Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.2 = 20%.
b) 0.5539 = 55.39%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
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.Researching this problem on the internet, it is found that the council has 15 members, of which 7 are Democrats and 8 are Republicans.
Item a:
The parameters are:
N = 15, n = 2, k = 7.
The probability is P(X = 2), hence:
[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 = 2) = h(2,15,2,7) = \frac{C_{7,2}C_{8,0}}{C_{15,2}} = 0.2[/tex]
Item b:
At most one Democrat, with n = 3, hence:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which:
[tex]P(X = 0) = h(0,15,3,7) = \frac{C_{3,0}C_{8,3}}{C_{15,3}} = 0.1231[/tex]
[tex]P(X = 1) = h(1,15,3,7) = \frac{C_{3,1}C_{8,2}}{C_{15,3}} = 0.4308[/tex]
Then:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1231 + 0.4308 = 0.5539[/tex]
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Simplify. x^2+5x-/14 x²+8x+7
please send a picture of it
the equation seems a lil bit complicated
Follow the steps to find the
area of the shaded region.
Now use the formula below
to find the area of the
triangle.
Triangle Area = bh
h = 6.2172 cm
Triangle Area = [?] cm²
Round to four decimal places.
129
8 cm
The area of the triangle will be 14.9835cm².
How fo you find the area of a triangle?Your information is incomplete and the complete question wasn't found. An overview will be given.
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.
Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.
In this case, let the assumed base be 4.82cm and the height is given as 6.2172cm.
The area will be:
= 1/2 × 4.82 × 6.2172
= 14.9835cm²
In conclusion, the area is 14.9835cm².
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he graphs of y = 3x and y = 3x are shown below.
In general, how does the growth of y = 3x compare to the growth of y = 3x?
The function y = 3x is growing slower than y = 3x.
The function y = 3x is growing faster than y = 3x.
The functions y = 3x and y = 3x are growing at the same rate.
The function y = 3x is growing slower than y = 3x.
The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.
Which answer choice correctly compares the growth of the graphs?The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.
Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.
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I need helping solving this :)
Answer: answer is B
Step-by-step explanation:
use Pythagorean theorem to find other side. And sine is opposite side over hypotenuse.
Geometry question please help!
Answer:
4
Step-by-step explanation:
Since,
The width of the Longer gear is 7, and the smaller gear has a width of 3..
7-3 = 4
Hope it helps...
Marking me as Brainliest would help me... :(
Suppose you pay back $575 on a $525 loan you had for 75 days. What was your simple annual interest rate? State your result to the nearest hundredth of a percent.
The simple annual interest rate for the $ 525 loan is equal to 46.35 %.
What is the interest rate behind a pay back?
In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:
575 = 525 · (1 + r/100)
50 = 525 · r /100
5000 = 525 · r
r = 9.524
The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:
r' = 9.524 × 365/75
r' = 46.350
The simple annual interest rate for the $ 525 loan is equal to 46.35 %.
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Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
NEXT QUESTION
ASK FOR HELP
The expression that would be simplified to be a multiplicative identity is 2^0
How to determine the expression that would be simplified to be a multiplicative identity?The complete question is added as an attachment
Multiplicative identities are represented as:
a * 1 = a
This means that the definition of multiplicative identities is the product of a number and 1
From the list of options, we have
2^0
When the exponent of a non-zero number is 0, the result is 1.
This means that
2^0 = 1
Hence, the expression that would be simplified to be a multiplicative identity is 2^0
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Please Help Brainliest
Using the z-distribution, the p-value would be of:
b) 0.0086.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, equivalent to a subtraction of 0, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, we test if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex].[tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex].For the distribution of differences, it is given by:
[tex]\overline{x} = \mu_D - \mu_C = 12 - 14 = -2[/tex].[tex]s = \sqrt{s_D^2 + s_C^2} = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
z = -2/0.76
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
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HELPP WILL GIVE BRAINLIEST
which graph represents the function f(x) = sqrt(x) + 3
Answer:
the real answer is 2 I hope that
What is the product?
2
12 64
78 30
6
32
78 30
(050
69
78 30
899
32
39 15
66 8
64
38 30
Answer:
the product is 1.32057606543E32
what is 73 division 84,649
73 division 84, 649 would give 8. 64 × 10^-4
How to determine the valueIn order to determine the value of the division, we have
= [tex]\frac{73}{84649}[/tex]
Using the calculator, put the values in
We would have
= 8. 64 × 10^-4
Thus, 73 division 84, 649 would give 8. 64 × 10^-4
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Differentiate between different types of plane with example
Answer:
The three planes of motion are the sagittal, coronal (or frontal) and transverse planes.
Sagittal Plane: Cuts the body into left and right halves. Forward and backward movements.
Coronal (or Frontal Plane): Cuts the body into front and back halves. ...
Transverse Plane: Cuts the body into top and bottom halves.
Consider the dot plot below. Of the following statements, which two characteristics of this dot plot make the median a better choice than the mean to summarize the center of the distribution?
A dot plot with an axis marked from 0 to 10 at increments of 1 is shown. Plot shows 8 dots at 10, 7 dots at 9, 6 dots at 8, 3 dots at 7, 2 dots at 0 and 6, and 1 dot at 5.
The mean is equal to the median and the data are symmetric.
The peak is equal to the median and the data are skewed.
The data are symmetric and there are outliers.
The data are skewed and there are outliers.
The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.
What Characteristics of a Dot Plot Makes Median a Better Choice?In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.
IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.
Therefore, the answer is: A. The data are skewed and there are outliers.
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A bag contains five yellow tickets numbered one to five. The bag also contains five green tickets numbered one to five. You randomly pick a ticket. It is green or has a number greater than four. Find the probability of this occuring.
The probability of picking a ticket that is green or has a number greater than four is 3/5
How to determine the probability?The given parameters are:
Yellow = 1 - 5
Green = 1 - 5
Total = 10
There are 2 cards whose numbers are greater than 4 i.e. Yellow 5 and Green 5
So, we have:
P(Number greater than 4) = 2/10
There are 5 green cards.
So, we have:
P(Green) = 5/10
Also, 1 green card is numbered greater than 4
So, we have:
P(Green greater than 4) = 1/10
The required probability is:
P = P(Green) + P(Number greater than 4) - P(Green greater than 4)
This gives
P = 5/10 + 2/10 - 1/10
Evaluate
P = 6/10
Simplify
P =3/5
Hence, the probability of picking a ticket that is green or has a number greater than four is 3/5
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he cone below has a radius of 3 inches, a height of 4 inches, and a slant height of 5 inches.
What is the approximate lateral area of the cone? Use 3.14 for π and round to the nearest whole number.
38 in.2
47 in.2
75 in.2
94 in.2
The lateral area of the cone is calculated as: B. 47 in.².
How to Find the Lateral Area of a Cone?Lateral area = πrl
Given the following:
Slant height (l) = 5 inches
Radius (r) = 3 inches.
π = 3.14
Plug in the values
Lateral area = (3.14)(3)(5)
Lateral area ≈ 47 in.²
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What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark
{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}
The domain of the rational function is:
{x ∈ ℝ| x ≠ –2, 2}
What is the domain of the rational function?
Here we have the rational function:
[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]
We want to get the domain of that function. First, we can rewrite the numerator and denominator as:
[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]
[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]
Then we can rewrite the rational function as:
[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]
This can be simplified to:
[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]
Now, the domain will be the set of all real numbers, minus the values of x that generate problems.
In this case, the values:
x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so we conclue that the domain is:
{x ∈ ℝ| x ≠ –2, 2}
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Amy and Vince want to save $7,000 so that they can take a trip to Europe in four years. How much must they save each month to have the money they need if they can get 3% per year, compounded monthly, on their savings?
Answer:
10
9
0
Step-by-step explanation:
you subtract the number of all your answers
Choose the correct simplification of (4x − 3)(3x2 − 4x − 3).
the expression simplified is:
[tex]12x^3 - 25x^2 + 9[/tex]
How to simplify the given expression?
Here we have the expression:
[tex](4x - 3)*(3x^2 - 4x - 3)[/tex]
We just need to distribute the product, we will get:
[tex](4x - 3)*(3x^2 - 4x - 3)\\\\(4x)*(3x^2 - 4x - 3) - 3*(3x^2 - 4x - 3)\\\\12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9[/tex]
Now we just need to group terms with the same exponent of x:
[tex]12x^3 - 16x^2 - 12x - 9x^2 + 12x + 9\\\\12x^3 + (-16 - 9)x^2 + (-12 + 12)x + 9\\\\12x^3 - 25x^2 + 9[/tex]
That is the expression simplified
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Question 7 (1 point) The two tables below show the amount of tip, y, included on a bill charging x dollars. A 2-column table with 3 rows titled Restaurant A. Column 1 is labeled x with entries 10, 20, 30. Column 2 is labeled y with entries 1, 2, 3. A 2-column table with 3 rows titled Restaurant B. Column 1 is labeled x with entries 25, 50, 75. Column 2 is labeled y with entries 5, 10, 15. Which compares the slopes of the lines created by the tables?
The slope of restaurant B is twice that of restaurant A
How to compare the slopes?The tables of values are given as
X(Bill) Y(Tip) X(Bill) Y(Tip)
Rest A 10 1 Rest B 25 5
Rest A 20 2 Rest B 50 10
Rest A 30 3 Rest B 75 15
The slopes are calculated using
Slope = (y2 - y1)/(x2 - x1)
Using the table of values, we have:
Rest A = (2 - 1)/(20 - 10)
Rest A = 0.1
Rest B = (10 - 5)/(50 - 25)
Rest B = 0.2
By comparing the slopes, we have:
Rest B = 2 * Rest A
This implies that the slope of restaurant B is twice that of restaurant A
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Joy wants to invest $3000 in a savings account. Determine the interest rate (simple interest) required for Joy 's investment to double in value in 18 years. Round your answer to the nearest tenth of a percent.
The interest rate needed to double the investment in 18 years is 6%.
What is the interest rate?Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)
Interest rate = interest earned / (amount invested x time )
$3000 / ($3000 x 18) = 6%
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Which parent function is f(x) = x²?
A. The quadratic parent function
B. The linear parent function
C. An exponential parent function
D. The absolute value parent function
Answer:
A
Step-by-step explanation:
It is the quadratic parent function
If two points on a line are A(10, −3) and B(12, 9), the rise is __________, and the run is __________, so the slope of the line is __________.
The rise is the difference in y-coordinates:
y₂ - y₁ = 9 - (-3) = 12The run is the difference in x-coordinates:
x₂ - x₁ = 12 - 10 = 2The slope is the quotient of rise over run:
m = 12/2 = 6========================
If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.
Which of the following terms completes the sentence below?
A sign chart helps you record data about a function's values around its
and
asymptotes.
The terms that completes the sentence are zeros; vertical. Option A
Function of a sign chart
The functions of a sign chart include;
It helps in the record of information about the functions values around its zeros and vertical asymptotesA sign chart indicates the sign of the result any mathematical operation between unknowns.From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.
Thus, the terms that completes the sentence are zeros; vertical. Option A
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Evaluate functions from their graph Problem g(3) =
See attached for the correct answer!
The notation g (3), left parenthesis, 3 refers to the output of the function when the input is x=. If the point (3, b) is on the graph, then g (3) =b.
We should look for the point on the graph whose x- coordinate is 3 is the point )3, 4).
The point on the graph whose x-coordinate is 3 is the point (3,4).
Therefore, g (3) = 4
The value of g(3) is g(3) = 4
How to evaluate the function?The function value is given as:
g(x)
The notation g(3) implies that:
We determine the value of g(x) when x = 3
From the graph, the function has a point at (3,4)
This means that:
When x = 3, g(x) = 4
i.e. g(3) = 4
Hence, the value of g(3) is g(3) = 4
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4x + 4y = 40
2x - 4y = 8
Answer:
x=8 y=2
Step-by-step explanation:
solve for x
1. 4x+4y=40
2. subtract 4y from both sides
3. 4x=40-4y
4. divide both sides by 40
5. [tex]\frac{4x}{4} = \frac{40-4y}{4}[/tex]
6. dividing by four undoes the multiplication by four
7. [tex]x=\frac{40-4y}{4}[/tex]
8. divide 40 - 4y by 4
9. x=10-y
10. use the last equation to solve the rest
Pakistan scored 270 runs and fell short of India's score by 10%. How much did
India score?
Answer:
India score 290 more than pakistan
Step-by-step explanation:
India score 20 more
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: A = JIH
B = GJH
C = GH
D = 300
E = 60
Step-by-step explanation:
A) <JIH is a inscribed angle
B) GJH is a major arc
C) GH is a minor arc
D) m GH = m<GFh = 60
If x^y = z is there any way to find y if you know x and z?
We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
How to solve for y?The expression is given as:
x^y = z
The above expression is an exponential expression.
Start by taking the logarithm of both sides
y log(x) = log(z)
Divide both sides by log(x)
[tex]y = \log_x(z)[/tex]
Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z
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The solving to this question
This is a simple harmonic motion exercise. The proof that the resultant force on the particle, at time t, is -225 Newtons is indicated below.
What is the proof that the resultant force on the particle, at time t, is -225x newtons?Note that we have been given the following:
Mass = 9kg,
Y = 45 N
ζ = 0.4 m
Then, Y/ζ = 45N/0.4m
= 112.5 N/m
Hence, the spring constant =
K = 112. 5N/m
From this point we can resolve the Amplitude (A):
Amplitude is given as:
A = CB - PB
= 0.6 - 0.5
A = 0.1m
I) So because one spring is elongated by x and the other is compressed by x, Hence, the spring force is:
F[tex]_{net}[/tex] = - Kₓ - Kₓ
= - 2Kₓ
= -2 x 112.5 x* X
F[tex]_{net}[/tex] = -225x Newton ..........Lets call this expression 1
From equation 1 above, we know that
Ma = -225x
a = (-225/m) x
⇒ a ∝ - x,
Hence, the motion is is simple harmonic in nature.
The time period, T = 2 π√m/K[tex]_{eq}[/tex]
Where, K[tex]_{eq}[/tex] = 2K
= 2π√(9/225)
= 2π * 3/15
= 2(22/7) * (3/15)
= 1.25714285714; thus
T ≈ 1.26 secs...............lets call this expression 2
What is the speed of the particle when it is 0.05 meters from C?Note that Angular Frequency is = 2π/T
= 2π/1.26
= 4.9866550057
ω = 4.99 rad/s
Since the velocity at any point x from the mean position is given by
V = ω √ (A² - x²); hence
V = 4.99 √[(0.1)² - (0.05)²
V = 4.99 x 0.0866
V = 0.432134
V ≈ 0.432..........Lets call this expression 3
What is the expression of x in terms of t?Along the x-axis, A simple harmonic motion can be depicted as:
x = A sin (ωt + Ф) ..........lets call this expression 4
where, Ф = Phase constant
At t = 0; x = A
A = A sinФ
⇒ SinФ = 1
⇒ Ф = π/2
Expression 4 becomes:
x = A sin (ωt + π/2)
Inserting the values of ω and A, we have
x = 0.1 sin (4.99t + π/2).........Lets call this expression 5a
or x = 0.1 cos (4.99t).......Lets call this expression 5b
Hence,
Sin(π/2 + Ф) = CosФ
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PLSS HELPPPPP ASAPP
Answer:
Step-by-step explanation:
area=length×width
=(2x+3)(3x-5)
Area=6x²-10x+9x-15
=6x²-x-15