Your Turn: In the diagram, AB = 12, BX = 2.5, and DX = 5. Find CD. Show all work. *
Answers
Related Questions
△EFG≅△JKL. What is m∠K?
Answers
Answer:
62
Step-by-step explanation:
4747% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.
Answers
p = 47% = 0.47, the probability that a man considers himself a professional baseball fan.
q = 1 - p = 0.53, the probability that a man does not consider himself a professional baseball fan.
n = 10, the number of men surveyed.
(a) Calculate the probability that exactly 5 of 10 men surveyed consider themselves as professional baseball fans.
P(5 of 10) = ₁₀C₅ p⁵q⁵ = 252*0.47⁵*0.53⁵ = 0.242
Answer: 0.242 or 24.2%
(b) Calculate the probability of at least 6 out of 10.
P(at least 6 of 10)
= ₁₀C₆ p⁶q⁴ + ₁₀C₇ p⁷q³ + ₁₀C₈ p⁸q² + ₁₀C₉ p⁹q + ₁₀C₁₀ p¹⁰ q⁰
= 0.1786 + 0.0905 + 0.0301 + 0.0059 + 0.0
= 0.3057
Answer: 0.3057 or 30.6%
(c) Calculate the probability of less than 4 of 10.
P(less than 4 of 10)
= ₁₀C₁ pq⁹ + ₁₀C₂ p²q⁸ + ₁₀C₃ p³q⁷
= 0.0155 + 0.0619 + 0.1464
= 0.2238
Answer: 0.2238 or 22.4%
The probability of a binomial distribution is given by:
[tex]P(X)=\left(^n_x)p^x(1-p)^{n-x}[/tex]
Part A:
The probability that the number who consider themselves baseball fans is exactly five is given by:
[tex]P(5)=\left(^{10}_{\,5}\right)(0.47)^5(1-0.47)^{10-5} \\ \\ =252(0.022935)(0.041820)=\bold{0.2417}[/tex]
Part B:
The probability that the number who consider themselves baseball fans is at least six is given by:
[tex]P(X\geq6)=P(6)+P(7)+P(8)+P(9)+p(10) \\ \\ =\left(^{10}_{\,6}\right)(0.47)^6(1-0.47)^{10-6}+\left(^{10}_{\,7}\right)(0.47)^7(1-0.47)^{10-7} \\ +\left(^{10}_{\,8}\right)(0.47)^8(1-0.47)^{10-8}+\left(^{10}_{\,9}\right)(0.47)^9(1-0.47)^{10-9} \\ +\left(^{10}_{10}\right)(0.47)^{10}(1-0.47)^{10-10} \\ \\ =210(0.010779)(0.078905)+120(0.005066)(0.148877) \\ +45(0.002381)(0.2809)+10(0.001119)(0.53)+1(0.000526)(1) \\ \\ =0.1786+0.0905+0.0301+0.0059+0.0005=\bold{0.3056}[/tex]
This can be approximated using normal distribution as I will illustrate in part c.
Part C:
The probability that the number who consider themselves baseball fans is less than four is given by:
[tex]P(X\ \textless \ 4)=P(0)+P(1)+P(2)+P(3)[/tex]
We can approximate this using normal distribution by subtracting 0.5 from the least value and adding 0.5 to the greatest value.
This gives [tex]P(0-0.5\ \textless \ X\ \textless \ 3+0.5)=P(-0.5\ \textless \ X\ \textless \ 3.5)[/tex]
The mean of a binomial distribution is given by [tex]\mu=np[/tex], while the standard deviation is given by [tex]\sigma= \sqrt{np(1-p)} [/tex].
Thus,
[tex]\mu=10(0.47)=4.7 \ and \ \sigma=\sqrt{10(0.47)(0.53)}=1.578[/tex]
The probability of a nomal distribution between two values (a, b) is given by:
[tex]P(a\ \textless \ X\ \textless \ b)=P\left( \frac{b-\mu}{\sigma} \right)-P\left( \frac{a-\mu}{\sigma} \right)[/tex]
Thus,
[tex]P(-0.5\ \textless \ X\ \textless \ 3.5)=P\left( \frac{3.5-4.7}{1.578} \right)-P\left( \frac{-0.5-4.7}{1.578} \right) \\ \\ =P(-0.7605)-P(-3.295)=0.2235-0.0005=\bold{0.223}[/tex]
rewrite the standard form equation below into slope-intercept form. x-2y=3 A. y=x+3 By=-3/2x-1/2 C.y=3/2x-1/2 D.y=1/2x-3/2
Answers
[tex]x-2y=3 \ \textgreater \ \mathrm{Subtract\:}x\mathrm{\:from\:both\:sides} \ \textgreater \ x-2y-x=3-x [/tex]
[tex]-2y=3-x \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}-2 \ \textgreater \ \frac{-2y}{-2}=\frac{3}{-2}-\frac{x}{-2}[/tex]
[tex]\frac{-2y}{-2} \ \textgreater \ \mathrm{Apply\:the\:fraction\:rule}:\ \frac{-a}{-b}=\frac{a}{b} \ \textgreater \ \frac{2y}{2}[/tex]
[tex]\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1 \ \textgreater \ y[/tex]
[tex]\frac{3}{-2}-\frac{x}{-2} \ \textgreater \ \mathrm{Apply\:rule}\:\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c} \ \textgreater \ \frac{3-x}{-2} [/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\ \textgreater \ -\frac{-x+3}{2} \ \textgreater \ y = -\frac{3-x}{2}[/tex]
[tex]Therefore... y=\frac{1}{2}x-\frac{3}{2} (Note: m=\frac{1}{2},\:b=-\frac{3}{2}) [/tex]
M is the slope and b is the y intercept.
Hope this helps!
If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 5, what is the equation of the new function?
A. g(x) = (5x)2
B. g(x) = x2
C. g(x) = 5x2
D. g(x) = (x)2
Answers
Answer:
g(x)= (1/5x) ^2
Step-by-step explanation:
Just did the test got a 100.
The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]² so none of the given option are correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
If we streatch a function f(x) horizontally by factor of c then the value of new function g(x) become f(x/c)
By stretching f(x) by 5 it will be
g(x) = f(x/5)
So replace x → x/5
Since,f(x) = x²
So,
g(x) = (x/5)²
Hence "The function f(x) = x² after stretching horizontally by a factor of 5 will be g(x) = [(1/5)x]²".
For more about the function,
brainly.com/question/23712366
#SPJ2
What number gives a result of -5 when 11 is subtracted from the quotient of the number and 6?
Answers
Final answer:
The answer explains how to find a number from an equation involving subtraction and division, providing step-by-step instructions.
Explanation:
To find the number that gives a result of -5 when 11 is subtracted from the quotient of the number and 6, we can create an equation:
Let the number be x.
The equation becomes: x/6 - 11 = -5
Solve for x:
Add 11 to both sides: x/6 = 6
Multiply both sides by 6: x = 36
Therefore, the number is 36.
I thought this was much more easier for you! :)
Answers
The base of the exponential is 12 which is also the base of the log as well. The only answer choice that has this is choice B.
======================================================================
Problem 2)
log(x) + log(y) - 2log(z)
log(x) + log(y) - log(z^2)
log(x*y) - log(z^2)
log[(x*y)/(z^2)]
Answer is choice D
======================================================================
Problem 3)
log[21/(x^2)]
log(21) - log(x^2)
log(21) - 2*log(x)
This matches with choice B
======================================================================
Problem 4)
Ln(63) = Ln(z) + Ln(7)
Ln(63)-Ln(7) = Ln(z)
Ln(63/7) = Ln(z)
Ln(9) = Ln(z)
z = 9
======================================================================
Problem 5)
Ln(5x-3) = 2
5x-3 = e^2
5x = e^2+3
x = (e^2+3)/5
This means choice A is the answer
An investment doubles in value every 9 years. What was the starting value of the investment if it is worth $4800 after 27 years.
Answers
If Jeremy walks 2 miles in 74 minutes, then how far will Jeremy walk in 84 minutes?
Answers
To find how far Jeremy will walk in 84 minutes, set up a proportion relating time and distance covered.
To find the distance he walks in 84 minutes, you can set up a proportion: 2 miles / 74 minutes = x miles / 84 minutes.
Solving for x, Jeremy will walk approximately 2.27 miles in 84 minutes. Jeremy walks at a speed of 2 miles in 74 minutes.
((Use the graph shown below to fill in the blank.))
If (4, y) is an ordered pair of the function, then y = a0.
Answers
Draw a vertical line (see side note below) through 4 on the x axis. I've done so in red (see attached image). The red line crosses the graph at the point (4,1) so this tells us that y = 1
Answer: y = 1
Side Note: you don't have to draw a vertical red line but it's handy to see how it works out. After you get used to these types of problems, you can visually be able to see the answer without these extra lines.
If (4, y) is an ordered pair of the function, then value of y = 1.
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
(4, y) is an ordered pair of the function.
Now, The point (4, y) has a known x coordinate of x = 4.
For the value of y at x = 4,
Draw a vertical line through 4 on the x axis.
Then, The vertical line crosses the graph at the point (4, 1).
Thus, The value of y is 1.
Thus, If (4, y) is an ordered pair of the function, then value of y = 1.
Learn more about the coordinate visit:
https://brainly.com/question/20362114
#SPJ2
The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is ___
Answers
53 plz help me with this
Answers
3 large beads cost 2.50 * 3 = 7.50
30-7.50 = 22.50
20-7.50 = 12.50
so they can spend between 12.50 and 22.50 on small beads
12.50 / 1.25 = 10
22.50/1.25 = 18
can buy between 10 and 18 small beads
1.25x >=12.50 and 1.25x<=22.50
I need the answer for 9
Answers
Set that expression equal to 1800 and solve for n, the number of sides.
180(n - 2) = 1800
Divide both sides by 180
n - 2 = 10
Add 2 to both sides
n = 12
The polygon has 10 sides.
so you can use this to find out how many sides of this polygon
(n-2) × 180° = 1800
n - 2 = 10
n = 12
this polygon has 12 sides
Find the sum of each group of numbers. You may add the numbers in any order. Then, check your work by adding the numbers again in a different order. a. 110, 83, and 328 b. 92, 37, 14, and 66 c. 432, 11, 157, and 30
Answers
1. 110 + 83 + 328 = 521
2. 92 + 37 + 14 + 66 = 209
3. 432 + 11 + 157 + 30 = 630
It does not matter how much you re-arrange the numbers in each group, you will keep arriving at the same answers, this is because the sum of a particular set of numbers will always remain the same.
Answer:
1. 110 + 83 + 328 = 521
2. 92 + 37 + 14 + 66 = 209
3. 432 + 11 + 157 + 30 = 630
Determine the value of r so the line passing through each pair of points has the given slope
(6,3) (r,2), m=1/2
Answers
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{1}{2}=\frac{2-3}{r-6}[/tex]
[tex](r-6)=2(-1)[/tex]
[tex]r-6=-2[/tex]
[tex]r=4[/tex]
0.5(7d+4)=7−1.5d
solve for d
Answers
Let's solve your equation step-by-step.0.5(7d+4)=7−1.5dStep 1: Simplify both sides of the equation.0.5(7d+4)=7−1.5d(0.5)(7d)+(0.5)(4)=7+−1.5d(Distribute)3.5d+2=7+−1.5d3.5d+2=−1.5d+7Step 2: Add 1.5d to both sides.3.5d+2+1.5d=−1.5d+7+1.5d5d+2=7Step 3: Subtract 2 from both sides.5d+2−2=7−25d=5Step 4: Divide both sides by 5.5d5=55d=1Answer:d=1
Which is best definition of contrapposto?
a. an active pose
b.an s-shaped pose
c. a block-shaped pose
Answers
The answer is an s shaped pose. Contrapposto is an Italian word that means counterpose. It is practiced in visual arts to depict a human figure standing with the majority of its heaviness on one foot so that its shoulders and arms curl off in an axis from the hips and legs forming a letter s.
I just finished the quiz the answer is B. an S-shaped pose
What is the number to the right of the decimal point called?
Answers
A square has an area of 121 yd^2 what is the length of each side
Answers
a= 11 inches
The side of the square having an area of 121 yards² is 11 yards
What is the area of a square?
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be Y = 121 yards²
Now , let the side of the square be = a
And the equation for the area of the square is
Area of the square = a²
where a is the side of the square
So , substituting the values in the equation , we get
a² = 121 yards²
Taking square root on both sides , we get
a = 11 yards
Therefore , the value of a is 11 yards
Hence , The side of the square having an area of 121 yards² is 11 yards
To learn more about area of square click :
https://brainly.com/question/17707380
#SPJ5
Your company gives you a cell phone plan which allows you 600 minutes to talk per month. So far this month, you have used 330 minutes and you have 10 days left on this month's plan. Which inequality could you use to determine how many minutes at most you can use per day so that you don't go over your monthly plan minutes?
A.)10x+330≥600
B.)10x+330>600
C.)10x+330≤600
D.)10x+330<600
Answers
We use the ≤ since you are allowed to use the 600th minute.
When we subtract 330 from both sides, it makes a bit more sense
10x ≤ 270
270 is the number of minutes left your plan since you've already used 330, and you have 10 days left in the month.
Round 103.468 to the nearest liter
Answers
How many solutions does the equation have?y+7=y–3many solutions1 solutionno solutions?
Answers
Subtract y on both sides, giving you...
7= -3
Which is false
Which logical form represents this statement?
Either it is not cold today or i am wearing woolen coat.
p: It is cold today.
q: I am wearing woolen coat.
~p ∧~q
~p ∧ q
~p ∨ q
~(p∨ q)
Answers
That's what I put for my answer.
Answer:
The correct answer is:
~p ∨ q
Step-by-step explanation:
p: It is cold today.
q: I am wearing woolen coat
~p: It is not cold today
V represents either...or...
Hence, ~p V q represents:
Either it is not cold today or i am wearing woolen coat.
Hence, the correct option is:
~p ∨ q
Determine f(2) where f(x)= x+1/4x-2
Answers
F(2)=3/6
F(2)= 1/2
What steps would you do to solve n/7 + 3 ≥ -4? Multiply by seven, then subtract three. Add three, then multiply by seven. Subtract three, then multiply by seven. Subtract three, then divide by seven.
Answers
Step 2: Subtract 3 from both sides.17n+3−3≥−4−317n≥−7
Step 3: Multiply both sides by 7.7*(17n)≥(7)*(−7)n≥−49
Answer:n≥−49
HELP!! WHAT IS THE VALUE OF X ?
Answers
solve the following equation by completing the square
Answers
Bonnie filled her car’s tank. She put in 10 1/2 gallons and paid $15.26. Determine the cost of gasoline per gallon.
Answers
Find the missing angle.
Answers
make sure your calculator is in Degree mode.
but will run you about 36.8698976458° and 53.13010235415598°.
Point m is the midpoint between A (-4,4) and B(-1,-6) find the location of M
Answers
((x1+x2)/2,(y1+y2)/2), where x1=-4, x2=-1, y1=4 and y2=-6
So, we have
M=(-4-1/2,4-(-6)/2)
M=(-5/2, 5)
What is the term for the point where angle bisectors of a triangle meet?