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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13)
Medical officials want to determine if birth weights are lower than usual in Southeast Asia. They randomly weigh 100 babies, and they determine that the average birth weight is 6 pounds 8 ounces.
State the variable.
What are the units for the variable?
State the population.
State the sample.
POINTS Out OF
7
What is the individual.
What is the Parameter.
What is the statistic.
See below for the response to each question
The variableThis is the item that is being surveyed.
The surveyed item is birth weights
Hence, the variable is birth weights
The units of the variableFrom the question, we have:
Average birth weight is 6 pounds 8 ounces.
Hence, the units of the variable are pounds and ounces
The populationThis is the total number of babies in Southeast Asia
Hence, the population of interest is the babies in Southeast Asia
The individualThis is the people in the survey
Hence, the individual in the study is the 100 babies that were randomly surveyed
The parameter of interestThis is the value that gives the required information.
Hence, the parameter of interest is the average birth weight
What is the statistic involvedThe statistic is the average
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In the following diagram, line m is parallel to line n and line q intersects the parallel lines at
Answer:
108°
Step-by-step explanation:
We know for a theorem that A = B, so:
4x + 28 = 2x + 68
Isolating the x:
2x = 40
x = 20
Now let's plug in the equation for A:
4(20) + 28 = 108°
Explain how to draw a line segments that measures 2 7/16 inches. d
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches
According to the tables used by insurance companies, a 47-year old woman has a 0.179% chance of passing away during the coming year. An insurance company charges $204 for a life insurance policy that pays a $100,000 death benefit. What is the expected value for the person buying the insurance?
The expected value for the person buying the insurance is -25.
How the expected value is calculated?The expected value is the average gain or loss of an event if the event is repeated a number of times.
Expected value = ∑xP(x)
Calculation:It is given that,
The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179
The death benefit = $100,000 - $204 = $99,796
The loss from living = -204
Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25
Therefore, the expected value for the person buying the insurance is -25.
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Find the area of the triangle with sides 40, 50, and 60.
The area of the triangle is 1000 unit square
What is the area of a triangle?
The area of a triangle is half the base multiplied by the height
The formula is given as;
Area = 1/2 × b × h
From the information given, the base is given as 50 and the height is 40
Area = 1/ 2 × 50 × 40
Area = 1/ 2 × 2000
Area = 1000 unit square
Thus, the area of the triangle is 1000 unit square
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At full price, Melvin would pay 1.679 dollars per liter of gasoline. Using his loyalty card, Melvin only pays 1.439 dollars per liter
He pays $0.24 less when using his loyalty card.
How much less does Melvin pay per liter when using his credit card?
We know that, without the card, he would pay $1.679 dollars per liter of gasoline.
With his card, he would pay $1.439
To find the relation between the two prices, we just need to take the difference between the two values (a difference is a subtraction).
d = $1.679 - $1.439 = $0.24
He pays $0.24 less when using his loyalty card.
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Write the measure of minor arc CE as the sum of the measures of minor arcs.
HELP !! anyone please i need this done in less than in hour JUST ANSWERS WILL DO
Answer:
Step-by-step explanation:
calendario matematico la necesito ya porfa.
The common difference based on the sequence given is 15.
How to illustrate the sequence?It should be noted that the sequence given Isa arithmetic sequence.
The common difference will be the second term minus the first term. This will be:
= 101 - 86
= 15
In conclusion, the difference is 15.
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F(x) = | sin 3x | -3 find the maximum and minimum value
Answer:
-2 and -3
Step-by-step explanation:
The minimum of |sin 3x| is 0 and the max is 1 (since the sine function ranges from -1 to 1)
Therefore, the maximum is 1 - 3 = -2 and the minimum is 0 - 3 = -3.
which integer is closest to the third root of -23
Answer:
The number 23 is prime. Therefore, the cube root of 23 = ∛23 = 2.8439.
Step-by-step explanation:
Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.
In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.
To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.
On comparing, we get a is the coefficient of x², that is, a = -3.
On comparing, we get b is the coefficient of x, that is, b = -5.
On comparing, we get c is the constant term, that is, c = 9.
Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.
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The provided question is incomplete.
The complete question is:
"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.
What are the values a, b, and c in the following quadratic equation?
- 3x² - 5x + 9 = 0
A. a = 5, b = 9, c = 0B. a = 3, b = 5, c = 9C. a = −3, b = −5, c = 9D. a = −5, b = 9, c = 0."What is the center of the circle given the following equation? (x-h)² + (y-k)² = r²
Answer:
on a coordinates plane :
The point of coordinates (h , k) is the center of the circle.
Step-by-step explanation:
by definition the expression:
(x-h)² + (y-k)² = r²
is the equation of the circle (in standard form)
Where r is the radius and (h , k) is the center of the circle.
It is the general equation of a circle
Correct answer:
The general equation of a circle is [tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) represents the location of the circle's center, and r represents the length of its radius. if we take some entities as [tex]h=4,k=-3[/tex] first has the equation of [tex](x - 4)^2 + (y + 3)^2 = 29[/tex]. This means that its center must be located at (4, –3), and its radius is √29.
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A ship leaves port on a bearing of 36.0° and travels 12.1 mi. The ship then turns due east and travels 6.1 mi. How far is the ship from port, and what is its bearing
The bearing angle exists 53.49°.
How to estimate the bearing angle of a ship?A bearing of 36° corresponds to the corresponding angle of
θ = 90 -36 = 54°
The (x, y) values for the position of the ship after achieving its first heading exist:
[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m
[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m
Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore
[tex]x_2[/tex] = 6.1 mi
[tex]y_2[/tex] = 0 mi
To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:
Δx [tex]= x_1+x_2[/tex]
= 7.11 mi + 6.1 mi = 13.21 mi
Δy [tex]=y_1+y_2[/tex]
= 9.78 mi + 0 mi = 9.78 mi
[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]
[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]
= 16.43 mi
The direction of the displacement vector exists given by
tan θ = Δy/Δx
θ = arc tan (Δy/Δx)
= arc tan (9.78/13.21)
= 36.51°
The question requested for the bearing angle, which exists just this angle subtracted from 90°:
90° - 36.51° = 53.49°.
Therefore, the bearing angle exists 53.49°.
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What type of motion transforms the letter “p” into a “b”?
The type of motion which transforms the letter “p” into a “b” is; Reflection.
What type of motion transforms the letter “p” into a “b”?It follows that the task content demands that the type of motion which maps p to b be identified. On this note, it follows that the type of motion in discuss is Reflection. More particularly, a reflection over the horizontal axis most definitely causes this transformation.
Therefore, the motion which transforms the letter “p” into a “b” is; Reflection.
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write an equation in slope -intercept form for the line that passes through the points (8,-3) and has a slope of 3 over 2
Answer:
y = 3/2x -15
Step-by-step explanation:
y = mx + b this is the slope intercept form. We need the slope and the y intercept. The slope (m) has been given (3/2), we just need the b (y-intercept). We will use the point given to find b. The point given is (8,-3). 8 is the x term and -3 is the y term. We will plug them into y = 3/2x + b to solve for b.
y = mx + b
y = (3/2) x + b The slope was given
-3 = (3/2)(8) + b Plugged in the given x and y from the point (8, -3)
-3 = 12 + b I can make 8 into a fraction by putting a 1 under it.
(3/2)(8/1). I can cross cancel to make the number easier to
2 and 8 both share the factor 2 so I will divide both numbers
by 2 and I will now have (3/1)(4/1). 3x4 is 12 and 1x1 is 1, so
12/1 is the same as 12.
-15 = b Subtract both sides by 12. -3-12 is -15
Now that I have the m and the b, I can write the equation in the slope intercept form. y = 3/2 + (-15) or y = 3/2 -15
3
If a product costs $15,000 for the first unit and there is
a 15% discount starting on the second unit, a 30%
discount (from the original price) starting on the 4th
unit, what would be the cost for 7 units?
It would cost $72,000 for 7 units of that product.
The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price. It is simply to say, 'discount' is a percentage of the listed price. A discount is a kind of price deduction in products that is noticed in consumer transactions, where the buyers have proposed a percentage of rebates on various products in order to boost sales. This rebate offered by the seller to buyer is known as a discount.
Original cost of product = $15,000.
For the second product there is a discount of 15%, thus selling price for the second product = $15,000 x 0.85 = $12750
For the fourth product and on there is a discount of 30%, thus selling price for the fourth product and on = $15,000 x 0.70 = $10500.
Thus total price of 7 units = $15,000 + $12750x2 + $10500x3
= $15,000 + $25,500 + $31500
= $72,000
Thus it would cost $72,000 for 7 units of that product.
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What is the complete factorization of the polynomial below?
x³ + 2x² + 4x+8
A. (x-2)(x+ 2i)(x+2i)
B. (x-2)(x+2i)(x-2i)
C. (x+2)(x + 2i)(x+2i)
D. (x+2)(x+2i)(x-2i)
The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).
What is the complete factorisation of the given polynomial; x³ + 2x² + 4x+8?It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.
It follows from observation that one of the zeros of the polynomial expression is at; x = -2.
Consequently, one of the factors of the polynomial in discuss is; (x+2).
x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)
= (x+2)(x+2i)(x-2i)
Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).
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fertilizer you put 2 qts for every 50 gal of water I only want to use 15gal of water how many qts,pts,cups??? do i put
If 36^12-m = 6^2m, what is the value of m?
=
Answer:
The answer to your question is m = 6
Step-by-step explanation:
I hope this helps and have a good day!
Answer:
36^12 - m = 6^2m
6^2(12 - m) = 6^2m
24 - 2m = 2m
24 = 4m
m = 6
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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NO LINKS!!! Please help me with this problem
Answer:
length: 8end points: (-8, 1), (0, 1)Step-by-step explanation:
In the quadratic form ...
(x -h)² = 4p(y -k)
The value 4p is the length of the latus rectum. It also tells the distance between the vertex (h, k) and the focus (h, k+p).
ApplicationThe value of 4p is given as 8. This means p = 8/4 = 2.
The length of the latus rectum is 8.
The end points of the latus rectum have the same y-value as the focus:
y = k +p = -1 +2 = 1
The end points of the latus rectum have x-values that are h±2p.
x = h ± 2p = -4 ± 2·2 = {-8, 0}
The end points of the latus rectum are (-8, 1) and (0, 1).
A single card is drawn from each of two decks of 52 cards. What is the probability of getting a heart from the first deck and then a diamond on the second deck?
a)0.09%
b) 6.25%
c)13%
d)52%
A single card is drawn from each of two decks of 52 cards. The probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.
Probability means possibility.
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
There are 52 cards in a standard deck.
So, the total number of possible outcomes=52
We have to pick a single card from each of decks of 52 cards.
In a deck of 52 cards there are 13 heart cards and 13 diamond cards.
Therefore the probability of getting a heart from the first deck=13/52
And the probability of getting a diamond from the second deck=13/52
Hence the probability of getting a heart from the first deck and then a diamond on the second deck=(13/52)×(13/52)=6.25%
Thus, the probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.
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Answer:
6.25%
Step-by-step explanation:
I got it right on the test.
At the city museum, child admission is $5.60 and adult admission is $9.30. On Sunday, 141 tickets were sold for a total sales of 974.60. How many child tickets were sold that day?
x = child tickets
y = adult tickets
x + y = 141
5.60x + 9.30y = 974.60
y = 141 - x
5.60x + 9.30 ( 141 - x ) = 974.60
5.60x + 1311.3 - 9.30x = 974.60
-3.70x + 1311.3 = 974.60
-3.70x = 974.60 - 1311.3
-3.70x = -336.7
x = 91
91 child tickets were sold that day
If sin(theta)=0.7 what is tan(theta)?
The value of tan theta from the given. expression is 7/√51
Trigonometry identityTrigonometry identity are expressions written in terms of sine, cosine and tangents.
Given the following trigonometry values as shown:
sin(theta)=0.7
Convert the decimal to fractions
sin(theta)= 7/10
According to SOH CAH TOA;
sin theta = opp/hyp
Determine the adjacent
adj = √hyp²-opp²
Substitute the values;
adj = √10²-7²
adj = √100-49
adj = √51
Determine the value of tan theta
tan(theta) = opp/adj
Substitute
tan(theta) = 7/√51
Hence the value of tan theta from the given. expression is 7/√51
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Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1700 fish. Absent constraints, the population would grow by 170% per year.
Answer: 2890
Step-by-step explanation:
a = b x p%
= 1700 x 170%
= 1700 x 1.7
= 2890
the population would be 2890 fish after one year
After flying at an altitude of 500m, a helicopter starts to descend when its ground distance from the landing pad is 11 kilometers. What is the angle of depression for the flight?
Answer:
2.603 degrees
Step-by-step explanation:
This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.
Height = 500
Base = 11,000
The hypotenuse ends up being 11,011.35777
in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!
a map has a scale of 2in: 6mi. if a two twons on a map is 10 in apart then how far apart are the real twons
Answer: 30 miles
Work Shown:
2 in : 6 mi
5*2 in : 5*6 mi
10 in : 30 mi
O. Find the distance between P (10,-7) and Q (7,- 10). Leave your answer in radical
form.
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=
[tex] \sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} } [/tex]
Also, for example the distance between A(a,b) and B(c,d)
is
[tex] \sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} } [/tex]
Answer:
[tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.
Step-by-step explanation:
To find the distance between two points, we can use the Distance Formula.
Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given:
P (10, -7) ⇒ x₁ = 10, y₁ = -7
Q (7, -10) ⇒ x₂ = 7, y₂ = -10
Substitute the given values into the formula and simplify.
[tex]\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}[/tex]
The distance between points P and Q is [tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.
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Create a problem with a quadratic equation that you would solve graphically and solve it.
The solutions to the quadratic problem are x = -1 and x= 4
Solving Quadratic equations graphicallyFrom the question, we are to create a problem with a quadratic equation and solve graphically
Consider the quadratic equation
x² -3x -4 = 0
The graph of the quadratic equation is shown below
We can observe that the graph cuts the x-axis at the point x = -1 and x = 4
Hence, the solutions to the quadratic problem are x = -1 and x= 4
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