[tex]x^4+4x^3-8x-32=0[/tex]
Can be factoried into:
[tex](x^3-8)(x+4)=0\\[/tex]
Now you're looking for which values of x will make the equations in the brackets equal to 0, since as long as one is equal to 0, they will be multiplied into 0.
First we'll do:
[tex]x^3-8=0[/tex]
We're looking for what number cubed is equal to 8, which is 2.
Note: -2 is also a possibility, but if you plug it in, you'll see that it doesn't work.
Second we'll do:
[tex]x+4=0[/tex]
This one's pretty easy, x will be -4.
So your solutions are:
x = 2, -4
The solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
What is a polynomial?Polynomials are sums of terms of the form k⋅xⁿ.
where k is any number
n is a positive integer.
Example:
2x + 4x - 7 is a polynomial
We have,
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 _______(1)
Divide into two parts.
[tex]x^{4}[/tex] + 4x³
-8x - 32
Take out the common from each part.
x³ ( x + 4 )
- 8 ( x + 4 )
Now,
We have,
x³ ( x + 4 ) - 8 ( x + 4 ) = 0
We can write this as:
(x³ - 8) (x + 4) = 0
Now,
We need to find the x values.
x³ - 8 = 0
x³ = 8
x = ±2
Put x = 2 in (1)
[tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0
x = 2
16 + 32 - 16 - 32
0 = 0
x = 2 is satisfied
Put x = -2 in (1)
16 - 32 + 16 - 32 = 0
-64 ≠ 0
x = -2 is not satisfied
x + 4 = 0
x = -4 putting in (1)
256 - 256 + 32 - 32 = 0
0 = 0
x = -4 is satisfied
Thus the solutions of the polynomial [tex]x^{4}[/tex] + 4x³ - 8x - 32 = 0 are 2 and -4.
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Given: f(x)
=
x - 2
x+8
Answer:
f×=×-2×+8=10×f=20xf=30×f
HELP
The coordinates of point T are (0,4). The midpoint of ST is (1,−3). Find the coordinates of point S.
The coordinates of S are (-1 , 11)
In the given statement is :
The coordinates of point T are (0,4). The midpoint of ST is (1,−3).
To find the coordinates of point S.
Now, According to the question:
Let the coordinate of point S are (x, y).
T (0, 4) is the mid point of ST
=> [tex]\frac{x+1}{2}=0 , \frac{y+(-3)}{2}=4[/tex]
=> x+1 =0 , y -3 = 8
=> x = -1 , y = 11
So, the coordinates of S are (-1 , 11)
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17. Higher Order Thinking The average rate
that human hair grows is 1.27 centimeters
per month. Elena let her hair grow for
3 months. Then she got 1.9 centimeters of
her hair cut off. If Elena's hair grows at the
average rate, how much longer is Elena's
hair now than 3 months ago? Explain how
to solve the problem. Then solve.
Elena's hair has grown in length overall net by. 1.81cm
It is given to us that the average rate at which human hair grows is 1.27 centimeters per month.
Elena allowed her hair to grow for three months, so that's a given. Then she had her hair chopped short by 1.9 cm.
Elena's hair naturally grows at a typical rate.
First, we'll figure out how much Elena's hair has grown in three months, and then from that figure, we'll deduct the length that has been trimmed.
Elena's hair grew 3.x*1.27=3.81 cm in three months.
The amount of hair that was removed was 1.9 cm.
Elena's hair has grown in length by 3.81 cm over the course of three months, minus the length that has been chopped, for a total net growth of 1.91 cm.
Growth in 3 months less the length that was removed is 3.81 – 1.9 = 1.91 cm
Hence, the total net growth of Elena's hair is 1.81cm
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The empire state building in new york city is about 1,450 feet high (including the antenna at the top) and 400 feet wide. Andre wants to make a scale drawing of the front view of the empire state building on an 8 1/2 inch by 11 inch piece of paper. select a scale that you think is the most appropriate for the scale drawing.
A. 1 inch to 1 foot
B. 1 inch to 100 feet
C. 1 inch to 1 mile
D. 1 centimeter to 1 meter
E. 1 centimeter to 50 meters
F. 1 centimeter to 1 kilometer
The scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters. (Correct choice: E)
What scale factor is the most appropriate to make an scale drawing of the Emipre State Building?
Scale factor are useful resources to make representations of huge and diminute representations of entire systems based on the application of length ratios defined below:
d / d' = r (1)
Where:
r - Length ratio, in feet per inchd - Real length, in feetd' - Scale length, in inchesNow we find the minimum reduction scale to fit the building in the paper.
Width
r' = 400 ft / 8.5 in
r' = 47.058 ft / in
Height
r' = 1,450 ft / 11 in
r' = 131.819 ft / in
The minimum reduction scale to fit the building in the paper is 131.819 ft / in (approx. 15.818 m / cm, that is 1 centimeter to 15.818 meters), that is, 1 centimeter to 131.819 feet. Then, the scale factor that is most appropriate for the scale drawing is 1 centimeter to 50 meters.
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50 points! with brainlyiest to first person!
given f(x)=3(4-x) what's the value of f(-4)
Answer:
f(-4) = 24
Step-by-step explanation:
f(x) = 3(4-x)
( substitute )
f(-4) = 3 x ( 4- (-4))
( calculate )
f(-4)= 24
9 Continuously compounded interest: word problems 82J
Learn with an example
Gigi opened a savings account and deposited $600.00 as principal. The account earns 3%
interest, compounded continuously. What is the balance after 2 years?
Use the formula A = Pe", where A is the balance (final amount), P is the principal (starting
amount), e is the base of natural logarithms (~2.718 28), r is the interest rate expressed as
a decimal, and t is the time in years.
Round your answer to the nearest cent.
$
Submit
The final amount in Gigi's amount after two years is $637.102.
Compound interest is also known as interest on principal and interest is the practice of adding interest to the principal amount of a loan or deposit.
Gigi opened a savings account.
The principal amount she deposited, P = $600
The interest rate, r = 3% = ( 3 / 100 ) = 0.03
The formula for the compound interest is given as:
[tex]A=Pe^{rt}[/tex]
Where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.
Then the amount in the account after t = 2 years will be:
[tex]A=Pe^{rt}\\A = 600 \times e^{(0.03 \times 2)}[/tex]
A = 600 × e⁰·⁰⁶
A = 600 × 1.06183654655
A = 637.101927927
A = $637.102
Therefore, the final amount in the account is $637.102.
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Find the smallest number by which 80 is multiplied to make it a perfect square?
Step-by-step explanation:
2*40=80
so, the smallest of 80 is 2
Step-by-step explanation:
question: find the smallest number by which 80 is multiplied to make a perfect square.
80 x 6 = 400
the square root of 400 = 20
therefore 6 is the smallest number that multiplies by 80 to give a perfect square.
GIVING BRAINIEST IF CORRECT!!!!
Express in simplest radical form.
Your answer is in the screenshot!
The ratio of stars to circles is 3 to 2. If
there are 28 circles, then how many stars are there?
Answer:
42
Step-by-step explanation:
3 to 2 can be represented as 3/2. Remember the numerator represents stars while the denominator represents circles. Set up a proportion the criss multiply. This ratio would be 3/2 = x/28. First multiply 28 x 3 and set it equal to 2x. This gives you 84=2x. Divide 2 by each side and you will get 42 stars.
11) What two numbers will √5 be between on a number line?
a) 2.01 and 2.24
62.0 and 3.25
2.1 and 2.156
d) 1.9 and 2.0
Answer:a
Step-by-step explanation:
it is 2.2360679775 which is in between 2.01 and 2.24
Answer: a. between 2.01 and 2.24
Step-by-step explanation:
√4=2
√9=3
9-4=5
5-4=1
1/5=0.2
√5=
√(4+1)=
√4+0.2=
2+0.2=2.2 ==> between 2.01 and 2.24: a
the total weight of henry peter and david is 123.peterr is 15 kg hevier than david. david is 3kg lighter than henry find henrys weight
The ages will be:
Henry's weight = 38kg
David =35kg
Peter = 50 kg
How to calculate the weight?Let Henry's weight be represented by x
David is 3kg lighter. This will be x-3.
Peter is 15kg heavier. This will be:
= x-3 + 15 = x +12
This will be:
x + x-3 + x + 12 = 123
3x + 9 = 123
3x = 123 - 9
3x =114
Divide
x = 114/3 = 38
Therefore, Henry's weight = 38kg
David =x - 3 = 38 - 3 = 35kg
Peter =35 + 15 50 kg
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the sum of 4 times a number and 9 is equal to 6
use the variable y for the unknown number
Answer:
-3/4
Step-by-step explanation:
4y + 9 = 6
4y = 6-9 = -3
y = -3/4
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5)
The line that is the perpendicular bisector of the segment is 12x - 2y= 13
How to determine the line that is the perpendicular bisector of the segment?The endpoints of the segment are
R(-1, 6) and S(5, 5)
Calculate the midpoint of the above segment using
RS = 1/2 * (x1 + x2, y1 + y2)
So, we have
RS = 1/2 * (-1 + 5, 6 + 5)
This gives
RS = (2, 5.5)
Calculate the slope of the segment using
Slope RS = (y1 - y2)/(x1 - x2)
So, we have
Slope RS = (5 - 6)/(5 + 1)
This gives
Slope RS = -1/6
The slopes of perpendicular lines are opposite reciprocal
This means that the slope of the perpendicular bisector is
m = -1/Slope RS
So, we have
m = -1(-1/6)
Evaluate
m = 6
The line that is the perpendicular bisector of the segment is calculated as
y = m(x - x1) + y1
Where
(x1, y1) = Midpoint RS = (2, 5.5)
So, we have
y = 6(x - 2) + 5.5
Evaluate
y = 6x - 12 + 5.5
y = 6x - 6.5
Multiply through by 2
2y = 12x - 13
Rewrite as
12x - 2y= 13
Hence, the line that is the perpendicular bisector of the segment is 12x - 2y= 13
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t the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.10 and the cost of a large greeting card is $4.15. How much would it cost to get 2 small greeting cards and 3 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The Total cost of 2 small and 3 large greeting cards is $16.65.
The Total cost of x small and y large greeting cards is $2.10x+$4.15y.
Given
Cost of the small greeting card =$2.10.
Cost of the large greeting card =$4.15.
We have to find the Total cost of 2 small and 3 large greeting cards and the total cost of x small and y large greeting cards.
First, we will find the Total cost of 2 small and 3 large greeting cards
Cost of 3 small greeting cards=2[tex]\times\\[/tex]2.10 =$4.2
Cost of 4 large greeting cards=3[tex]\times[/tex]4.15=$12.45
Total cost=$4.2+$12.45=$16.65
Therefore, the Total cost of 2 small and 3 large greeting cards is $16.65.
Now, the total cost of x small and y large greeting cards
Cost of x small greeting cards=x[tex]\times\\[/tex]2.10 =$2.10x
Cost of y large greeting cards=y[tex]\times[/tex]4.15=$4.15y
Total cost=$2.10x+$4.15y
Therefore, the Total cost of x small and y large greeting cards is $2.10x+$4.15y.
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Total cost, 2 small greeting cards and 3 large greeting cards: 16.65
Total cost, x small greeting cards and y large greeting cards: 2.10x+4.15y
I don’t understand this question
Answer:
f(-4) = - 64
f(3) = - 15
f(-a) = - 3a² - 4a
-f(a) = 3a² - 4a
f(a + h) = - 3a² - 6ah - 3h² + 4a + 4h
Pay careful attention that you do not miss the negative signs in some of these terms
Step-by-step explanation:
The function is f(x) = -3x² + 4x
To evaluate the function at any value of x, simply substitute for x in the function expression
f(-4)Order the following rational and irrational numbers from least to greatest.
square root of 20, -2 3/5, 10/3,3.9, 3 7/5
The order of the number from the least to the greatest is -2 3/5, 10/3,3.9, 3 7/5, 20.
What are the order of the numbers?A rational number is a number that can be expressed as the fraction of two numbers in which the decimal is not zero. A rational number can be positive or negative. An example of a rational number is 3, -1.2.
An irrational number is a number that cannot be expressed as the fraction of two numbers. An example of a irrational number is 1/3, 22/7.
In order to order a number, all the numbers should have the same form. Thus, all the numbers would be converted to decimals where possible.
-2 3/5 = -2.6
10 /3 = 3.33
3 7/5 = 4.5
In order to order the numbers, note that the farther a negative number is from zero the smaller the number is and the farther a positive number is to zero, the greater the number is.
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MOWING Cordell is mowing his front lawn. His mailbox is on the edge of the lawn. Cordell starts mowing near the mailbox and moves away from the mailbox, towards his house. He continues to move back and forth between the edge of the lawn and the house. Select a reasonable graph that shows the distance Cordell is from the mailbox as he mows. Let the horizontal axis show the time and the vertical axis show the distance from the mailbox.
The graph of the distance that Cordell moves between the home and the mailbox and time period will be a repeating graph.
Let us assume that the distance between the lawn and the mailbox of Cordell is L.
He starts moving from his home towards the mailbox. After reaching the mailbox, he returns back to the home. Let say the time when he first returns back to his home is T₁.
The graph will show that the value of distance will first increase till L and after that he will come back to his home and the distance will decrease and become zero and the time period will be T₁. This show that he had return back to his home.
Similarly, the time well he again starts from his home and reaches till the mailbox and then again reaches to his home again is T₂. The graph is again plotted in the same manner as it was done in the first case.
It is because the distance L between mailbox and his home is same.
So, we can conclude that the graph will be a repeating graph. The shape of graph will be Saw-tooth like shape.
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the perimeter of a square to be 37 meters. Find the length of one side.
Answer:
9.25 Meters
Step-by-step explanation:
a square has 4 sides so:
37 divided by 4= 9.25 or 9 1/4
what is the y intercept in 5x -2y
Answer:
0
Step-by-step explanation:
y intercept means that the x is 0, so we make the equation like this:
-2y = -5x
-2y = -5(0)
y = 0/-2
y = 0
For the piecewise function, find the values h(-8), h(1), h(3), and h(8).
The output values of h(-8), h(1), h(3), and h(8) in the given piecewise function are 16, 3, 11 and 16 respectively.
What are the output values of h(-8), h(1), h(3) and h(8) in the given piecewise function?Given the piecewise function in the question;
-4x - 16, for x < -7
h(x) = { 3, for -7 ≤ x < 3x + 8, for x ≥ 3
h(-8) = ?h(1) = ? h(3) = ?h(8) = ?Determine the output value of h(-8), -8 falls in the domain of x < 7,
Hence;
h(x) = -4x - 16
h(-8) = -4(-8) - 16
h(-8) = 32 - 16
h(-8) = 16
Determine the output value of h(1), 1 falls in the domain of -7 ≤ x < 3,
Hence;
h(x) = 3
h(1) = 3
Determine the output value of h(3), 3 falls in the domain of x ≥ 3,
Hence;
h(x) = x + 8
h(3) = 3 + 8
h(3) = 11
Determine the output value of h(8), 8 falls in the domain of x ≥ 3,
Hence;
h(x) = x + 8
h(8) = 8 + 8
h(8) = 16
Therefore the output values of h(-8), h(1), h(3), and h(8) in the given piecewise function are 16, 3, 11 and 16 respectively.
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9n - 50 = 4, what does n equal?
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{9n - 50 = 4}[/tex]
[tex]\large\text{Add 50 to both sides:}[/tex]
[tex]\mathsf{9n - 50 + 50= 4 + 50}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{9n = 4 + 50}[/tex]
[tex]\mathsf{9n = 54}[/tex]
[tex]\large\text{Divide 9 to both sides:}[/tex]
[tex]\mathsf{\dfrac{9n}{9} = \dfrac{54}{9}}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{n = \dfrac{54}{9}}[/tex]
[tex]\mathsf{n = 6}[/tex]
[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{n = 6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
(01.01 LC)
What is the simplified form of
a
b
C
d
45√x
√√4x
√√x.√√x-√√x-√√x?
Answer:
Step-by-step explanation:
An image shows two right triangles A B C and D E F. Triangle A B C: Side A B is 3. Side B C is 5. Side C A is 4. Triangle D E F: Side D E is 6. Side E F is 10. Side F D is 8. Which statement about the two triangles is correct? ~ because You cannot tell if the triangles are similar because the angles are not given. is not similar to , because , while . is congruent to
If the ratio of the sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles. Then the correct option is B.
What is the triangle?
Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
A picture shows triangle ABC and triangle DEF.
Triangle ABC: Side AB is 3, Side BC is 5, and Side CA is 4.
Triangle DEF: Side DE is 6, Side EF is 10, and Side FD is 8.
The ratio of the sides of the triangles ΔABC and ΔDEF will be given below.
AB/DE=BC/EF=CA/FD
3/6=5/10=4/8=1/2
If the ratio of the sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles.
The diagram is shown below.
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Two right triangles—A B C and D E F. The triangles ΔABC and ΔDEF are comparable triangles if the ratio of their sides is the same.
Given that,
Two right triangles—A B C and D E F. Triangle A B C has a side of 3, a side of 5, and a side of 4.
Triangle D E F: sides D and E , side E and F and side F and each 6, 10, and 8.
Because the angles are not provided, making it impossible to determine whether the triangles are identical is not comparable to.
We have to find which of the two triangles' respective claims is true.
Describe the triangle.
The polygonal shape known as a triangle has three sides and three angles. The sum of the triangle's angles is 180 degrees.
Triangle ABC and triangle DEF are depicted in an image.
Triangle ABC has sides AB at 3, BC at 5, and CA at 4.
Triangle DEF has sides.
Sides DE at 6; EF at 10; and FD at 8.
The triangles ΔABC and ΔDEF side ratio will be provided below.
AB/DE=BC/EF=CA/FD
3/6=5/10=4/8=1/2
Therefore, The triangles ΔABC and ΔDEF are comparable triangles if the ratio of their sides is the same.
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A baseball team has home games on Friday and Sunday. The two
games together earn $3546.00 for the team. Friday's game
generates $374.00 less than Sunday's game. How much money
was taken in at each game?
The money earned on friday is $1586 and on sunday is $1960.
What is meant by linear equation in one variable?A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable.
Let us assume the money generated by Friday game is 'F'.
Let us assume the money generated by Sunday game 'S'.
The two games together earn $3546.00 for the team.
Equation will become;
F + S = 3546.00 ........(equation 1)
Friday's game generates $374.00 less than Sunday's game. Thus,
F = S - 374.00
Since, F = S - 456.50 use the substitution method and put this value in equation 1.
(S - 374.00) + S = 3546.00
Simplifying the equation;
2S = 3546.00 + 374.00
2S = 3920
S = 1960.
Put this value in equation 1 and find F.
F + S = 3546.00
F + 1960 = 3546.00
F = 1586.
Thus, the money generated on friday is $1586 and on sunday is $1960.
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Help please! I need this urgently
Answer: step-by-step
Step-by-step explanation:
first one is paralell
second one is perpindicular
third one is neither
lmk if wrong, good luck!
Determine the number of solutions of this equation.
2(x-1)=3(x-4)
Infinitely many solutions
One solution
No solutions
Answer:
One solution.
Step-by-step explanation:
2(x-1)=3(x-4)
2x - 2 = 3x - 12
-2 + 12 = 3x - 2x
10 = x.
Ahmad and Dante wash cars in the neighborhood and charge $5 per car. Last year, they worked very hard and were able to wash 450 cars in the year. They have done a little market research and found that for every $0.20 that the price is reduced, they can get 50 more customers.
1. b. If they decreased the price by $0.20 how much would they earn?
The amount earned if they decreased the price by $0.20 will be $2400.
How to calculate the value?From the information, they found that for every $0.20 that the price is reduced, they can get 50 more customers.
The amount earned if they decreased the price by $0.20 will be:
= ($5 - $0.20) × (450 + 50)
= $4.80 × 500
= $2400
Therefore, the amount is $2400.
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event 8) is
0.40. The probability of Roger winning the tournament, given that Stephan wins, is O. The probability of Stephan winning the tournament.
given that Roger wins, is 0. Given this information, which statement is true?
O A
Events A and Bare not independent because P(AB) # PA)
The true statement is that C. Events A and B are not independent because P(A|B) ≠ P(A).
How to illustrate the information?The probability that Roger wins a tennis tournament (event A) is 0.45 i.e. P(A)=0.45
The probability that Stephan wins the tournament (event B) is 0.40 i.e. P(B)=0.40
It should be noted that if A and are independent events, then P(B|A) = P(B). This isn't possible in this situation.
Therefore, the true statement is that events A and B are not independent because P(A|B) ≠ P(A).
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The probability that Roger wins a tennis tournament (event A) is 0.45, and the probability that Stephan wins the tournament (event B) is 0.40. The probability of Roger winning the tournament, given that Stephan wins, is 0. The probability of Stephan winning the tournament, given that Roger wins, is 0. Given this information, which statement is true?
1.Events A and B are independent because P(A|B) = P(A).
2.Events A and B are independent because P(A|B) ≠ P(A).
3. Events A and B are not independent because P(A|B) ≠ P(A).
4. Events A and B are not independent because P(A|B) = P(A).
Nick buys a bag of cookies that contains 9 chocolate chip cookies, 6 peanut butter cookies, 7 sugar cookies and 7 oatmeal cookies. What is the probability that Nick randomly selects a sugar cookie from the bag, eats it, then randomly selects a chocolate chip cookie? Express you answer as a reduced fraction.
Answer: 2/29
Step-by-step explanation: because he has 29 cookies in total therefor if he just randomly picks a cookie from the bag this would be 2/29 as he randomly chose 2 cookies out of 29 total cookie. we have no idea what he could have chose and all the cookies are mixed in a bag.
================================================
Explanation:
There are 7 sugar cookies
This is out of 9+6+7+7 = 29 total cookies
The probability of getting a sugar cookie is 7/29
After that cookie is selected, the total drops to 29-1 = 28 cookies. The probability of getting a chocolate chip on the second selection is 9/28
Multiply the fractions mentioned to get the final answer
(7/29)*(9/28) = (7*9)/(29*28) = (7*9)/(29*7*4) = 9/(29*4) = 9/116
A survey of 279 SPC students was taken at registration. Of those surveyed: 51 students had signed up for a Language Arts course 36 students had signed up for a Humanities course 18 students had signed up for both a Math and Language Arts course 8 students had signed up for both a Math and Humanities course 9 students had signed up for both a Language Arts and Humanities course 4 students had signed up for all three courses students did not sign up for any of these classes How many students signed up for only Math (of these three)?
Treating the amounts as Venn sets, we have that 161 students signed up for only Math, considering that 40 did not sign for any.
What are the Venn sets?For this problem, we consider the following sets:
Set A: Students that have signed up for Arts.Set B: Students that have signed up for Humanities.Set C: Students that have signed up for Math.4 students had signed up for all three courses students, hence:
(A ∩ B ∩ C) = 4.
8 students had signed up for both a Math and Humanities, hence:
(B ∩ C) + (A ∩ B ∩ C) = 8
(B ∩ C) = 8.
18 students had signed up for both a Math and Language Arts, hence:
(A ∩ C) + (A ∩ B ∩ C) = 18
(A ∩ C) = 14.
9 students had signed up for both a Language Arts and Humanities, hence:
(A ∩ B) + (A ∩ B ∩ C) = 9
(A ∩ B) = 5.
36 students had signed up for a Humanities course, hence:
B + (A ∩ B) + (B ∩ C) + (A ∩ B ∩ C) = 36
B + 5 + 8 + 4 = 36
B = 19.
51 students had signed up for a Language Arts course, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 36
A + 5 + 14 + 4 = 51
A = 28.
Considering that there are 279 students, and supposing 40 did not sign for any course, we have that:
A + B + C + (A ∩ B) + (B ∩ C) + (A ∩ C) + (A ∩ B ∩ C) + 40 = 279.
28 + 19 + C + 5 + 8 + 14 + 4 + 40 = 279
118 + C = 279
C = 161
161 students signed up for only Math, considering that 40 did not sign for any.
More can be learned about Venn sets at https://brainly.com/question/24388608
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