To find the number of ways six people can be allocated to three different cars with the man alone, we consider the man's three choices and then partition the five women into the remaining two cars in all possible ways, then multiply by the man's choices.
Explanation:The question asks for the number of different ways six people can be allocated to three different cars, ensuring the man is alone. Since there are three cars, the man has three choices of cars to be alone in. After the man has chosen his car, we have five women and two remaining cars. The five women can be distributed in these cars in a 5-partition of two numbers, which means the number of ways we can divide five into two groups without considering order.
The possible partitions for the five women are (3,2), (4,1), and (5,0). For each partition, there are combinations of woman that can occupy the cars. For example, for partition (3,2), we have 5 choose 3 ways to choose which three women are in the first car and the remaining two automatically go to the second car. We repeat this process for each partition. Finally, we must multiply the number of ways for each partition by the three initial choices the man had to get the total number of combinations.
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?
Answer:
40
Step-by-step explanation:
Got it on edge
How many 1/3 can go into 8/10
Answer:
2/3
Step-by-step explanation:
8/10 is 0.800, and 1/3 is 0.333333333337, so without going over 1 but saying below 0.800 would be 2/3 or 0.66666666667
1/3= 0.333
8/10=0.8
so 2 1/3 can go into 8/10
Tara bought 4 souvenirs during 2 days of vacation. After 8 days of vacation, how many total souvenirs will Tara have bought? Solve using unit rates
which number is prime? 4. 13. 26. 15.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.
so 13
13. A prime number is a number which cannot be factored anymore. 4 can be factored as 2 x 2, 26 can be factored as 13 x 2, and 15 can be factored as 3 x 5.
find the missing part to make the sentence true 5+4= +3
You are a cook. You just got orders for 2 steaks at table 6, 4 steaks at table 7, and 4 steaks at table 11. How many steaks should you put on the grill?
Correct me if I am wrong.
10 Steaks
2 Steaks for Table 6
4 Steaks for Table 7
4 Steaks for Table 11
2 + 4 + 4 = 10
ya i say 10 as well.
I’m super confused on number one
The equivalent ratios are calculated as;
1) 16/20
2) 8/12
3) 8/9
4) 9/21
5) 4/5
6) 6/9
How to find the equivalent ratios?Equivalent ratio is a ratio that is equal to another ratio when broken down or when numerator and denominator are multiplied by same number.
1) The ratio is given as 4/5.
If the denominator is 20, then it means the equivalent numerator will be;
(20/5) * 4 = 16.
Equivalent ratio = 16/20
2) The ratio is given as 2/3.
If the denominator is 12, then it means the equivalent numerator will be;
(12/3) * 2 = 8.
Equivalent ratio = 8/12
3) The ratio is given as 24/27
If the denominator is 9, then it means the equivalent numerator will be;
(9/27) * 24 = 8
Equivalent ratio = 8/9
4) The ratio is given as 3/7.
If the numerator is 9, then it means the equivalent denominator will be;
(9/3) * 7 = 21.
Equivalent ratio = 9/21
5) The ratio is given as 8/10.
If the denominator is 5, then it means the equivalent numerator will be;
(5/10) * 8 = 4.
Equivalent ratio = 4/5
6) The ratio is given as 30/45.
If the numerator is 6, then it means the equivalent denominator will be;
(6/30) * 45 = 9.
Equivalent ratio = 6/9
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How do you factor this?
Step 1. Split the second term in 2x^2 - x - 21 into two terms
2x^2 + 6x - 7x - 21
Step 2. Factor out the common terms in the first two terms, then in the last two terms.
2x(x + 3) -7(x + 3)
Step 3. Factor out the common term x + 3
(x + 3)(2x - 7)
mario earned three times as much monry last year as his wife elena.the total amount that the two earned was 11,000.how much money did elena earn
Mrs. whimsey's class is having a pizza party . If there are 16 student and 4 pizzas cut into 8 slices , what answer choice represents the function of one pizza each student receives
Final answer:
Each student will receive 2 slices of pizza, as there are a total of 32 slices from 4 pizzas divided among 16 students.
Explanation:
To determine the number of pizza slices each student receives, we need to calculate the total number of slices available and then divide this by the number of students. Given that there are 4 pizzas and each pizza is cut into 8 slices, we have:
Multiply the number of pizzas by the number of slices per pizza: 4 pizzas × 8 slices/pizza = 32 slices.
Divide the total number of slices by the number of students: 32 slices ÷ 16 students = 2 slices/student.
Therefore, the function that represents the number of pizza slices each student receives is 2 slices per student.
Evaluate using distributive property
16 x ( -3/8)+16 x 1/4
Final answer:
The expression 16 x (-3/8) + 16 x 1/4 is evaluated using the distributive property to get -6 + 4, which equals -2.
Explanation:
To evaluate the expression 16 x ( -3/8) + 16 x 1/4 using the distributive property, we will distribute the 16 into the terms inside the parentheses.
Here is the step-by-step process:
Multiply 16 by (-3/8): 16 × (-3/8) = -6.
Multiply 16 by 1/4: 16 × 1/4 = 4.
Add these two results together: -6 + 4 = -2.
Therefore, the evaluation of the expression 16 x ( -3/8) + 16 x 1/4 is -2.
the table shows a power of exponents.
powers of 5 value
5^3 125
5^2 25
5^1 5
5^0 1
5^-1 1/5
5^-2 1/25
A. subtract 5 from the previous value
B. subtract 100 from the previous value
C. divide the previous value by 5
D. divide the previous value by 25
Answer:
c
Step-by-step explanation:
Find the equation of the line that is parallel y=3x-2 and contains the point (2,11).
The equation of the line parallel to y=3x-2 and containing the point (2,11) is y=3x+5.
Explanation:The equation of a line that is parallel to y=3x-2 will have the same slope as this line. Since the slope of the given line is 3, the parallel line will also have a slope of 3. The equation of a line can be represented in the form y=mx+b, where m is the slope and b is the y-intercept. We can find the equation of the parallel line by substituting the given point (2,11) into the equation.
Start with the equation y=3x+b and substitute x=2 and y=11.
11=3(2)+b
Now solve for b.
11=6+b
b=11-6
b=5
The equation of the parallel line is therefore y=3x+5.
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How can you split 112 so you can divide it by seven
well, 112 divided by 7 is 16 :)
you dont need to split it because 112 can already be divided by 7, youre answer sould be 16. I hope this helps!!!
a manufacturer keeps track of her monthly costs by using a cost function this assigns a total cost for a given number of manufactured items X the function is C(x)=5,000 + 1.3x
what is the reasonable domain of this function what is the cost of 2,000 items that the cost must be kept below 10,000 this month what is the greatest number of items she can manufacturer need these answers ASAP please help
Answer:
a)Domain is all positive integers.
b)C(2000)=$7600
c) For C(x)<10000, less than 3846 items should be manufactured.
Step-by-step explanation:
Given that cost function is C(x)=5000+1.3x, where x is the number of manufactured items.
a) The domain of C(x) means the range of values x can take. Since x is the number of manufactured items, it cannot be negative and fraction.
Hence domain is all positive integers.
b)To find the cost of 2000 items, we should plugin x=2000 in C(x).
That is cost of 2000 items, C(2000)=5000+1.3(2000)=5000+2600=$7600
c) We are asked to find the number of items such that cost is kept below 10,000 that is C(x)<10000
5000+1.3x<10000
Subtract 5000 from both sides
1.3x<5000
Divide with 1.3 on both sides
[tex]x<\frac{5000}{1.3}[/tex]
x<3846.2
Hence number of items must be less than 3846 for C(x)<10000
Final answer:
The reasonable domain of the cost function is x >= 0. The cost of 2,000 items that must be kept below $10,000 is $7,600. The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).
Explanation:
The reasonable domain of the cost function is x >= 0 since the number of items manufactured cannot be negative. In other words, the function is valid for all non-negative values of x.
To find the cost of 2,000 items that must be kept below $10,000, we substitute x = 2,000 into the cost function:
C(2,000) = 5,000 + 1.3 × 2,000
Simplifying this equation, we get:
C(2,000) = 5,000 + 2,600 = $7,600
To determine the greatest number of items that can be manufactured with a cost below $10,000, we need to solve the inequality:
5,000 + 1.3x < 10,000
Simplifying this inequality, we have:
1.3x < 5,000
Dividing both sides of the inequality by 1.3, we obtain:
x < 3,846.15
The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).
what is the simplified form of this
y^5 is your answer hope it helps!
What is 119.63 rounded to the nearest whole number ?
120
bc its grater than four in this case forty
A rectangle has a width of 2cm and a perimeter of 25cm. Find the length and the area .
2w + 2l = 25
2 * 2 + 2l = 25
Simplfiy.
4 + 2l = 25
Subtract 4 from both sides.
2l = 21
Divide both sides by 2.
l = 10.5
Now that we have the value of l, we can find the area.
A = lw
A = 10.5 * 2
A = 21.
The length is 10.5cm.
The area of the rectangle is 21cm^2
Joanna has 45 postcards in her postcard collection, which is 180% of the number of postcards Kyle has. How many postcards does kyle have?
Answer:The answer is 25
Step-by-step explanation:Hope this helps:)It’s 100% correct
The clean up hitter on a baseball tean batted 1/4 of the runs the team scored. The hitter batted in 5 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
A.1/4n=5
B.n/4=1/4
C.5n=1/4
D.5n=4
Answer:
A. [tex]\frac{1}{4}n=5[/tex]
The solution is: n=20
Step-by-step explanation:
1. You have the following information given in the problem above:
- The hitter batted [tex]\frac{1}{4}[/tex] of the runs the team scored.
- The hitter batted in 5 runs.
2. If [tex]n[/tex] is the number of run the team scored, then [tex]\frac{1}{4}[/tex] of [tex]n[/tex] must be equal to five runs batted by the hitter. Therefore, the equation is:
[tex]\frac{1}{4}n=5[/tex]
3. Solve for [tex]n[/tex], as following:
[tex]\frac{1}{4}n=5\\n=(5)(4)\\n=20[/tex]
Lainey bought a set of 20 markers for $6 what is the cost of one market
since you know Lainey has 20 markers and the total cost is $6, all you have to do is solve 20/6 to find the cost of each marker. So, the answer would be about $2.33 dollars, since 20/6 would equal $2.333333333... and I just rounded it up. Hope I helped you! Good luck (:
What is 495/220 in simplest form
495/220 can be simplified to 9/4 by dividing the numerator and denominator by 55
the answer to what is 495/220 in simplest form is 9/4
4 1/5 divided by 2/3 express your answer as a mixed number in Simplest form
I started off by changing 4 1/5 into 21/5 to make the division easier.
To divide the mixed number 4 1/5 by the fraction 2/3, first convert the mixed number to an improper fraction. The operation becomes (21/5) ÷ (2/3). By multiplying 21/5 by the reciprocal of 2/3, which is 3/2, we find that the result is 63/10. When converted back to a mixed number, 63/10 is expressed as 6 3/10.
Explanation:The task is to do the operation 4 1/5 divided by 2/3 and expressing the answer as a mixed number in simplest form. To divide fractions, we usually multiply by the reciprocal. First, convert 4 1/5 to an improper fraction which gives us 21/5.
Take the reciprocal of 2/3, we get 3/2.Multiply 21/5 by 3/2: (21/5) * (3/2) = 63/10.Now, convert this improper fraction back to a mixed number. 63 ÷ 10 = 6 Remainder 3. Hence, the mixed number is 6 3/10.Learn more about Dividing Fractions here:https://brainly.com/question/18511795
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Write an inequality that represents eight less than three times a number is more than 22
Answer:
3n - 8 > 22
Step-by-step explanation:
Let the number be n. Then "eight less than three times the number" is represented by 3n - 8 > 22.
Answer:
i need help too yall
Step-by-step explanation:
what is the value of "m" equal?
First, let's convert the radical terms to exponents. Remember the following:
[tex]\sqrt[n]{x^m} = x^\frac{m}{n}[/tex]
[tex]\sqrt{x^5} = x^{\frac{5}{2}}[/tex]
[tex]\sqrt[4]{x^9} = x^{\frac{9}{4}}[/tex]
[tex]\sqrt[6]{x^5} = x^{\frac{5}{6}}[/tex]
After substituting in the values we just found, our expression looks like:
[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]
Now, remember that we can add the exponents of terms that have the same base and are being multiplied by each other. Also, remember that we can subtract the exponents of terms with the same base that are being divided by each other. This is represented as:
[tex]x^a \cdot x^b = x^{(a + b)}[/tex]
[tex]\dfrac{x^c}{x^d} = x^{(c - d)}[/tex]
Thus, we can simplify our expression even more:
[tex]\dfrac{(x^{\frac{5}{2}})(x^{\frac{9}{4}})}{x^{\frac{5}{6}}}[/tex]
[tex]\dfrac{x^{\frac{19}{4}}}{x^{\frac{5}{6}}}[/tex]
[tex]x^{\frac{47}{12}}[/tex]
Our answer is [tex]\boxed{m = \dfrac{47}{12}}[/tex].
Would 3z + 2 = 5 when z is 1 be an expression?
A manufacturing company has the following fixed monthly costs and unit variable costs: Rent = $2,200 Utilities = $375 Variable costs for materials and assembly = $13.25/unit Monthly labor = $750 If its product sells for $24.99 per unit, how many units must it sell in a month to break even? Round your answer to the nearest whole number.
A manufacturing company has the following fixed monthly costs and unit variable costs:
Rent = $2,200
Utilities = $375
Variable costs for materials and assembly = $13.25/unit
Monthly labor = $750
Given is the product is sold at $24.99 per unit
Let the number of units sold be x
Adding total cost = [tex]2200+375+750=3325[/tex]
Equation becomes:
[tex]3325+13.25x=24.99x[/tex]
[tex]11.74x=3325[/tex]
x= 283.21
So, rounding it to nearest whole number we get, 283 units.
A boy is X years old. His sister is twice as old he is. The sum of their age is 27, How old is the boy?
The boy is 9
9x2=18
18+9=27
In this explanation, we'll determine the age of the boy using algebraic equations based on the given information. Let's represent the boy's age as X and his sister's age as 2X.
Let's set up the equations based on the information provided:
1. The boy's age: X years
2. His sister's age: 2X years (twice as old as the boy)
3. The sum of their ages: 27 years
Using these three pieces of information, we can create an equation to find the value of X (the boy's age).
1. The first equation represents the sum of their ages:
X + 2X = 27
2. Simplify the equation by combining like terms:
3X = 27
3. Now, isolate X by dividing both sides of the equation by 3:
X = 27 / 3
4. Calculate X:
X = 9
So, the boy is 9 years old.
Let's represent the boy's age as X and his sister's age as 2X. The sum of their ages is given as 27 years.
1. We can express the sum of their ages in an equation:
X + 2X = 27
2. Combine the like terms on the left side of the equation:
3X = 27
3. To find the value of X, isolate X on one side of the equation. We do this by dividing both sides of the equation by 3:
X = 27 / 3
4. Simplify the expression:
X = 9
Thus, the boy is 9 years old, and his sister is twice as old, which makes her 18 years old (2 * 9 = 18).
The sum of their ages, 9 + 18, indeed equals 27.
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If a die is rolled one time find these probabilities
-of getting less than 7
-Getting a number greater than or equal to 3
In probability, the outcomes of rolling a die are considered. The probability of getting a number less than 7 is 1 or 100% and the probability of rolling a number greater than or equal to 3 is 2/3 or approximately 66.67%
Explanation:This question falls under the topic of probability in Mathematics. In the case of a single die, there are 6 possible outcomes because a die has 6 faces.
For the probability of getting a number less than 7, all outcomes (1,2,3,4,5,6) are less than 7. Thus, the probability is 6 out of 6 or 1.
For the probability of getting a number that's greater than or equal to 3, the favorable outcomes are 3,4,5,6. So, there are 4 such outcomes. The probability, in this case, is 4 out of 6, which simplifies to 2/3.
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Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (-9,9) and parallel to the line whose equation is 2x-5y-3=0. The equation of the line in point slope form is ___. The equation of the line in general form is ____= 0. PLEASE HELP ASAP.
The equation of a parallel line through point (h, k) can be found by altering the given line's equation this way:
remove any constant (or replace it with 0, as appropriate)replace x with (x-h)replace y with (y-k)To change this equation to point-slope form, solve for y (without expanding the x-term). If there is any constant added to the x-term, add its opposite (so it appears with y).
Here, that looks like ...
... 2(x+9) -5(y-9) = 0
... -5(y-9) = -2(x+9) . . . . add the opposite of the x-term
... y - 9 = 2/5(x +9) . . . . this is the point-slope form you want
_____
To put the equation in general form, multiply by the common denominator of any fractions, and subtract the stuff on the right side of the equal sign. Factor out any common factors of the integer coefficients and constant, and multiply by -1 if the leading coefficient is negative.*
Here, we multiply by 5 (and eliminate parentheses) to get
... 5y -45 = 2x +18
... -2x +5y -63 = 0 . . . . right side subtracted
... 2x -5y +63 = 0 . . . . . leading coefficient made positive. This is your general form.
___
* Actually, I can find no requirement that General Form have a positive leading coefficient. Nor is there a requirement that the coefficients be mutually prime. However, these are requirements for the very similar Standard Form, which has the constant on the right side of the equal sign, instead of the left. Since leading minus signs tend to get lost, IMO, it is a good idea to make the leading coefficient positive, even if it is not a requirement.