The total cost of a catered meal for the Armstrong family reunion was to be split equally by the 20 people who came. Before the meal started, five more Armstrong's unexpectedly appeared. The total cost was shared equally among the 25 people, and so each person in the original group owed $4 less. What was the total cost of the catered meal?
Answer:
$400
Step-by-step explanation:
Let the initial total cost be represented = $X.
Hence, for 20 family members
= $ x/20 each .......1
Now that they are 25 members
= $x/25 each.......2
Each in the original group which is equation 1 owed $4 less.
That is,
x/20 - 4 ........ 3
Now equate 2 and 3
X/20 - 4/1 = X/25
Taking the LCM of both sides
X-80/20 = X/25
Cross multiply both sides
25( x-80 ) = 20x
25x-2000 = 20x
Collecting like terms
25x-20x = 2000
5x = 2000
Divide through by 5
X = 2000/5
X = 400
The total cost for the catered meal is $400.
To check if it was correct
Put 400 into equation 1 and 2 and then minus whatever you get from each other, you will get $4
From equation 1
400/20 = $20
From equation 2
400/25 =$16
$20-$16 = $4
Thanks
what is the area of the figure below
Answer:
Step-by-step explanation:
this is sorta a thought process to figure this out. so think it thur with me. b/c they are saying that the line is the same length with the lines thur it... see them? so then that means that two sides of the right triangle are of a certain length so that means we know the base and length of the sides of a box, if we were to add the other right triangle to it.. see that?
so we can say that 6*7.5 = box and we'll have two total boxes, see that? the top portion of the parallelogram and the bottom are each a box .. but cut down the middle and put as two opposite parts of a triangle.
so
2*(6*7.5) = 90 [tex]in^{2}[/tex]
Find two negative consecutive integers such that the square of the first is five more than the second. Find the integers.
Answer:
the two consecutive negative integers are -2 and -1.
Step-by-step explanation:
Represent these negative integers by m and n.
Then (because the integers are consecutive) n = m + 1, and m^2 = n + 5.
Substituting m + 1 for n in the second equation, we get:
m^2 = m + 1 + 5, or
m^2 - m - 6 = 0
This factors into (m - 3)(m + 2) = 0. The only negative root is -2.
Thus, the two consecutive negative integers are -2 and -1.
Check: Is the square of the first five more than the second?
Is (-2)^2 = -1 + 5? YES
The integers aer -2 and -1.
pls answer this i have no clue
Answer:
90 degrees
Step-by-step explanation:
The three angles of a triangle always add up to 180 degrees, so knowing this, all three of the measures given should add up to 180.
First, you need to solve for x:
S(x+10) + R(2x+60) + T(50+x) = 180
Add up all of the like terms:
10 + 60 + 50 = 120
x + 2x + x = 4x
So now you are left with 4x + 120 = 180
And solve for x:
4x/4 + 120/4 = 180/4
x + 30 = 45
x + 30-30 = 45-30
x = 15
Now that we have the value of x, plug it into the measure given for angle R:
(2x+60)
= (2(15)+60)
= (30 + 60)
= 90
So the measure of angle R is 90 degrees.
I hope this helped! :)
Please answer correctly! I will mark you Brainliest!
Answer:
d=18 feet
Step-by-step explanation:
The volume of a sphere is represented by the equation [tex]V=\frac{4}{3}\pi r[/tex]³, where r is the radius. If the volume is 972[tex]\pi[/tex],
[tex]972\pi =\frac{4}{3}\pi r[/tex]³
Divide [tex]\pi[/tex] from each side,
[tex]972=\frac{4}{3} r[/tex]³
Multiply each side by 3/4 to get rid of the fraction,
[tex]r[/tex]³[tex]=729[/tex]
Using the cube root, we find that 729 is actually a perfect cube.
[tex]r=9[/tex]
Now, the diameter is 2 times the radius, so
9×2=18
So, the measure of the diameter is 18 feet.
Helpppp please and ty
Answer:
-2, -1, 0, 1
Step-by-step explanation:
you hover over the stars
PLEASEEEEE ILL MARK BRAINIEST
Answer:
5. 18 that is what i think the answers are
6. 13.75
5 2 11 8 35 32
Right will be marked brainlist
Answer:
the answer is 3,107.21
The answer to that question is that one
What is the mode of the data set? {32, 29, 35, 25, 32, 22, 30} Enter your answer in the box.
Answer:
beleive its 35
Step-by-step explanation:
Answer:
The mode hear is 32
Step-by-step explanation:
The mode is the number seen the most in a selected group.
Here is a Mnemonic to help remember what the 3 M's are:
'Hey diddle, diddle
the medians in the middle
add and divide for the mean
the mode is the one that you see the most
and the range is the difference between'
T=21and u =4 what is \sqrt(t+U)
Answer: 5
Step-by-step explanation: 21 + 4 = 25
square root of 25 = 5
Answer and Step-by-step explanation:
T = 21
U = 4
[tex]\sqrt{ 21 + 4} \\\\\\\sqrt{25} \\\\\\5[/tex]
5 is the answer to the expression.
#teamtrees #PAW (Plant And Water)
Can someone help me with this. Will Mark brainliest.
Answer:
√53
Step-by-step explanation:
Use the distance formula to find the distance between the two coordinates
Can someone help me with this. Will Mark brainliest.
Answer:
B ( -1, -8)
Step-by-step explanation:
A ( -7, -6)
midpt (-4, -7)
Equation:
(x + 3, y - 1)
Solve for B:
(-4, -7)
(x + 3, y - 1)
( -1, -8)
Using the information from the previous question, find the equation in standard form for the area of the fenced-in section in terms of the length of the field.
(area = length • width)
Answer:
y = x2 − 500x + 60,000
Step-by-step explanation:
area of the fenced-in section = length • width
y = (x − 200)(x − 300)
= x² − 300x − 200x + 60,000
= x² − 500x + 60,000
Help me please it’s due today
Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark. How much shorter with their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead?
Answer:
If they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.
Step-by-step explanation:
Given that Gigi's Family left their house and drove 14 miles south to a gas station and then 48 miles east to a waterpark, to determine how much shorter would their trip to the waterpark have been if they hadn't stopped at the gas station and had driven along the diagonal path instead the following calculation must be performed, using the Pythagorean theorem:
14 ^ 2 + 48 ^ 2 = X ^ 2
196 + 2,304 = X ^ 2
√ 2500 = X
50 = X
14 + 48 - 50 = X
62 - 50 = X
Thus, if they hadn't stopped at the gas station and had driven along the diagonal path, their trip would have been 12 miles shorter.
How does the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to
the volume of a cylinder with a radius of 8 inches and a height of 6 inches?
Answer:
they are the same
Step-by-step explanation:
We can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to compare the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to the volume of a cylinder with a radius of 8 inches and a height of 6 inches.
Volume of cylinder 1 will be -
V(1) = πR²h = 6 x 6 x 8π = 36 x 8π = 288π
Volume of cylinder 2 will be -
V(2) = πR²h = 8 x 8 x 6π = 64 x 6π = 384π
So, we can write that -
V(1)/V(2) = (288π)/(384π)
V(1)/V(2) = (288)/(384)
V(1)/V(2) = 3/4
Therefore, we can conclude that the volume of cylinder 1 is 3/4 times the volume of cylinder 2.
To solve more questions on cylinders, visit the link below-
https://brainly.com/question/16134180
#SPJ3
i get alot of these please help
Answer:
18 is 3 more than 9- false
18 is 3 times as much as 6 - true
9 is 3 times as much as 27- false
9 is 3 more than 6 - true
Select the correct answer.
What is the domain of the function shown on the graph?
A. -∞ < x < ∞
B. x ≤ 2
C. x ≤ 1
D. -10 < x < 2
Option B is correct, x ≤ 2 is the domain of the function shown on the graph.
What is a function?A relation is a function if it has only One y-value for each x-value.
We have to find the domain of the given graph.
Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis.
The graph has x values less than or equal to two.
x ≤ 2 is the domain of the given function.
Hence, option B is correct, x ≤ 2 is the domain of the function shown on the graph.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ3
ect
Use the number line interactive to evaluate the
following expressions.
8 + 3 =
+
16
(-8) + (-5) =
<
(-8) + 2 =
Answer:
1. 11
2. -13
3. -6
Step-by-step explanation:
Hope this helps. Have a great day! (I got this correct on edge :})
2) Michael decides to go for a cycle ride. He rides a
distance of 80 km at an average speed of 24 km/h.
Work out how long Michael’s ride takes
Step-by-step explanation:
REMEMBER D/S×T (triangle)
therefore, finding time
D/S
80/24
make sure to press the degrees button on your calculator
3 hours and 20 minutes
Plzzz help me!!!!!!!!
m - 12 = 11
A. -23
B. -1
C. 1
D. 23
Answer:
D. 23
Step-by-step explanation:
m-12-(11)=0
m-23 = 0
m = 23
Find the Area of the composite figure below:
Answer:
24
Step-by-step explanation:
added all the sides hope this helps
What is the surface area of the prism below?
A
216 ft2
B
312 ft2
C
432 ft2
D
10,800 ft2
What is the answer when you simplify it?[tex]7^{2} +2(\sqrt{81} +\sqrt{49} )[/tex]
I would just like some solving steps or the answers.
Help help help help help
Answer:
6 ft
Step-by-step explanation:
The triangle CDE is half of the size of triangle ABC, so if you match up the corresponding sides, DE is half of AC. AC is 12 so DE is 6.
hope is helped!
Are there outliers in the set of data below? Hint: Use your formulas from the lesson
52, 58, 62, 66, 67, 68, 68, 70, 70, 72, 73, 74, 76, 84, 90
Question 1 options:
52 and 90
68 and 70
There are no outliers
pls help
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
Answer:
hi
Step-by-step explanation:
hope it helps
have a nice day
Answer:
3.14, 5.8, 0.3, negative 2
Step-by-step explanation:
3.14 is found bn 2 and 3 but very close to 3 u can just take 3.1 and for 5.8 it's bn 5 and 6 very close to 6 but not six , and we'll negative 2 is right on negative 2
help asap please i need to get thru this
Answer:
The Scale Factor is 1/4.
Step-by-step explanation:
if you multiply each side (of figure A) by 1/4, the product matches with figure B's corresponding sides. for example, 56 to 14, 28 to 7, and 64 to 16.
the scale factor is just how much a chosen shape is multiplied by to get the next shape.
to get bigger shapes into a smaller shape, multiply the sides by fractions like we did this problem.
