Answer:168
Step-by-step explanation:
56 x 3 = 168
A bag contains 7 good apples and 3 bad apples. Nick takes two apples at random from the box, WITHOUT replacement.
This problem deals with dependent events in probability. The probability of picking two good apples in a row from a bag containing 7 good and 3 bad apples, without replacement, is calculated as (7/10)*(6/9), which equals 0.467.
Explanation:The subject of this question is Mathematics, specifically probability. When Nick picks two apples without replacement, we are dealing with dependent events, since the outcome of the second event depends on the outcome of the first event. Dependent events require a different calculation for the probability.
The total apples in the bag initially are 7 good + 3 bad = 10 apples. The probability of picking a good apple on the first draw is 7/10 or 0.7. When one apple is taken out, there are now 9 apples left in the bag. If the first apple was good, the probability of picking the second good apple is now 6/9 or 2/3.
Since these are dependent events, the total probability of picking two good apples in a row would be (7/10) * (6/9) which reduces to 14/30 or approximately 0.467.
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Tickets for a baseball game cost a? dollars for adults and c? dollars for children. The expression 2a+3c represents the cost (in dollars) for a family to go to the game. What is the cost for the family when an adult ticket is $17? and a child ticket is $12??
To find the total cost for the family to attend the baseball game, we substitute the given ticket prices into the expression 2a + 3c, where a is the cost of an adult ticket and c is the cost of a child ticket, resulting in a total cost of $70.
Explanation:The student is asking about the cost for a family to attend a baseball game with the given prices for adult and child tickets.
Given the cost of an adult ticket as $17 and a child ticket as $12, we use the expression provided (2a + 3c) to calculate the total cost for the family.
Substituting the given values into the expression, we get 2(17) + 3(12), which equals 34 + 36.
Summing up these two products gives us a total of $70.
Therefore, it will cost the family $70 to attend the baseball game.
Which is a root of [tex]f(x)=0[/tex] with a multiplicity of 2?
Answer:
3
Step-by-step explanation:
The zero at the point x=3 is a result of a factor of even degree, because the function does not change sign as the value of (x -3) changes sign. Since a cubic only has 3 factors, the even degree must be 2. That is, (x -3)² is a factor of f(x) and the root at x=3 has multiplicity 2.
There were 50 students in the chess club. The membership went up by 10%. How many more students joined the club?
The membership went up by 10%.
There are now 55 total students in the club.
The formula for calculating the percentage change is
[tex]p=\frac{N-O}{O}.100[/tex]
where p is the percent change, N is the New Value and O is the Old Value.
In this problem we are given the Old Value (50) and the percent change (10). We can substitute this into the formula and solve for N:
[tex]10=\frac{N-50}{50} .100\\10=2(N-50)\\5=N-50\\N=55[/tex]
There are now 55 total students in the club.
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Saul in third in line. Enid is last in line. There are 3 children between them. What position is Enid in line?
Final answer:
Starting with Saul in the 3rd position and counting the 3 children between him and Enid, Enid is determined to be in the 7th position in the line.
Explanation:
To find the position of Enid in line, we start with Saul who is third in line. If there are 3 children between Saul and Enid, and Enid is last, we need to count the positions:
Saul is 3rd in line.
1st child after Saul is in the 4th position.
2nd child after Saul is in the 5th position.
3rd child after Saul is in the 6th position.
Enid is after the 3rd child, placing her in the 7th position.
Therefore, Enid is in the 7th position in line.
Find f(x) if it is known that f(x−2)=2x−4
Answer:
f(x) = 2x
Step-by-step explanation:
Remark
What I'm about to do is probably not the best way to do this question, but it is right. The plan is to take out a common factor on the right of f(x - 2) and then derive f(x) from that.
Solution
f(x - 2) = 2x - 4 Take out a common factor on the right of f(x -2)f(x - 2) = 2(x - 2) Now what that means is that in the original equation, wherever you saw an x, you put in x - 2. So the original equation must have beenCheck
f(x) = 2x To check this put x - 2 back inf(x - 2) = 2(x -2) Remove the brackets. f(x - 2) = 2x - 4 which is what it should be.Final answer:
To find f(x), replace x - 2 with y to get f(y) = 2(y + 2) - 4, simplify to f(y) = 2y, then revert y back to x to find f(x) = 2x.
Explanation:
To find the function f(x) when you know that f(x - 2) = 2x - 4, you need to replace x - 2 with y so that x = y + 2. Therefore, f(y) = f(x - 2) = 2x - 4 becomes f(y) = 2(y + 2) - 4.
Simplifying this, we get:
f(y) = 2y + 4 - 4
f(y) = 2y.
Now, to revert back to the original function, replace y with x to get f(x) = 2x. This is the function we were looking to find.
A recursive rule for a geometric sequence is a1=3;an=1/2an−1.
What is the explicit rule for this sequence?
Enter your answer in the box.
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=3\\\\a_n=\dfrac{1}{2}a_{n-1}\to \boxed{r=\dfrac{1}{2}}[/tex]
--------------------------------------------------
Exciplit rule:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=3\left(\dfrac{1}{2}\right)^{n-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot\left(\dfrac{1}{2}\right)^{-1}=3\cdot\left(\dfrac{1}{2}\right)^n\cdot2\\\\\boxed{a_n=6\cdot\left(\dfrac{1}{2}\right)^n}[/tex]
Answer:
The answer is: a_n = 6*(1/2)^n
pease help, thank you
Answer: -2
=====================================================
Draw a vertical line through 4 on the x axis. This vertical line crosses the parabola at some point (which we'll call point A). Draw a horizontal line from point A to the y axis and note how it lands on y = 12. Therefore the point (4,12) is on this parabola.
Repeat the same steps as before to find that (8,4) is also on the parabola
We need to find the slope of the line through (4,12) and (8,4)
m = (y2 - y1)/(x2 - x1)
m = (4-12)/(8 - 4)
m = -8/4
m = -2
The slope of this line is -2 meaning that the average rate of change from x = 4 to x = 8 is -2.
The line goes down 2 units each time you move to the right 1 unit.
Hey y'all please help me with this geometry problem,would really appreciate it :)
180-(x+50)+180-4x+180-(2x+40)+180-3x=360
720-x-50-4x-2x-40-3x=360
630 - 10x=360
-10x=360-630
-10x=-270 /:(-10)
x=27
One number is five more than another and their sum Is there less than three times the smaller find the numbers
Answer:
The numbers are 8 and 13
Step-by-step explanation:
In order to find this, we set the smaller number as x. Then we can set the larger one as x + 5, since it is 5 more than the smaller.
Given these two, we can then set them equal to 3x - 3, since the answer is three less than three times the larger.
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
5 = x - 3
8 = x
Now to find the larger number, put into the larger number equation.
x + 5
(8) + 5
13
The numbers are 8 and 13.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''One number is five more than another and their sum Is there less than three times the smaller''.
Now,
Let the smaller number = x
Then, The another number = x + 5
Write the expression as;
x + x + 5 = 3x - 3
2x + 5 = 3x - 3
2x - 3x = - 3 - 5
- x = - 8
x = 8
And, The another number = x + 5
= 8 + 5
= 13
Thus, The numbers are 8 and 13.
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A dartboard is divide into sections numbered 1-20. Leon throws a dart at the board 30 times. 8 times the dart lands on the number 2. What is the experimental probability that the dart lands on number 2?
Answer:
4/15
Step-by-step explanation:
Experimental probability is the actual times the event occurs divided by the number of trials
Actual times : 8
Number of trials: 30
Experimental probability of a 2: 8/30 = 4/15
A triangle has two sides of lengths 4 and 15.What value could the length of the third side be? Check all that apply.. A:12 B:13 C:4 D:15 E:11 F:19
If a, b and c are the lengths of the sides of a triangle then
if a ≤ b ≤ c, then a + b > c.
A: 4, 12, 15
4 + 12 = 16 > 15 CORRECT :)
B: 4, 13, 15
4 + 13 = 17 > 15 CORRECT :)
C: 4, 4, 15
4 + 4 = 8 < 15 INCORRECT :(
D: 4, 15, 15
4 + 15 = 19 > 15 CORRECT :)
E: 4, 11, 15
4 + 11 = 15 INCORRECT :(
F: 4, 15, 19
4 + 15 = 19 INCORRECT :(
Answer: A: 12, B: 13, D; 15Our Einstein has baked a cake and cut it into 8 slices. If he hands out 3 slices to his guests, what fraction of the cake is left?
Answer:
[tex]\frac{5}{8}[/tex]
Step-by-step explanation:
We have been given that our Einstein has baked a cake and cut it into 8 slices. So each slice will be equal [tex]\frac{1}{8}[/tex].
He hands out 3 slices to his guests. Let us find out part of the cake given to guests.
[tex]\text{The part of the cake given to guests}=\frac{1}{8}+\frac{1}{8}+\frac{1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{1+1+1}{8}[/tex]
[tex]\text{The part of the cake given to guests}=\frac{3}{8}[/tex]
To find the fraction of left cake we will subtract [tex]\frac{3}{8}[/tex] from 1 as Einstein has 1 whole cake.
[tex]\text{fraction of cake is left}=1-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8}{8}-\frac{3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{8-3}{8}[/tex]
[tex]\text{fraction of cake is left}=\frac{5}{8}[/tex]
Therefore, [tex]\frac{5}{8}[/tex] of the cake is left.
Answer:
As per the given statement: Our Einstein has baked a cake and cut it into 8 slices.
⇒ Total slice of cake Einstein has baked = 8
Also, it is given that if he hands out 3 slices to his guests.
⇒ Number of slice he hands out to his guests = 3
Remaining slice of a cake Einstein left with = 8 -3 = 5.
We have to find the fraction of the cake is left.
Fraction states that a fraction is a number that represents a part of a whole. Also, It consists of a numerator and a denominator, where numerator represents the number of equal parts of a whole, while the denominator is the total number of parts.
Fraction of the cake is left = [tex]\frac{\text{Slices of cake left}}{\text{Total number of slices of a cake}}[/tex]
Substitute the given values we get;
[tex]\text{Fraction of the cake is left} =\frac{5}{8}[/tex]
therefore, the fraction of the cake is left is, [tex]\frac{5}{8}[/tex]
the function f(x) varies inversely with x and f(x)=0.5 when x =0.3. what is f(x) when x=2.4?
Answer:
0.0625
Step-by-step explanation:
If the function f(x) varies inversely with x, then this function is of the form
[tex]f(x)=\dfrac{a}{x},[/tex]
where a is unknown number.
Since f(x)=0.5 when x =0.3, then
[tex]0.5=\dfrac{a}{0.3},\\ \\a=0.5\cdot 0.3=0.15.[/tex]
Therefore, the function is
[tex]f(x)=\dfrac{0.15}{x},[/tex]
Now when x=2.4,
[tex]f(2.4)=\dfrac{0.15}{2.4}=\dfrac{15}{240}=\dfrac{1}{16}=0.0625.[/tex]
A football signs a contract that pays him $16 million over 4 years. What is his average pay per year?
Answer:
the footballer's average pay would be $4 million/annum.
What is the area of the rhombus shown below?
Answer:
B
Step-by-step explanation:
The interior of the 4 triangles in the rhombus are right angle triangles. In addition AC is bisected by BD and BD is bisected by AC. Those form the sides of the right angle triangle.
So the sides of the right angle are
1/2 17 = 8.5 and1/2 15 = 7.5The area of one right angle is
1/2 * 8.5 * 7.5 = 1/2 * 63.75 = 31.875But there are 4 of themArea of the rhombus = 4 * 31.875 = 127.5The answer is B
Answer:
B. 125.5 square units
Step-by-step explanation:
The area of a rhombus is half the product of the diagonals.
If the diagonals have lengths a and b, then the are is:
area = ab/2
area = (17)(15)/2
area = 255/2
area = 127.5
Answer: B. 125.5 square units
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The quotient of a number and 18 is 109.8.
which statements are correct?
It can be solved by using the division property of equality.
It can be solved by using the multiplication property of equality.
The equation should be x/18=109.8
The equation should be 18x=109.8
The answer is 6.1.
The answer is 1,976.4.
Answer:
2. It can be solved by using the multiplication property of equality.
3. The equation should be: [tex]\frac{x}{18}=109.8[/tex]
6. The answer is 1,976.4.
Step-by-step explanation:
Let x be the number.
We have been given that the quotient of a number and 18 is 109.8.
Since we know that in a division problem the number which is being divided called dividend and by which number we divide is called divisor.
[tex]\text{Dividend}\div \text{Divisor }=\text{ Quotient}[/tex]
We can represent our given information as:
[tex]\frac{x}{18}=109.8[/tex]
By using multiplication property of equality we will get,
[tex]18*\frac{x}{18}=18*109.8[/tex]
[tex]x=18*109.8[/tex]
[tex]x=1976.4[/tex]
Upon looking at our given choices we can see that 2nd, 3rd and 6th statements are correct choices.
can someone help me with this question?
Answer: [tex]\bold{(A)\ \dfrac{\text{51 miles}}{\text{1 hour}}}[/tex]
Step-by-step explanation:
Consider the formula "distance (d) = rate (r) x time(t)" and solve for r.
d = r · t
÷ t ÷ t
[tex]\dfrac{d}{t}=r[/tex]
Now plug in the given d and t values from the table to solve for r:
[tex]r=\dfrac{\text{204 miles}}{\text{4 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex] simplified the fraction
You can check this by plugging in the other 3 values from the table:
[tex]r=\dfrac{\text{306 miles}}{\text{6 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{408 miles}}{\text{8 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
[tex]r=\dfrac{\text{510 miles}}{\text{10 hours}}[/tex]
[tex]=\dfrac{\text{51 miles}}{\text{1 hour}}[/tex]
Phyllis Doran worked at Symmes Medical Center for 7 1/2 hours on Monday and from 8:00 a.M. Until 1:00 p.M. On Tuesday What is the total number of hours she worked
Answer:
Step-by-step explanation:
The coordinates of the vertices of trapezoid ABCD are A (2,6), B (5,6), C (7,1), and D (-1,1). The coordinates of the vertices of trapezoid A'B'C'D' are A' (-6, -2),B' (-6, -5), C' (-1, -7), and D' (-1, 1). Which statement correctly describes the relationship between trapezoid ABCD and trapezoid A'B'C'D' ?
A. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then across the y-axis.
B. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can rotate trapezoid ABCD 180°about the origin and then translating it 4 units left.
C. Trapezoid ABCD ≅ trapezoid A'B'C'D'
You can reflect trapezoid ABCD across the x-axis and then rotating it 90°clockwise.
Answer:
if you still need the answer, its C.
Step-by-step explanation:
Ben and Jerry’s ice cream company estimates that for every 32 people that they serve their delicious ice cream to, they need to make 128 ounces of ice cream. How many people can they serve if they make 704 ounces of ice cream?
Set up a proportion and solve.
The first part of the proportion would be the known values of 32 people to 128 ounces.
The second part of the proportion is X ( the number of people) for 704 ounces.
This is written as 32/128 = X/704
To solve for X Cross multiply:
32 * 704 = 128x
Simplify:
22528 = 128x
Solve for X by dividing both sides by 128:
x = 22528 / 128
x = 176 people
helps please i need it
Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4).
A) y = 3x - 26
B) y = -3x + 16
C) y = 1/3 x-2
D) y = -1/3 x+6
Answer:
D) y = -1/3 x+6
Step-by-step explanation:
If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope. Knowing y= mx+b we need to find the slope of the old line.
3x+9y=7
Subtract 3x from each side
3x-3x +9y = -3x+7
9y = -3x+7
Divide each side by 9
9y/9 = -3x/9 + 7/9
y = -1/3 x + 7/9
We know the slope of the old line is -1/3, so the slope of the parallel line is -1/3.
If we know the slope of the line and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y-4 = -1/3(x-6)
Distribute the -1/3
y-4 = -1/3 x -1/3*-6
y-4 = -1/3x +2
Add 4 to each side
y-4+4 = -1/3x +2+4
y = -1/3x+6
Stephanie bought 3 pizzas for a total of $9.00. Which expression shows p, the cost of each pizza?
Answer:
the answer is 3
Step-by-step explanation:
3 pizzas equal $9.00 so in order to know how much each pizza was, we will have to do division:
9 divided by 3
9/3
3
A builder uses 32 wooden slats to make 4 fence panels. Fatima wants to know how many slats are needed for 1 panel. Gerard wants to know how many slats he will need to make 8 panels. Drag an expression to answer each question.
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Wooden slates required to make 4 fence panels = 32
To find wooden required to make 1 panel, use ratio property,
4 fence panels = 32 wooden slates
1 fence panel = 8 wooden slates
Also, to find wooden required to make 8 panels, use ratio property,
4 fence panels = 32 wooden slates
8 fence panels = 64 wooden slates
1 fence panel required 8 wooden slates and 8 fence panels required 64 wooden slates.
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Final answer:
Gerard needs 64 slats to make 8 panels, as it is a proportional relationship.
Explanation:
To find out how many slats are needed for one panel, we simply divide the total number of slats by the number of panels. Since a builder uses 32 slats to make 4 panels, for one panel, Fatima would need:
Number of slats for one panel = Total number of slats \/ Number of panels
Number of slats for one panel = 32 / 4 = 8 slats
For Gerard's question, if 1 panel requires 8 slats, then to make 8 panels he would need:
Number of slats for 8 panels = Slats per panel x Number of panels
Number of slats for 8 panels = 8 x 8 = 64 slats
It's a straightforward example of a proportional relationship in mathematics, where the number of slats scales directly with the number of fence panels.
There are 120 students surveyed (30 from each grade). Use the table below to determine that probability that a student selected at random is in 11th grade or selected Math as their favorite subject?
Find P (11th or math)
a. 7/120
b. 1/2
c. 67/120
d. 59/120
Answer: 59/120 (choice D)
Add up the values in the "math" column and the "11th" row to find the total number of people who are either in 11th grade, in math, or in both.
So,
(12+10+8+7) + (14+5+3) = 59
represents the number of people who are in either category. This is out of 120 (given). This is where 59/120 comes from.
What percentage is the fraction `2/(10)` equal to?
Answer:
20%
Step-by-step explanation:
Percentage means out of 100
We need to get 2/10 to be out of 100
Multiply by 10/10
2/10*10/10
= 20/100
This is 20%
If a solid piece of an aluminium cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, what is the length of the piece of aluminium rod?
Answer: 10 cm
Step-by-step explanation:
Given: The volume of a solid piece of an aluminium cylindrical rod =[tex]200\cm^3[/tex]
The base area of cylinder = [tex]20\ cm^2[tex]
We know that the volume of cylinder is given by :-
[tex]\text{Volume]=\text{base area}\times \text{height}\\\\\Rightarrow200\=20\\times h\\\\\Rightarrow\ h=\frac{200}{20}=10[/tex]
Hence, the length of the piece of aluminium rod = 10 cm
To find the length of the aluminum rod with a volume of 200 cm³ and a base area of 20 cm², divide the volume by the base area. The length is 10 cm.
If a solid piece of an aluminum cylindrical rod has a volume of 200 cm3 and a base area of 20 cm2, to find the length of the aluminum rod, we can use the formula for the volume of a cylinder, which is Volume = Base Area imes Height (or length in this case, since it's a rod). Given the volume (V) is 200 cm³ and base area (A) is 20 cm², the length (L) can be calculated as L = V / A.
When you divide 200 cm³ by 20 cm², the result is:
L = 200 cm³ / 20 cm² = 10 cm.
Therefore, the length of the aluminum rod is 10 cm.
Last month, dory biked 11 times as many miles as karly. Togetherthey biked a total of 156 miles . How many miles did dory bike last month
Answer:
143 miles
Step-by-step explanation:
Let the distance Karly biked be x
Then Dory biked 11x
So x+11x=156
x=156/12=13
So Dory biked 11 ⋅ 13= 143 miles
Is this correct?
Anita does the same number of jumping jacks each day over a period of several days. On the fifth day, she has completed a total of 325 jumping jacks. By the eighth day, she has completed a total of 520. What value equals the slope of the line of the total number of jumping jacks when graphed against the day?