The total cost for 53 people attending the school banquet is $1,665.
What is the cost of the school banquet for 53 people?Given the parameter:
The cost of a school banquet is expressed as:
$75 + 30n, as n is the number of people attending.
To determine the cost for 53 people attending the school banquet, you can plug the value of n (which is 53) into the given cost function:
Cost = $75 + 30n
Plug in n = 53
Cost = $75 + 30( 53 )
Cost = $75 + 1590
Cost = $1,665
Therefore, the total cost will be $1,665.
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A yogurt shop allows its customers to add, for no charge, 3 toppings to any yogurt purchased. If the store has 15 possible toppings, how many different 3-topping combinations can a customers choose?
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)
if y varies directly as X and Y is 48 when X is 6 what is expression can be used to find the value of y when X is to
The expression y = kx can be used to find the value of y when x is given. In this case, the value of y when x is 2 is 16.
Explanation:To find the expression to determine the value of y when x is 2, we need to use the fact that y varies directly as x. This can be represented by the equation y = kx, where k is the constant of variation.
We are given that when x is 6, y is 48. Plugging these values into the equation, we have 48 = k * 6. Solving for k, we find that k = 8.
Now we can use this value of k in our equation to find y when x is 2. Substituting 8 for k and 2 for x, we have y = 8 * 2 = 16. Therefore, the value of y when x is 2 is 16.
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The scores on a psychology exam were normally distributed with a mean of 57
and a standard deviation of 4. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?
Answer:
Cutoff for a failing score is 49 and 2.28% students failed.
Step-by-step explanation:
We have been given that scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 4.
2 standard deviation below mean would be,
[tex]57-2(4) =57-8= 49[/tex]
Therefore,Cutoff far a failing score is 49.
Now let us find out the z-score for our given values,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{49-57}{4}=\frac{-8}{4} =-2[/tex]
Now let us look up the probability from normal distribution table.
[tex]P(z<-2) =0.02275[/tex]
Therefore, percentage of students failed is 2.28%.
HELP ME PLEASE THANKS SO MUCH !
The answer is C,
200 is the original distance
plus the increasing 5 yards everyday
Nina earns $15 for each yard she mowes. she wants to buy a dress that coasts $109. how many yards will she need to mow to earn money for the dress? explain
she will need to mow 8 yards because 109 divided by 15 equals 7.2 but she cant just mow 7.2 yards so you round up to 8 yards
The graphs below show the number of honor roll students in each grade at Bridgeport Middle School. Which statement is true??
A. According to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll.
B. The scale on Graph 1 does not distort the differences in the number of students.
C. The two graphs use completely different data
D.both: “according to Graph 2, there are more than twice as many sixth graders on the honor roll than eighth graders on the honor roll” and “the two graphs use completely different data”
What is the standard form of the number shown in this calculator display?
3.82e+7
38.9e i think 60% sure
find the slope of the line
the slope is 3/-5!!!! if u go up 3 and to the LEFT 5 that means it is negative.
[tex] - 12 + - 33 \leqslant 39[/tex]
whats the answer of the problem peter is 3 years older than his sister Anna. if times their combined age is 85 . determine Annas age
Answer:
Anna is 41 years old.
Step-by-step explanation:
Easiest way to do this is by building a equation,
Lest say Anna's age is [tex]x[/tex].
Then as Peter is 3 years older than Anna Peter's age should be [tex]x+3[/tex].
Then the combined ages of the two people is given as 85. So we can write an equation as,
[tex]x+(x+3)=85[/tex]
[tex]x+x+3=85[/tex]
[tex]2x+3=85[/tex]
[tex]2x+3-3=85-3[/tex] (deducting 3 from both sides of the equation)
[tex]2x=82[/tex]
[tex]x=41[/tex]
As we originally took Anna;s age as [tex]x[/tex]
We can say Anna is 41 years old.
What is x > -3 as an interval notion?
(- 3, ∞ )
the parenthesis at both ends indicates x ≠ - 3 or ∞
if x ≥ - 3 then {- 3, ∞ )
the square bracket on the left indicates x can equal - 3
Final answer:
The inequality x > -3 in interval notation is (-3, ∞), which means that the solution set for x includes all values greater than -3, but does not include -3 itself.
Explanation:
When the inequality x > -3 is written in interval notation, it means that the solution set for x includes all values greater than -3, but does not include -3 itself. In interval notation, we use a round bracket to indicate that -3 is not included in the solution set. The interval notation for x > -3 is (-3, ∞). This notation represents a half-open interval, where -3 is excluded but all values greater than -3 are included. The symbol ∞ represents infinity, indicating that there is no upper bound for the values of x in this inequality.
Evaluate the expression when a=-3 and b=7 7a-b
The amount a babysitter earns is given by the equation y=7.5x where x is the number of hours and y is the amount earned in dollars. Is this relationship proportional?
Yes, this relationship is proportional.
Answer:
Yes, the relationship is proportional
Step-by-step explanation:
This is because the number of hours (x) is multiplied by the same number, 7.5, meaning that all of the values will be proportional (create a straight/linear line on a graph when the points are plotted).
The figure shows two parallel lines KL and NO cut by the transversals KO and LN:
Which statement best explains the relationship between Triangle KLM and Triangle ONM?
Triangle KLM is similar to triangle ONM because measure of angle 3 equals measure of angle 4 and measure of angle 1 equals measure of angle 5
Triangle KLM is similar to triangle ONM because measure of angle 3 equals measure of angle 6 and measure of angle 1 equals measure of angle 4
Triangle KLM is congruent to triangle ONM because measure of angle 3 equals measure of angle 4 and measure of angle 1 equals measure of angle 5
Triangle KLM is congruent to triangle ONM because measure of angle 3 equals measure of angle 6 and measure of angle 1 equals measure of angle 4
Answer:
Triangle KLM is congruent to triangle ONM.
Step-by-step explanation:
All three angles of triangles are equal, that is both triangles are congruent.
Please share the figure to show the numbering of angle you are using. So that I can describe you which angle is equal to which one.
Nikita invest 2000 into a bank account with a 4% annual interest rate. In seven years which is the most expensive item she can afford to buy
a) 2,700.
B) 2,500
c) 2,200
D) 3,000
Answer:
The correct option will be: B) 2,500
Step-by-step explanation:
Nikita invest 2000 into a bank account with a 4% annual interest rate.
So, the amount of interest in one year will be: [tex](2000*0.04)= 80[/tex]
and the amount of interest in 7 years will be: [tex](80*7)=560[/tex]
Thus, the total money in her account after 7 years [tex]=(2000+560)=2560[/tex]
So, the most expensive item she can afford to buy will be: 2500
Answer:
The answer is (a mountain bike priced at $2,500) In Plato
Step-by-step explanation:
In kite WXYZ , m∠XWY=38° and m∠ZYW=15° .
What is m∠WXY ?
Enter your answer in the box.
PLEASEE HELPPP!!!
°
AC = CB, hence ΔABC is isosceles
the base angles 34 and x - 5 are therefore equal
x - 5 = 34 ( add 5 to both sides )
x = 39
and 4y = 180 - ( 2 × 34 ) = 112
4y = 112 ⇒ y = 28
Answer:
x=39° ,y=28°
Step-by-step explanation:
In the given figure
Side AC = Side BC
Hence ΔABC is an isosceles triangle.
⇒∠CAB =∠CBA (∵ angles opposite to equal sides are equal)
⇒ (x - 5)° = 34°
⇒ x = 39
Also in Δ ABC
∠ABC + ∠ACB + ∠CAB = 180°
(∵ Sum of all the interior angles of a triangle)
⇒ 34° + 34° + 4 y = 180°
⇒ 4 y =180°-68°
⇒ y=112°÷ 4
⇒y= 28°
Hence, x = 39° , y = 28°
The top of a refrigerator has an area of 0.6 m^2. The height of the refrigerator is 180 CM. What volume does the refrigerator occupy in CUBIC METERS?
Note: all measurements of the refrigerator need to be in meters, make sure you have IDENTICAL units.
SHOW WORK PLEASE
THANKS IN ADVANCE! :)
the volume (V ) of a cuboid is V = Ah
where A is the area of the base or top and h is the height
h = 180 cm = 1.8m
V = 0.6 × 1.8 = 1.08 m³
The volume of the refrigerator is calculated by converting its height from centimeters to meters (180 cm = 1.8 m) and then multiplying it by the given area of the top (0.6 m²), resulting in a volume of 1.08 cubic meters.
To calculate the volume of the refrigerator, we need to use the formula for the volume of a rectangular prism, which is Volume = length x width x height. We already have the area of the top of the refrigerator, which is a product of its length and width, and we're given the height. However, firstly we need to ensure that all units are in meters.
Convert the height from centimeters to meters: 180 cm = 1.8 m.
Now, we can calculate the volume: Volume = Area x Height = 0.6 m² x 1.8 m = 1.08 m³.
Therefore, the refrigerator has a volume of 1.08 cubic meters.
Rubin has 6 rolls of pennies containing 50 coins each, 5 rolls of nickels containing 40 coins each, 4 rolls of dimes containing 50 coins each l, and 3 rolls of quarters containing 40 coins each. How much money does he have?
6•50=$3.00 pennies
5•40=$2.00 nickels
50•10=$5.00 dimes
25•40=$10.00 total $20.00
Answer: $63
Step-by-step explanation:
Penny = $0.01
Nickel = $0.05
Dime = $0.1
Quarter= $0.25
Number of pennies = 6(50) = 300
Number of nickels = 5(40)= 200
Number of dimes = 4(50)= 200
Number of quarters = 3(40) = 120
Total amount of money:
300(0.01)+ 200(0.05) + 200(0.1) + 120(0.25) = $63
What is the value of x?
3(x−2)+5x=18
X = ????
3(x-2)+5x=18
the correct answer is x=3
first simply the equation
8x=18+6
Now rid of alike terms resulting in
8x=24
now divide 24 by 8
x=3
Solve -3 1/2 = 1/2x + 1/2x + x
- 3 1/2 = 2x
-7 /2 = 2 x
-7 /4 = x
-1 3/4 = x
Mr. Glidden is expanding the size of his garden. His new garden will be 3 times as long and 2 times as wide as his original garden. The perimeter of his original garden is 30 feet and the length is 11 feet. What will be the perimeter, in feet of his new garden?
Method One:
Step One: Figure out how long the width is, witch is 19 feet.
Step Two: Multiply 2*19 and 3*11 because it is 2 times as long and three times as wide
Step Three: Add 38+33
The new perimeter will be 71 feet.
The original garden's width is determined to be 4 feet. Upon expanding the garden to triple its length and double its width, the new garden's perimeter is calculated to be 82 feet.
The question is about calculating the perimeter of a new garden based on given dimensions and scale factors for its expansion. The original garden has a perimeter of 30 feet and a length of 11 feet. To find the width, we use the formula for the perimeter of a rectangle, P = 2l + 2w, which gives us 30 = 2(11) + 2w. Solving for w, we find that the width of the original garden is 4 feet.
Given that Mr. Glidden is expanding his garden to be 3 times as long and 2 times as wide, the new dimensions will be 3(11) feet by 2(4) feet, or 33 feet by 8 feet.
Therefore, the new perimeter will be 2(33) + 2(8), which equals 66 + 16, resulting in a new perimeter of 82 feet.
10p-2(3p-6)=4(3p-6)-8p please show work
What does |-2 + (-1)| equal too
[tex]|-2 + (-1)|[/tex]
Well, first, we must subtract-2 by 1, as the negative sign next to 1 is inside the parentheses.
[tex]|-2 -1|[/tex]
[tex]|-3|[/tex]
Now remember, since it is an absolute value, meaning the distance from that number to zero, we will now disregard the negative sign and get our answer: 3
When the absolute value of the slope gets smaller, the graph of a line gets
_______.could you use?
a. shorter
b.steeper
c.longer
d.less steep
The graph of the line would get less steep.
(APEX approved~)
Answer:
D) Less steep.
what is the m<PHJ
A. 100°
B. 120°
C. 140°
D. 160°
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
∠PML = 140°
∠KHP = 20°
We need to find the measure of ∠PHJ.
Let m ∠PHJ = x°
From the graph, we conclude that
∠PML = ∠PHJ + ∠KHP (Vertically opposite angle)
[tex]140^\circ=x+20^\circ\\\\140^\circ-20^\circ=x\\\\120^\circ=x[/tex]
Hence, Option 'B' is correct.
if 75 is added to a number, the result is 39 less than three times the number.find the number
First, we would set the number to x.
Then, we turn the words into an equation.
x+75 = 3x-39
Isolate the x.
-2x = -114
So...
x = 57
The Number is 57.
Let's call the number you're trying to find "x."
According to the information given, if 75 is added to x, the result is 39 less than three times the number, which can be expressed as:
x + 75 = 3x - 39
To solve for x, you can first get all the x terms on one side of the equation and the constant terms on the other side:
75 + 39 = 3x - x
Now, simplify the equation:
114 = 2x
To isolate x, divide both sides by 2:
x = 114 / 2
x = 57
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Miguel babysits for 3 hours and earns $15. Which represents the unit rate?
The unit rate is $/Hr. Since the hours are the unit being considered.
To find the unit rate, divide both sides by three
(Let x = hourly rate)
3x = 15
x = 5
Miguel Makes $5 per Hour
Answer:
He Earns 5 Per Hour
Holly
has 25 fish in her aquarium. Tommy has one-fifth the number of fish that Holly has. Jared has three times as many fish as Tommy. If they combine all their fish in the new school aquarium, how many fish would there be in all?
Complete each number pattern
8,625 8,725 ______ ______ 9,024
862 962 _____ 1,162 ______
6,215 _____ 6,015 _______ ______
one number is three less than four times another. if their sum is decreased by seven, the result is twenty. find the numbers
x = 21
y = 6
x = 4y - 3
x + y - 7 = 20
Because we have a value for x, we can put it in the second equation to find the value of y.
4y - 3 + y - 7 = 20
Combine like terms.
5y - 10 = 20
Add 10 to both sides.
5y = 30
Divide both sides by 5.
y = 6
Now we can place this value of y back into the equation to find the exact value of x.
x + 6 - 7 = 20
Combine like terms.
x - 1 = 20
Add 1 to both sides.
x = 21