Question says that a yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. Also the store has 15 possible toppings.
Now we need to find about how many different 3-topping combinations can a customers choose.
To find that we just need to apply combination formula
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
which is used to select r items out of n items
we have to find combination of 15 toppings into 3 toppings so we calculate C(15,3) using above formula
[tex]C(15,3)=\frac{15!}{3!(15-3)!}[/tex]
[tex]C(15,3)=\frac{15!}{3!*12!}[/tex]
[tex]C(15,3)=\frac{15*14*13*12!}{3!*12!}[/tex]
[tex]C(15,3)=\frac{15*14*13}{3!}[/tex]
[tex]C(15,3)=\frac{2730}{6}[/tex]
[tex]C(15,3)=455[/tex]
Hence final answer is 455.
Answer:
only 455
Step-by-step explanation:
i have a ? how do you know when its C(n,r) and not P(n,r)
The price of a used car is reduced by 25% to $6,000. What was the original price of the car in dollars? Round your answer to the nearest dollar.
The original price of the used car, before the 25% reduction, was approximately $8,000. This was calculated by considering that $6,000 represents 75% of the original price.
Explanation:The question is related to percentage and price, which falls under the realm of Mathematics. To find the original price of the car, you must consider that the price after the 25% discount was $6,000. This 25% reduction means that $6,000 represents 75% of the original price because 100% - 25% equals 75%. To find the original price (which is 100%), you can set up a simple equation and solve for the original price using cross multiplication. The equation will look like this:
75/100 = 6000/x
When you cross multiply and solve for x, the result is $8,000. So, the original price of the car was approximately $8,000.
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What is the square root of 25
The square root of 25 is 5.
Your just trying to find what number you can multiply with its self to make that number. So 5x5 = 25
Another example is lets say 64, the square root of 64 is 8 because 8x8 = 64.
Hope this makes sense!!
Hope this Helps!!
What is the square root of 25?
5 * 5 = 25
√25 = 5
your answer is 5
The coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
To determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. This states that if the diagonals , then the quadrilateral is a parallelogram.
The midpoint of HJ is and the midpoint of IK is (2, 2).
Therefore, HIJK is a parallelogram because the diagonals , which means they bisect each other.
Answer: The quadrilateral HIJK is a parallelogram.
Explanation:
It is given that the coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).
The parallelogram diagonal theorem states that the quadrilateral is a parallelogram if both diagonal bisects each other.
If HIJK is a quadrilateral, then HJ and IK are the diagonals of HIJK.
First we find the midpoint of HJ.
[tex]\text{Midpoint of HJ}=(\frac{0+4}{2}, \frac{5-1}{2})[/tex]
[tex]\text{Midpoint of HJ}=(2,2)[/tex]
Now, find the midpoint of IK.
[tex]\text{Midpoint of IK}=(\frac{3+1}{2}, \frac{3+1}{2})[/tex]
[tex]\text{Midpoint of IK}=(2,2)[/tex]
The midpoint of both diagonal are same. It means the diagonals of HIJK bisects each other.
By parallelogram diagonal theorem, we can say that the quadrilateral HIJK is a parallelogram.
Answer: IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.
Step-by-step explanation:
Bi-weekly mortgage is $576. Monthly phone charges are $44.95. The electric bill last month was $105.88. Groceries cost about $98/week. What is a good estimate of your monthly expenses?
Final answer:
To estimate the monthly expenses, we calculate each monthly cost including the bi-weekly mortgage paid twice a month, phone charges, electric bill, and groceries multiplied by the average number of weeks per month for a total of $1,728.64.
Explanation:
To estimate the monthly expenses based on the provided costs, we need to calculate the monthly totals of each category. Here's the breakdown:
Bi-weekly mortgage: Since a month roughly consists of 4 weeks, a bi-weekly amount would be paid twice. Therefore, $576 × 2 = $1,152 for the mortgage per month.
Monthly phone charges: This cost is already on a monthly basis, so it's $44.95 for the phone.
Electric bill: The electric bill from last month was $105.88 and we'll use this as an estimate for the current month as well.
Groceries: Groceries cost about $98/week. As there are roughly 4.345 weeks in a month (52 weeks in a year divided by 12 months), we'll multiply the weekly cost by this factor: $98 × 4.345 ≈ $425.81 for groceries.
Adding these expenses, the total estimated monthly expenses would be $1,152 (mortgage) + $44.95 (phone) + $105.88 (electric) + $425.81 (groceries) = $1,728.64.
What is the difference between 76.82 and 2.761
74.059 is the answer.
Hope this helps...
The difference usually means to subtract so I am going to subtract 76.82 - 2.761 to get an answer of 74.059.
Abby has 2 4/5 lb of potting soil. She needs 2 1/2 times that amount for her plants.
How much potting soil does she need?
Express your answer in simplest form
Insert the brackets to make each statement true.
40 ÷ 2 +3 x 2^2 -3 =23
(3x)^2 write in expanded form use parentheses to indicate multiplication
Expand (3x)^2
When you see ^2, it means that the term(s) inside the parenthesis should be copied once, and multiplied.
(3x)^2 = (3x)(3x)
(3x)(3x) is your expanded form
~Rise Above the Ordinary
Will give the brainiest to whoever answers first
4.What are the coordinates of the vertex of y = –x2 – 12x – 32?
5.What's the y-intercept of y = –x2 – 12x – 32?
6.Find any zeros of y = –x2 – 12x – 32.
Question 1:
For this case we have:
The value of the x coordinate of the vertex is with the equation given by:
[tex]x = -\frac{b}{2a} \\[/tex]
Where b = -12 and a = -1
therefore,
[tex]x =- \frac{-12}{2(-1)} \\\\x = -6\\[/tex]
To find the coordinate and substitute in the equation:
[tex]y = - (- 6) ^ 2-12 (-6) -32\\\\y = 4\\[/tex]
Answer:
The coordinates of the vertex are (-6.4)
Question 2:
For this case we have the following equation:
[tex]y = -x ^ 2 - 12x - 32\\[/tex]
By definition, to find the intercept point with the y axis, we make x = 0 and substitute as shown below:
[tex]y = - (0) ^ 2-12 (0) -32\\\\y = -32\\[/tex]
Thus, the intercept point with the y axis is given by (0, -32)
Answer:
the y-intercept is (0, -32)
Question 3:
For this case we have the following equation:
[tex]y = -x ^ 2 - 12x - 32\\[/tex]
The zeros of the function are given by the cut points with the x axis, so, equaling the equation to zero and clearing x we have:
[tex]0 = -x ^ 2 - 12x - 32\\[/tex]
Rewriting the equation we have:
[tex]0 = x ^ 2 + 12x +32\\[/tex]
Factoring has the following:
[tex](x + 4) (x + 8) = 0\\[/tex]
Thus, the solutions are given by:
[tex]x = -4 \\\\x = -8\\[/tex]
Therefore, the zeros of the equation are (-4.0) and (-8.0)
Answer:
(-4.0) and (-8.0)
Polygon ABCD is translated to create polygon A’B’C’D’. Point A is located at (1,5) and point A’ is located at (-2,3). Which expression defines the transformation of any point (x,y) to (x’,y’) on the polygons?
Answer:
The translation is 3 units left and 2 units down
Step-by-step explanation:
we know that
Point A is located at (1,5) and point A’ is located at (-2,3)
so
The rule of the translation is
(x,y) -----> (x+a,y+b)
(1,5) ----> (-2,3)
Find the values of a and b
1+a=-2 ----> a=-2-1 ----> a=-3
5+b=3 ----> b=3-5 ----> b=-2
so
The rule of the translation is
(x,y) -----> (x-3,y-2)
That means -----> The translation is 3 units left and 2 units down
Answer:
x’ = x - 3
y’ = y - 2
Step-by-step explanation:
In one baseball season peter hit twice the difference of the number of home runs Alice hit and 6.altogether they hit 18 home runs how many home runs did each player hit that season?
Answer:
Peter hit 12 home runs, Alice hit 6.
Step-by-step explanation:
If peter hit twice the amount of Alice then you multiply how many she got by 2 and you get 12.
Just one math question. Thank you :)
Tamar wants to select an integer that is closer to zero on the number line than -3 is. How many possible choices other than zero does she have?
A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The number are 1, 2, -1, -2. Thus, the number of possible choices Tamar have is 4.
What is a number line?A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.
Tamar wants to select an integer that is closer to zero on the number line than -3 is. Since the distance between 0 and -3 is 3 units, therefore, we need to find the integers that are either 1unit or 2 units away from zero. Hence, the number are 1, 2, -1, -2. Thus, the number of possible choices Tamar have is 4.
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Zero is not an element of the set of natural numbers. True or false
true is the answer to this problem yah yah yah
Zero is neutral because it is not negative or positive so it is neutral
9.1÷3576 rounded to the nearest whole number
Answer:
Answer is 0
Step-by-step explanation:
[tex]\frac{9.1}{3576}=0.0025447427[/tex]
Whole numbers are the set of numbers represented by {0,1,2,3.......}, So basically counting numbers with a 0. Whole numbers does not contain fractions or negative numbers.
Rounding off is a way of simplifying a number so that it is close to the value of the original number. 0.0025447427 lies in between the whole number 0 and 1. But is is a very small value and is close to 0 than 1. So the closet whole number is 0.
The partment rents for 3 times as much as it did 10 years ago now partment was $270 per month 10 years ago how much does that apartment cost now
Original cost of a sled: $99.50 ; markup by 33%
you are simply doing 99.5x33% + 99.5
and to save you some time, the answer would be 132.34
What is the value of the expression?
6.4−2.4÷0.1
Enter your answer in the box as a decimal.
The answer is -17.6
Scott has 25 baseball cards in his collection. On his birthday, Scott’s grandfather gives him his collection of 100 baseball cards. Scott trades 50 of his cards at the baseball card shop. How many cards did Scott not trade?
Answer:
Scott did not trade 75 cards! Hope this helps!
Step-by-step explanation:
Answer:
he didnt trade 75 cards ooooooooooooooooooooooooooo
Step-by-step explanation:
In the lunch room at your school, 5 people can sit at one table. If you put two tables together, 8 people can sit. If you put three tables together, 11 people can sit. How many people can sit if you put 20 tables together?
Based on the pattern, with each added table, 3 more people can sit. Now, let's see, how many people can sit when we put 20 tables together.
1. First, count the number of 'extra' tables after the first one. With 20 tables in total, we subtract 1 for the initial table to obtain 19 extra tables.
2. We know that for each extra table, 3 more people can sit. So, we then multiply the 19 extra tables by 3, which results in 57.
3. Recall that with the first table, 5 people could sit.
4. To get the total number of people that can sit, we then add the calculated extra seats, which is 57, to the initial 5 seats. So, 57 + 5 equals 62.
So, when you put 20 tables together, 62 people can sit according to the pattern we have noticed.
(Will give brainliest to first correct answer) Multiply.
5⋅2/3 (fraction)
Enter your answer as an improper fraction, in simplified form, in the box.
Answer:
10/3
Step-by-step explanation:
put 5 over 1 and multiply across and you get 10/3
Ari has 10 boards that are 7.8ft long. What is the total length of all the boards Ari has
"10 boards that are 7.8ft long" can be interpreted as 10 * 7.8
When multiplying a number by 10, just move the decimal one point over.
7.8 * 10 = 78
Ari has 78 feet worth of boards.
Help!!!!!!! Plz and thank yu
a) 0/8 = 0
b) -1/1 = -1
c) 4.5 / -1 = -4.5
what is 2/3x+4=4/5x-2
Hey there!
Apply fraction cross multiply: if a/b = c/d , then a *d = b*c
2 ( 5x - 2 ) = ( 2x + 4 ) * 4
expand : 2 (5x-2 ) => 2*5x - 2*2 => 10x - 4
expand : ( 2x +4 ) * 4 => 2x * 4 + 4*4 => 8x + 16
10x - 4 = 8x+16
add 4 to both sides:
10x-4+4 = 8x+16+4
simplify :
10x = 8x + 20
subtract 8x from both sides:
10x -8x = 8x+20-8x
simplify:
2x = 20
Therefore:
x = 20 / 2
x = 10
Hope that helps!
Step 1. Simplify 2/3x to 2x/3
2x/3 + 4 = 4/5x - 2
Step 2. Simplify 4/5x to 4x/5
2x/3 + 4 = 4x/5 - 2
Step 3. Multiply both sides by 15 (the LCM of 3,5)
10x + 60 = 12x - 30
Step 4. Subtract 10x from both sides
60 = 12x - 30 - 10x
Step 5. Simplify 12x - 30 - 10x to 2x - 30
60 =2x - 30
Step 6. Add 30 to both sides
60 + 30 =2x
Step 7. Simplify 60 + 30 to 90
90 = 2x
Step 8. Divide both sides by 2
90/2 = x
Step 9. Simplify 90/2 to 45
45 = x
Step 10. Switch sides
x = 45
Solve y−3x=13 for y.
Answer:
y=13+3x
Step-by-step explanation:
The equation y - 3x = 13 can be solved for y as y = 13 + 3x after adding 3x both sides.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The linear equation is:
y - 3x = 13
It is required to solve for x
The expression can be defined as the combination of constants and variables with mathematical operators.
Make the subject as y:
Add 3x on both sides:
y - 3x + 3x = 13 + 3x
y = 13 + 3x
Thus, the equation y - 3x = 13 can be solved for y as y = 13 + 3x after adding 3x both sides.
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(Will give brainliest to first correct answer) What is the product of −2 1/4 and 2 1/2? (Fractions with whole numbers)
Enter your answer as a mixed number, in simplified form, in the box.
The square of a number x is 92. The number x is between what two consecutive whole number
Answer:
i think 9 and 11 i might be wrong sry\
Step-by-step explanation:
what is 30 feet = yrds
it would be 10 yards
It’s ten yards, 1 foot = 0.333 yard
For each order pair ,determine whether is it a solution to 7x+4y=-23
Simplifying
7x + -4y = 23
Solving
7x + -4y = 23
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y' to each side of the equation.
7x + -4y + 4y = 23 + 4y
Combine like terms: -4y + 4y = 0
7x + 0 = 23 + 4y
7x = 23 + 4y
Divide each side by '7'.
x = 3.285714286 + 0.5714285714y
Simplifying
x = 3.285714286 + 0.5714285714y
An order pair is a solution to the given equation 7x+4y=-23 if substituting the values of the order pair into the equation makes the equation correct. Using this method it can be determined for instance that (1,-6) is not a solution whereas (-1,-5) is a solution to the equation.
Explanation:To determine whether an order pair is a solution to the given equation 7x+4y=-23, you'll need to substitute the values of x and y from the order pair into the equation and see if both sides of the equation balance out.
For instance, if your order pair is (1, -6), you would substitute x=1 and y=-6 into the equation. The equation would then become: 7(1) + 4(-6) = -23. Simplifying this, you get 7 - 24 = -23, which is incorrect.
If you were to take the order pair (-1,-5), the equation 7(-1) + 4(-5) = -23 simplifies to -7 - 20 = -23 , which is indeed correct. Therefore, the order pair (-1,-5) is a solution to the given equation.
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what is a transformation that shrinks or stretches a figure
A dilation is a transformation that shrinks or stretches a figure by multiplying or dividing each point by a scale factor.
Explanation:A transformation that shrinks or stretches a figure is called a dilation. A dilation is a transformation that changes the size of the figure without changing its shape. It can either shrink the figure, making it smaller, or stretch it, making it larger.
During a dilation, each point of the figure is multiplied or divided by a scale factor. If the scale factor is greater than 1, the figure is stretched. If the scale factor is between 0 and 1, the figure is shrunk.
For example, if we have a triangle and apply a dilation with a scale factor of 2, each side of the triangle will be multiplied by 2, resulting in a larger triangle.
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