Answer: 1320 ways.
Step-by-step explanation:
For this problem you should use the formula for variations in combinatorics. You use this when choosing a few objects from a group in which the order of the objects is of importance:
[tex]P^{12} _{3}=\frac{12!}{(12-3)!}=\frac{12 \cdot 11\cdot 10\cdot ...\cdot 1}{9 \cdot 8 \cdot ... \cdot 1} = 12 \cdot 11 \cdot 10 = 1320[/tex]
where ! stands for factorial.
Which inequality is equivalent to 22 ≤x-9?
(A) 13sx
(B) 13zx
(C) 31sx
(D) 31zx
Answer:
31 ≤ x
Step-by-step explanation:
22 ≤ x - 9;
22 + 9 ≤ x - 9 + 9;
31 ≤ x
Find the mean for n = 200 and p = 0.24 when the conditions for the binomial distribution are met.
The mean value of expected value for a binomial distribution is given by the next formula:
[tex]\mu_x=n\cdot p[/tex]Where n is the number of trials and p is the probability of success. So, using the given data:
[tex]\begin{gathered} \mu_x=200\cdot0.24 \\ \mu_x=48 \end{gathered}[/tex]So the expected value or mean is 48
(07.02 HC)
Barbara draws pens randomly from a box containing 5 pens of the same shape and size. There is 1 green pen, 3 red pens, and 1 blue pen. She draws 1 red pen and then
another red pen without replacing the first one. Find the probability of drawing 1 red pen followed by another red pen, and show the equation used.
Answer: She already got rid of two red pens, so there's one red pen left.
5-1=4-1=3. 1 red 1 blue 1 green. 100/3=33.3333333… so her chance of getting another red pen is 33.3333333333333333333333% and a 66.66666666666666666666% chance of not.
Step-by-step explanation
you are playing a game of hide - and - seek with two friends . while one of your friends counts , you and your other friend are given a chance to hide in one of five possible hiding spots . you are each allowed to pick a hiding spot , and are permitted to share a hiding spot . your friend finishes counting and checks one of the five hiding spots . assuming that everyone's decisions are made uniformly at random , what are the chances that your friend does not find anyone in the first spot that they check ?
The probability the friend finds no one in the first spot is 60%.
What is probability?Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.
For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.
The two friends can only hide in 2 spots, leaving 3 spots with nobody.
The number of hiding spots = 5
The number of friends hiding = 2
The number of counting friends = 1
The number of spots they can hide = 2 out of 5
The probability of finding a person in a hiding spot = 2/5 or 40%
The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).
The chances that your friend finds anyone in the first spot are 60%.
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i really need help can anyone help solve the attatched question
WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZYX has a measure of 34 degrees. Find the measure of angle ZWY.
Angle ZWY has a measure of what
degrees.
Angle ZWY has a measure of 13 degrees.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given,
Angle WXY has a measure of 133 degrees
Angle ZYX has a measure of 34 degrees
Angle ZWY:
= 180 - 133 -34
= 13
Angle ZWY has a measure of 13 degrees.
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Does anyone know why this is wrong??
[tex]=-10x^4-4x^3+6x^2[/tex]
PLEASE HELP!!!!!!!!!!!!
The stem-and-leaf plot shows kilometers walked by participants in a charity benefit walk. Use it to answer the questions.
A stem and leaf plot shows the number of kilometers walked for charity.
The plot is titled 'Kilometers Walked for Charity.' The numbers 12, 13, 14, 15, 16, and 17 are in a vertical column to the left of a vertical line.
· On the same line as 12 but on the right of the vertical line are the numbers 3, 3, 6, 7, 9, and 9.
· On the same line as 13 but on the right of the vertical line are the numbers 1, 1, 4, 5, and 5.
· On the same line as 14 but on the right of the vertical line are the numbers 0, 0, 2, 3, 3, 8, 8, and 9.
· On the same line as 15 but on the right of the vertical line are the numbers 2, 2, 2, 2, 2, 3, 5, 5, and 7.
· On the same line as 16 but on the right of the vertical line are the numbers 4, 5, 5, 9, and 9.
· On the same line as 17 but on the right of the vertical line are the numbers 3 and 5.
The key to the stem and leaf plot identifies that 12 vertical line 3 means 12.3.
a. How many people participated in the walk?
b. How many of the walkers traveled more than 14 kilometers?
Answer:
35 participants for A
22 participants traveled more than 14 km for B.
Step-by-step explanation:
type the correct answer in each box. use numerals instead of words if neasary
This is given point in the fourth quadrant.
In this point, the adjacent is
[tex]\frac{5}{13}[/tex]The opposite is y.
Find hypotenuse h using the pythagorean theorem:
[tex]\begin{gathered} h^2=(\frac{5}{13})^2+y^2 \\ h=\sqrt[]{\frac{25}{169}+y^2} \end{gathered}[/tex][tex]\sec (\theta)[/tex]is equal to hypotenuse by adjacent.
[tex]\cot (\theta)[/tex]is equal to adjacent by opposite.
In the fourth quadrant,
[tex]\sec \theta[/tex]is positive , and
[tex]\cot \theta[/tex]is negative.
So,
[tex]\begin{gathered} \sec \theta=\frac{h}{\frac{5}{13}} \\ =\frac{13\sqrt[]{\frac{25}{169}+y^2}}{5} \\ \cot \theta=\frac{\frac{5}{13}}{-y} \\ =-\frac{5}{13y} \end{gathered}[/tex]If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6
Since y varies directly with x then
[tex]\begin{gathered} \frac{y}{x}=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}[/tex]So,
[tex]\frac{y}{x}=\frac{-3}{-12}=\frac{3}{12}=\frac{1\cdot3}{4\cdot3}=\frac{1}{4}[/tex]Then, 1/4 is the constant of proportionality. So that,
[tex]\begin{gathered} \frac{y}{x}=\frac{1}{4} \\ \frac{-6}{x}=\frac{1}{4} \\ -\frac{6}{x}\cdot x=\frac{1}{4}\cdot x \\ -6=\frac{x}{4} \\ 4\cdot-6=\frac{x}{4}\cdot4 \\ -24=x \end{gathered}[/tex]-3(0.5+3p)=-6(p-5.9) show work
help
Answer:
p=12.3
Step-by-step explanation:
-1.5-9p= -6p+35.4
36.9=3p
p=12.3
f(x)=4x+2; Find f(8)
We have:
[tex]f(x)=4x+2[/tex]And want to find f(8), for this we simply replace x with 8 and operate:
[tex]f(8)=4(8)+2\Rightarrow f(8)=34[/tex]a ball dropped from rest and falls for 8 seconds
whats the final velocity
and whats te average velocity
how far did it fall
There are two spinners. one spinner has three equally sized sectors that are numbered 1, 2, and 4. the second spinner has four equally sized sectors that are labeled a, b, c, and d. each spinner is spun once. how many outcomes do not show c? responses 4 4, 6 6, 7 7, 9
The number of outcomes that do not show c is calculated to be 9 if each spinner is spun once.
The three possible outcomes of the first spinner are 1,2 and 4 and the possible outcomes of the second spinner are a,b,c and d; so if the two spinners are spun together, the possible outcome will be:
a1, a2, a4
b1, b2, b4
c1, c2, c4
d1, d2, d4
Therefore, there are a total of 12 possible outcomes, and 3 out of these possible outcomes show c. Now the outcomes that do not show c can be calculated by subtraction as follows;
Outcome not showing c = Total outcomes - Outcomes showing c
Outcome not showing c = 12 - 3
Outcome not showing c = 9
Therefore, 9 outcomes do not show c if each spinner is spun once.
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Answer: 6
Step-by-step explanation:
write an equation of the line below.
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is where x = 0. Therefore, the y-intercept would be 3. To find the slope, you do Δy/Δx (Δ = Change In). To find that, you go up 4 times, then move to the right 2 times to reach the second dot. Now, you do 4 / 2, which equals 2. Your final equation will be y = 2x + 3.
If you write every whole number from I to
100. how many times will you write the digit
"2"?
Answer:
20 times
Step-by-step explanation:
Digit 2 appears 20 times in first 100 natural numbers
101x^2+231x-334=-2 find the A,B,C
The roots of the equation is 1 and 3.28
The given equation is a quadratic
To find the roots of a quadratic equation, the formula is
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]
The equation is 101x^2+231x-334=-2 we need to find the A,B,C
101x^2+231x-332 = 0
here a is 101, b is 231, and c is -332
[tex]\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 + \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 + \sqrt{53361 + 134128 } }{202}\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + \sqrt{187489 } }{202}\\\\\frac{-231 + 433 }{202}\\\\=\frac{202}{202}\\\\ 1[/tex]
[tex]\frac{-b - \sqrt{b^{2} - 4ac } }{2a}\\\frac{-231 - \sqrt{231^{2} - 4(101)(-332) } }{2(101)}\\\frac{-231 - \sqrt{53361 + 134128 } }{202}\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 - \sqrt{187489 } }{202}\\\\\frac{-231 -433 }{202}\\\\=\frac{664}{202}\\\\ 3.28[/tex]
Therefore, the roots of the equation is 1 and 3.28
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please help thank you
Answer:
%25 of customers ordered ice tea.
Step-by-step explanation:
To find percentage = Part/Whole x 100
35/140 x 100 = 0.25 x 100 = %25
Why are there two possible solutions to the equation, X2 = 100?
Answer:
100 is perfect square
Step-by-step explanation:
in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100
Please answer only if you know the answer.
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.
What is the slope-intercept form?
The slope-intercept form of a line is y=mx + c.
Where, x and y are coordinates. m = slope and c = y intercept.
Given, slope (m) = 3/4
Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:
-4 = (3/4) × 5 + c
⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4
Now, putting the value of c in the standard equation:
y = (3/4)x - 31/4
⇒ 4y = 3x - 31
⇒ 3x - 4y = 31
Answer is Option C
A guy wire runs from the top of a cell tower to a metal stake in the ground. Hannah
places a 6-foot tall pole to support the guy wire. After placing the pole, Hannah
measures the distance from the stake to the pole to be 1 ft. She then measures the
distance from the pole to the tower to be 12 ft. Find the length of the guy wire, to the
nearest foot.
The length of the guy wire, to the nearest foot is 1548 ft.
What is the Pythagoras theorem?The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized
After sketching the information given, we have two similar right triangles, ΔABE and ΔCDE.
CD = 6 ft
DE = 1 ft
BD = 12 ft
Since ΔABE ~ ΔCDE, therefore,
AB/CD = BE/DE (proportional sides)
Plug in the values
AB/6 = (12 + 1)/2
AB/6 = 13/2
Cross multiply
AB = 13(3)
AB = 39 ft
AE = √(AB² + BE²)
AE = √(39² + 12²)
AE = 1548 ft (nearest foot)
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Answer: The length of the guy wire, to the nearest foot is 1548 ft.
Step-by-step explanation:
Divide write the answer as a fraction in simplest form 7/8 divided by 6 =
Answer:
[tex]\frac{7}{48}[/tex]Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.
Dividing and simplifying gives us following:
[tex]\frac{7}{8}\text{ Divied 6}\rightarrow\frac{7}{8}\times\frac{1}{6}=\frac{7}{48}=\frac{7}{48}[/tex]which integers represent each situation? a) a debt of $10b) 6 degrees below 0 c) deposit of $25 someone please help fast
An integer that represent the debt of $10 can be express below
[tex]-\text{ \$10}[/tex]An integer that represent 6 degree below 0 is expressed below
[tex]0-6=\text{ -6 degre}e[/tex]An integer that represent a deposit of $25 can be express below
[tex]+\text{ \$25= \$25}[/tex]Write the equation of the line in y=mx+b form using the following two points:
(-2,-1) and (-1,-2)
Enter you equation here: type your answer....
10 points
Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:
y= -1.00x + -3.00
(results are in decimal form, rounded to the nearest 100th)
i hope i helped it is for if it was for like slope intercept form
Step-by-step explanation:
A bag contains twelve balls labeled 1 through 12. One ball will be randomly picked.
What is the probability of picking an even number?
Write your answer as a fraction in simplest form
Hello there!
If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:
1 2 3 4 5 6 7 8 9 10 11 12
When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.
In this example: What is the probability of picking an even number?
Ask yourself: What are we trying to find?
We are trying to find the probability of even numbers.
Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?
The bag consists of: 1 2 3 4 5 6 7 8 9 10 11 12
Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.
Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.
Finally, think about: What is the total amount of samples in this bag?
We know that there are 12 balls, so 12 would be the total amount.
To conclude, we can find 6 even numbers in a bag of 12 balls;
Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].
Tom surveyed 150 students at his school to find out each student's favorite color. His results are shown in the circle graph above. Candace asked 15 of her friends from the same school to choose their favorite color, and 5 people chose yellow. According to Tom's survey, how many of Candace's friends would have been expected to choose yellow?
We have that in Tom's survey he obtained that 20% of the students like the yellow color (see graph above).
Then, in Candance's (small) survey, she asked 15 friends. According to Tom's survey, Candance should have obtained that 20% of her friends like the yellow color.
Therefore, we need to find 20% of 15 (friends) to find the expected number of friends that Candance should have had using the results of Tom's survey. Then, we have:
[tex]\frac{20}{100}\cdot15=\frac{300}{100}=3[/tex]Hence, according to Tom's survey, Candance's friends would have been expected to be 3 to choose (of her 15 friends) yellow (3 is 20% of 15).
I just need a little help
Which table represents a function?
Answer:
A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.
Step-by-step explanation:
5x^2-25=100 solve by taking square root
Answer:
x=5,−5
Step-by-step explanation:
14. Consider this system of equations.y = -2x2 + 9y = 4x + 3What values of x are solutions to the system of equations?A.x = -9 and x = 7B.x= -7 and x = 9C.x = -3 and x = 1D.x = -1 and x = 3
SOLUTION:
Step 1:
In this question, we are given the following:
Consider this system of equations:
[tex]\begin{gathered} y=-2x^2\text{ +9} \\ y\text{ = 4x + 3} \end{gathered}[/tex]Step 2:
The details of the solution are as follows:
CONCLUSION:
The values of x that are the solutions to the system of equations are:
[tex]x\text{ =- 3 and x = 1 -- OPTION C}[/tex]
the scale of topographical of map is 1:50000.what is the area of a dam which is represented on the map by an area of 3.5 centimeter square
The scale of a topographical map is 1:50000. This means that 1 cm on the map is 50 000 cm on reality.
[tex]1\operatorname{cm}\rightarrow50000\operatorname{cm}[/tex]Now, we can take the