,309 = $2,254
agent's commission = 7% x $547,000 = $38,290
seller's net = $547,000 - $480,000 (mortgage) - $38,290 (agent's commission) - $360 (home warranty) - $2,254 (property taxes) = $26,096
Answer:
26,096
Step-by-step explanation:
Proration using 365-day method:
Buyer days are June - December 210 days (June 30 + July 31 + August 31 + September 30 + October 31 + November 30 + December 31 - June 4 days)
Seller days are January - June 155 days (January 31 + February 28 + March 31 + April 30 + May 31 + June 30 - June 26 days)
Formula with closing day to buyer: 210/365 x $5,309 = $3,054.49 --> $5,309 - $3,054.49 = $2,254.51 property taxes
Commission:
$547,000 sale price x .07 commission fee = $38,290 commission
Seller Net:
$547,000 sale price - $480,000 mortgage = $67,000 - $38,290 commission = $28,710 - $360.00 home warranty = $28,350 - $2,254.51 = $26,096
solve the inequality:8x+3>2x-15
8x + 3 > 2x - 15
8x - 2x > -15 - 3
6x > -18
x > -3
Answer:
x > -3
Step-by-step explanation:
8x + 3 > 2x - 15
Add -3 and -2x on both sides.
8x - 2x > -15 - 3
6x > -18
Divide 6 into both sides.
x > -18/6
x > -3
The formula for converting temperature from Fahrenheit(F) to Celsius(C) is C = 5 (F – 32°). If the
temperature
is 77° Fahrenheit, what is it in Celsius?
Answer:
25C
Step-by-step explanation:
C=(F-32)*5/9
c=(77-32)*5/9
c=25C
How many palindromes of length 5 can you form using letters with the following properties: they start with a consonant, and the consonants and vowels alternate; no letter appears more than twice. (Note: assume letters "a", "e", "i", "o", and "u" are the vowels of the English alphabet).
Answer:
2100
Step-by-step explanation:
There are 21 consonants that can serve as the first and last letters. There are 5 vowels that can serve as the 2nd and 4th letters. There are 20 remaining consonants that can serve as the 3rd letter. (The same consonant cannot appear in all three places.)
So, the total number of 5-letter palindromes that start with a consonant and alternate with a vowel will be ...
21×5×20 = 2100 . . . different palindromes
2100 palindromes of length 5 can you form using letters.
What is palindrome?A palindrome is a word, number, phrase, or other sequence of characters which reads the same backward as forward, such as madam or racecar.
As, there are 21 consonants that can be the first and last letter.
and, there 5 vowels that be the second and fourth letter .
lastly, the 20 remaining consonants that can be the 3rd letter.
So, the total number of 5-letter palindromes will be,
= 21×5×20
= 2100
Learn more about palindrome here:
https://brainly.com/question/19052372
#SPJ2
Which is the first step in simplifying 4(3x-2)+6x(2-1)
Answer:
4(3x-2)+6x(2x-1)
12x-8+12^2x-6x
12x-6x +12^2x-8
6x+12^2x-8
Answer:
the first step in simplifying 4(3x-2)+6x(2-1) is to do subtract 1 from 2 in the second set of parenthesis. That will get you 4(3x-2)+6x(1)
The equation completely simplified is 18x-8
-look in the step-by-step explanation if you want to know all the steps to simplifyinh the equation
Step-by-step explanation:
Now if you want to know the rest here it is:
Then use the Distributive Property:
-distribute the 4 into (3x-2) to get 12x-8
-then distribut the 6x into (1) to get 6x
Your equation is now 12x-8+6x
Finally, add 12x and 6x to simplify the equation as much as you can
you get 18x-8 as you final, most simplified answer
James currently has $215 in a savings account. Every month, he deposits an additional $45 into his account. James had to replace the wooden fence around his house for a total of $4,100, and his zero-interest payment plan requires $168 per month. If James uses all of his budgeted savings to help pay off the fence, in addition to the monthly payment, what will be the remaining balance on the fence after 12 months?
Answer:
James still owes 1,261 dollars after 12 months
Step-by-step explanation:
Second attempt :P
James currently has 215 dollars, every month for 12 months, he deposits 45 dollars into his account
215 + 12 x 45
215 + 540 =755
Now we know how much money James will have after 12 months, we need to find out how much he will owe.
James has to pay 168 per month for 12 months
168 x 12 = 2016
After 12 months the total amount James owes will be 2,016 dollars.
He makes 755 for the whole 12 months
2,016 - 755 = 1,261
James still owes 1,261 dollars after 12 months
Simplify the expression. 641/3
Answer:213.7
Step-by-step explanation:
How many gallons of 20% moonshine and how many gallons of 30% moonshine have to be mixed together to make 100 gallons of 28% moonshine? x = gallons of 20% moonshine y = gallons of 30% moonshine
Answer:
20 and 80
Step-by-step explanation:
x+y= 100
0.2x+0.3y= 0.28*100
0.2x+0.3*(100-x)= 280.2x- 0.3x +30= 280.1x= 2x= 20 ⇒ y= 80
At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there are only one lane and one inspector, who can inspect vehicles ar the rate of per hour in an exponentially distributed fashion.
A. What is the average length or the waiting line?
B. What is the average total time it takes for a vehicle to get through the system?
C. What is the utilization of the inspector?
D. What is the probability that when you arrive there will be three or more vehicles ahead of you?
Answer:
no❤️Step-by-step explanation:
PLSSSSSSS HELP WILL MARK BRAINLIEST Doug owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If he has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?
Answer:
i think this person answered but idrk perseusharrison79
Step-by-step explanation:
For 2 parallelograms, the corresponding side lengths are 1 inch and x inches, and 2 inches and 6 inches.
Not drawn to scale
StartFraction 1 over x EndFraction = StartFraction 2 over 6 EndFraction
StartFraction 1 over x EndFraction = StartFraction 6 over 2 EndFraction
StartFraction 1 over 6 EndFraction = StartFraction 2 over x EndFraction
One-half = StartFraction 6 over x EndFraction
Step-by-step explanation:
Simplify.
35 - (42 + 5)
━━━━━━━☆☆━━━━━━━
▹ Answer
-12
▹ Step-by-Step Explanation
35 - (42 + 5)
35 - 47 = -12
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
Hello!
~~~~~~~~~~~~~~~~~~~~~~~~~
35 - (42 + 5) =
-12
~~~~~~~~~~~~~~~~~~~~~~~~~
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice. ❤︎
A random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen, resulting in the accompanying data (from "Engineering Properties of Soil," Soil Science, 1998: 93–102).1.10 5.09 0.97 1.59 4.60 0.32 0.55 1.450.14 4.47 1.20 3.50 5.02 4.67 5.22 2.693.98 3.17 3.03 2.21 0.69 4.47 3.31 1.170.76 1.17 1.57 2.62 1.66 2.05The values of the sample mean, sample standard deviation,and (estimated) standard error of the mean are2.481, 1.616, and .295, respectively. Does this data suggestthat the true average percentage of organic matterin such soil is something other than 3%? Carry out atest of the appropriate hypotheses at significance level.10. Would your conclusion be different if a 5 .05 hadbeen used? [Note: A normal probability plot of the datashows an acceptable pattern in light of the reasonablylarge sample size.]
Answer:
We conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
We conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
Step-by-step explanation:
We are given a random sample of soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen;
1.10, 5.09, 0.97, 1.59, 4.60, 0.32, 0.55, 1.45, 0.14, 4.47, 1.20, 3.50, 5.02, 4.67, 5.22, 2.69, 3.98, 3.17, 3.03, 2.21, 0.69, 4.47, 3.31, 1.17, 0.76, 1.17, 1.57, 2.62, 1.66, 2.05.
Let [tex]\mu[/tex] = true average percentage of organic matter
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 3% {means that the true average percentage of organic matter in such soil is 3%}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu \neq[/tex] 3% {means that the true average percentage of organic matter in such soil is something other than 3%}
The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean percentage of organic matter = 2.481%
s = sample standard deviation = 1.616%
n = sample of soil specimens = 30
So, the test statistics = [tex]\frac{2.481-3}{\frac{1.616}{\sqrt{30} } }[/tex] ~ [tex]t_2_9[/tex]
= -1.76
The value of t-test statistics is -1.76.
(a) Now, at 10% level of significance the t table gives a critical value of -1.699 and 1.699 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is something other than 3% at 10% significance level.
(b) Now, at 5% level of significance the t table gives a critical value of -2.045 and 2.045 at 29 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the true average percentage of organic matter in such soil is 3% at 5% significance level.
y-3x=3 and x-2y=4 using elimination method
Answer:
x = -2, y = -3
Step-by-step explanation:
y - 3x = 3
x - 2y = 4
-3x + y = 3
x - 2y = 4
-6x + 2y = 6
x - 2y = 4
Add the equations.
-5x = 10
x = -2
Substitute -2 for x in the first original equation and solve for y.
y - 3x = 3
y - 3(-2) = 3
y + 6 = 3
y = -3
Answer: x = -2, y = -3
Step-by-step explanation:
[tex]y-3x=3--------(1) \\ x-2y=4 --------(2)\\ -3x +y =3 ----------(1)\\x-2y =4-----------(2)\\Multiply -equation(1)-by-the-coefficient-of x -in-equation(2)\\Multiply -equation(2)-by-the-coefficient-of x -in-equation(1)\\ -3x +y =3 ----------(1)\times 1\\x-2y =4-----------(2)\times -3\\\\-3x+y = 3 -----(3)\\-3x +6y = -12----(4)\\Subtract -equation(4)-from-equation(3)\\-5y =15\\\frac{-5y}{-5} =\frac{15}{-5} \\y = -3\\[/tex]
[tex]Substitute ; -3 -for;y -in -equation (1) or (2)\\-3x +y =3 ----------(1)\\-3x + (-3)=3\\-3x-3 =3\\-3x= 3+3\\-3x=9\\\frac{-3x}{-3} = \frac{9}{3} \\x = -2[/tex]
Find the slope of the line shown
Answer:
4/3
Step-by-step explanation:
We can find the slope by using the formula
m = (y2-y1)/(x2-x1)
We need two points ( 5,1) and ( 8,5)
m = ( 5-1)/(8-5)
= 4/3
The table shows the average number of pounds of trash generated per person per day in the United States from 1970 to 2010. Use the statistics calculator to calculate the mean and median. Round the answers to the nearest hundredth
Answer:
Table needed to help
Step-by-step explanation:
Mean vs Median
The mean (informally, the “average“) is found by adding all of the numbers together and dividing by the number of items in the set: 10 + 10 + 20 + 40 + 70 / 5 = 30.
The median is found by ordering the set from lowest to highest and finding the exact middle. The median is just the middle number: 20.
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two side
bf this triangle?
O 5 cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
It's (D) 8 cm and 9 cm. Hope this helps you!
Step-by-step explanation:
The other 2 sides added have to be greater than 13.
Answer:
8 and 9
Step-by-step explanation:
The triangle inequality states that the sum of the two shortest sides must be greater than the longest side.
Let's check the first one. 5 + 8 > 13 → 13 > 13 which is false.
6 + 7 > 13 → 13 > 13 which is false.
7 + 2 > 13 → 9 > 13 which is false.
8 + 9 > 13 → 17 > 13 which is true.
please answer someone
Answer:
answer C
Step-by-step explanation:
hello
set A is [tex]10^x[/tex]
set B is 1000+50(x-1)
so set A is an exponential function and the values increase at a faster rate than set B
hope this helps
7 + x - 15 = -2.67 solve for x
Answer:
5.33
Step-by-step explanation:
Move your numbers so that they're separate from the variables. You should now have x = -2.67 + 8; x = 5.33
Answer:
x=5.33
Step-by-step explanation:
7+x-15=-2.67
7-15+x=-2.67
Add 7 and -15
-8+x=-2.67
Add 8 on both sides
which equal to 5.33
x=5.33
Which one of the following groups of numbers includins all prime numbers? a)2,3,5 b)7,17,63,67 c)3,11,63,67 d)1,3,11,23
Answer:
a) 2, 3, 5
Step-by-step explanation:
2, 3, 5
All numbers are prime.
7, 17, 63, 67
63 is not a prime number.
3, 11, 63, 67
63 is not a prime number.
1, 3, 11, 23
1 is not a prime number.
6th grade math , please help
Answer: 4 to 10 then it’s 6 to 20 then it’s 8 to 25 Then it’s 10 to 30 then it’s 12 to 35 I hope this is the answer
Step-by-step explanation:
Step-by-step explanation:
Ava is walking at a constant rate of 5 feet each 2s so :
5 ft ⇒ 2 sWe should keep adding 2s in the time and 5 feet in the distance
Let's complete the chart:
0⇒02⇒54⇒106⇒158⇒2010⇒25The mean arrival rate of flights at Philadelphia International Airport is 195 flights or less per hour with a historical standard deviation of 13 flights. To increase arrivals, a new air traffic control procedure is implemented. In the next 30 days, the arrival rate per day is given in the data vector below called flights. Air traffic control manager wants to test if there is sufficient evidence that arrival rate has increased.
flights <- c(210, 215, 200, 189, 200, 213, 202, 181, 197, 199,
193, 209, 215, 192, 179, 196, 225, 199, 196, 210,
199, 188, 174, 176, 202, 195, 195, 208, 222, 221)
a) Find sample mean and sample standard deviation of arrival rate using R functions mean() and sd().
b) Is this a left-tailed, right-tailed or two-tailed test? Formulate the null and alternative hypothesis.
c) What is the statistical decision at the significance level α = .01?
Answer:
a) The sample mean is M=200.
The sample standard deviation is s=13.19.
b) Right-tailed. The null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
c) At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Step-by-step explanation:
We start by calculating the sample and standard deviation.
The sample size is n=30.
The sample mean is M=200.
The sample standard deviation is s=13.19.
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{30}(210+215+200+. . .+221)\\\\\\M=\dfrac{6000}{30}\\\\\\M=200\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{29}((210-200)^2+(215-200)^2+(200-200)^2+. . . +(221-200)^2)}\\\\\\s=\sqrt{\dfrac{5048}{29}}\\\\\\s=\sqrt{174.07}=13.19\\\\\\[/tex]
This is a hypothesis test for the population mean.
The claim is that the arrival rate is significantly higher than 195. As we are interested in only the higher tail for a significant effect, this is a right-tailed test.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=195\\\\H_a:\mu> 195[/tex]
The significance level is 0.01.
The standard deviation of the population is known and has a value of σ=13.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{13}{\sqrt{30}}=2.373[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{200-195}{2.373}=\dfrac{5}{2.373}=2.107[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.107)=0.018[/tex]
As the P-value (0.018) is bigger than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
At a significance level of 0.01, there is notenough evidence to support the claim that the arrival rate is significantly higher than 195.
Write the numbers in scientific notation.
8. 5,100,000
9. .00000698
10. 3.000052
Write the numbers in standard form.
11. 6.548 x 10-3
12. 5.854 x 10' 58.54
13. 2.25 x 106
Answer:
8)5.1*10⁶
9)6.98*10 to the power of -6
10) 3.000052*10⁰
11)0.006548
2. How much interest is earned by investing $2100 for three years at 4.5% compounded
monthly?
Answer:
The final balance is $2,402.92.
The total compound interest is $302.92.
Step-by-step explanation:
A = P(1 + r/n)^{nt}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
A=2100(1+.045/12)^(3*12)
A=2100(1.00375)^(36)
A=2100*1.442478322
A=2402.92
gain of 302.92
I NEED HELP PLEASE, THANKS! :)
Answer:
see below
Step-by-step explanation:
The coefficients are 19Cr for r from 0 to 19, as shown in the first and last choices. The sum of the powers of the factors is 19, as shown in the first and last choices. The only difference between the first and last choices is the order of terms in the sum. Both have the same total, and both are equivalent expansions of the given expression.
If you prefer the higher powers of m to appear first, then the last choice is appropriate.