Answer:
P(X = 0) = 0.25
P(X = 1) = 0.75
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The probability distribution of X.
3 red balls out of 4, one picked, so we can have either 0 red balls or 1 red ball. The probability disitribution is the probability of each outcome.
[tex]P(X = 0) = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = \frac{3}{4} = 0.75[/tex]
What is the height of a triangle of base 10m and an area of 60m²
A = 0.5*b*h
60 = 0.5*10*h
60 = 5h
5h = 60
h = 60/5
h = 12
Answer: The height is 12 meters.
Answer:
6 m
Step-by-step explanation:
Since the area is 60 m squared and the base is 10 m, the height is 12.
Formula: base x height / 2 = area
= 10 x height / 2= 60 m squared
60 / 10 = 6 x 2 = 12.
Hope this helps!
What is the area of triangle ABC? Round to the nearest whole number
9514 1404 393
Answer:
C. 837
Step-by-step explanation:
The remaining angle is ...
C = 180° -A -B = 180°-62° -67° = 51°
The law of sines tells us that the length AC is ...
AC/sin(B) = AB/sin(C)
AC = AB·sin(B)/sin(C) = 40·sin(67°)/sin(51°)
Using the area formula given, we now have ...
area = 1/2(AB)(AC)sin(A)
= (1/2)(40)(40·sin(67°)sin(62°)/sin(51°) ≈ 836.7
The area of the triangle is about 837 square units.
the division method of 680624 and 165649
9514 1404 393
Answer:
680624 = 2^4 · 7 · 59 · 103165649 = 11^2 · 37^2Step-by-step explanation:
Using the division method, you find prime divisors that give integer quotients until the final quotient is a prime. For small divisors, it is beneficial to make use of divisibility rules. For larger ones, you just have to try the list of primes to see what you get.
680624The last two digits are divisible by 4, so the number can be divided by 2 twice (at least). We can keep dividing by 2 as long as the 1s digit is even.
680624/2 = 340312
340312/2 = 170156
170156/2 = 85,078
85078/2 = 42539
The next prime is 3. The divisibility rule for 3 is the sum of digits must be divisible by 3. 4+2+5+3+9 = 23, not divisible by 3.
The next prime is 5. For divisibility by 5, the number must end in 0 or 5. This is not divisible by 5.
The next prime is 7. For divisibility by 7, there are several possible rules you can use. One I find relatively easy to remember is to subtract double the 1s digit from the rest of the number and see if that is divisible by 7. Here, that gives ...
4253 -2(9) = 4235; 423 -2(5) = 413; 41 -2(3) = 35 . . . divisible by 7
Continuing, we have ...
42539/7 = 6077
There are additional divisibility rules for 11 and 13 that can be applied. For divisibility by 11, we can add pairs of digits: 77 +60 = 137, not divisible by 11.
For divisibility by 13, we can add 4 times the last digit to the rest:
4253 +4(9) = 4289; 428 +4(9) = 464; 46 +4(4) = 62 . . . not divisible by 13
__
After this point, it is a matter of trying the primes one by one to see what the number may be divisible by. This "trial and error" will show you ...
6077/59 = 103 . . . 103 is prime, so we're done
The final factorization is ...
680624 = 2^4 · 7 · 59 · 103
__
165649As luck would have it, this is a perfect square, so we can immediately reduce the problem to something a little easier.
√165649 = 407
We can see "immediately" that this is not divisible by 2, 3, 5, or 7. However, 04+07 = 11, so this is divisible by 11.
407/11 = 37 . . . 37 is prime, so we're done
The final factorization is ...
165649 = 11^2 · 37^2
_____
As you can probably tell, it is convenient to have a list of prime numbers available. Here is a list of the first few primes.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103
_____
Additional comment
If you start with the smallest primes, (2, 3, 5}, once you find a prime divisor, you only need to try primes greater than or equal to that one on the quotient. In any event, you only need to try primes up to the square root of the value you're trying to factor. If none of those work, then the number itself is a prime.
In the first problem, once we got to 6077, we would only need to try primes up to √6077 ≈ 77. That is, if 6077 turned out to be not divisible by any prime equal to 73 or less, then 6077 would be the last prime factor. (As we found, 6077 is composite, not prime, so using that number is just to illustrate the point regarding the largest value needed to be tested.)
Two balls are picked at random from a box containing 5 red balls and 3 green balls. What is the probability that 1 red ball and 1 green ball are selected?
Answer:
Step-by-step explanation:
Answer:
3/8 x 5/8= 15/64
Step-by-step explanation:
What proportion of the students scored at least 23 points on this test, rounded to five decimal places
This question is incomplete, the complete question is;
The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.
What proportion of the students scored at least 23 points on this test, rounded to five decimal places?
Answer:
proportion of the students that scored at least 23 points on this test is 0.30850
Step-by-step explanation:
Given the data in the question;
mean μ = 22
standard deviation σ = 2
since test closely followed a Normal Distribution
let
Z = x-μ / σ { standard normal random variable ]
Now, proportion of the students that scored at least 23 points on this test.
P( x ≥ 23 ) = P( (x-μ / σ) ≥ ( 23-22 / 2 )
= P( Z ≥ 1/2 )
= P( Z ≥ 0.5 )
= 1 - P( Z < 0.5 )
Now, from z table
{ we have P( Z < 0.5 ) = 0.6915 }
= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850
P( x ≥ 23 ) = 0.30850
Therefore, proportion of the students that scored at least 23 points on this test is 0.30850
Use the graph of the function y=g(x) below to answer the questions.
Answer:
Step-by-step explanation:
g(5) = 2 > 0
:::::
g(x) = 0 for x = -2, 2, 4
:::::
g(x) < 0 for -3 ≤ x < -2
Please help!!! Find the domain of the function y = 2 cot(5∕8x).
A) All real numbers except odd integer multiples of 8π∕5
B) All real numbers except 0 and integer multiples of 8π∕5
C) All real numbers except 0 and integer multiples of 4π∕5
D) All real numbers except odd integer multiples of 4π∕5
Answer:
Function 
Step-by-step explanation:
) Domain is defined as the set of possible values of x where function is defined.
For domain,
So,
The value of x is define as
The domain of the function is all real numbers except
The range is defined as all the y values for every x.
So, The range of the function is all real numbers.
2) The general form of the cot function is
Where, Period is
On comparing, B=3
So, The period of the given function is
3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.
The vertical asymptote is at where function is not defined.
The two vertical asymptote is
Put n=0,
Put n=1,
So, The two vertical asymptote are
Answer:
B.)
Step-by-step explanation:
took test
urgent help needed !!!!!!
Answer:
use gauthmath
Step-by-step explanation:
you will thank me later
Y+10 like terms from expression 2
Answer:
y+10=2
y=-8
Step-by-step explanation:
y=2-10
y=-8
For questions #1 and #2:
A) Write one sentence in your own words, describing the step you need to solve the problem.
B) Write the answer
EXAMPLE:
x/3 = 5
A. Multiply both sides by 3.
B. Answer is 15.
Question #1:
x - 3 = 10
Question #2:
2x = 8
I need help pleaseeeeee
Answer:
question 1
if you want x to stand alone
you will take the -3 off by crossing it to the other side
NB when a negative number crosses the equal sign it becomes positive
x =10+3= ×=13 is the final answer
Step-by-step explanation:
question 2
you will divide both sides by 2(because we want x to stand alone)
so final answer is ×=4
A 20 foot ladder is leaning against the outside of the house while a painter is painting. The ladder makes an angle of 72∘ with the ground. What is the distance between the foot of the ladder and the house? Round your answer to the nearest foot. the answer is not 19.02
Cos (72°) = x/20
x=cos(72°)×20
x=6.2
x≈6
Answer:
x=6
Step-by-step explanation:
I need help plzzz I do understand what they want me to do plz help I’m in summer school right now!!!
Answer:
B.
Step-by-step explanation:
Vertical line test is a test in which you draw a line that goes up and down through the function. If at any point it goes through the function twice, then the function is no longer a function. cheers
Part G
You’ve seen two methods for finding the area of ΔABC—using coordinate algebra (by hand) and using geometry software. How are the two methods similar? How are they different? Why might coordinate algebra be important in making and using geometry software?
PLSS HELP ME
Answer:i need this too lol
Step-by-step explanation:
Find the length of a side of a cubic die, if the volume of the die is 343/4 cubic inches
O 1.25 in.
0 1.50 in.
0 1.75 in.
01.95 in.
Answer:
The length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.
Step-by-step explanation:
The volume of a cube is given by:
[tex] V = l^{3} [/tex]
Where:
l: is the length =?
V: is the volume = 343/4 in³
By solving the above equation for "l" we have:
[tex] l = (V)^{1/3} = (343/4 in^{3})^{1/3} = 4.41 in [/tex]
Therefore, the length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.
None of the options are correct for the given volume.
I hope it helps you!
Can someten help me find the answer?
Answer:
D
Step-by-step explanation:
It subtracts.
Write each set in the indicated form.
If you need to use "
…" to indicate a pattern, make sure to list at least the first four elements of the set.
Answer:
a. Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}
Or
{y | y is a natural number and 11 < y < 16}
b. Rooster form: {3, 4, 5 ,6, ...}
Step-by-step explanation:
a. Rooster form: {12, 13, 14, 15}
All four numbers are natural numbers, therefore we would write this set of numbers in set builder form such that they will all have the same property. Thus:
Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}
Or as
{y | y is a natural number and 11 < y < 16}
b. Set-builder form: {y | y is a natural number and y > 2}
Since natural numbers are positive integers, this tells us that all values of the set are not less than or equal to 2. Therefore, they are integers that range from 3 and above.
Thus:
Rooster form: {3, 4, 5 ,6, ...}
If P(x) = 2x2 – 3x + 7 and Q(x) = 8 - x), find each function value.
15. P(-3)
16. Q(2)
17. P(4)
18. Q(-3)
Answer:
15. 52
16. 6
17. 59
18. 11
Step-by-step explanation:
For each year t, the number of trees in Forest A is represented by the function A(t) = 72(1.025). In a neighboring forest, the number of trees in Forest B is represented by the function B(t) = 63(1.029).
Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?
Round your answer to the nearest tree.
Forest A or B will have _________ more trees.
Answer:
Forest A will have 6 more trees.
Step-by-step explanation:
The number of trees in Forest A is represented by the function:
[tex]A(t)=72(1.025)^t[/tex]
And Forest B is represented by:
[tex]B(t)=63(1.029)^t[/tex]
And we want to determine which forest will have the greater number of trees after 20 years.
So, evaluate both functions for t = 20. For Forest A:
[tex]\displaystyle \begin{aligned} A(20)&=72(1.025)^{20} \\ &=117.9803...\\ &\approx 118 \text{ trees} \end{aligned}[/tex]
And for Forest B:
[tex]\displaystyle \begin{aligned} B(20) &= 63(1.029)^{20} \\ &=111.5958... \\ &\approx 112 \end{aligned}[/tex]
Therefore, after 20 years, Forest A will have 6 more trees.
help pls ik the answers i just don’t k is how to show work :(
include the notation and just do the work on the page
Find y on this special right triangle
Answer:
Cos(x) = adjacent side/hypotenuse[tex]cos(45)=\frac{\frac{7\sqrt{2} }{2} }{x} \\\\cos(45)x=\frac{7\sqrt{2} }{2}\\\\\frac{\sqrt{2} }{2}x=\frac{7\sqrt{2} }{2}\\\\x=\frac{\frac{7\sqrt{2} }{2}}{\frac{\sqrt{2} }{2}} =\frac{7\sqrt{2} }{2}*\frac{2}{\sqrt{2}} =7[/tex]
Use the Pythagorean Theorem to find y[tex]y^{2} +(\frac{7\sqrt{2} }{2} )^{2} =x^{2} \\\\y^{2} =7^{2}-(\frac{7\sqrt{2} }{2} )^{2} \\\\y^{2}=49-\frac{49(2)}{4} =49-\frac{49}{2}=\frac{49(2)}{2}-\frac{49}{2}=\frac{98-49}{2}=\frac{49}{2} \\\\y=\sqrt{\frac{49}{2} } =\frac{7}{\sqrt{2} } =\frac{7\sqrt{2}}{\sqrt{2}(\sqrt{2})} =\frac{7\sqrt{2}}{2}[/tex]
I need a fully completed (or at least for the 8th grade) khan academy account!!!
Please help me!!
Answer:
so you need a khan academy account?
Please help with this function problem
Answer:
-2
-1
-2
Step-by-step explanation:
really ? this is a problem ? why ?
f(0) means the functional value for x = 0.
is x = 2 ? no.
so, automatically the other case applies, and f(0) = -2
f(2) means x=2
is x = 2 ? yes.
so that case applies, and f(2) = -1
f(5) means x=5
is x = 2 ? no.
so again, the case for x <> 2 applies, f(5) = -2
If computers sell for $1160 per unit and hard drives sell for $ 102 per unit, the revenue from x computers and y hard drives can be represented by what expression? If computers sell for $ per unit and hard drives sell for $102 per unit, the revenue from x computers and y hard drives can be represented by
What is the domain of the function graphed below?
Answer:
x<7
Step-by-step explanation:
Write an equation in point slope form for each line. Slope is 0 and (1 , 2) is on the line
Answer:
y -2 = 0(x-1)
Step-by-step explanation:
Point slope form is
y -y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y -2 = 0(x-1)
y-2 =0
IMPORTANT NEED ANSWER ASAP !!
The stem plot shows the number of mini-marshmallows eaten in one minute by a group of people competing in a contest.
Row1 with a 2 to the left of the bar with a 9 to the right. Row 2 with a 3 to the left of the bar with 8, 9 to the right. Row 3 with a4to the left of the bar with 2, 6, 7, 8, 8to the right. Row 4 with a5to the left of the bar with 3, 5, 5, 5 to the right. Row 5 with a 6to the left of the bar with 1, 3, 7to the right.
Key: 2|9 = 29 mini-marshmallows
Which of the following is a correct statement about the distribution?
There are no outliers.
The distribution is skewed left.
The center is around 44.
The distribution is bimodal.
Step-by-step explanation:
mark me as brainlist...........
Answer:
I got to say, the other guy got it good. Thanks dude.
Step-by-step explanation:
What is |-2.24|? i need this question answered quickly
i think the answer is 2.24
The profit, in dollars, of selling n items is given by P(n) = 0.86n - 2800. Identify the slope and the y-intercept.
Answer: 0.86 and -2800 (choice A)
Explanation:
Think of the given equation as y = 0.86x - 2800
Then compare it to y = mx + b
We see that m = 0.86 is the slope and b = -2800 is the y intercept.
Answer:
Slope: 0.86 , Y-intercept:-2800
Step-by-step explanation:
Linear equations go by the form of y=mx + c
where m is the gradient(slope of the graph) and c is the y-intercept
21 × 6 ÷ 7 + 12 - 15
Answer:
15
Step-by-step explanation:
By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.
21*6 = 126
126/7 = 18
18 + 12 = 30
30 - 15 = 15
Answer:
15
Step-by-step explanation:
21 × 6 ÷ 7 + 12 - 15
= 126 ÷ 7 + 12 - 15
= 18 + 12 - 15
= 30 - 15
= 15
Find the area of 11 by 2
