The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.
The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:
4 has two prime factors: 2 and 2 (2 squared).6 has two prime factors: 2 and 3.The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.
Thus, the probability of rolling a number with exactly two prime factors is:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 6 = 1 / 3
Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).
Find the value of each variable.
How do you solve 3x^3+6x^2=72x
which values are solutions to the inequality below? check all that apply
In which graph does y vary directly as x? It’s not C, I got it wrong.
The angle of inclination of a ramp is 6° and the ramp is 14 feet long. Approximately how high off the ground is the end of the ramp? 0.8 ft 1 ft 1.5 ft 1.8 ft
Answer:
1.463 ft.
Step-by-step explanation:
As you can see in the image, we can use the sin(6) to calculate the high.
sin(6°) = x/14
x = sin(6°)*14
x = 1.463 ft.
Find the length of a rectangle with area of 16 sq. cm. and width of 8 cm.
2 cm
8 cm
128 cm
multiply and simplify 12 and 2 / 3 3 + 1 / 4
Use the parabola tool to graph the quadratic function f(x)=x^2+10x+24.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabol
Answer:
See the attachment
Step-by-step explanation:
You want a graph of the parabola defined by f(x) = x² +10x +24.
VertexWe can add and subtract the square of half the x-coefficient to put the equation into vertex form:
f(x) = x² +10x +24 . . . . . . . . . . given
f(x) = x² +10x +25 +24 -25 . . . . add and subtract (10/2)² = 25
f(x) = (x +5)² -1 . . . . . . . . . write in vertex form
Comparing to the vertex form equation f(x) = (x -h)² +k, we see that ...
(h, k) = (-5, -1).
These are the coordinates of the vertex.
Another pointThe coefficient of x² is 1, so another point can be found by adding (1, 1) to the vertex. That means a second point on the parabola is ...
(-5, -1) +(1, 1) = (-4, 0)
GraphThe attached graph shows the parabola with vertex (-5, -1) through point (-4, 0).
__
Additional comment
When the coefficient of x² is not 1, the process is a little different. If you start with f(x) = ax² +bx +c, you can factor 'a' from the first two terms to help you get vertex form.
f(x) = a(x² +(b/a)x) +c
f(x) = a(x² +(b/a)x +(b/(2a))²) + c - a(b/(2a))²
f(x) = a(x +b/(2a)x)² +(c -b²/(4a))
The vertex is (-b/(2a), c -b²/(4a)).
The second point can be found by adding (1, a) to the vertex coordinates.
The following question has two parts. First, answer part A. Then, answer part B.
Isabella's mother has a garden with a total area of
10/23 square feet. She plans her planting season like this:
1/4 of the garden will be used for planting peas. And,
3/4 of the garden will be used for planting corn.
Which of the following graphs represents the equation x >-3y+9
Explain how you know 21/100 is greater than 1/5
This problem can be solved using equivalent fractions. The first step in resolving this problem is to realize that fractions are best compared when they both have the same denominator. In this case, I will choose to make that common denominator 100. There is no need to rewrite the fraction [tex]\frac{21}{100}[/tex] as the denominator for this fraction is already 100. The fraction [tex]\frac{1}{5} =\frac{20}{100}[/tex] . This is achieved by multiplying both the numerator and denominator by 20. Now that the two fractions have the same denominator, we can easily see that [tex]\frac{21}{100}[/tex] is greater than [tex]\frac{1}{5}[/tex] because it is greater than its equivalent fraction.
A 60 kg dog requires fluids at 50 mL/kg over 24 hours. Using a 10 gtt/mL set how many gtts/min will you set?
To set the infusion rate for a 60 kg dog, calculate the total fluid needed (3000 mL), the total number of drops (30,000 gtts), and then determine the drops per minute (20.83 gtt/min), rounding to approximately 21 drops per minute.
To calculate the infusion rate for a 60 kg dog that needs 50 mL/kg of fluids over 24 hours using a 10 gtt/mL set, follow these steps:
Firstly, calculate the total volume of fluids required by the dog:Therefore, you will set the infusion to approximately 21 drops per minute (rounding to the nearest whole number).
Please help, math question.
Identify the variable and the categories represented in this problem. Set up and fill in a two-way table to represent the frequencies in this problem.
A player shoots a basketball from a height of 6 feet. The equation, h = -16t 2 + 25t + 6, gives the height, h , of the basketball after t seconds. Describe the height, rounded to the nearest tenth of a foot, of the basketball after 1.5 seconds, assuming no other player touches the ball.
Answer:
The height of the ball after t =1.5 second is 7.5 feet.
Description:
The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.
Therefore, the basketball thrown at the rate of 1 feet/per second.
Step-by-step explanation:
Given: A player shoots a basketball from a height of 6 feet. The equation,
h(t) = [tex]-16t^2 + 25t + 6[/tex]
We need to find the height of the ball when t = 1.5 and describe the height.
plug in t = 1.5 in h(t) = [tex]-16t^2 + 25t + 6[/tex]
h(1.5) = [tex]-16(1.5)^2 + 25(1.5) + 6[/tex]
Simplifying the above expression, we get
h(1.5) = -36 + 37.5 + 6
h(1.5) = -36+43.5
h(1.5) = 7.5 feet
The height of the ball after t =1.5 second is 7.5 feet
Description:
The basket ball shoots from a height of 6 feet, it increase the height 1.5 feet after 1.5 seconds.
Therefore, the basketball thrown at the rate of 1 feet/per second.
Two jets leave an airport at the same time, flying in opposite directions. The first jet is traveling at three hundred seventy-seven mph and the other at two hundred seventy-five mph. How long will it take for the jets to be 9128 miles apart?
Leanne can clean a fish tank in 30 minutes. Karl can clean a fish tank in 20 minutes. If they work together, how many minutes does it take them to clean a fish tank? (2 points)
Answer:
12 minutes
Step-by-step explanation:
Just took the test and got it right
Apply the distributive property to create an equivalent expression. 2(3-8y)
Answer:
An equivalent expression is [tex]6 - 16y[/tex]
Step-by-step explanation:
The distributive property consists in removing the parenthesis. For this problem, it is done by multiplying the number outside the parenthesis by each term inside the parenthesis and then performing a subtraction between the results because of the minus sign inside.
For the expression [tex]2(3-8y)[/tex], when applying the distributive property, you would get:
[tex]2\times 3 - 2\times 8y[/tex]
[tex]6 - 16y[/tex]
Thus, an equivalent expression is [tex]6 - 16y[/tex].
The distributive property to remove the parentheses in the expression 2(3 - 8y) is 6 - 16y
Using the distributive property to remove the parenthesesFrom the question, we have the following parameters that can be used in our computation:
2(3 - 8y)
When the expression is expanded, we have the following
2(3 - 8y) = 2 * 3 - 2 * 8y
Evaluate the products
This gives
2(3 - 8y) = 6 - 16y
Lastly, we have
2(3 - 8y) = 6 - 16y
Hence the expression when simplified is 6 - 16y
Read more about expression at
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If we consider the toss of four coins as an experiment, how many equally likely outcomes does the sample space have?
The no. of equally likely event is 10.
What is probability ?Probability is chance of occurrence of a certain event out of all the possible events that can occur in a given situation.
According to the given question Tossing of four coins simultaneously as an experiment let us find he sample space and assuming that all these 4 coins are unbiased.
S = { HHHH, HHHT, HHTT, HTTT, TTTT, TTTH, TTHH, THHH, HTTH, THHT }.
∴ N(s) = 10.
As these 4 coins are unbiased there for all the events in the sample space are equally likely to happen.
So, The no. of equally likely outcome is 10.
learn more about probability here :
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please helppp its too hard!!!
Can you please help me?
find the 8th term of the expansion of (1/2x-y)^10
a 5x^3y^7
b 70x5y5
c -14x3y7
d -15x3y7
Answer:
d. [tex]-15x^3y^7[/tex]
Step-by-step explanation:
By the binomial theorem,
[tex](p+q)^n=\sum_{r=0}^{n} ^nC_r (p)^{n-r} q^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Thus,
[tex](\frac{1}{2}x-y)^{10}=(\frac{x}{2}+(-y))^{10})=\sum_{r=0}^{n} ^10C_r (\frac{x}{2})^{10-r} (-y)^{r}[/tex]
For the 8th term, r = 7,
Thus, the 8th term would be,
[tex]^{10}C_7 (\frac{x}{2})^{10-7} (-y)^{7}[/tex]
[tex]=\frac{10!}{7!(10-7)!} (\frac{x}{2})^3 (-y)^7[/tex]
[tex]=-\frac{10\times 9\times 8}{3\times 2\times 1}\times \frac{x^3}{8}\times y^7[/tex]
[tex]=-\frac{720x^3y^7}{48}[/tex]
[tex]=-15x^3y^7[/tex]
Hence, option 'D' is correct.
which equation represents a proportional situation?
A. y = 9x
B. y = -2x + 23
C. y = - 3x + 4
D. y = 3x - 12
what is the length of AC?
What is the probability that a unit chosen at random has between four and six rooms?
how many solutions 2x+3y=-3 and 3x + 5y = -9
Which is the best approximation for the solution of the system of equations
Answer:
Solution of the system of the equations is (0.882, 0.647)
Step-by-step explanation:
As shown in the figure equations are [tex]y=-\frac{2}{5}x+1[/tex] and y = 3x - 2
Solution of the system of equations will be the common point or point of intersection of these lines.
To get the point of intersection we will solve these equations.
We will equate these equations to get the value of x.
[tex]-\frac{2}{5}x+1=3x-2[/tex]
[tex]-2x+5=15x-10[/tex]
15x + 2x = 10 + 5
17x = 15
[tex]x=\frac{15}{17}[/tex]
x = 0.882
By putting x = 0.882 in y = 3x - 2
y = 3(0.882) - 2
y = 0.647
So the solution of systems of equations is (0.882, 0.647)
Four gallons of paint are used to paint 25 chair. If each chair used the same amount of paint how many gallons are used to paint each chair? Between what two whole number does your answer lie
∆FGH , the measure of <H=90, FH=48,GF=73,and, HG=55 What is the value of the sine of <F to the nearest hundredth
According to Coldwell Banker Real Estate Corporation, a home selling for $189,000 in Austin, Texas, would sell for $437,850 in Denver, Colorado. How much would a $350,000 home in Denver sell for in Austin? Round to the nearest $1000.
Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.