Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
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.In this problem, we have that the values of the parameters are:
N = 10, k = 4, n = 2.
The probability that both are green 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(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333[/tex]
0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.
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Translate the shape A three squares right and one square down.What are the coordinates of the vertices of the image?
If the shape A is translated four squares right and two squares up, the resulting coordinate point will be at (-2, 5), (-2, 2) and (0, 2)
Translation of coordinatesTranslation is a transformation technique of changing the position of an object on the xy plane
Given the coordinates of the vertices (1, 4), (1, 1), (3,1)
If the shape A is translated three squares right and one squares up, the resulting coordinate point will be at (-2, 5), (-2, 2) and (0, 2)
Note that 4 was subtracted from the x-axis and 2 added to the y-coordinates.
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Uv has endpoints at u(4, 6) and v(10, 4). find the midpoint m of uv.
write the coordinates as decimals or integers.
m =
submit
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ U(\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad V(\stackrel{x_2}{10}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 10 +4}{2}~~~ ,~~~ \cfrac{ 4 +6}{2} \right)\implies \left( \cfrac{14}{2}~~,~~\cfrac{10}{2} \right)\implies (7~~,~~5)[/tex]
Can someone say happy birthday to me do it for how every many point this question is gonna give yoouuu
Answer:
Happy birthday <3
Step-by-step explanation:
:)
please help if u know :D
Answer:
B.
Step-by-step explanation:
We can start by dividing 3.5 and 0.75.
3.5/0.75 is 4.67.
Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.
1*4.67 is 4.67.
Determine the value of "a" for which g(h(a)) = 13
Answer:
a = 6
Step-by-step explanation:
g(x) = 5x - 2
h(x) = √(x + 3)
g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2
g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2
5[tex]\sqrt{a+3}[/tex] - 2 = 13
5[tex]\sqrt{a+3}[/tex] = 15
[tex]\sqrt{a+3}[/tex] = 3
( [tex]\sqrt{a+3}[/tex] )² = 3²
a + 3 = 9
a = 6
help pls im being timed
The trigonometric ratios show that the angle FHE is 48.59°.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex](hypothenuse)^2=(leg_1)^2+(leg_2)^2[/tex]. And the main trigonometric ratios are:
[tex]sin(\alpha) =\frac{opposite \;leg }{hypotenuse} \\ \\ cos(\alpha) =\frac{adjacent\;leg }{hypotenuse} \\ \\ tan(\alpha) =\frac{sin(\alpha )}{cos(\alpha )}= \frac{opposite \;leg }{adjacent\;leg } \\ \\[/tex]
It is important to remember that the sum of internal angles for any triangle is 180°.
From the question, it is possible to see 2 right triangles (HGF and FHE).
You can find the hypotenuse of the triangle HGF from the trigonometric ratio: sen Θ
[tex]sin45=\frac{opposite\; leg }{hypotenuse} =\frac{\sqrt8}{hypotenuse}\\ \\ \frac{\sqrt{2} }{2} =\frac{\sqrt{8} }{hypotenuse} \\ \\ \sqrt{2}*hypotenuse=2\sqrt{8} \\ \\ hypotenuse=\frac{2\sqrt{8} }{\sqrt{2}} =2\sqrt{4} =2*2=4[/tex]
The hypotenuse of triangle HGF is one of legs for the triangle FHE. The, you can find the angle FHE from the trigonometric ratio: tan β. Thus,
[tex]sin \beta =\frac{opposite\; leg }{adjacent\; leg} =\frac{3}{4}\\ \\ sin \beta=\frac{3}{4}=0.84806\\ \\ arcsin\beta =48.59^{\circ \:}[/tex]
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c) What is the equation of line a? (2 points)
The line a is an illustration of a proportional linear equation, and the equation of line a is y = 1.4x
How to determine the equation of the data?The line a passes through the following points:
(x,y) = (0,0) and (1.3, 1.82(
The above means that line a is a proportional linear equation
The constant of proportionality (k) is calculated using:
k = y/x
Using the values on the table, we have:
k = 1.82/1.3
Divide
k = 1.4
Substitute k = 1.4 in k = y/x
y/x = 1.4
Multiply both sides by 1.4
y = 1.4x
Hence, the equation of the line a is y = 1.4x
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What is the value of n?
38°
Answer: 247 the Answer
A map of a public park shows a circular pond. There is a bridge along a diameter of the pond that is 0.25 mi long. You walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. How much farther does your friend walk? Round your answer to the nearest hundredth. Use 3.14 for π.
Your friend walks about
miles farther than you.
The distance further the friend walked is 0.41 miles.
How much farther did the friend walk?The distance the friend walked can be determined by calculating the circumference of a semicircle.
Circumference of a semicircle = πr + 2r
r = 0.25 / 2 = 0.125mi
3.14 x 0.125 + 0.25 = 0.66 mi
Difference in the distance = 0.66 - 0.25 = 0.41 miles
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3. A farmer needs to dig a rectangular pit that is 5m long, 4m wide and 6m deep. How many cubic meters of soil must he removed?
156 m3
120 m3
231 m3
345 m3
wrong answer/nonsense = report
Answer:
120 m3
Step-by-step explanation:
The volume of a rectangular prism is l*w*h. plug in the 3 measurements and get 5*4*6 = 120
Is b=2a+10 equal to 4a+2b=10
Answer:
Yes
Step-by-step explanation:
ch statement is true about the graphs of the two lines y=-6 and x =
dx= -1/?
The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope that is
ndefined, and the graph of x = is a vertical line with a slope of 0.
The lines are perpendicular to each other because the graph of y=-6 is a vertical line with a slope that is
ndefined, and the graph of x = is a horizontal line with a slope of 0.
The lines are perpendicular to each other because the graph of y = -6 is a vertical line with a slope of 0, and th
aph of x = is a horizontal line with a slope that is undefined.
he lines are perpendicular to each other because the graph of y=-6 is a horizontal line with a slope of 0, and
e graph of x = is a vertical line with a slope that is undefined.
Answer:
IT'S A !
Step-by-step explanation:
Took the quiz on edge 2022 .
the correct statement is:
"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Find correct statement is true about the graphs of the two lines y=-6 and x = dx
Since, horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope.
Therefore, the correct statement is:
"The lines are perpendicular to each other because the graph of y = -6 is a horizontal line with a slope of 0, and the graph of x = dx is a vertical line with an undefined slope."
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Your mortgage is a 30-year fixed at 8% on $150,000. you are considering refinancing at 3.5% fixed for 30 years. the bank charges you 1.5% of your debt in closing fees. approximately how long will it take you to recoup the closing fees from the reduced loan payment amount?
Zane works for a catering company and is bringing a total of 160 servings of food to a conference. If 40 people come to the conference, there would be enough for each person to have 4 servings of food. If 80 people come to the conference, there would be enough for each person to have 2 servings of food.
Does this situation represent an indirect variation? If so, what are the independent and dependent variables?
A.
No, this is not an indirect variation. The product of the variables is not constant.
B.
Yes, this is an indirect variation. The number of servings per person is the independent variable, and the number of people is the dependent variable.
C.
Yes, this is an indirect variation. The number of people is the independent variable, and the number of servings per person is the dependent variable.
D.
Yes, this is an indirect variation. However, because the number of people is undetermined, the variables cannot be determined.
Answer:
D
Step-by-step explanation:
Since we don't know how many people we don't know how many servings would be consumed. therefore this is an indirect variation
Find an algebraic expression equivalent to 3 over 2 left paren 6 x squared minus two over 3 x right paren
The equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x
How to determine the equivalent expression?The expression is given as:
3/2(6x^2 - 2/3x)
Open the bracket
3/2*6x^2 - 3/2*2/3x
Evaluate the product
9x^2 - x
Hence, the equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x
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10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).
determine the area of abcd.
Answer: 80
Step-by-step explanation:
We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.
By the distance formula,
[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]
So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]
What equation has the same solution as 3x-5=5x + ll
Answer: -5=2x+11
Step-by-step explanation:
3x-5=5x+11
subtract 3x to both sides
3x-5 - 3x =5x+11 - 3x
simplify
-5 = 2x +11
answer is -5=2x+11
TIME SENSITIVE!!! What will the first row of this multiplication be? (first image is the problem, second is the options)
Answer:
the first option
Step-by-step explanation:
hope the answer helps...
Ayuda porfa doy corona
Answer:
goto chrome and search spankbang
Step-by-step explanation:
thet the answer
How to convert no. Ito persentage
To turn a number (either an integer or a decimal) into a percent, simply multiply by 100. That is the same as moving the decimal point two places to the right. You may need to round to the desired precision. Add a percent (%) sign.
What is percentage? :A percentage is a way of expressing one number as a portion or share of a whole number, and percentages are always based on their relation to 100, which represents the whole number or object.For example, 75% is the same as 75 out of 100. Any percentage lower than 100 is just part of the whole or total.Definition of a number : A number is an arithmetic value used for representing the quantity and used in making calculations.What is Maths? : MATH stands for "Mathematics" in its entire form. Mathematics is a branch of science that studies the logic of form, quantity, and arrangement.Learn more about Mathematics, refer:
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Please help, thanks!!!
Problem 4
Draw any right triangle you want. Afterward, draw a perpendicular segment that goes from the 90 degree angle to the hypotenuse. Call this new segment the altitude. It might help to have the hypotenuse laying flat or horizontal.
The length of this altitude can be found using the geometric mean formula. Search out "geometric mean for triangles" (or similar) and you should get a diagram that visually summarizes what is going on. I've provided a screenshot of an example using GeoGebra. See below.
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Problem 5
The two special types of right triangles are: the 45-45-90 triangle and the 30-60-90 triangle.
If x is the leg length of the first triangle type mentioned, then [tex]x\sqrt{2}[/tex] is the hypotenuse. We can confirm this using the pythagorean theorem. Recall that the legs of any 45-45-90 triangle are the same, meaning we have an isosceles triangle.
For the second type of triangle, the short leg x leads to the hypotenuse 2x and long leg [tex]x\sqrt{3}[/tex]
==========================================================
Problem 6
If you know say the opposite and adjacent sides of a right triangle, then you can use the tangent ratio because tan = opposite/adjacent.
Sine is used for opposite/hypotenuse, while cosine is used for adjacent/hypotenuse. Those are the main 3 trig functions. Technically there are 3 more, but they are just reciprocals of the previous three.
==========================================================
Problem 7
Use inverse trig functions to find the missing angles if you know the sides. The inverse trig functions have an exponent of -1.
For instance, let's say the triangle has an opposite side of 10 and hypotenuse of 15
The reference angle would be...
[tex]\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(x) = \frac{10}{15}\\\\x = \sin^{-1}\left(\frac{10}{15}\right)\\\\x \approx 41.81^{\circ}\\\\[/tex]
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Problem 8
Imagine looking completely horizontal at the horizon. The angle in which you are currently looking is 0 degrees. If you look upward, say 10 degrees, then the angle of elevation is 10 degrees. Looking down means we have an angle of depression. These two types of angles help us determine various distances and lengths.
Use the alternate interior angle theorem to help show that angles of depression are congruent to angles of elevation. It will depend on context which type of angle is more useful.
Find the midpoint of A and B where A has coordinates (8, 2)
and B has coordinates (3,8).
Answer:
(5.5, 5 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then
midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )
What is the average rate of change for this function for the interval from x=3 to x=5
The average rate of change is 12 the interval from x=3 to x=5.
How to find the average rate of change of something?Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
Given:
Interval; x = 3 to x = 5
We can represent these by
[tex]x_1 = 3\\x_2 = 5[/tex]
The corresponding y values are as follows
When x = 3, y = 8
When x = 5, y = 32
This will also be represented
[tex]y_1 = 8\\y_2 = 32[/tex]
The average rate of change is then calculated as follows
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\\\m = \dfrac{32 -8}{5-3}\\\\m = \dfrac{24}{2}\\\\m = 12[/tex]
Hence, the average rate of change is 12.
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11/12 - 7/9
5/36
5/72
25/36
25/72
c
Step-by-step explanation:
What is the common ratio for this geometric sequence?
16, 8, 4, 2, ...
Which shows the equation of the line containing the point (4, 6) and having a slope of 4 in slope-intercept form?

4y=x−28
y=4x−10
y=−4x+10
y=−52x+4
Answer:
y=4x-10
Step-by-step explanation:
See attached image
solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb
Answer:
a = z/mb
Step-by-step explanation:
Given:
[tex]\displaystyle \large{z=mab}[/tex]
To solve for a, divide both sides by the variables mb to isolate a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]
Simplify the expression and we finally have solved for a-term.
[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]
Therefore, the answer to this question is a = z/mb.
Please let me know if you have any questions regarding my answer or explanation!
Whic
the following is an angle? (3 points
Figure A has two rays connected at a vertex, Figure B is a line with one endpoint and the other end has an arrow, Figure C is a line with two endpoints, and Figure D is a line with an arrow at each end
Figure A
Figure B
Figure C
Figure D
Figure A which has two rays connected at a vertex is an angle in this scenario.
What is an Angle?This is formed when two rays share a common endpoint with there being different types of angles.
The common endpoint shared forms a vertex which is why Figure A was chosen as the most appropriate choice.
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A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?
Help me please I dont know what the answer is here...
If you can, please write the steps so i can understand better next time.
For this problem, let's think of this shape as a rectangle and a triangle put together. We'll calculate the area of each shape and add them together to get the total area.
For the rectangle, the equation is b*h. Here the base = 7 cm and the h = 4cm
For the triangle, the equation is 1/2 * (b*h). Here the base is a little tricky to find. We know the total length is 12cm and the rectangle length was 7cm. So 12-7= 5cm, which is the base of the triangle. The height would be the same (4cm).
Once you calculate those two areas and add them up, you'll have the total area of this shape.