Answers
Answer:
2 a. 210 ways
b. 50 ways
c. 28 ways
d. 0.205
4 a. 1716 ways
Step-by-step explanation:
2. a. The number of ways, [tex]n_w[/tex] of selecting without restriction is given as follows;
[tex]\dbinom{10}{4}[/tex] = 10!/(4!(10 - 4)!) = 210
b. The number of ways of selecting 3 boys from 5 is 5!/(3!(5 - 3)!) = 10 ways
The number of ways of selecting the remaining 1 girl from 5 = 5!/(1!(5 - 1)!) = 5 ways
The number of ways of the selection where there must be three boys = 5×10 = 50 ways
c. Given that Maggie and Marley must be chosen, each of whom can be chosen only one way, we have;
Selection of 2 from 8 gives;
8!/(2!(8 - 2)!) = 28
Therefore, the number of ways of the selection where there must be Maggie and Marley is 28 × 1 × 1 = 28 ways
d. The probability of no boys is given by the relation;
P(k success from n trials) = [tex]_nC_r \cdot p^k \cdot (1 - p)^{n-k}[/tex]
Where n = number of persons = 10
k = Number of person in the group = 4
p = Probability of success of girls = 1/2
Therefore, we have for no boys;
[tex]\dbinom{10}{4} \times \left (\dfrac{1}{2} \right )^4\times \left (1-\dfrac{1}{2} \right )^{10-4} = \dfrac{210}{16 \times 64} = \dfrac{105}{512} = 0.205[/tex]
4a) The number of ways of selecting 9 softball players from 15 where Rylea and Emily must be included;
Given that Rylea and Emily are already selected, we have;
The number of ways of selecting 7 softball players from 13 given as follows;
13!/(7!(13 - 7)!) = 1716 ways
Given that Rylea and Emily can both be selected in only one way, the total number of ways = 1×1×1716 = 1716 ways
Related Questions
The area of the parallelogram is____________________
the area of the quadrilateral.
What goes in the blank?
Answers
Answer:
double
Step-by-step explanation:
126,720 inche are equal to how many miles ?
Answers
Answer:
The answer is
2 milesStep-by-step explanation:
63, 360 inches = 1 mile
126,720 = 126,720 / 63 , 360 × 1 mile
Which is equal to
2 miles
Hope this helps you
An amusement park has 20 rides. Ethan has enough time to ride 3 rides before the park closes. How many different ways could Ethan pick to ride the 3 rides? PLZZZZ HELLPPPP MEEEE
Answers
Answer:
20*19*18 = 6840
UNLESS...............
he is allowed to ride the same ride again , over and over....
then it is 20 x 20 x 20 = 8000
Step-by-step explanation:
If a space of 18 inches is allowed for each person, how many persons can be seated in a row of bleacher seats 90 feet long?
Answers
Answer:
31 people
Step-by-step explanation:
think of it like a line,
first person at zero then add 3 feet per person so...
1 + 90/3 = 31 people
kinda funny that the problem isnt accounting for the size of the people
I NEED HELP!!
The chef at a school cafeteria asked 100 male and 100 female students
whether they like peas. 58 of the males said they like peas. 36 of the females
said they dislike peas. Which two-way table correctly shows these results?
Answers
Answer:
d
Step-by-step explanation:
The table shows the result of the statement given below.
What is data table?A data table is a range of cells in which you can change values in some of the cells and come up with different answers to a problem.
here, we have,
Given that,
the chef at a school cafeteria asked 100 male and 100 female students whether they like peas.
42 of the males said they like peas. 64 of the females said they dislike peas.
The number of males who like peas=42 and the number of males who dislikes peas=58.
The number of females who like peas=36 and the number of females who dislikes peas=64.
The table shows the result of the statement given below.
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Solve the following system of equations: x − 2y = 14 x + 3y = 9 (1, 12) (−1, −12) (12, −1) (12, 1)
Answers
Answer:
work is shown and pictured
answer is c
Answer:
the correct answer among the choices is C
Step-by-step explanation:
How can (4x⁵/2x²)³ be solved in 2 different ways
Answers
We assume that we need to simplify the expression in two different ways.
Answer:
One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.
Second way: Simplify the terms inside parentheses, and then raise the result to the third power.
The result of both ways is the same: [tex] \\8x^{9}[/tex]
Step-by-step explanation:
One way
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]
[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]
[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]
[tex] \\8x^{9}[/tex]
This is the first simplification.
Second way
Simplify the terms inside parentheses, and then raise the result to the third power.
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]
[tex] \\ (2*x^{5-2})^{3}[/tex]
[tex] \\ (2*x^{3})^{3}[/tex]
[tex] \\ (2^{3}*x^{3*3})[/tex]
[tex] \\ (8*x^{9})[/tex]
or [tex] \\ 8x^{9}[/tex].
What is the leading coefficient of a cubic polynomial that has a value of −208 when x=1, and has zeros of 5, 5i, and −5i?
Answers
Answer:
2
Step-by-step explanation:
We already have the zeros, so we can write the cubic polynomial in this general form:
[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]
Where:
[tex]x_1 = 5[/tex]
[tex]x_2 = 5i[/tex]
[tex]x_3 = -5i[/tex]
So we have that:
[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]
[tex]y = a(x -5)(x^2 + 25)[/tex]
To find the value of the leading coefficient 'a', we can use the point (1, -208) given:
[tex]-208 = a(1 -5)(1 + 25)[/tex]
[tex]-208 = a(-4)(26)[/tex]
[tex]a = -208 / (-104) = 2[/tex]
So the leading coefficient is 2.
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 x , a = −2
Answers
Answer:
4x
Step-by-step explanation:
The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.
For the given function, f(x) = 4x and a = -2
So, f(a) = f(-2) = 4(-2) = -8
f'(a) = f'(-2) = 4
All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0
Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have
f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...
= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...
= -8 + 4(x + 2) + 0 + 0
= -8 + 4x + 8
= 4x
Explain in your own words why a polynomial can’t be a quadratic if a= 0?
Answers
If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.
So [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.
As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).
In triangle ABC, points N and M lie on sides AB and AC, respectively.Given AM = AN = BM = NC = BC, find m∠BAC.
Answers
Answer:
36°
Step-by-step explanation:
Please refer to the attached figure.
Triangles ANC, AMB, BCN, CBM are all isosceles by virtue of the given congruences. By symmetry, we also claim that ΔABC is isosceles (AB≅AC).
We aren't sure how their internal angles relate, but we can write a couple of equations.
Let x = m∠BAC, y = m∠BCN.
∠NCA = ∠NAC = ∠MBA = ∠MAB = x
∠BCM = ∠BMC = x +y
∠BMC = ∠MBA +∠MAB = 2x
So, we have ...
∠BMC = x +y = 2x ⇒ y = x
And the sum of angles around ΔABC is ...
x +(2x) +(2x) = 180°
x = 180°/5 = 36°
The measure of angle BAC is 36°.
Press the attachment it’s a picture of the question. PLEASE HELP ME MY LAST DAY IS TODAY AND I NEED HELP! I WILL GIVE YOU BRAINLIEST
Answers
Answer:
210 vegetable in 7 rows
Step-by-step explanation:
first step is to figure out how many vegetable can she grow in one row:
convert feet to inches : 6.25 feet* 12 inches=75 inches
(75/2 1/2) (2 /12 is 3/2 or 2.5)
(75/2.5)= 30 vegetable in one row
in 7 rows : 30*7=210 vegetable in 7 rows
whats the square root of 83
Answers
Answer:
9.110434
Step-by-step explanation:
√83 ≈ 9.110434
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees based on the region of the country the warehouse is located. She randomly selects 35 employees who work in warehouses on the East Coast (Group 1) and 35 employees who work in warehouses in the Midwest (Group 2) and records the number of parts shipped out from each for a week. She finds that East Coast group ships an average of 1299 parts and knows the population standard deviation to be 350. The Midwest group ships an average of 1456 parts and knows the population standard deviation to be 297.Using a 0.01 level of significance, test if there is a difference in productivity level. What is the p-value? (Round to four decimal places) p-value =
Answers
Answer:
The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).
p-value = 0.0473
Step-by-step explanation:
To perform this test we first define the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).
Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).
The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁
The null hypothesis is represented as
H₀: μ = 0 or μ₂ = μ₁
The alternative hypothesis is represented as
Hₐ: μ ≠ 0 or μ₂ ≠ μ₁
So, to perform this test, we need to compute the test statistic
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = average productivity level of the East Coast group = 1299 parts shipped
n₁ = sample size of East Coast group surveyed = 35
s₁ = standard deviation of the East Coast group sampled = 350
μ₂ = average productivity level of the Midwest group = 1456 parts shipped
n₂ = sample size of Midwest group surveyed = 35
s₂ = standard deviation of the Midwest group sampled = 297
σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59
We will use the t-distribution as no information on population standard deviation is provided
t = (1456 - 1299) ÷ 77.59
= 2.02
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68
Significance level = 0.01
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = 0.047326
0.047326 > 0.01
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Hope this Helps!!!
I NEED HELP PLEASE, THANKS! :)
Answers
Answer:
Option B
Step-by-step explanation:
Rewrite each of the options given to us in standard form. That way we can identify the parabola properties of each -
[tex]Standard Form = 4\cdot \:2\left(y-\left(-9\right)\right)=\left(x-8\right)^2,\\\left(h,\:k\right)=\left(8,\:-9\right),\:p=2\\-----------------\\Standard Form = 4\cdot \:2\left(y-8\right)=\left(x-\left(-9\right)\right)^2,\\\left(h,\:k\right)=\left(-9,\:8\right),\:p=2[/tex]
Right away you can tell that the second option is correct. The vertex is known to be ( - 9, 8 ) and extends at an exponential rate of 2. This is our solution, Option b!
After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of
Answers
Answer:
Every decade, the number of species decays by a factor of 0.0834.
Step-by-step explanation:
Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:
[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]
Every decade, the number of species decays by a factor of 0.0834.
Answer:
28% subtracted
Step-by-step explanation:
khan
Which of these numbers is prime? 13, 30, 49, 65, 87
Answers
Explanation: 13 = prime
30 = composite
49 = composite
65 = composite
87 = composite
Answer:
13
Step-by-step explanation:
factors of 13 : 1, 13
factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
factors of 49: 1, 7, 49
factors of 65: 1, 5, 13, 65
factors of 87: 1, 3, 29, 87
Consider the y-intercepts of the functions. f(x)= 1/5 [x-15] g(x)= (x-2)^2 The y-coordinate of the greatest y-intercept is..
Answers
Answer:
4
Step-by-step explanation:
I used Desmos
We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).
How to find the y-intercepts?For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.
So, for the first function:
[tex]f(x) = (1/5)*|x - 15|[/tex]
The y-intercept is:
[tex]f(0) = (1/5)*|0 - 15| = 15/5 = 3[/tex]
For the second function:
[tex]g(x) = (x - 2)^2[/tex]
The y-intercept is:
[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]
Then we can see that g(x) has a greater y-intercept than f(x).
If you want to learn more about y-intercepts:
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The sugar content of the syrup in canned peaches is normally distributed. A random sample of n=25 cans yields a sample standard deviation of s=6.9 milligrams. Construct a 99% one-sided lower confidence bound for the population variance.
Answers
Answer:
99% one-sided lower confidence bound = 26.77
Step-by-step explanation:
We have to calculate a 99% one-sided lower confidence bound for the population variance.
The sample size is n=25.
The degrees of freedom are then:
[tex]df=n-1=25-1=24[/tex]
The critical value of the chi-square for this confidence bound is:
[tex]\chi^2_{0.01, \,24}=42.98[/tex]
Then, the lower confidence bound can be calculated as:
[tex]LB=\dfrac{(n-1)s^2}{\chi^2_{0.01,24}}=\dfrac{24\cdot(6.9)^2}{42.98}=\dfrac{1,142.64}{42.68}=26.77[/tex]
Exponential properties
Answers
Answer:
none of the above
Step-by-step explanation:
f(x) = 5 * 2^x
Let x = 3
f(3) = 5 * 2^3
= 5 * 8
= 40
Prove that 2x3 + 3x² + x is always divisible by 6 if x is an integer.
PLEASE I NEED THIS ANSWERED ASAP.
USE PROOF BY EXHAUSTION.
Answers
Answer: see proof below
Step-by-step explanation:
Proof by exhaustion means to input several numbers that satisfy the claim and if they all prove to be true then you have proven the claim.
Claim: (2x³ + 3x² + x)/(6) ∈ Z (integer)
Let's choose x = {1, 2, 3, 4)
Case 1: x = 1
2(1)³ + 3(1)² + (1) = 12
12/6 = 2
2 ∈ Z [tex]\checkmark[/tex]
Case 2: x = 2
2(2)³ + 3(2)² + (2) = 30
30/6 = 5
5 ∈ Z [tex]\checkmark[/tex]
Case 3: x = 3
2(3)³ + 3(3)² + (3) = 84
84/6 = 14
14 ∈ Z [tex]\checkmark[/tex]
Case 4: x = 4
2(4)³ + 3(4)² + (4) = 180
180/6 = 30
30 ∈ Z [tex]\checkmark[/tex]
Since each case was shown to be true we have proven the claim is true by exhaustion.
When 6r − 17r = -66 is solved, the result is: A. 6 B. -6 C. -11 D. 11
Answers
Answer:
A
Step-by-step explanation:
6r - 17r = -66
Subtract like terms.
-11r = -66
Divide both sides by -11.
r = -66/-11
r = 6
Answer:
6
Step-by-step explanation:
6r-17r=-66
-11r=-66
r=6
Finding missing angles
Answers
Answer:
C. 105° = (5x - 70)°
Step-by-step explanation:
Vertically opposite angles are equal in size.
105° = (5x - 70)°
The correct answer is choice C.
Meant to put the letter C
solve both equations 8x + 7y = 39 4x – 14y = –68
Answers
Answer:
x=1/2, y=5
Step-by-step explanation:
This can be solved using substitution!
Hope this helped!
Answer:
{x,y}={ 1/2, 5)
Step-by-step explanation:
[1] 8x + 7y = 39
[2] 4x - 14y = -68
Solve equation [2] for the variable x
[2] 4x = 14y - 68
[2] x = 7y/2 - 17
// Plug this in for variable x in equation [1]
[1] 8•(7y/2-17) + 7y = 39
[1] 35y = 175
// Solve equation [1] for the variable y
[1] 35y = 175
[1] y = 5
// By now we know this much :
x = 7y/2-17
y = 5
// Use the y value to solve for x
x = (7/2)(5)-17 = 1/2
Find the gradient of the line 2y = 8x + 1 =
. Find the y-intercept of the line 4y + 8x = -8 =
Does the point (1 ,12) lie on the line y = 3x + 8 ? =
Does the point (-2 ,10) lie on the line y = 14 + 2x ? =
Answers
Answer:
56 46 38 2 12
Step-by-step explanation:
Which of the following numbers would be used to get the variable by itself in the equation 7x = 12?
Answers
Answer:
Divide by 7 or multiply by 1/7
Step-by-step explanation:
7x = 12
Divide each side by 7
7x/7 = 12/7
x = 12/7
We could also multiply each side by 1/7
7x * 1/7 = 12*1/7
x = 12/7
A soccer player has made 3 of her last 10 field goals, which is a field goal percentage of 30%. How many more consecutive field goals would she need to make to raise her field goal percentage to 50%?
Answers
Answer:
x = 4
Step-by-step explanation:
What is the equation of a line whose slope is 2 and passes through the point (-6,9)
Answers
Answer:
y = 2x + 21
Step-by-step explanation:
Step 1: Write out known variables
y = mx + b
m = 2
y = 2x + b
Step 2: Find b
9 = 2(-6) + b
9 = -12 + b
b = 21
Step 3: Rewrite linear equation
y = 2x + 21
Translate into an algebraic expressions: b is decreased by 40% and decreased again by 40% . What is the result ?
Answers
Answer:
Result = 9b/25 or 36b/100
Step-by-step explanation:
The number is b
step 1
b is decreased by 40%
value of 40% of b = 40/100 *b = 4b/10
New value after this change = b - 40% decreased value of b = b -4b/10
= (10b-4b)/10 = 6b/10
Step 2 The new value obtained is again decreased by 40%
value of 40% number found in step 1 = 40% of value found in step 1
value of 40% number found in step 1 = 40/100 * 6b/10 = 24b/100
This value (24b/100) is subtracted from value found in step 1(6b/10) as given that value obtained is decreased by 40%
new value found after 40% decrease = 6b/10 - 24b/100
new value found after 40% decrease = 60b/100 - 24b/100= 36b/100
new value found after 40% decrease = 36b/100 = 9b/25
Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25
Which expression has a positive value?
A - Negative 4 + (negative 5) (negative 6) divided by (negative 3)
B - 8 Left-bracket 10 divided by (2) (negative 2) Right-bracket
C - 3 (negative 64 divided by 8) + 25
D - Negative 2 (negative 5) (negative 3) divided by 10
Answers
Answer:
C - 3 (negative 64 divided by 8) + 25 =1
Step-by-step explanation:
Answer:
C is correct answer
Step-by-step explanation: