Complete the table of values below:
x -3 -2 -1 0 1 2 3 How the graph relates to y=2x
y=2x Answer
Answer
Answer
Answer
Answer
Answer
Answer
Not applicable
y=-2x Answer
Answer
Answer
Answer
Answer
Answer
Answer
multiplied by Answer
y=(3)(2x)
Answers
Answer:
The values of x are:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a [tex]y = 2^x[/tex]
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. [tex]y = -2^x[/tex]
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. [tex]y = (3)(2^x)[/tex]
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Answer:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b.
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c.
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Related Questions
Find the area of the composite figure in square mm. Round your
answer to the nearest square milimeter. (Enter only a number as
your answer.)
Answers
Answer:
521
Step-by-step explanation:
Composite figure.
Draw a straight down from C to line segment AB. This forms a triangle.
Now, the area of this figure=
Area of semicircle+area of rectangle+ area of triangle.
Rectangle area formula = l times w
Length - 20
Width =14
14 times 20 = 280
Area of rectangle = 280
Semicircle area = area of circle/2
Area of circle = π[tex]r^2[/tex]
Diameter =20= 2r
r=10
π[tex]r^2[/tex]= π 10^2 =100π
100 times 3.14 =314
314/2 = 157
Area of semicircle = 157
Area of triangle= bh/2
Triangle's base= 32-20=12
Triangles height = 14
14 times 12 = 168
168/2 = 84
Area of triangle: 84
Area of semicircle+area of rectangle+ area of triangle.
157+280+84 =521
Simplify by combining like terms: 5x + 3x + 10x
Answers
Answer:
answer is 8x+10x
18x
is the answer
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answers
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region? A square is inscribed in a circle with a diameter of 12 StartRoot 2 EndRoot millimeters. Everything outside of the square is shaded. Recall that in a 45 – 45 – 90 triangle, if the legs each measure x units, then the hypotenuse measures x units. (72π – 144) mm2 (72π – 72) mm2 (288π – 288) mm2 (288π – 144) mm2
Answers
Answer: A. (72π - 144) mm²
Step-by-step explanation:
[tex]A_{shaded}=A_{circle}-A_{square}\\\\\\A_{circle}=\pi \cdot r^2\\.\qquad \ =\pi \bigg(\dfrac{12\sqrt2}{2}\bigg)^2\\\\.\qquad \ =\pi (6\sqrt2)^2\\.\qquad \ =72\pi\\\\\\A_{square}=side^2\\.\qquad \quad =\dfrac{12\sqrt2}{\sqrt2}^2\\\\.\qquad \quad =12^2\\\\.\qquad \quad =144\\\\\\\large\boxed{A_{shaded}=72\pi-144}[/tex]
The area of shaded region is (72π – 144) square millimeters.
To understand more, check below explanation.
Area of shaded region:It is given that,
The diameter of circle is [tex]12\sqrt{2}[/tex] millimeters.
Since, radius = diameter/2
So that, radius of circle[tex]=12\sqrt{2}/2=6\sqrt{2}[/tex]
now, we have to find area of circle,
[tex]Area=\pi *r^{2} \\\\Area=\pi *(6\sqrt{2} )^{2} \\\\[/tex]
Area = 72π square millimeters
The side of inscribed square[tex]=12\sqrt{2} /\sqrt{2}[/tex] = 12mm
Since, area of square= (side)^2
Area of square= 12 * 12 = 144 square millimeters
To find the area of shaded region, subtract area of square from area of circle.
Area of shaded region = area of circle - area of square
Area of shaded region = (72π – 144) square millimeters.
Learn more about the area of circle here:
https://brainly.com/question/14068861
Write the expression in standard form. -3 + yi = x + 6i
Answers
Answer:
The expression in standard form is -3 + 6i
Step-by-step explanation:
Writing complex equation in standard form we have;
-3 + yi = x + 6i
We transfer the real and imaginary parts to be on different sides of the equation as follows;
yi - 6i = x + 3
We factorize the imaginary part;
i(y-6) = x + 3
We note that the real portion on the left hand side of the equation is zero, therefore, we have;
i(y-6) + 0= x + 3
x + 3 = 0
Therefore, x = -3
Substituting the value of x in the first equation, we have;
-3 + yi = -3 + 6i
Comparing gives;
y = 6
The expression in standard form is -3 + 6i.
Find an equation for the nth term of the sequence. -3, -12, -48, -192, ... (1 point)
Answers
a = -3
common ratio(r) = -12/(-3) = 4
nth term = a.r^(n-1)
= -3.(4)^(n-1)
Please can someone help!
Answers
Answer:
51 mph
Step-by-step explanation:
→ The first thing we need is a formula which links speed, distance and time so,
Speed = Distance ÷ Time
Speed = mph
Distance = metres/miles
Time = hours
→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,
Speed = Distance ÷ Time
→ Rearrange to get distance as subject
Distance = Speed × Time
→ Substitute in the values
Distance = 45 × 40
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
40 ÷ 60 = 0.666666667
→ Substitute in the time value multiplied by the speed
Distance = 45 × 0.666666667 = 30
⇒ 30 metres/miles is overall distance for the first part of the journey
→ Now we have to work out the distance for the second part of the journey. State the distance formula.
Distance = Speed × Time
→ Substitute in the values into the distance formula
Distance = 60 × 25
→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60
25 ÷ 60 = 0.416666667
→ Substitute in the time value multiplied by the speed
Distance = 60 × 0.416666667 = 25
⇒ 25 metres/miles is overall distance for the second part of the journey
→ Now we have to add the distance of both the journeys together
25 + 30 = 55
→ Then we add the times of the journey together
40 minutes + 25 minutes = 65 minutes
→ Convert 65 minutes into hours
65 ÷ 60 = 1.08333 hours
→ Substitute both values into the speed = distance ÷ time formula
Speed = 55 ÷ 1.08333 = 50.76923077
→ The question says to round it to the nearest whole number so,
50.76923077 = 51 mph
Miss Smith bought 60 notebooks and 72 pencils to make identical packages with some notebooks and some pencils for her students. She used everything she bought, and every student got a package. What is the largest number of packages she can make? How many notebooks and pencils would be in each package?
Answers
Answer: 12 packages with 5 notebooks and 6 pencils in each package.
Step-by-step explanation:
The greatest common factor of 60 and 72 is 12. Thus divide both numbers(60 and 72) by 12 to get 5 and 6. Thus, Miss Smith made 12 packages with 5 notebooks and 6 pencils in each package.
Answer:
12 packages with 5 notebooks and 6 pencils in each package.
Step-by-step explanation:
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x − 4)3 − 7. The point (0, 0) on the graph of f(x) corresponds to which point on the graph of g(x)?
Answers
Answer:
The point (0, 0) in the graph of f(x) corresponds to the point (4, -7) in the graph of g(x)
Step-by-step explanation:
Notice that when we start with the function [tex]f(x)=x^3[/tex], and then transform it into the function: [tex]g(x)=(x-4)^3-7[/tex]
what we have done is to translate the graph of the function horizontally 4 units to the right (via subtracting 4 from the variable x), and 7 units vertically down (via subtracting 7 to the full functional expression).
Therefore, the point (0, 0) in the first function, will now appeared translated 4 units to the right (from x = 0 to x = 4) and 7 units down (from y = 0 to y = -7).
then the point (0, 0) after the translation becomes: (4, -7)
Answer:4, -7
Step-by-step explanation:
1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Answers
Step-by-step explanation:
68$53++83(-$(7(3($++$
Explanation:
(x+2)(9-x)
= 9x - x^2 + 18 - 2x
= -x^2 + 7x + 18
Solve the equation 2q – 4 = 26 for q.
Answers
Answer:
q = 15
Step-by-step explanation:
2q – 4 = 26 (add 4 to both sides)
2q = 26 + 4
2q = 30 (divide both sides by 2)
q = 30/2
q = 15
A item in a shop is increased in price by 20% and then decreased in price by 20% a month later.
Is there an overall increase or
decrease in price and by how
much?
please give the method too
Answers
Answer:
Decrease of 4% ($4).
Step-by-step explanation:
Suppose the initial price was $100. An increase of 20% will make the price $120.
Now we decrease it 20% which brings it to 120 - 0.20 * 120
= 120 - 24
= $96.
So that's an overall decrease of $4 or 4%.
What is the solution to this equation?
4x-3 + 2x= 33
O A. x= 15
B. x = 18
O c. x = 5
O D. x = 6
Answers
Answer:
4x – 3 + 2x = 33
6x = 36
x = 6
D. x = 6
If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t^2 + 120t. How long will it take the rocket to return to the ground? Group of answer choices
Answers
Answer:
[tex]Time = 7.5\ seconds[/tex]
Step-by-step explanation:
Given
[tex]Equation:\ h(t) = -16t^2 + 120t[/tex]
[tex]Initial\ Velocity = 160ft/s[/tex]
Required:
Determine the time taken to return to the ground
From the equation given; height (h) is a function of time (t)
When the rocket returns to the ground level, h(t) = 0
Substitute 0 for h(t) in the given equation
[tex]h(t) = -16t^2 + 120t[/tex]
becomes
[tex]0 = -16t^2 + 120t[/tex]
Solve for t in the above equation
[tex]-16t^2 + 120t = 0[/tex]
Factorize the above expression
[tex]-4t(4t - 30) = 0[/tex]
Split the expression to 2
[tex]-4t = 0\ or\ 4t - 30 = 0[/tex]
Solving the first expression
[tex]-4t = 0[/tex]
Divide both sides by -4
[tex]\frac{-4t}{-4} = \frac{0}{-4}[/tex]
[tex]t = \frac{0}{-4}[/tex]
[tex]t =0[/tex]
Solving the second expression
[tex]4t - 30 = 0[/tex]
Add 30 to both sides
[tex]4t - 30+30 = 0+30[/tex]
[tex]4t = 30[/tex]
Divide both sides by 4
[tex]\frac{4t}{4} = \frac{30}{4}[/tex]
[tex]t = \frac{30}{4}[/tex]
[tex]t = 7.5[/tex]
Hence, the values of t are:
[tex]t =0[/tex] and [tex]t = 7.5[/tex]
[tex]t =0[/tex] shows the time before the launching the rocket
while
[tex]t = 7.5[/tex] shows the time after the rocket returns to the floor
Help me with 2a and 2b please
Answers
Answer:
Step-by-step explanation:
A∩B={x| x∈a and x∈B}
a) A∩B={4,6}
b) A∩B={ 4,9}
c) A∩B={yellow,green}
Find the pattern and fill in the missing numbers: 0, …, 9, 18, 30, 45, ...
Answers
it is 9
and it is also 54
Answer:
3 and 63.
Step-by-step explanation:
The sequence formula is [tex]\frac{3n(n+1)}{2}[/tex].
Resulting in a sequence of 0, 3, 9, 18, 30, 45, 63.
Solve for x. − 6 ≥ 10 − 8x.
Answers
Answer:
2</x or x>/2
Step-by-step explanation:
-6>/10-8x
-10 -10
-16>/-8x
divide both sides by -8
2</x or x>/2
the reason the sign is bc u r dividing by a - number.
Answer:
x ≥ 2
Step-by-step explanation:
-6 ≥ 10 - 8x
Subtract 10 on both parts.
-6 - 10 ≥ 10 - 8x - 10
-16 ≥ -8x
Divide both parts by -8 remembering to reverse sign.
-16/-8 ≤ (-8x)/-8
2 ≤ x
Switch parts.
x ≥ 2
What are two integers whose sum is -2 and product is -80?
Answers
Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
help if you can but this is kinda urgent any help is welcome tho
Answers
Answer:
(Change in y)/(change in x) is defined as the average rate of change.
For a linear equation:
y = a*x + b
A is the average rate of change, and is called the "slope" of the linear equation, and this is a constant.
Then the sentence will be:
"The average change between two ordered pairs (x,y) is the ratio (change in x)/(change in y)
In a linear function, this is called the slope, and it is constant"
What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060
Answers
Answer:
Option (D)
Step-by-step explanation:
Sum of interior angles of a polygon is represented by the expression,
Sum of interior angles = n(n - 1)×180°
Here n is the number of sides of a polygon
If n = 18,
Sum of 18 sided polygon = (18 - 1) × 180°
= 7 × 180°
= 3060°
Therefore, sum of interior angles of a 18 sided polygon will be 3060°.
Option (D) will be the answer.
Answer:
2880
Step-by-step explanation:
SUM=_-2=
18-2=16
16*180 = 2880 OR
18*160 = 2880 degrees
A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h
Answers
Answer:
d) 405 = 15 times 4.5 times h
The height of the prism 'h' = 6 inches
Step-by-step explanation:
Explanation:-
Given Volume of prism
V = 405 cubic inches
Given length of the prism
L = 15 inches
Given width of the prism
W = 4.5 inches
The volume of the prism
V = l w h
405 = 15 ×4.5× h
405 = 67.5 h
Dividing '67.5' on both sides , we get
h = 6 inches
Final answer:-
The height of the prism 'h' = 6 inches
Answer: V = l w h. 405 = 15 times 4.5 times h
Step-by-step explanation:
Given the following :
Volume of prism = 405 in^3
Length = 15 inches
Height = h
Width = 4.5 inches
Recall :
The volume of a prism is the product of the Base and the height.
That is;
Volume = Base × height
However, Base of prism is given by the area of the base shape of the prism.
From our parameters Base shape of the prism is a rectangle.
Therefore, Area of rectangle = Length × width
= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism
Therefore, Volume of prism equals ;
Volume = 15 × 4.5 × h
Volume = 405in^3
Volume = Base × height
405 = 15 × 4.5 × h
PLLLLLLLLLLLLLLLEEEEEEEEEAAAAAAAASSSSSSSE HEEEEEEEEELP As soon as a new car that costs $25,000 is driven off the lot, it begins to depreciate at a rate of 24.9% annually. About how much money is the car worth after the second year?
Answers
Answer:
The value of the car after two years is $14,100.025
Step-by-step explanation:
Here, we want to calculate the value of a car after its second year, given the depreciation percentage.
To get the value of the car year after year at the fixed percentage level, what we do is to set up an exponential equation;
V = I(1-r)^t
where V is the present value
I is the initial value = $25,000
r is the rate = 24.9% = 24.9/100 = 0.249
t is the number of years = 2 in this case
So we substitute these values in the depreciation case and have;
V = 25000(1-0.249)^2
V = 25000(0.751)^2
V = $14,100.025
The number 5600 is first decreased by 15 % . The value obtained is next increased by 10 % . Find the final number.
Answers
Answer:
5236
Step-by-step explanation:
the original number is equal to 100%
Therefore 5600=100% how about 85 %(which is what is left after decreasing 15%)
85×5600÷100=4760
the new original is(100%)=4760
4760=100% how about 110%(which is what you'll have after adding 10%)
4760×110÷100=5236
Is 19⁄18 an improper fraction or a mixed number?
Answers
Answer:
Improper fraction.
Step-by-step explanation:
19/18 is an improper fraction. If it were a mixed number, you would have an integer followed by a fraction, like 1 and 1/18.
Hope this helps!
Answer:
It would be an improper fraction.
A mixed number would be 1 whole, while the other part is a fraction.
[tex]1\frac{1}{18}[/tex]
A improper fraction is when the numerator is greater than the denominator, such as
[tex]\frac{19}{18}[/tex]
Hope this helps
Answer by
~[tex]Fishylikeswater[/tex]~
What is the solution to this equation?
4x + 2(x + 6) = 36
O A. x = 7
B. x = 5
O c. x = 4
D. x = 8
Answers
Simplifying
4x + 2(x + 6) = 36
Reorder the terms:
4x + 2(6 + x) = 36
4x + (6 * 2 + x * 2) = 36
4x + (12 + 2x) = 36
Reorder the terms:
12 + 4x + 2x = 36
Combine like terms: 4x + 2x = 6x
12 + 6x = 36
Solving
12 + 6x = 36
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 6x = 36 + -12
Combine like terms: 12 + -12 = 0
0 + 6x = 36 + -12
6x = 36 + -12
Combine like terms: 36 + -12 = 24
6x = 24
Divide each side by '6'.
x = 4
Simplifying
x = 4
Complete the following equivalent fractions. 18/54 = ?/3
Answers
Answer:
1
Step-by-step explanation:
do 18 times 3
then do 54 divided by 54
to find the following number
hope this helps
A box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted. A pair of contact lenses is drawn at random from the box.Find the probability that it is not tinted.What is the answer:2/3 2/5
Answers
Answer:
[tex]\dfrac{2}{3}.[/tex]
Step-by-step explanation:
It is given that a box contains 2 dozen pairs of contact lenses ,of which 8 pairs are tinted.
1 dozen = 12 units
Total pairs of contact lenses [tex]=2\times 12 = 24[/tex]
Tinted pairs of contact lenses = 8
Pairs of contact lenses not tinted = 24 - 8 = 16
If a pair of contact lenses is drawn at random from the box, then we need to find the probability that it is not tinted.
[tex]P(\text{Not tinted})=\dfrac{\text{Pairs of contact lenses not tinted}}{\text{Total pairs of contact lenses}}[/tex]
[tex]P(\text{Not tinted})=\dfrac{16}{24}[/tex]
[tex]P(\text{Not tinted})=\dfrac{2}{3}[/tex]
Therefore, the required probability is [tex]\dfrac{2}{3}.[/tex]
‼️10 points‼️
9. Match the graph with its equation.
A. x= 4
B. y= 4
C. x= -4
D. y= -4
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
C. x = -4
▹ Step-by-Step Explanation
The line passes through the point -4, and a vertical line represents x. Therefore, the answer is x = -4.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
x= -4
Step-by-step explanation:
The graph shows that the line crosses -4 and stays paralell with y-axis so the equation is x=-4
I need help please help me.
Answers
Answer:
20°.
Step-by-step explanation:
According to both the diagram and the presented angle measure, m∠RPS + m∠QPR = m∠QPS.
(4x + 27) + (9x - 115) = 107
4x + 9x + 27 - 115 = 107
13x - 88 = 107
13x = 195
x = 15
Now that we have the value of x, we can find the m∠QPR.
9x - 115
= 9 * 15 - 115
= 135 - 115
= 20
So, m∠QPR is 20°.
Hope this helps!
i will mark brainliest for correct answers!!
200 students attend a school which offers French and History. 10% of those who take History also take French and 4 times as many students take History as take French. 8% of the students take neither History or French. By drawing a Venn Diagram find the probabilty that a student picked at random does History and French. Give your answer as a percentage.
Answers
Answer:
8%
Step-by-step explanation:
Hello,
8% of the students take neither History or French
so we have 8*200/100=8*2=16 students out of French and History
let s say that
a is the number of students taking only History
b is the number of students taking both History and French
c is the number of students taking only French
10% of those who take History also take French
so 0.10(a+b)=b <=> 0.10a+0.10b=b
<=> 0.10a+0.10b-0.10b=b-0.10b=0.9b
<=> 0.10a=0.90b
let's multiply by 10 it comes a = 9b
4 times as many students take History as take French
so a + b = 4 (b + c)
it comes 9b + b = 10b = 4b + 4c
<=> 10b-4b=4b+4c-4b=4c
<=> 6b=4c
<=> 3b=2c
<=> c = 3b/2
and we know that a + b + c = 200 - 16 = 184
so
9b + b + 3b/2 = 184 we can multiply by 2 it comes
20 b + 3b = 184*2
23b = 184*2 = 23 * 8 *2 = 23*16
b = 23*16/23 = 16
so b = 16
c = 3*16/2 = 24
c = 24
a = 9b = 144
a = 144
you can see the Venn diagram below
and then the probability that a student picked at random does History and French is 16/200 = 8%
so the answer is 8%
hope this helps