Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
A technology company is forming a task force of six members to deal with urgent quality issues. The positions will be filled by randomly chosen qualified applicants. The qualified applicants consist of five managers and ten engineers.
Required:
a. What is the probability that the chosen applicants are either all managers or all engineers?
b. What is the probability that the number of managers is the same as the number of engineers on the task force?
c. What is the expected number of engineers chosen?
d. What is the probability that at least one manager is chosen for the task force?
Answer:
a. 0.042 = 4.2% probability that the chosen applicants are either all managers or all engineers.
b. 0.2398 = 23.98% probability that the number of managers is the same as the number of engineers on the task force.
c. The expected number of engineers chosen is 4.
d. 0.958 = 95.8% probability that at least one manager is chosen for the task force.
Step-by-step explanation:
The positions are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
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]
In this question:
5 + 10 = 15 applicants, which means that [tex]N = 15[/tex]
10 are engineers, which means that [tex]k = 10[/tex]
Six members are chosen, which means that [tex]k = 6[/tex]
a. What is the probability that the chosen applicants are either all managers or all engineers?
Not possible having all managers(five applicants are manager, while there are 6 open positions), so this is P(X = 6), that is, all engineers.
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 6) = h(6,15,6,10) = \frac{C_{10,6}*C_{5,0}}{C_{15,6}} = 0.042[/tex]
0.042 = 4.2% probability that the chosen applicants are either all managers or all engineers.
b. What is the probability that the number of managers is the same as the number of engineers on the task force?
3 engineers, so this is P(X = 3).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,15,6,10) = \frac{C_{10,3}*C_{5,3}}{C_{15,6}} = 0.2398[/tex]
0.2398 = 23.98% probability that the number of managers is the same as the number of engineers on the task force.
c. What is the expected number of engineers chosen?
The expected value of the hypergeometric distribution is:
[tex]E(X) = \frac{nk}{N}[/tex]
So
[tex]E(X) = \frac{6(10)}{15} = 4[/tex]
The expected number of engineers chosen is 4.
d. What is the probability that at least one manager is chosen for the task force?
At most five engineers, which is:
[tex]P(X \leq 5) = 1 - P(X = 6)[/tex]
Since in item a. we already have P(X = 6).
[tex]P(X \leq 5) = 1 - 0.042 = 0.958[/tex]
0.958 = 95.8% probability that at least one manager is chosen for the task force.
what is the length of a rectangular solid with a volume of 180 cu ft, if it is 9 ft high and 4ft wide?
Answer:
5 ft
Step-by-step explanation:
The formula for Volume is V=lwh, or Volume = length x width x height.
The equation would be:
[tex]180=l(4)(9)[/tex]
or
[tex]180=36l[/tex]
To find the answer, divide by 36.
[tex]\frac{180}{36} =\frac{36l}{36}[/tex]
[tex]5=l[/tex]
jill number has a prime factorization with 6 numbers. Jamal number had a prime factorization with 3 numbers. Whos is bigger. jill says hers is but jamal jays not true explain.
Answer:
not enough information
Step-by-step explanation:
jill could have 2*2*2*2*2*2
and Jamal 113*113*113
but if Jill's number is made from all high primes and Jamals from low ones, it's vice versa
For a two-tailed test with a sample size of 20 and a .20 level of significance, the t value is _____. Selected Answer: d. 1.328
Answer:
1.328
Step-by-step explanation:
Given :
Sample size, n = 20.
Degree of freedom, df = n - 1
df = 20 - 1 = 19
α = 0.2
Using the T-distribution calculator :
Since it is two - tailed:
Tα/2 ; 19 = T0.2/2 ; 19 = T0.1, 19 = 1.3277 = 1.328
Using a t-distribution calculator, it is found that the t-value is of t = 1.328.
How to find the critical value of the t-distribution?In a calculator, these following inputs are needed:
The number of degrees of freedom, which is one less than the sample size.The level of significance.Whether the test is one-tailed or two-tailed.In this problem, inputting the data given in a calculator, it is found that the t-value is of t = 1.328.
More can be learned about the t-distribution at https://brainly.com/question/13873630
The following expression gives an approximate value of the total average credit card debt in a U.S. household (in dollars) t years after 1995.
400t + 5750
Use this expression to predict what the total average credit card debt will be in the year 2025.
Answer: In the year 2025, the total average credit card debt for a U.S. household will be ------------ dollars.
Answer:
In 2025, t=30. so D=418*30+6000 = 18540
Find RS. Can anyone help?
The segment XT splits the trapezoid exactly in half. The average of RS and Q will give us XT because of the properties of a trapezoid.
We find the area of a trapezoid by averaging the bases as well.
RS + Q / 2 = XT
RS + 26 / 2 = 22
RS + 26 = 44
RS = 18
Hope this helps!
A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 3521 people made credit card purchases. Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form. Identify the population and the sample.
Answer:
The population is the population of 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
Step-by-step explanation:
Department mails customers satisfactions forms to those who make credit cards purchase at the store, totaling 3521 people. Thus, the population is the population of 3521 people who made credit card purchases.
Surveys are mailed to 278 of these people, chosen at random, and 172 people return the survey form.
Thus the sample, that is, those from whom the data will be taken and expanded to the rest of the population, is the 172 people who returned the survey form.
The population is all 3521 people who made credit card purchases.
The sample is the 172 people who returned the survey form.
help PLSS HELP ASAP
TAN^2 X + SQRT3 TAN X =[0}
Answer:
Step-by-step explanation:
[tex]tan^2x+\sqrt{3} tanx=0\\tanx(tanx+\sqrt{3} )=0\\either~tan~x=0=tan~n\pi \\x=n\pi \\where~n~is~an~integer.\\if~x \in[0,2\pi )\\then~x=0,\pi \\or\\tan~x+\sqrt{3} =0\\tan~x=-\sqrt{3}=tan~(\pi-\frac{\pi }{3} ),tan~(2\pi -\frac{\pi }{3} )\\tan~x=tan(\frac{2\pi}{3} ),tan(\frac{5\pi}{3} )\\x=\frac{2\pi }{3},\frac{5\pi }{3}[/tex]
Ten pairs of points yielded a correlation coefficient r of 0.790. If a =0.05, which of the following statements is correct if H.: P = 0? (Do not calculate a t-value.) A) Because 0.790 is greater than 0.632, the nullliy pothesis is not rejected. Because 0.790 is greater than 0.602, che null hypothesis is not rejected. Because 0.790 is greater than 0.632, che null hypothesis is rejected. OD) There is no correlation between the variables
Step-by-step explanation:
Ten pairs of points yielded a correlation coefficient r of 0.790. If a =0.05, which of the following statements is correct if H.: P = 0? (Do not calculate a t-value.) A) Because 0.790 is greater than 0.632, the nullliy pothesis is not rejected. Because 0.790 is greater than 0.602, che null hypothesis is not rejected. Because 0.790 is greater than 0.632, che null hypothesis is rejected. OD) There is no correlation between the variables
Please help me with this question.
Answer:
B
Step-by-step explanation:
In a triangle, the sum of any two sides must be bigger than the third.
For the first one, 10+20=30 is not greater than 30, so this is not correct.
For B, 122+137 = 259 > 257, 257+137>122 , and 257 + 122 > 137. This works
For C, 8.6 + 2.7 = 11.3 < 12.2, so this does not work
For D, 1/6 + 1/5 = 5/(6*5) + 6/(6*5) = 5/30 + 6/30 = 11/30 < 1/2 = 15/30, so this does not work
What are the zeroes of f(x) = x2 - X - 2?
x= -2,1
x = 2, -1
x= -2, -1
x = 2,1
Answer:
x=2 x=-1
Step-by-step explanation:
f(x) = x^2 - X - 2
0= x^2 -x-2
Factor
0 =(x-2)(x+1)
Using the zero product property
x-2 =0 x+1 =0
x=2 x=-1
Answer:
x=2, -1
Step-by-step explanation:
Hi there!
We want to find the zeros of this function: f(x)=x²-x-2
The zeros are the values of x that will make f(x)=0
So that means in order to find the zeros, set f(x) as 0
In that case,
x²-x-2=0
Now let's solve the quadratic equation
We can do it by factoring
-x is the sum of two numbers, while -2 is the product of those two same numbers
Now think: which two numbers add up to -1, but multiply to get -2?
Those numbers are -2 and 1
Now factor the polynomial by FOIL:
(x-2)(x+1)=0
Split and solve
x-2=0
x=2
x+1=0
x=-1
The zeros are x=2, -1
Hope this helps!
An automobile assembly line operation has a scheduled mean completion time, , of minutes. The standard deviation of completion times is minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of completion times under new management was taken. The sample had a mean of minutes. Can we support, at the level of significance, the claim that the mean completion time has decreased under new management
The question is incomplete. The complete question is :
An automobile assembly line operation has a scheduled mean completion time, μ, of 15.5 minutes. The standard deviation of completion times is 1.7 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 90 completion times under new management was taken. The sample had a mean of 15.4 minutes. Can we support, at the 0.1 level of significance, the claim that the mean completion time has decreased under new management?
Solution :
The given data :
n = 90
μ = 15.5
σ = 1.7
[tex]$\overline x$[/tex] = 15.4
So, the null hypothesis is : [tex]$H_0: \mu = 15.5$[/tex] is been tested against
Alternate hypothesis : [tex]$H_1 : \mu < 15.5 $[/tex] (one-tailed test)
Since, the sample size is sufficiently large and the sample deviation is known, we use the Z-test.
Under this test, the test statistic is given as :
[tex]$Z=\frac{\overline x - \mu}{\sigma/\sqrt{n}} \sim N(0,1)$[/tex]
Under [tex]H_0[/tex], we have
[tex]$Z_0=\frac{\overline x - \mu}{\sigma/\sqrt{n}} $[/tex]
[tex]$Z_0=\frac{15.4-15.5}{1.7/\sqrt{90}} $[/tex]
[tex]$Z_0=-0.56$[/tex]
The critical value for the test is [tex]$Z_{\alpha} = Z_{0.1} = -1.28$[/tex]
We observe that (-0.56 > -1.28), and so we fail to reject the null hypothesis.
No, there is no evidence to support the claim that the mean completion time has decreased.
Thus, we conclude that the mean completion time is 15.5 minutes.
By which number should (2/5)^-3 be multiplied to get (1/2)^4 as a product ?
Answer:
[tex]\frac{2}{5}^{-3}[/tex]×[tex]x=\frac{1}{2}^{4}[/tex]
[tex]x=\frac{2}{5} ^{3} \\[/tex]×[tex]\frac{1}{2}^{4}[/tex]
(negative in the exponent means reciprocal of the fraction)
x= [tex]\frac{1}{250}[/tex]
Brainliest please
Bus X and bus y traveled the same 80-mile route. If bus X took 2 hours and bus y traveled at an average speed that was 50 percent faster than the average speed of bus X, how many hours did bus y take to travel the route?
Answer:
1 hr , 18 mins
Step-by-step explanation:
that is the procedure above
Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)
Answer:
Hello,
Answer A (-4,0) and (0,0)
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]
[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]
Bobby wants to bring popsicles to a summer barbecue. He decides to try a new recipe for pineapple-orange popsicles, so he makes a small batch with 1 cup of pineapple juice and 3 cups of orange juice to taste. He likes the combination, so he uses 3 cups of pineapple juice and 7 cups of orange juice to make a larger batch for the barbecue. Which batch of popsicles tastes more like oranges?
Answer:The first would taste more like oranges
Step-by-step explanation:
Find the missing pieces of the triangle round to the nearest tenth
Answer:
8√3
Step-by-step explanation:
Missing side,
√(19²-13³)
= 8√3
Answered by GAUTHMATH
what is the radius of a circle in it in if the area is 36m²?
A.0.339 m
B.3.39 m
C.78.5 m²
D.339 m
Answer:
B. 3.39 m
Step-by-step explanation:
r² = A/π
= 36/3.14
= 11.465
r = √11.465 = 3.39
PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!
It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.
A map has a scale in which 1.25 inches represents 250 miles.
How many miles does 1 inch represent?
Answer: 200 miles
Work Shown:
(1.25 inches)/(250 miles) = (1 inch)/(x miles)
(1.25)/(250) = 1/x
1.25x = 250*1 ..... cross multiplication
1.25x = 250
x = 250/(1.25)
x = 200 miles
Find the distance between the points: (-1, 5) and (3, -3). In your final answer, include the formula and calculations that you used to find the distance.
Answer:
[tex]4\sqrt{5}[/tex] units
Step-by-step explanation:
The distance between any two points on the x y plane (a,b) and (c,d) has one of two formulas. [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex] or [tex]\sqrt{(c-a)^2+(d-b)^2}[/tex] if you use c-a you have to also use d-b, and the other way around for a-c and b-d. You can rearrange which order you add though. So with (-1,5) and (3,3) here is the math
[tex]\sqrt{(3-(-1))^2+((-3)-5)^2} \\\sqrt{4^2+(-8)^2} \\\sqrt{16+64}\\\sqrt{80}[/tex]
You could simplify this to [tex]4\sqrt{5}[/tex]
Let me know if there was anything you didn't understand.
one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year
Answer:
it should be 8.333333%
Step-by-step explanation:
In the figure, triangles ABC and DEF are congruent.
Find the measure of DF.
a. 13m
b. 12m
c. 7m
d. 13.928m
Choose the correct solution for the given equation x^2-6x=40
Answer:
10,-4
Step-by-step explanation:
not sure where the options are but if you were to solve this equation first bring everything to one side.
x^2 - 6x - 40 = 0
factor it
(x-10)(x+4) = 0
set each part to 0
x-10 = 0 and x+4 = 0
solutions are 10 and -4
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?
Answer:
15
Step-by-step explanation:
3/8 = 9
9÷3= 3
the remainder of 3/8 is 5/8 so
5x3=15
Which of the statements is true for the two division problems below? A: (x^2-3x-18)/(x-6) B. (x^3-x^2-5x-3)/(x^2+2x+1)
Answer:
B is the right statement
Answer:
add the answer choices
Step-by-step explanation:
Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)
9514 1404 393
Answer:
rightacuteobtuserightobtuseStep-by-step explanation:
When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.
A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...
f = a² +b² -c²
and interpreted as follows:
f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)
Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.
__
The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.
Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity] ln(5x) 5x Step 1 As x → [infinity], ln(5x) → and 5x → .
Answer:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]
Step-by-step explanation:
L'Hopital's rule says that, if both numerator and denominator diverge, then we can look at the limit of the derivates.
Here we have:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x}[/tex]
The numerator is ln(5x) and when x tends to infinity, this goes to infinity
the denominator is 5x, and when x tends to infinity, this goes to inifinity
So both numerator and denominator diverge to infinity when x tends to infinity.
Then we can use L'Hopithal's rule.
The numerator is:
f(x) = Ln(5x)
then:
f'(x) = df(x)/dx = 1/x
and the denominator is:
g(x) = 5*x
then:
g'(x) = 5
So, if we use L'Hopithal's rule we get:
[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]
Mr Gardner is making 6 treat bags. He has 185 chocolate-covered raisins to share evenly among the treat bags.
Answer:
✎There will be 30 Chocolate-Covered raisins in each bag.
✎ And 5 Remaining.
Step-by-step explanation:
Take 185 and divide it by 6 and you should get 30 per bag with a remainder of 5 :)
A town recently dismissed 8 employees in order to meet their new budget reductions. The town had 9 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that at least 7 employees were over 50? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
The probability that at least 7 employees were over 50 is 0.0073%.
Step-by-step explanation:
Given that a town recently dismissed 8 employees in order to meet their new budget reductions, and the town had 9 employees over 50 years of age and 16 under 50, if the dismissed employees were selected at random, to determine what is the probability that at least 7 employees were over 50, the following calculation must be performed:
9/25 x 8/24 x 7/23 x 6/22 x 5/21 x 4/20 x 3/19 = X
0.36 x 0.33 x 0.304 x 0.272 x 0.238 x 0.2 x 0.157 = X
0.000073 = X
100X = 0.0073
Therefore, the probability that at least 7 employees were over 50 is 0.0073%.
