The portion of cake Mike ate is 1/6.
The numbers given are expressed as fractions. Fractions are numbers that consist of numerators and denominators. For example, in the fraction 2/3, 2 is the numerator and 3 is the denominator.
The first step is to determine which portion of the cake that was stored in the freezer.
Portion kept in the freezer = 2/3 x 3/4 = 1/2
The second step is to determine the amount of cake Mike ate.
2/3 - 1/2
[tex]\frac{4 - 3}{6}[/tex] = [tex]\frac{1}{6}[/tex]
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The portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
The given parameters:
Original fraction of cake Mike possessed = 2/3Fraction of the cake Mike stored = 3/4The portion of the cake that Mike wrapped and stored in the freezer is calculated as follows;
[tex]= \frac{3}{4} \times \frac{2}{3} \\\\= \frac{1}{2}[/tex]
The portion of the cake that Mike ate is calculated as follows;
[tex]remaining = original - portion \ stored\\\\remaining = \frac{2}{3} - \frac{1}{2} = \frac{4 - 3}{6} = \frac{1}{6}[/tex]
Thus, the portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].
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Which values of a, b , and c correctly represent the answer in the simplest form?
Answer:
a=1 b=5 c=9
Step-by-step explanation:
Answer: answer is A
Step-by-step explanation:
A recipe uses 1 1/4 cups of oil to make 20 servings. If the same amount of oil is used for each serving, how many servings can be Made with one gallon of oil ?
Answer:
Step-by-step explanation:
1 1/4 (or 1.25) cups to 20 servings = 1 gallon (16 cups) to x servings
1.25 16
--------- = -------- cross multiply
20 x
(1.25)(x) = (20)(16)
1.25x = 320
x = 320/1.25
x = 256 servings <===
Last year 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. Find the percent of decrease.
Answer:
17.25%.
Step-by-step explanation:
We have been given that last ear 225 students attended the annual school dance at CCMS. This year 211 students attended the dance. We are asked to find the percent of decrease.
We will use percent decrease formula to solve our given problem as:
[tex]\text{Percent decrease}=\frac{|\text{Final - Original}|}{\text{Original}}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|211-255|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{|-44|}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=\frac{44}{255}\times 100\%[/tex]
[tex]\text{Percent decrease}=0.1725490\times 100\%[/tex]
[tex]\text{Percent decrease}=17.25490\%[/tex]
[tex]\text{Percent decrease}\approx 17.25\%[/tex]
Therefore, percent decrease is approximately 17.25%.
Complete the steps in order to write the inverse of f(x) = x + 5
Answer:
[tex]f^{-1}[/tex](x) = x - 5
Step-by-step explanation:
Let y = f(x) and make x the subject
y = x + 5 ( subtract 5 from both sides )
y - 5 = x
Change y back into terms of x, thus
[tex]f^{-1}[/tex](x) = x - 5
6. 40 adults and 26 kids went to
see a movie for $486.70. At the
same price, another group of 20
1 adults and 31 kids went to see
the same move for $332.45.
How much was an adult ticket
and how much was a kid ticket?
The cost of adult and kid tickets, we set up two equations representing the total cost for separate groups and use the elimination method to solve the system of linear equations. Once we solve for one ticket type, we can use its value to find the cost of the other ticket type.
The problem presented is a system of linear equations where we have two unknowns: the cost of an adult ticket and the cost of a kid ticket. We can set up the two equations based on the given information:
40A + 26K = 486.70 (First group's total cost)
21A + 31K = 332.45 (Second group's total cost)
To solve this system, we can use either substitution or elimination methods. For simplification, let's use the elimination method:
Multiply the second equation by 2: (2 x 21A) + (2 x 31K) = 2 x 332.45, which gives us 42A + 62K = 664.90.
Now subtract the first equation from this new equation: (42A + 62K) - (40A + 26K) = 664.90 - 486.70, resulting in 2A + 36K = 178.20.
Divide the entire equation by 2: A + 18K = 89.10.
We now have an easier equation to work with along with our original first equation.
To find the value of one variable, we could substitute the value of A from the first equation (using the second simplified equation) into the second equation and solve for K.
Once we have the value of K, we can substitute it back into either original equation to solve for A.
These steps will give us the exact cost of an adult ticket (A) and a kid ticket (K).
Does (-3,5 make the equation y=X+-2 true
Answer:
No.
Step-by-step explanation:
x+(-2)=-3+(-2)=-3-2=-5, not 5.
The graphs of y=x2- 3 and y = 3x -4 intersect at
approximately
1) (0.38,-2.85), only
2) (2.62,3.85), only
3) (0.38, -2.85) and (2.62,3.85)
4) (0.38, -2.85) and (3.85,2.62)
Answer:
Option 3) (0.38, -2.85) and (2.62,3.85)
Step-by-step explanation:
we have
[tex]y=x^{2}-3[/tex] ----> equation A
[tex]y=3x-4[/tex] ----> equation B
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs
using a graphing tool
The intersection points are (0.38,-2.85) and (2.62,3.85)
see the attached figure
therefore
The graphs intersect approximately at (0.38,-2.85) and (2.62,3.85)
(04.01 LC)
Marneshia walked of a mile in of an hour. What equation can be used to calculate her unit rate in miles per hour? (1 point)
Question 2 options:
1)
= mile per hour
2)
= miles per hour
3)
= miles per hour
4)
= mile per hou
The answer is 1 mile an hour
HELP HELP I DONT UNDERSTAND THIS
Answer:
1) angle bisector
2) w = 72°
3) t = 44°
4) t = 51°
5) FG = 16 units
Step-by-step explanation:
1) Given that, ∠VYW ≅ ∠WYV
The line which cuts any angle into equal halves is angular bisector of the angle
⇒ YW is angle bisector
2) In a triangle, sum of two interior angle is equal to exterior angle of other side.
⇒ w-41° + w-31° = w.
⇒ w = 72°
3) Sum of interior angles in a pentagon is 540°
(For a n sided it is (n-2)180° )
⇒ 149° + 139° + t+32° + 3t +t = 540°
⇒ t = 44°
4) sum of all exterior angles taken one at each vertex = 360°
⇒ 2t-50° + 46° + 2t + 34° + 2t-50° + 34° + 40° = 360°
⇒ t = 51°
5) Here, by comparing ΔHGF and ΔHIF
∠GHF = ∠IHF
∠HGF = ∠HIF
and HF is common side for both triangles
⇒ ΔHGF ≡ ΔHIF ; i.e) ΔHGF , ΔHIF are congruent triangles
⇒ FG = FI = 16 units
In a square or rectangle. How do you find the distance from the top left corner to the bottom right corner diagonally
Answer:
You use the Pythagorean theorem.
Step-by-step explanation:
https://math.stackexchange.com/questions/33549/calculating-the-distance-from-top-left-corner-to-bottom-right-corner-on-a-rectan
If my rent is 2795 a month, I agree to pay 75 more than my roommate how much do I owe and how much does my roommate owe
Answer:
The rent owe by me is Rs 1435
The rent owe by roommate is Rs 1360
Step-by-step explanation:
Given as :
The total rent of the room = x = Rs 2795
Let The room rent pay by friend = Rs y
And The room rent pay by me = Rs z
Now, According to question
The room rent pay by me = Rs 75 + room rent pay by roommate
i,e Rs z = Rs 75 + Rs y
Now, Again
The total rent of the room = The room rent pay by me + room rent pay by roommate
Or, x = Rs z + Rs y
Or, Rs 2795 = (Rs 75 + Rs y) + Rs y
Or, 2795 = 75 + 2 y
Or, 2 y = 2795 - 75
Or, 2 y = 2720
∴ y = [tex]\dfrac{2720}{2}[/tex]
i.e y = Rs 1360
So, room rent pay by friend = y = Rs 1360
And,The room rent pay by me = Rs 75 + room rent pay by roommate
Or,The room rent pay by me = Rs 75 + Rs 1360
So,he room rent pay by me = Rs 1435
Hence,The rent owe by me is Rs 1435
And ,The rent owe by roommate is Rs 1360 Answer
Select the expressions that are equivalent to 12x - 6.
@ -6(2x - 1)
® 6(2x - 1)
© 6x(2-1)
-6x(2x - 1)
@ -6(-2x + 1)
® 6x(-2x + 1)
Answer:
® 6(2x - 1); @ -6(-2x + 1)
Step-by-step explanation:
12x - 6 = 6(2x- 1) Factored out 6
12x - 6 = -6(-2x + 1) Factored out -6
what is the volume of a square pyramid with base edges 24ft and slant height 20ft
The volume of the square pyramid is: 3072 ft³
What is the volume of the square pyramid?
The volume (V) of a square pyramid can be calculated using the formula:
V = ⅓ × base area × height
The base area of a square pyramid is given by the formula:
base area = base edge²
Given that the base edges (a) is 24 ft and the slant height (s) is 20 ft, we can calculate the height (h) of the pyramid using the Pythagorean theorem.
h = √(20² - (24/2)²)
h = √256
h = 16 ft
Thus:
Volume = ⅓ * 256 * 16
Volume = 3072 ft³
Simplify: 6(3 + 5)
48
65
47
15
Answer:
48
Step-by-step explanation:
Step #1, Use PEMDAS,(Purple,Eyed,Monster,Drinks,A,Soda
Step #2, Add (3+5)
(8)
Step #3, Multiply 8×6
Step #4, No You
Answer:
48
Step-by-step explanation:
Matthew earned $75 in interest on
his savings account in one year.
The bank paid a simple interest
rate of 5%. What was the initial
amount of money Matthew put
into his savings account?
Answer:
Step-by-step explanation:
The formula for simple interest is
I = Prt,
where I is the interest earned,
P is the initial investment amount,
r is the interest rate in decimal form, and
t is the time in years. For us,
I = 75,
P = ?
r = .05
t = 1
Filling in what we were given:
75 = P(.05)(1) and
.05P = 75 so
P = 1500
6. (08.02 MC)
Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490n. What is the percent change in volume between cylinders A and b
Answer:
The percentage change in volume between cylinder A and cylinder B is 50%
Step-by-step explanation:
The volume of a cylinder is given by the formula
V= πr^2h
For cylinder A, where r=7 and h= 5, π=22/7
V= π * 7^2 * 5
V= π * 49 * 5
V= 769.69 cubic inch
For cylinder B
V= 490π
V= 1539.3804 cubic inch
The percentage change in volume between cylinder A and cylinder B
=[ (VA- VB)/VB] *100
=( 1539.3804 - 769.69) / 1539.3804
= 0.5000 * 100
= 50%
The percentage change in the volume between cylinder A and cylinder B is 50%
What is a cylinder?
A cylinder is a three-dimensional object. It is a prism with a circular base.
volume of a cylinder = πr²h
π= 22/7
r = radius
h = height
Volume of cylinder A = π(7² x 5) = 245π
Percentage change in volume = (245 / 490) - 1 = 50%
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Which equation can be solved to find one of the missing side lengths in the triangle?
60
12 units
O cos(609) = 12
O cos(600) =
O COS(60°) = 6
Answer:
[tex]cos(60^o)=\frac{a}{12}[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
In the right triangle of the figure
The cosine of the angle of 60 degrees is equal to divide the adjacent side to the angle of 60 degrees (BC) by the hypotenuse (AB)
so
[tex]cos(60^o)=\frac{BC}{AB}[/tex]
we have
[tex]BC=a\ units\\AB=12\ units[/tex]
substitute the values
[tex]cos(60^o)=\frac{a}{12}[/tex]
The correct equation that represents the side length is Cos 60 = a/12
Trigonometry identityFrom the triangle given, we have the following
Adjacent = aHypotenuse = 12Using the soh cah toa identity
Cos theta = adj/hyp
Cos 60 = a/12
Hence the correct equation that represents the side length is Cos 60 = a/12
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I have a 100 question study guide it is worht 20 points in total how many points is it
Answer:
2000 points
Step-by-step explanation:
Given:
Number of questions in a study guide (Q) = 100
Number of points for 1 question (n) = 20
Now, total number of points is calculated using unitary method by multiplying number of questions and number of points in one question.
Therefore, the total number of points is given as:
Total points = [tex]n\times Q[/tex]
Total points = [tex]20\times 100[/tex]
Total points = [tex]2000[/tex]
Hence, the study guide is worth 2000 points.
Answer:
10
Step-by-step explanation:
PLEASE HELP ITS URGENT!!
Given: △ABC is isosceles; 1 ≅ 3
Prove: AB || CD
Answer:
AB ║ CD. (Proved)
Step-by-step explanation:
See the attached diagram of the triangle.
It is given that Δ ACD is an isosceles triangle.
Therefore, AC = AD and ∠ ACD = ∠ ADC, ⇒ ∠ 3 = ∠ 4 .......... (1)
Again, given that ∠ 1 = ∠ 3 ........... (2)
Now, from equations (1) and (2) we can write, ∠ 1 = ∠ 4
Now, AB and CD are two straight lines and AD is the transverse line and hence, ∠ 1 and ∠ 4 are alternate angles that are equal.
Therefore, AB and CD are parallel straight lines and AB ║ CD. (Proved)
PLEASE HELP WILL GIVE BRAINLIEST! One fifth of the student a Riverview Elementary walk to school each day. There are 350 students in the school. How many students walk to school?
A.) 50
B.) 100
C.) 270
D.) 150
E.) 70
The right answer is Option E.
Step-by-step explanation:
Given,
Total number of students in school = 350
Students who walk to school = [tex]\frac{1}{5}\ of\ total\ students[/tex]
Number of students who walk to school = [tex]\frac{1}{5}*350[/tex]
Number of students who walk to school = 70
70 students walk to the school.
The right answer is Option E.
Keywords: fraction, division
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Final answer:
The calculation shows that 70 students at Riverview Elementary walk to school.
Explanation:
The question is asking us to calculate what fraction of the total number of students at Riverview Elementary walk to school each day.
Since one fifth of the students walk to school, we need to divide the total number of students by 5 to find the number of students who walk to school.
To find one fifth of 350 students, we calculate:
350 ÷ 5 = 70
Therefore, 70 students walk to school each day at Riverview Elementary.
Celia uses 4 ounces of yogurt for each smoothie she makes.she makes.she has 1 quart of yogurt.how many smoothies can she make with the yogurt? explain your thinking
You can use the fact that 1 quart is equal to 32 ounces.
Next, you can use the division fact, 32 divided by 4 equals 8.
And so, Celia can make 8 smoothies.
What is 4 7/8 x 28 in simplest form
Answer:
164 and one over two
Step-by-step explanation:
47 over 8 *28
=1316 over 8
=164 and four over eight
=164 and one over two
[tex] \frac{47}{8} \times 28 \\ = \frac{1316}{8} \\ = 164 \frac{4}{8} \\ = 164 \frac{1}{2} [/tex]
Hope that helps
Find the value ox X:
A 20
B 18
C 15
D 11
Answer:
x =15°
Step-by-step explanation:
Given that the horizontal line is 90° to the vertical line, then both the angles have to necessarily add up to 90° i.e
(5x-10)° + 25° = 90°
5x - 10 + 25 = 90
5x + 15 = 90 (subtract 15 from both sides)
5x = 90 - 15
5x = 75 (divide both sides by 5)
x = 75 / 5 = 15°
what percent of 108 is 81?
Answer: 133.33
Just do 108/81x100 to get 133.33
Hope this helps!
Answer:
75%
Step-by-step explanation:
You start driving north for 11 miles, turn right, and drive east for another 60 miles.
How many miles must you travel to return directly back to your starting point?
Answer:
61 miles.
Step-by-step explanation:
Given: driving north for 11 miles and drive east for another 60 miles.
As given in the question, the travelling pattern show a right angle triangle, where hypotenuse line is the way to return back directly to starting point. As shown in picture attached.
∴ we can say, adjacent (a) is 11 miles and opposite (b) is 60 miles
Now, using Pythagoras theorem to get distance to return.
[tex]h^{2} = a^{2} +b^{2}[/tex]
⇒ [tex]h^{2} = 11^{2} +60^{2}[/tex]
⇒ [tex]h^{2} = 121+3600= 3721[/tex]
⇒ [tex]h= \sqrt{3721}[/tex]
∴[tex]h= 61[/tex]
∴ 61 miles need to be travel to return back directly to starting point.
50 PINTS！！！！！！！！ PLEASE HELP QUICK!!!!!!!!!!! What is the slope of the line shown in the graph? (4 points) A coordinate plane is shown with points graphed at 2 comma 2 and 0 comma 1. The points are joined by a line. −2 −1 −1 over 2 1 over 2
We are given, [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] where [tex]P_1(2,2),P_2(0,1)[/tex].
Using slope formula we obtain
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{0-2}=\dfrac{-1}{-2}=\boxed{\dfrac{1}{2}}[/tex]
Hope this helps.
Answer:
1/2
Step-by-step explanation:
I took the test :)
soledads regular pay rate is $7.50 per hour. If she works more than 40 hours in one week, she receives 1.5 times
her regular pay rate for each additional hour. How many hours would Soledad have to work in one week to earn a
total of $345?
43
45
46
44
Answer:
44
Step-by-step explanation:
pay for 40 hours: 7.50 * 40= 300
pay for 1 hour of overtime pay: 1.5 * 7.5= 11.25 per hour
11.25 * 4= 45
45 + 300= 345
40 + 4= 44
Two parallel lines are crossed by a transversal. Parallel lines r and s are cut by transversal q. On line s where it intersects with line q, the uppercase left angle is 125 degrees and the bottom right angle is d degrees. What is the value of d? d = 55 d = 75 d = 125 d = 155
Answer:
d=125
Step-by-step explanation
edge 2020
The value of d, which is the bottom right angle formed on line s when cut by transversal q, is 125 degrees due to the alternate exterior angles being congruent on parallel lines.
Explanation:When two parallel lines are crossed by a transversal, certain angles are equal due to the properties of parallel lines. The upper left angle on line s when intersected with the transversal q is given as 125 degrees; this is the alternate exterior angle relative to the bottom right angle formed on line s also intersected by q, which is known as d degrees in the question.
According to the alternate exterior angles theorem, these two angles are equal because the lines r and s are parallel. Therefore, the bottom right angle on line s, or d degrees, is also 125 degrees, because alternate exterior angles are congruent when two parallel lines are cut by a transversal.
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Mo’s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
Answer:
Step-by-step explanation:
a + p = 165......a = 165 - p
1.75a + 2.5p = 337.50
1.75(165 - p) + 2.5p = 337.50
288.75 - 1.75p + 2.5p = 337.50
-1.75p + 2.5p = 337.50 - 288.75
0.75p = 48.75
p = 48.75 / 0.75
p = 65 <==== 65 lbs of peaches were sold
a + p = 165
a + 65 = 165
a = 165 - 65
a = 100 <=== there were 100 lbs of apples sold
check...
1.75a + 2.5b = 337.50
1.75(100) + 2.5(65) = 337.50
175 + 162.50 = 337.50
337.50 = 337.50 (correct)
Mathematics MH helpo
The inequalities that require flipping the sign are:
-5x - 10 > 5
[tex]\frac{x}{-7} + 3 \leq 4[/tex]
Solution:
Let us the inequalities one by one
You can perform on operations on both sides of inequality, and have its truth value unchanged
But if we multiply or divide by a negative number , we must flip the sign
option 1)-5x - 10 > 5
Move -10 from L.H.S to R.H.S
-5x > 5 + 10
-5x > 15
Divide the above expression by 5
[tex]-x > 3[/tex]
Divide the above inequality by -1, so we must flip the sign
x < -3
option 2)[tex]7x - 5 \leq 16[/tex]
Move the constant term from L.H.S to R.H.S
[tex]7x \leq 16 + 5\\\\7x \leq 21\\\\[/tex]
Divide the above inequality by 7
[tex]x \leq 3[/tex]
This does not required flipping the symbol
option 3[tex]\frac{x}{5} - 6 > -11[/tex]
Move the constant term from L.H.S to R.H.S
[tex]\frac{x}{5} > -11 + 6\\\\\frac{x}{5} > -5[/tex]
Multiply both the sides by 5
[tex]x > -25[/tex]
This does not required flipping the symbol
option 4[tex]x + 12 \leq 29[/tex]
Move the constant term from L.H.S to R.H.S
[tex]x \leq 29 - 12\\\\x \leq 17[/tex]
This does not required flipping the symbol
option 5[tex]\frac{x}{-7} + 3 \leq 4[/tex]
Move the constant term from L.H.S to R.H.S
[tex]\frac{x}{-7} \leq 4-3\\\\\frac{x}{-7} \leq 1\\\\[/tex]
Multiply both the sides by -7, so we must flip the sign
[tex]x \geq -7[/tex]
Thus this requires flipping the sign
Answer: -5x - 10 > 5
Step-by-step explanation: