Answer:
20 people
Step-by-step explanation:
At the movie theater, they give out a free drink to every 75th customer and a free bag of popcorn to every 30th customer.
On Monday, 3,000 customers came to the theater.
To find the number of people who got both free items, we will calculate the Least Common Multiple (LCM) of 30 and 75.
LCM of 30, 75
= 5 × 3 × 5 × 2
= 150
Each 150th customer will receive both free items.
Total number of people who receive both free items = 3000 ÷ 150
= 20 people
On Monday 20 people will receive both free items.
If anyone can do this for me step by step i will give you 30 points please help me out
Answer:
after 10 months
Step-by-step explanation:
Let x be the number of months and y be the amount they still owe.
Sin Ian borrows $1000 from his parents, then the y-intercept b= 1000 since he owes $1000 when x = 0. He pays them back $60 each month The slope is then m = -60 . Substituting in b = 1000 and m = -60 into the slope-intercept form of a line then gives y= mx + b=-60x +1000.
Sin Ken borrows $600 from his parents, then the y-intercept b = 600 since he owes $600 When x= 0. He pays them back $20 per month so the amount he owes decreases $20 each month. The slope is then m = -20 . Substituting in
b= 600 and m = -20 into the slope-intercept form then gives y = mx +b = -20x + 600.
They will owe the same amount when they have the same y-coordinate. Therefore -60x+ 1000= y= -20x+600. Solve this equation for x:
-60x+ 1000 = -20x+ 600
1000 = 40x+ 600
400 = 40x
10=x
They will then owe the same amount after 10 months.
Simplify:{x(6x - 1
A)
B)
2x-1
9
2x
x-
2x7.5
D
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {D. \:= 2 {x}^{2} - \frac{1}{3} x}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] \frac{1}{3} x \: ( \: 6x - 1 \: )\\[/tex]
[tex] = \frac{x \: ( \: 6x - 1 \: )}{3}\\[/tex]
[tex] = \frac{6 {x}^{2} - x}{3} \\[/tex]
[tex] = \frac{6 {x}^{2} }{3} - \frac{x}{3}\\ [/tex]
[tex] = 2 {x}^{2} - \frac{1}{3} x\\[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
solve the system of equations y=x-7 y=x^2-9x+18
9514 1404 393
Answer:
(x, y) = (5, -2)
Step-by-step explanation:
Equating expressions for y, we have ...
x^2 -9x +18 = x -7
x^2 -10x +25 = 0 . . . . . add 7-x to both sides
(x -5)^2 = 0 . . . . . . . . factor
The value of x that makes the factor(s) zero is x=5. The corresponding value of y is ...
y = x -7 = 5 -7 = -2
The solution is (x, y) = (5, -2).
Answer and I will give you brainiliest
Answer:
x = 60 degree
Step-by-step explanation:
90 + 90 + 2x - 10 + 2x + 2x + 10 = 540 degree (sum of 5 interior angles)
180 + 6x = 540
6x = 540 - 180
x = 360/6
x = 60 degree
Help with this Geometry question please
Answer:
Angle A = [tex]77^{o}[/tex]
Step-by-step explanation:
cos A = adjacent / hypotenuse
cos A = 18/82
cos A = 0.22
A = [tex]cos ^{-1}[/tex]0.22
A = [tex]77^{o}[/tex]
Use the graph to answer the question.
What is [tex]\frac{AD}{AB}[/tex] in simplest form?
A. [tex]\frac{10}{3}[/tex]
B. [tex]\frac{1}{3}[/tex]
C. [tex]\frac{17}{5}[/tex]
D. 3
Answer:
D. 3
Step-by-step explanation:
Distance between A and D = AD = 9 units
Distance between A and B = AB = 3 units
[tex] \frac{AD}{AB} = \frac{9}{3} [/tex]
Simplify by dividing
[tex] \frac{AD}{AB} = \frac{3}{1} [/tex]
[tex] \frac{AD}{AB} = 3 [/tex]
The answer is 3
Bill can hit a bucket of 323 golf balls in 17 hours.
How many golf balls can Bill hit in 23 hours?
I was wondering if someone could answer this :)
Answer:
17
Step-by-step explanation:
2a+30 = 4a-4
+4 +4
2a+34 = 4a
-2a -2a
34 = 2a
÷2 ÷2
a=17
Hope this helps! :)
Answer:
A = 17
Step-by-step explanation:
Opposite angles are congruent in a parallelogram
Hence 2a + 30 = 4a - 4
( Note that we've just created an equation that we can use to solve for a)
We now solve for a
2a + 30 = 4a - 4
Add 4 to both sides
2a + 34 = 4a
Subtract 2a from both sides
34 = 2a
Divide both sides by 2
a = 17
0.0543 nearest whole number
Answer:
0
Step-by-step explanation:
Ignore the next 2 numbers after 0.05. To the nearest whole number, round 0.05 to the nearest tenth, 0.1. Then round that to the nearest whole number, 0, which is your answer.
A technical machinist is asked to build a cubical steel tank that will hold of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest .
Answer:
The smallest possible length is 0.83m
Step-by-step explanation:
Given
[tex]Volume = 565L[/tex]
Required
The smallest length of the tank
Since the tank is cubical, then the volume is:
[tex]Volume = Length^3[/tex]
This gives:
[tex]565L= Length^3[/tex]
Express as [tex]m^3[/tex]
[tex]\frac{565m^3}{1000} = Length^3[/tex]
[tex]0.565m^3 = Length^3[/tex]
Take cube roots of both sides
[tex]0.8267m = Length[/tex]
Rewrite as:
[tex]Length = 0.8267m[/tex]
Approximate
[tex]Length = 0.83m[/tex]
X Y
-10 2
-15 3
-25 5
Determine whether y varies directly with x. If so, find the constant of variation and write the equation
Answer:
x = -5y
Step-by-step explanation:
x = ay
-10 = 2a
a = -5
x = ay
-15 = 3a
a = -5
x = ay
-25 = 5a
a = -5
Solve for X in the triangle. Round your answer to the nearest tenth
Answer:
[tex]\displaystyle x \approx 9.9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] sinθ = opposite over hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 64°
Opposite Leg = x
Hypotenuse = 11
Step 2: Solve for x
Substitute in variables [sine]: [tex]\displaystyle sin(64^\circ) = \frac{x}{11}[/tex][Multiplication Property of Equality] Multiply 11 on both sides: [tex]\displaystyle 11sin(64^\circ) = x[/tex]Rewrite: [tex]\displaystyle x = 11sin(64^\circ)[/tex]Evaluate: [tex]\displaystyle x = 9.88673[/tex]Round: [tex]\displaystyle x \approx 9.9[/tex]Prove the formula that:
((∃x)(F(x)∧S(x))→(∀y)(M(y)→W(y)))∧((∃y)(M(y)∧¬W(y)))
⇒(∀x)(F(x)→¬S(x))
Step-by-step explanation:
Given: [∀x(L(x) → A(x))] →
[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for
arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof
technique.
Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
We need to show that the above expression is unsatisfiable (False).
¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))
∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))
E.I with respect to x,
(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a
(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))
E.I with respect to y,
(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b
U.I with respect to y,
(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b
Since P ∧ Q is P, drop L(a) from the above expression.
(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b
Apply distribution
(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))
Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to
(L(b) ∧ H(a, b) ∧ ¬A(b))
U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace
¬A(b) in the above expression with ¬L(b). Thus, we get,
(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.
This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows
from the premise.
15
What is the value of z in the equation 3z+9=z?
NEED HELP ASAP PLEASE
Assume that a three-month CD purchased for $3000 pays simple interest at an annual rate of 10%. How much total interest does it earn?
$ ____
What is the balance at maturity? ______
Answers:
interest = $75balance at maturity = $3075=============================================================
Explanation:
The simple interest formula is
i = p*r*t
where in this case,
p = 3000 = principal (amount deposited)r = 0.10 = annual interest rate in decimal formt = 3/12 = 0.25 = number of yearsSo,
i = p*r*t
i = 3000*0.10*0.25
i = 75 is the amount of interest earned
This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)
The balance at maturity is p+i = 3000+75 = 3075 dollars
---------------
In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.
Consider the following equation. -2x + 6 =[-2/3] + 5
Answer:
that's my answer
hope it helps
Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(y2 − 4) = x2(x2 − 5) (0, −2) (devil's curve)
Answer:
Step-by-step explanation:
Given that:
[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]
at point (0, -2)
[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]
Taking the differential from the equation above with respect to x;
[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]
Collect like terms
[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
Hence, the slope of the tangent line m can be said to be:
[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]
At point (0,-2)
[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]
[tex]\dfrac{dy}{dx}= 0[/tex]
m = 0
So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:
(y - y₁ = m(x - x₁))
y + 2 = 0(x - 0)
y + 2 = 0
y = -2
HELPPPPOOOPPPPOPPPPPPPP
Answer:
Your answer would be B
Step-by-step explanation:
So right away you can get rid of a and d since they are positive numbers, there is no positive numbers in the graph were the line is.
So we know that the y-intercept is -2 (as you can see the line pass through (0,-2))
And we know the y intercept is -8 (since the line pass through (-8,0))
so you are left with b and c, c is incorrect because the -2 goes through the y-intercept not the x.
The right choice is b, it states that the x-intercept -8 pass through the line, the y-intercept is -2
Your welcome and hoped this helped!
Margot surveyed a random sample of 180 people from the United States about their favorite sports to watch. Then she sent separate, similar, survey to a random sample of 180 people from the United Kingdom. Here are the results:
Favorite sport to watch United States United kingdom Total
Basketball 60 51 111
Football 67 14 81
Soccer 28 86 114
Tennis 25 29 54
Total 180 180 360
Margot wants to perform a x^2 test of homogeneity on these results. What is the expected count for the cell corresponding to people from the United Kingdom whose favorite sports to watch is tennis?
Answer:
27
Step-by-step explanation:
The expected count in a χ² test can be obtained thus :
Expected count for each each point in a two way table ::
(row total * column total) / total
Therefore, expected count for cell corresponding to people from United Kingdom whose favorite sport is tennis :
Row total = (51+14+86+29) = 180
Column total = (25 + 29) = 54
Total = 360
Hence,
Expected count = (180 * 54) / 360
Expected count = 27
Which state ment is true regarding the graphed function
F(4)= g(4)
F(4)= g(-2)
F(2)= g(-2)
F(-2)= g(-2)
Answer:
F(-2)= g(-2)
Step-by-step explanation:
F(-2)= g(-2), both function have the same points of intersect.
In △CDE, DE=14, CE=9, and m∠E=71∘. What is the length of CD⎯⎯⎯⎯⎯⎯? Enter your answer, rounded to the nearest hundredth, in the box.
Answer:
13.96units
Step-by-step explanation:
To get the length of CD, we will use the cosine rule as shown:
CD² = DE²+CE²-2(DE)(CE)cos m<E
Substitute the given values
CD² = 14²+9²-2(14)(9)cos71
CD² = 196 + 81 - 252cos71
CD² =277 - 252cos71
CD² = 277 - 82.0431
CD² = 194.95682
CD = √194.95682
CD = 13.96 units
Hence the length of CD of 13.96units
Pls help ASAP!!!!!!!!!!! I NEED HELP IMMEDIATELY!!!
Jaime had ten posters, but only five could fit on his closet door. How many different ways can he arrange the five posters out of the ten on his closet door?
A. 252
B. 648
C. 6,048
D. 30,240
Answer:
its c
Step-by-step explanation:
Find the value of X
Answer:
100°
Step-by-step explanation:
the lower right angle is 180-149 = 31°
the sum of all three angles in a triangle is 180°.
so the solution is 180-31-49
HELP plsssss I will GIVE YOU BRAINLYEST
Answer: B
Step-by-step explanation:
Answer:
-5ºC < 5ºC is an inequality that compares temperatures.
B is the correct answer for the multiple choice question.
PLEASE HELP ME I HAVE TO PASS THIS TEST
30 POINTS
Answer:
Hi, there the answer is
These are the equations with exactly one solution
-5x + 12 = –12x – 12
-5x + 12 = 5x + 12
-5x + 12 = 5x – 5
Hope This Helps :)
Step-by-step explanation:
First degree equations
A first degree equation has the form
ax + b = 0
There are some special cases where the equation can have one, infinitely many or no solution
If , the equation has exactly one solution
If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0
If a=0 and the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.
We have been given some equations, we only need to put them in standard form
-5x + 12 = –12x – 12
Rearranging
7x + 24 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = 5x + 12
Rearranging
-10x + 0 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = 5x – 5
Rearranging
-10x + 17 = 0
It has exactly one solution because a is not zero
.......................
-5x + 12 = -5x – 12
Rearranging
0x + 24 = 0
It has no solution, no matter what the value of x is, it's impossible that 24=0
Answer: These are the equations with exactly one solution
-5x + 12 = –12x – 12
-5x + 12 = 5x + 12
-5x + 12 = 5x – 5
simplify -5-√-44
i have no idea
Answer:
Undefined
Step-by-step explanation:
The square root of a negative number does not exist in the set of real numbers so it would be Undefined
Can somone help me solve this
Answer:
solid shade above
Step-by-step explanation:
graph line same way you would if it was an equal sign
all the y's that are greater are above the line
its solid because is greater than OR equal to. Equal to includes the line itself as a set of solutions
I need big help on this one
simplify the expression (2r^4y4xy^2) completely
Step-by-step explanation:
we can simplify the stuff inside the parentheses to
[tex] \frac{ {x}^{3} }{2y} [/tex]
now we need to multiply it with itself, giving us
[tex] \frac{ {x}^{6} }{4 {y}^{2} } [/tex]
so yeah, D is the correct answer
What is the area of the parallelogram shown?
Answer:
Area = 96 square m
Step-by-step explanation:
[tex]Area = base \times height = 12 \times 8 = 96 \ m^2[/tex]
Answer:
The area of parallelogram is 96 m ².
Step-by-step explanation:
According to the question , we have given a parallelogram with base 12 m and height is 8 m. We need to find the area of parallelogram.
Solution :-Using Formula
Area of parallelogram = Base × Height
Substitute the values into this formula
Area of parallelogram = 12 m × 8 m
multiply, we get
Area of parallelogram = 96 m²
Therefore, The area of parallelogram is 96 m ².
