Answer:
Whats the question?
Step-by-step explanation:
You bought a magazine for $3 and some
candy bars for $2 each. You spent a total.
of $19. How many candy bars did you do
buy?
Answer:
8 candy bars
Step-by-step explanation:
Transform the question to an equation:
3 + 2x = 19
Solve:
2x = 16
x = 8
Check the answer:
3 + 2 (8) = 19
3 + 16 = 19
True
Hello There!
A magazine costs $3 and some candy bars. Let’s represent the number of candy bars as “X”
19-3=16 so that’s how much money is spent on candy bars.
If $16 is spent on candy bars then 8 candy bars were bought.
How many point(s) define a space?
Answer:
four pointsStep-by-step explanation:
Two points define a straight line (look at the picture #1).
Three non-collinear points define a plane (look at the picture #2).
Four points not lying in one plane, define space (look at the picture #3).
Given triangle ABC, (1,8), (-5, 13) and (7, 13) what type of triangle do these points make
Check the picture below.
so the vertex at the bottom is exactly half-way of the opposite side, and equidistant from the other two vertices, meaning the two slanted sides are twins, and thus this is an isosceles triangle.
hich is the lowest common denominator that would be used to add these four fractions?
3⁄8, 5⁄16, 2⁄3, 1⁄2
A. 48
B. 96
C. 32
D. 128
Step-by-step explanation:
To find the LCM, we must check and find the value that all four denominators can divide without a remainder.
Let's take 48
Therefore: 48/8= 6
48/16= 3
48/3= 16
48/2= 24
So, we can see that clearly 48 is our LCM
Therefore; 6(3/8)+3(5/16)+16(2/3)+24(1/2)
=18/48+15/48+32/48+24/48
=(18+15+32+24)/48
=89/48
Answer:
Its 48 to clarifiy instead of a long paragraph
Step-by-step explanation:
Which parent function is represented by the table?
Can someone please help?
Answer:
A. f(x) = x²
Step-by-step explanation:
Observing the values
when x= -2..............f(x)= 4..................this is x²............-2²= 4
when x= -1..............f(x)= 1......................this is x²............ -1² = 1
when x= 0..............f(x)=0.....................this is x².......... 0²= 0
when x= 1.............f(x)= 1........................this is x²........ 1²= 1
When x=2........... f(x) = 2...................... this is x²........ 2² = 4
⇒The first option is correct.
ANSWER
The correct answer is A.
EXPLANATION
We can see from the table that:
[tex]f( - 2) = {( - 2)}^{2} = 4[/tex]
[tex]f( - 1) = {( - 1)}^{2} = 1[/tex]
[tex]f(0) = {(0)}^{2} = 0[/tex]
[tex]f(1) = {( 1)}^{2} = 1[/tex]
[tex]f(2) = {(2)}^{2} =4[/tex]
In general we can conclude that,
[tex]f(x) = {( x)}^{2} = {x}^{2} [/tex]
Therefore the parent function represented by the table is
[tex]f(x) = {x}^{2} [/tex]
find the volume in terms of pi
[tex]A=100\pi\text{ ft}^2\\V=?\\\\V=\dfrac{4}{3}\pi r^3\\r=?\\\\100\pi=4\pi r^2\\r^2=25\\r=5\text{ ft}\\\\V=\dfrac{4}{3}\pi \cdot 5^3=\dfrac{500}{3}\pi \text { ft}^3[/tex]
Evaluate
2a + 3b for a = -1 and b = 0.
1. -1
2.-2
3. 1 1/2
4. 1/2
ANSWER ASAP PLEASE!
Answer:
So it's B.
Step-by-step explanation:
Because 2a+3b, a= -1 and b = 0
so, 2(-1) + 3(0)
-2 + 0 = -2
Hope my answer has helped you and if not i'm sorry.
Naomi made a triangular pyramid from cardboard. The triangular base has a height of 4 inches and a base length of 15 inches. The height of the pyramid is 6 inches. If Naomi wants to double the volume of the pyramid, which method can she use? She can double the base length of the base so that the new volume is 120 cubic inches. She can double the base length of the base so that the new volume is 360 cubic inches. She can double both the base length and height of the base so that the new volume is 240 cubic inches. She can double both the base length and height of the base so that the new volume is 720 cubic inches.
Answer:
She can double the base length of the base so that the new volume is 120 cubic inches
Step-by-step explanation:
The method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.
What is triangular pyramid?A tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedral and the only one that has fewer than 5 faces.
Volume of triangular pyramid :
Volume of triangular pyramid = 1/3 × Base Area × Height
According to the question
Naomi made a triangular pyramid from cardboard.
The triangular base has a height = 4 inches
The triangular base has a base length = 15 inches
The height of the pyramid = 6 inches
Therefore,
Base area of triangular pyramid
= [tex]\frac{1}{2} * Base\ of\ triangle * Height\ of\ triangle[/tex]
= [tex]\frac{1}{2} * 15 * 4[/tex]
= 30 [tex]inches ^{2}[/tex]
So,
Volume of triangular pyramid = 1/3 × Base Area × Height
= [tex]\frac{1}{3}[/tex] × 30 × 6
= 60 [tex]inches ^{3}[/tex]
Now,
Naomi wants to double the volume of the triangular pyramid
i.e
New Volume of triangular pyramid = 120 [tex]inches ^{3}[/tex]
Which can be obtain if she can double the base length of the base
Hence, the method she can use to double the volume of triangular pyramid is she can double the base length of the base so that the new volume is 120 cubic inches.
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Multiply the polynomials. (x – 5)(x2 + 4x – 2)
the cheap answer is simply
(x-5)(x²+4x-2)
we can simply multiply the terms on one by the terms of the other and then add like-terms and simplify.
[tex]\bf (x-5)(x^2+4x-2)\implies \begin{array}{cllll} x^2+4x-2\\ \times x\\ \cline{1-1}\\ x^3+4x^2-2x \end{array}+ \begin{array}{cllll} x^2+4x-2\\ \times -5\\ \cline{1-1}\\ -5x^2-20x+10 \end{array} \\\\\\ x^3+4x^2-2x-5x^2-20x+10\implies x^3+4x^2-5x^2-2x-20x+10 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill x^3-x^2-22x+10~\hfill[/tex]
Answer:
51x
Step-by-step explanation:
What is the equation of the line represented by the table below?
There are two ways to solve this question:
1. The quickest way to solve this question is perhaps to try substitute an x-value from the table into each of the possible answer equations and seeing if it returns the same y-value as in the table.
Let us use point (0, 2) from the table:
A. y = 12x - 5
if x = 0: y = -5
The value we wanted is 2, therefor A is not correct
B. y = -5x + 2
if x = 0, y = 2
This is correct, however to check if it really is this equation we should substitute a few more points in.
if x = -2: y = -5(-2) + 2 = 12 (correct)
if x = -1: y = -5(-1) + 2 = 7 (correct)
Given that the first three values are correct, we can say that the answer is B. y = -5x + 2.
To make sure even further however we may also substitute x = 0 into C. and D.
C. y = 10x - 5
if x = 0: y = -5 (not correct)
D. y = -2x + 2
if x = 0: y = 2 (this is correct so we must try substituting another value from the table)
if x = -2: y = -2(-2) + 2 = 6 (the value from the table for x = -2 is y = 12, therefor this is not correct)
Thus the answer is B. y = -5x + 2
2. The second method is to find the equation of the line itself without testing points. The first step is to find the gradient. We can do this using any two points, (x1, y1) and (x2, y2), and the formula for the gradient of a straight line:
m = (y2 - y1)/(x2 - x1)
Let's use the first two points from the table (-2, 12) and (-1, 7). Thus:
m = (7 - 12)/(-1 - (-2))
m = (-5)/1
m = -5
Now we can substitute this and one point (let's take (0, 2) into the formula for a straight line y - y1 = m(x - x1), where (x1, y1) is our point. Thus:
y - 2 = -5(x - 0)
y - 2 = -5x
y = -5x + 2
Therefor, looking at the possible answers, we can see that this matches answer B.
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 12) and (x₂, y₂ ) = (- 1, 7) ← 2 ordered pairs from table
m = [tex]\frac{7-12}{-1+2}[/tex] = - 5
note that (0, 2) is where the graph crosses the y- axis ⇒ c = 2
y = - 5x + 2 → B
Kenji and Antwan have jobs that pay differently. Antwan gets paid an hourly wage of $20. Kenji gets paid an hourly
wage of $15 and receives $35 a day in tips.
Both men worked h hours on Tuesday and earned the same amount of money.
if the equation 20h = 15h + 35 models this situation, how many hours did each man work?
Each worked 7 hours
Each worked 1 hour
Each worked 1 day.
Each earned $7.
Answer:
The answer is 7 hours
Step-by-step explanation:
20 times 7 is 140 and 15 times 7 is 105 so 105 plus 35 is 140 hence the answer is 7 hours.
The number of hours that each man works will be 7 hours. Then the correct option is A.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Kenji and Antwan have jobs that pay differently. Antwan gets paid an hourly wage of $20. Kenji gets paid an hourly wage of $15 and receives $35 a day in tips.
Both men worked h hours on Tuesday and earned the same amount of money. If the equation 20h = 15h + 35 models this situation.
Then the solution to the equation will be
20h = 15h + 35
5h = 35
h = 7 hours
The number of hours that each man works will be 7 hours. Then the correct option is A.
More about the solution of the equation link is given below.
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An angle that measures between 90 and 180° is called a(n)___angle,
Answer:
Obtuse
Step-by-step explanation:
An angle that measures between 90 and 180° is called an obtuse angle.
It must be above 90 degrees and below 180 degrees to be obtuse
Hope this helped!
~Just a girl in love with Shawn Mendes
If f(x)=6x^2-4 and g(x) =2x+2,find (f-g) (x).
Answer:
[tex]\large\boxed{(f-g)(x)=6x^2-2x-6}[/tex]
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)\\\\f(x)=6x^2-4,\ g(x)=2x+2\\\\\text{substitute:}\\\\(f-g)(x)=(6x^2-4)-(2x+2)\\\\=6x^2-4-2x-2\qquad\text{combine like terms}\\\\=6x^2-2x+(-4-2)\\\\=6x^2-2x-6[/tex]
Answer:
6x^2-2x-6 don't listen to these words it has to be 20 characters long
Which scatterplot shows no correlation?
There are three types of correlation.
1) Positive correlation: Two variables are said to be positively correlated when one variable increase then other variable will also increase or one is decrease then other will also decrease.
2) Negative correlation between two variables means when x is increasing but y is decreasing or vice versa.
3) No correlation: When the is scattred and we won't be able to find any distinct relationship then there will be no relation.
Notice in the first and third graph it has positive slope which means if x is increasing then y is also increasing. So, first and third graph is positively correlated.
Whereas in the second graph if x is increasing then y is decreasing. So, second graph is negatively correlated.
But in the last graph there is no such relationship as the data scattered randomly everywhere in the graph. So, it's shows no correlation.
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The last graph shows no correlation.
Option D is the correct answer.
What is correlation?Correlation is a statistical measure that indicates how strongly two variables are related or associated with each other.
It is a way of expressing the degree to which one variable is related to another variable.
We have,
The correlation is of different types.
- Positive correlation:
As one variable increases, the other variables also increase.
- Negative correlation:
As one variable increases, the other variables also increase.
- No correlation:
The variable increase and decrease as one variable increases.
Now,
We see that,
The last graph shows no correlation.
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the length of a flower garden is 9 meters. the width of the garden, w, is unknown. if the area of the garden is greater than 45 square meters, what are the possible values of w, its width, in meters?
Answer:
The width should be more than 5 m. So it can be 6,7 ...
Step-by-step explanation:
The length of a flower garden is = 9 m
The width of a flower garden is = w
The area of a flower garden > 45 sq. m
The area of a flower garden = l * b
l * b > 45
9 * b > 45
the width should be more than 5 m. So it can be 6,7 ...
Answer:
w > 36
Step-by-step explanation:
i got it right on edgeinuity
Which of the following equations is not equivalent to the others?
O y=-3X-4
O y=-3x+(-4)
O y=-4 + 3x
Oy=-4-3x
Mrs. Roberts poured 2 glasses of lemonade. The first glass contained 5 oz of lemon juice and 8 oz of water. The second glass contained 3 oz of lemon juice and 7 oz of water. Which glass of lemonade had a stronger lemon flavor? Show me or explain to me how you know. (Prove to me that your answer is correct!)
Answer:
The first glass
Step-by-step explanation:
I believe that first, you must find the ratio of lemonade to water in each glass.
[Remember that you can write a ratio in 3 ways (assume that x and y are numbers):
x : y
x / y
x to y
Now, our first glass of lemonade can be written as 5/8. If you were to write 5/8 as a decimal, you'd get 0.625.
Now, our second glass of lemonade can be written as 3/7. If you were to write 3/7 as a decimal, you'd get 0.428 (I rounded it to the nearest thousandth.)
0.625 > 0.428
0.625 is greater than 0.428, so therefore, the first glass had a stronger lemon flavor.
I hope this helps! :)
Step-by-step explanation:
The first glass has a total volume of 5 oz + 8 oz = 13 oz. Of the 13 oz, 5 oz is lemon juice, so the fraction of lemon is 5/13.
The second glass has a total volume of 3 oz + 7 oz = 10 oz. Of the 10 oz, 3 oz is lemon juice, so the fraction of lemon is 3/10.
We need to compare these fractions. To do that, we need to find the common denominator. In this case, 10×13 = 130.
5/13 = 50/130
3/10 = 39/130
So the first glass has the stronger lemon flavor.
ha diameter of 9 inches?
15. What is the area of a circle with a diameter of
is of 6.8 meters
a. 14.13 inches b. 28.26 inches c. 63
6 What is the volume of a cylinder with a radius of 6.8
and a height of 14 meters?
a. 95.2 meters b. 289.93 meters c. 2032 21
meters
7 What is the volume of a cylinder with a diameter of 5 feet
and a height of 7.4 feet?
b. 145.23 feet C. 580.9 feet
a. 37 feet
5 inches long,
8. How many bricks that are il inches long, 5 inches wide
and 3 inches deep can fit into a crate that is 55 inches lo
20 inches wide, and 12 inches deep?
b. 100
c. 120
a. 80
Question 1:
For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle.
They tell us that the diameter is 9 inches, then the radius is 4.5 inches. substituting we have:
[tex]A = \pi * (4.5) ^ 2\\A = \pi * 20.25\\A = 63.59[/tex]
Thus, the area of the circle is[tex]63.59 \ in ^ 2[/tex]
ANswer:
Option C
QUestion 2:
For this case we have that by definition, the volume of a cylinder is given by:[tex]V = \pi * r ^ 2 * h[/tex]
Where:
r: It's the radio
h: It's the height
According to the data we have to:
[tex]r = 6.8 \ meters\\h = 14 \ meters[/tex]
Substituting in the formula:
[tex]V = \pi * (6.8) ^ 2 * 14\\V = \pi * 46.24 * 14\\V = 2032.71[/tex]
Finally, the volume of the cylinder is [tex]2032.71 \ m ^ 3[/tex]
Answer:
Option C
Question 3:
For this case we have that by definition, the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
r: It's the radio
h: It's the height
According to the data we have to:
[tex]r = \frac {5} {2} = 2.5 \ feet\\h = 7.4 \ feet[/tex]
Substituting in the formula:
[tex]V = \pi * (2.5) ^ 2 * 7.4\\V = \pi * 6.25 * 7.4\\V = 145.23[/tex]
Finally, the volume of the cylinder is [tex]145.23 \ ft ^ 3[/tex]
Answer:
Option B
Question 4:
For this case we have that the volume of the bricks comes given by:
[tex]V = 11 * 5 * 3\\V = 165[/tex]
The volume of each brick is [tex]165 \ in ^ 3.[/tex]
On the other hand, we have that the volume of the crate is also obtained by multiplying its three dimensions, that is:
[tex]V = 55 * 20 * 12V = 13,200[/tex]
Thus, the volume of the crate is [tex]13,200 \ in ^ 3[/tex]
We divide the volume of the crate between the volume of the brick to know the quantity:
[tex]\frac {13,200} {165} = 80[/tex]
Thus, 80 bricks fit.
Answer:
Option A
Answer:
5). Option C. 63 inches
6). Option C. 2032.71 m³
7). Option b. 145.23 ft³
8). Option a. 80
Step-by-step explanation:
To find the answers
Question 5
Here r = 9/2 = 4.5
Area of circle = πr²
= 3.14 * 4.5²
= 63.585 ≈ 63
Option c is the correct answer
Question 6
Here r = 6.8 m and h = 14 m
Volume of cylinder = πr²h
= 3.14 * 6.8² * 14
= 2032.71 m² Option C
Question 7
Here r = 6.8 m and h = 14 m
Volume of cylinder = πr²h
= 3.14 * 5² * 7.4
= 145.23 feet² Option b
Question 8
Volume of one brick = lbh
= 11 * 5 * 3
Volume of crate = 55*20*12
number of briks = Volume of crate /Volume of one brick
= (55*20*12)/(11 * 5 * 3)
= 80 Option a
Which equation represents the graphed function?
Answer:
y = -2x + 3
Step-by-step explanation:
The three is the y-intercept, so when x=0, y will equal 3. (0,3)
The slope is negative (-2x), because the minus is present infront of x. So the line's going down.
And we can confirm that it's the function
y = -2x + 3 by letting one point in the line from the graph enter the function.
For example (1,1)
1 = -2x + 3. (let y = 1.)
1 = -2(1) + 3 (let x = 1)
1 = 1
so we can see when we let 1 = -2(1) + 3 it equals the y value on the line.
Answer:
Step-by-step explanation:
y= -2x + 3
A restaurant bill is $25 and a 20 percent tip should be given to the waiter.Which expression can be used to find the total amount that will be paid?
Hugh brought some magazines that cost $3.95 each and some some books that cost $8.95 each. He spent a total of $47.65 let m represent the number of magazines and b represent the number of books. Which equation models the situation
Answer:
3.95m + 8.95b = 47.65
Step-by-step explanation:
From this problem, you get quite a handful of information.
The variable "m" represents the # of magazines Hugh bought.
The variable "b" represents the # of books Hugh bought.
One magazine [m] cost $3.95
One book [b] cost $8.95
The total cost of books and magazines is $47.65
Based on the information, you can create an equation with two variables, representing the total cost and how many of each magazine and book Hugh bought.
If one magazine cost $3.95, the amount of money he spent on magazines can be represented by 3.95m.
If one book cost $8.95, the amount of money he spent of magazines can be represented by 8.95b.
And lastly, if the total cost of magazines and books Hugh bought is $47.65, the following equation can be made:
3.95m + 8.95b = 47.65
So, "3.95m + 8.95b = 47.65" is the correct equation. I hope this helps! :)
-2.08333333 in fraction form
[tex]x=-2.08\overline{3}\\100x=-208.\overline{3}\\1000x=-2083.\overline{3}\\1000x-100x=-2083.\overline{3}-(-208.\overline{3})\\900x=-1875\\x=-\dfrac{1875}{900}=-\dfrac{25}{12}[/tex]
Please help me!!...............
Answer:
50.
Step-by-step explanation:
the range is the lowest number subtracted from the highest; in this case, 93-43.
what is the percent change from 45 to 56? round to the nearest percent
Step-by-step answer:
Percentage difference = (new value-old value)/old value*100%
=(56-45)/45*100%
=11/45%100%
= 24.4%
Answer: 24
Step-by-step explanation:
its just 24 have the same question ^^
choose the equation that represents a line that represents a line that passes through points -3, 2 and 2,1 A. 5x+y=-13 B. 5x-y=17 C. x-5y=13 D. x+5y=7
bearing in mind that standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-2}{2-(-3)}\implies \cfrac{-1}{2+3}\implies -\cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-2=-\cfrac{1}{5}[x-(-3)]\implies y-2=-\cfrac{1}{5}(x+3)[/tex]
[tex]\bf y-2=-\cfrac{1}{5}x-\cfrac{3}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5\left(y-2 \right)=5\left( -\cfrac{1}{5}x-\cfrac{3}{5} \right)}\implies 5y-10=-x-3 \\\\\\ 5y=-x+7\implies x+5y=7[/tex]
what is the factorization of 3x^2-8x+5
Final answer:
The quadratic expression 3x²-8x+5 is factored by finding two numbers that multiply to 15 and sum to -8, resulting in the factorization (3x-5)(x-1).
Explanation:
The factorization of the quadratic expression 3x²-8x+5 can be found by looking for two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 5), and also sum to give the coefficient of x (which is -8). These numbers are -5 and -3, as (-5) × (-3) = 15 (which is 3 × 5) and (-5) + (-3) = -8. Therefore, the expression can be factored as (3x-5)(x-1).
Given the frequency table, what percentage of the students in grades 9–10 like rap music? Round to the nearest whole percent. Band Preference for School Dance Rap Rock Country Row totals Grades 9–10 40 30 55 125 Grades 11–12 65 20 35 120 Column totals 105 50 90 245
Answer:
32%
Step-by-step explanation:
The given table in the correct format is attached in the image below. We need to tell what percentage of students from the grades 9 - 10 like rap music.
Total number of students in grades 9 - 10 = 125
Number of students in grades 9 - 10 who like rap music = 40
Percentage of students in grades 9 - 10 who like the rap music will be calculated as:
[tex]\frac{\text{Number of students in grades 9-10 who like rap music}}{\text{Total number of students in grades 9-10}} \times 100 \%[/tex]
Using the given values in above expression we get:
[tex]\frac{40}{125} \times 100\%\\\\= 32\%[/tex]
This means 32% of the students in grades 9 - 10 like rap music
Answer:
B: 32% I got it Correct on my test.
Step-by-step explanation:
Hope this helps :)
Sam bought brushes for $8, a palette for $5, and oil paints for $15. He paid $29.82 in all. What sale-tax rate did Sam pay?
Add the cost of the three items:
8 + 5 + 15 = $28
Subtract that amount from the total:
29.82 - 28 = $1.82 ( amount he paid in tax)
Divide the tax amount by the cost of the items:
1.82 / 28 = 0.065
Multiply that by 100:
0.065 x 100 = 6.5% sales tax rate
15. If the 8% tax on an item amounts to $0.96, what is the final price (tax included) of the item?
Answer:
The Total including sales tax would equal $1.04.
Step-by-step explanation:
The total tax added is $0.08.
Answer:
$1.04
Step-by-step explanation:
.96*.08=.08
.08+.96=1.04
11. The probability that a dessert sold at a certain cafe contains chocolate is 75%. The probability that a dessert containing chocolate also contains nuts is 23%. Find the probability that a dessert chosen at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.
The probability that a dessert chosen at random contains nuts given that it contains chocolate is 17.3%.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a dessert chosen at random contains nuts and chocolate - 75% x 23% = 17.3%
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The conditional probability that a dessert contains nuts given that it contains chocolate is approximately 30.7%, calculated by dividing the probability of both events occurring by the probability of the condition (chocolate presence).
The student is asking for the conditional probability that a dessert contains nuts given that it contains chocolate. Since we are given that the probability a dessert contains chocolate (P(C)) is 75%, and the probability that a dessert contains both chocolate and nuts (P(C AND N)) is 23%, we can find the conditional probability (P(N|C)) by dividing the probability of the joint event by the probability of the condition:
P(N|C) = P(C AND N) / P(C)
P(N|C) = 0.23 / 0.75
P(N|C) = 0.3067
Therefore, the probability that a dessert chosen at random contains nuts given that it contains chocolate is about 30.7% when rounded to the nearest tenth of a percent.