Total number of ways to select 3 people from the 5 total: 5!/(3! (5 - 3)!) = 10
• Number of ways of picking 0 women:
[tex]\dbinom20\times\dbinom33 = 1\times1 = 1[/tex]
• Number of ways of picking 1 woman:
[tex]\dbinom21\times\dbinom32 = 2\times3 = 6[/tex]
• Number of ways of picking 2 women:
[tex]\dbinom22\times\dbinom31 = 1\times3 = 3[/tex]
• Number of ways of picking 3 women: 0, since there are only 2 to choose from
Then X has the probability mass function
[tex]P(X=x) = \begin{cases}\frac1{10}&\text{if x=0}\\\frac6{10}=\frac35&\text{if }x=1\\\frac3{10}&\text{if }x=2\\0&\text{otherwise}\end{cases}[/tex]
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
The value of a car will “depreciate” over time. For example, a car that was worth $24 000 when it was new, is being sold for $13 500 three years later. Determine the annual depreciation rate on this car. Express your final answer as a percent, rounded to one decimal place.
Answer:
The car will depreciate at a rate of 21.14% per year.
Step-by-step explanation:
Given that the value of a car will “depreciate” over time, and, for example, a car that was worth $ 24,000 when it was new, is being sold for $ 13,500 three years later, to determine the annual depreciation rate on this car the following calculation must be performed:
13,500 x (1 + X) ^ 1x3 = 24,000
13,500 x (1 + 0.2114) ^ 3 = 24,000
X = 21.14%
Therefore, the car will depreciate at a rate of 21.14% per year.
in a group of boys the number of arrangments of boys 4 boys is 12 times the number of arrangment of 2 boys the number of boys in the group is
Answer:
4*12*2
Step-by-step explanation:
it will be the right answer
Answer:
There are 6 boys in group.
Step-by-step explanation:
Since we have given that
Number of arrangement of 4 boys = 12 times the number of arrangement of 2 boys.
So, Let the number of boys in the group be 'x'.
So, Number of boys in the group will be
\begin{gathered}x=\frac{12\times 2}{4}\\\\x=\frac{24}{4}\\\\x=6\end{gathered}
x=
4
12×2
x=
4
24
x=6
Hence, there are 6 boys in the group.
hope it helps you a follow would be appreciated
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
t > -25
t < -25
t ≤ -25
t ≥ -25
Answer:
t≥-25
Step-by-step explanation:
this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.
I NEED MAJOR HELP WITH THIS QUESTION
Instriction; using the following image, solve for tbe trigonometry ratios of < D and < F .
Answer:
Kindly check explanation
Step-by-step explanation:
Since the triangle is right angled ; we can solve for x using Pythagoras :
x = hypotenus ; hence ;
x² = opposite² + adjacent²
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17
Using Trigonometry :
Sin D = side opposite D / hypotenus = 8/17
Cos D = side Adjacent D / hypotenus = 15 / 17
Tan D = side opposite D / Adjacent side = 8/15
Sin F = side opposite F / hypotenus = 15/17
Cos F = side Adjacent F / hypotenus = 8 / 17
Tan F = side opposite F / Adjacent side = 15/8
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
please help me with this question.
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
p and q are two numbers.whrite down an expression of. a.) the sum of p and q. b) the product of p and q
The cost function in a computer manufacturing plant is C(x) = 0.28x^2-0.7x+1, where C(x) is the cost per hour in millions of dollars and x is the number of items produced per hour in thousands. Determine the minimum production cost.
9514 1404 393
Answer:
$562,500 per hour
Step-by-step explanation:
The cost will be a minimum where C'(x) = 0.
C'(x) = 0.56x -0.7 = 0
x = 0.7/0.56 = 1.25
The cost at that production point is ...
C(1.25) = (0.28×1.25 -0.7)1.25 +1 = -0.35×1.25 +1 = 0.5625
The minimum production cost is $562,500 per hour for production of 1250 items per hour.
_____
Additional comment
This is different than the minimum cost per item. This level of production gives a per-item cost of $450. The minimum cost per item is $358.30 at a production level of 1890 per hour.
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
9514 1404 393
Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
x -3,4,11,18 y -3,1,5,9
Is the relationship linear, exponential, or neither?
Choose 1 answer:
9514 1404 393
Answer:
linear
Step-by-step explanation:
The points all lie on a straight line. The relationship is linear.
Which of the following functions is graphed below?
20
15
10
-8-84
-2
42
-5
-10
-15
-20
9514 1404 393
Answer:
D.
Step-by-step explanation:
The linear portion of the curve is in the region x ≥ 2. The only function defined that way is the one in choice D.
Please help me thank you!!!
Answer:
B
Step-by-step explanation:
To solve this use a unit circle (see pic)
Go to the 300 degree
Then look at the y coordinate (y coordinate because it's cosine)
Which matches with answer choice B
In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is with a standard deviation of days. Assume the data to be approximately bell-shaped.
Required:
a. Between what two values will approximately 68% of the numbers of days be?
b. Estimate the percentage of customer accounts for which the number of days is between 18 and 46.
c. Estimate the percentage of customer accounts for which the number of days is between 11 and 53.
At the gas station, each liter of gas costs $3 but there's a promotion that for every beverage you purchase you save $0.20 on gas.
What is the product? (–3s + 2t)(4s – t)
Answer:
[tex] - 12 {s}^{2} + 11st - 2 {t}^{2}[/tex]Step-by-step explanation:
(–3s + 2t)(4s – t)
= -3s (4s - t) + 2t(4s - t)
[tex] = - 12 {s}^{2} + 3st + 8st - 2 {t}^{2} [/tex]
[tex] = - 12 {s}^{2} + 11st - 2 {t}^{2} (ans)[/tex]
Answer: -12s^2 + 11st -2t^2
Step-by-step explanation:
= (-3s + 2t)(4s - t)
= -12s^2 + 3st + 8st -2t^2
= -12s^2 + 11st -2t^2
Answer Provided by GauthMath please heart and comment thanks if you like.
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 30 batteries gave a sample variance of 16.3 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
Answer:
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=30[/tex]
Variance [tex]\sigma= 16.8[/tex]
Significance Level [tex]\alpha=0.05[/tex]
[tex]\sigma = 23[/tex]
Genet=rally the Hypothesis are as follows
Null [tex]H_0=\sigma^2=23[/tex]
Alternative [tex]H_a=\sigma^2 \neq 23[/tex]
Generally the equation for Chi distribution t is mathematically given by
t test statistics
[tex]X^2=\frac{(n-1)\sigma}{\sigma^2}[/tex]
[tex]X^2=\frac{(30-1)16.8^2}{23}[/tex]
[tex]X^2=355.86[/tex]
Therefore
Critical Value
[tex]P_{\alpha,df}[/tex]
Where
[tex]df=29[/tex]
[tex]P_{\alpha,df}=16.0471 and 45.7223[/tex]
[tex]X^2=45.7223[/tex]
Hence, we reject H_0 as There is sufficient evidence to show that population variance is not 23
Simplify (1 - sin x)(1 + sin x).
0 1
O cos^2 x
O sin^2 x
O tan^2 x
(2/3)x-1=27/8,find x
Answer:
x = 105/16
Step-by-step explanation:
2/3x - 1 = 27/8
Add 1 to each side
2/3x - 1+1 = 27/8+1
2/3x = 27/8 + 8/8
2/3x = 35/8
Multiply each side by 3/2
3/2 * 2/3x = 35/8 *3/2
x = 105/16
In the context of the Pearson r correlation coefficient, the absolute size of r is the:_____.
a. coefficient that indicates the measurement scale that applies to two variables.
b. direction of the relationship between two variables.
c. strength of the relationship between two variables.
d. curvilinear relationship between two variables.
Answer:
strength of the relationship between two variables.
Step-by-step explanation:
The Pearson r correlation Coefficient used to measure the relationship or association between two variables. The correlation Coefficient, R ranges between - 1 and 1. As it provides information on both the strength and type of the relationship. The type of relationship could be positive or negative.
The absolute size of r measures Tha strength of the relationship as it ignores the sign. As the Pearson r value moves closer to 1, the higher the strength of the relationship.
Whoever gets this problem right with proper work shown will get brainliest
Answer:
100 % or 1
Step-by-step explanation:
There are two dice
Each dice has a possible roll of 1,2,3,4,5,6
The possible sums are 2,3,4,5,6,7,8,9,10,11,12
The probability of getting a sum greater than 1 is 100 % or 1 since the outcomes are all greater than 1
There are 84 students in a speech contest. Yesterday, 1/4 of them gave their speeches. Today, 3/7 of the remaining students gave their speeches. How many students still haven't given their speeches?
Answer:
36
Step-by-step explanation:
Total students un the contest = 84
Number of students who gave their speech yesterday:-
[tex] \frac{1}{4} \: of \: total \\ = \frac{1}{4} \times 84 \\ = 21[/tex]
so 21 students gave their speech yesterday
remaining students = 84 - 21= 63
Number of students who gave their speech today:-
[tex] \frac{3}{7} \: of \: remaining \\ = \frac{3}{7} \times 63 \\ = 27[/tex]
Number of students who have given their speech:-
= 21 + 27
= 48
Number of students who still haven't given their speech :-
= total - 48
= 84 - 48
= 36
If land the domain of the following peicewise function f(x)={x^2 +2 if -6
Answer:
? what is this question asking
Step-by-step explanation:
Salma invested $8000 in a fund for 6 years and was paid simple interest. The total interest that she received on the investment was $1400. As a percentage, what was the annual interest rate of her investment? If necessary, refer to the list of financial formulas.
Answer: I don’t know lol maybe 1460
Step-by-step explanation:
Anyone willing to help on this worksheet?
Answer:
I am pretty sure it's #2 but wait for more ansawers because im not 100% sure.
Step-by-step explanation:
Answer:
Same I think it's B but I'm not entirely sure
Step-by-step explanation:
What is the factored form of the binomial expansion 625x4 – 3,000x3y + 5,400x2y2 – 4,320xy3 + 1,296y4?
(5x – 6y)4
(5x + 6y)4
(25x – 36y)2
(25x + 36y)2
Answer:
(5x – 6y)^4
Step-by-step explanation:
Given
[tex]625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Required
The factored form
Solving (a): (5x – 6y)^4
Expand using pascal triangle;
Exponent 4 is represented as: 1 4 6 4 1. So, we have:
[tex](5x - 6y)^4 = 1 * (5x)^4 + 4 * (5x)^3 * (-6y) + 6 * (5x)^2 * (-6y)^2 + 4 * (5x) * (-6y)^3 + 1 * (-6y)^4[/tex]
Expand:
[tex](5x - 6y)^4 = 1 * 625x^4 + 4 * 125x^3 * (-6y) + 6 * 25x^2 * 36y^2 + 20x * (-216y^3) + 1 * (1296y^4)[/tex]
Remove brackets
[tex](5x - 6y)^4 = 625x^4 - 3000x^3y + 5400x^2y^2 - 4320xy^3 + 1296y^4[/tex]
Hence, (a) is correct
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
9514 1404 393
Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
The side lengths of a triangle are 5,10, and 13. Is this a right Triangle?
No because 5^2 +10^2 is not equavalent to 13^2
by using the pythagoras' theorem
*REVERSE PROPORTION*
9514 1404 393
Answer:
33.3%
Step-by-step explanation:
The selling price of £42 is (1 +40%) times the total purchase price.
1.40 × purchase price = £42
purchase price = £42/1.40 = £30
The total profit is 40% of this, so is ...
£30 × 40% = £12
The purchase price of the skirt is ...
total cost - glove cost = skirt cost = £30 -3 = £27
The profit on the skirt is ...
total profit - glove profit = skirt profit = £12 -100% × £3 = £9
Then the percentage profit on the skirt is ...
skirt profit % = skirt profit / skirt cost × 100% = £9/£27 × 100% = 33.3%
The percentage profit on the cost of the skirt was 33.3%.
