1.
Platinum Gym charges a one-time registration fee of $60, and membership is $20 a month.
Super Fit charges a one-time registration fee of $150, and membership is $10 a month.
(a) Write a expression to represent the membership cost of Platinum Gym for x months.
Let x = months
20x + 60 is your expression
(b) Write an expression to represent the membership cost of Super Fit for x months
Let x = months
10x + 150 is your expression
(c) You are solving for both one month and twelve months of membership.
One month: Plug in 1 for x.
20(1) + 60 = 20 + 60 = 80
10(1) + 150 = 10 + 150 = 160
Platinum Gym is cheaper overall for one month by $80
One year: There are twelve months in a year. Plug in 12 for x.
20(12) + 60 = 240 + 60 = 300
10(12) + 150 = 120 + 150 = 270
Super Fit is cheaper than Platinum Gym overall for one year by $30
(d) Set the two expression equal to each other.
20x + 60 = 10x + 150
Isolate the x. Subtract 10x and 60 from both sides
20x (-10x) + 60 (-60) = 10x (-10x) + 150 (-60)
20x - 10x = 150 - 60
Simplify
20x - 10x = 150 - 60
10x = 90
Isolate the x. Divide 10 from both sides
10x/10 = 90/10
x = 9
It takes 9 months for the cost to be the same.
(e) It really depends on how long you want to work out at a gym. If you are working out for less than a year, than Platinum Gym is the better choice. If more than a year, then Super Fit is the better choice.
---------------------------------------------------------------------------------------------------------------------
hope this helps
Find the probability that event A will appear at least three times in four independent tests if the probability of occurrence of event A in one test equal to 0.4
This kind of problems are solved using Bernoulli's distribution. Everytime you have a win/lose scenario, and you know the probability [tex] p[/tex] of winning, and you want [tex]k[/tex] successes over [tex]n[/tex] trials, you have the following probability:
[tex]\displaystyle P(k\text{ successes over }n\text{ trials}) = \binom{n}{k}p^k(1-p)^{n-k} [/tex]
You want the probability of having at least three successes, i.e. you are interested in the cases k=3 and k=4. The corresponding probabilities are
[tex]\displaystyle P(3 \text{ successes}) = \binom{4}{3}0.6^3 \cdot 0.4 = 4\cdot 0.216 \cdot 0.4 = 0.3456[/tex]
[tex]\displaystyle P(4 \text{ successes}) = \binom{4}{4}0.6^4 = 0.1296 [/tex]
So, the total probability is [tex] 0.3456+0.1296 = 0.4752[/tex]
2x + 2y =6. 5x + 2y =4. Which of the following equations could be the result of multiplication and addiction to eliminate a variable in the system of equations?
A) 19x = 24
B) 19y = 22
C) 11y = 22
2x+2y=6
5x+2y =4
Multiply eq 1 by 5 and equation 2 by -2
10x+10y = 30
-10x - 4y = -8
Now adding we get
6y = 22
Divide by 2
3Y =11
What is the LCM for 14,8
Answer,
56
Hope this helps :-)
Hello there!
This question is super easy to me.
You had to find the prime factorization of 14.
7*2=14
Next, you had to find the prime factorization of 8.
2*2*2=8
7*2*2*2=56
Answer⇒⇒⇒56
The least common multiple of 14 and 8 is 56.
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
Use the graph below to fill in the blank with the correct number: f(1) = _______ X, Y graph. Plotted points negative 3, 0; negative 2, 2; 0, 1; and 1, negative 2.
Answer:
f(1) = -2
Step-by-step explanation:
Each point is (x, f(x)).
The point (1, f(1)) is given as (1, -2), so f(1) = -2.
Answer:
f(1) = -2
Step-by-step explanation:
Solve for sss.
0.5s+1=7+4.5s
The value of s from the given equation is -1.5.
The given equation is 0.5s+1=7+4.5s.
We solve the given equation for s.
What is an equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity.
Now, the given equation can be solved as follows:
0.5s+1=7+4.5s
⇒0.5s-4.5s=7-1
⇒-4s=6
⇒s=-6/4
⇒s=-1.5
Therefore, the value of s is -1.5.
To learn more about an equation visit:
brainly.com/question/22277991.
#SPJ6
Please answer! Will mark as Brainliest if correct.
Pedro, Lena, Harriet, and Yermin each plot a point to approximate the square root of 0.50.
(See picture)
Whose point is the best approximation of the square root of 0.50?
A: Pedro
B: Lena
C: Harriet
D: Yermin
Answer:
D. Yermin
Step-by-step explanation:
\sqrt(0.50) = 0.70710678
When rounded go to 0.7
Answer:It’s D
That’s the answer because I did this test before and got it right
Which operation would be completed second in the following expression?
7 2 - 3 + 9 × 8 ÷ 2
A. simplify the exponent
B. subtract
C. divide
D. multiply
Tommy has a pet monkey .Every day , his monkey eats 4 apples in the morning.the monkey also eats two bananas for every banana that tommy eats .
Write an equation to describe this situation where x is the number of banana tommy eats and y is the total number of pieces of fruit the monkey eats
WILL GIVE 20 POINTS I PROMISE !!!! PLEASE ANSWER FAST
If a piece of ribbon is 4 and 3/4. feet long, how long is it in inches?
A. 48 inches
B. 57 inches
C.60 inches
D. 62 inches
12 inches is equivalent to 1 foot. So 12 times 4 = 48. So, the answer is b because then u know that its a little more than 48.
Hope this helped! Comment if u have questions. :)
2 biscuits cost 80p how much do 12 cost
Well to find how much 12 biscuits cost, you must first find how much each biscuit costs. Therefore, you divide 80p by 2, and get 40p. Then multiply 40p by 12 (the total amount of biscuit). You get the answer, which is 480p.
at an amusement park, 360 visitors rode the roller coaster in 3 hours. write and solve a proportion to find the number of visitors at this rate who will ride the roller coaster in 7 hours
Answer:
840 visitors
Step-by-step explanation:
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope? 22 feet 26 feet 33 feet 44 feet
33 hope this helps thanks
Answer:
44
Step-by-step explanation:
The answer is 44 because 66-22=44, 44+22=66 44 is twice of 22
What is the exact circumference of a circle with a diameter of 43 cm in terms of pi?
So the corcumference is equal to the diameter tiems pi.
Youre given the diameter, so just multiply it by pi.
The answer is 43pi.
The circumference of a circle with a diameter of 43 cm can be calculated using the formula C = πd. Substituting 43 for d, the exact circumference in terms of pi is 43π cm.
Explanation:The circumference of a circle is determined by the formula C = πd, where C is the circumference, d is the diameter of the circle, and π (Pi) is a mathematical constant whose approximate value is 3.14. If we plug the given diameter of 43 cm into the formula, we get C = π * 43. Thus, the exact circumference in terms of pi is 43π cm.
Learn more about Circumference of a Circle here:https://brainly.com/question/31844715
#SPJ11
The same four friends buy tickets for two shows on consecutive nights. They use a coupon for $5 off each ticket. They pay a total of $416 for 8 tickets. Write and solve an equation to find the original price of the tickets.
Answer:
Original price of the ticket was $57.
Step-by-step explanation:
Four friends buy tickets for two shows.
Let the price of a ticket was $c
Then cost of 4 tickets = $4c
They use a coupon to get the discount = $5 on each ticket
So total discount on 4 tickets = 4×5 = $20
Cost of the tickets after discount = 4c - 20
Cost of the tickets for two consecutive nights = 2(4c - 20)
If they paid total amount = $416 for 8 tickets
Then the equation will be 2(4c - 20) = 416
Now we can solve this equation to get the original price of the ticket.
2(4c - 20) = 416
4c - 20 = 208
4c = 208 + 20
4c = 228
c = [tex]\frac{228}{4}[/tex]
c = $57
Therefore, original price of a ticket was $57.
Answer:
57
Step-by-step explanation:
I did this earlier.
use the distributive property to solve the equation 4x/5-x=x/10-9/2
15 i think sorry if its wrong
20 points- Help me please this is due today
You moved the decimal place, but didn't account for that in your exponent. It should no longer be 10.
The answer is 1.035*10¹¹
Adding and subtracting like terms
How do I solve w-w*2+-2w*2
Answer:
See two different cases, below:
Step-by-step explanation:
You cannot "solve" w-w*2+-2w*2, because this is not an equation. Rather, you want to simplify w-w*2+-2w*2 by combining like terms. You have w - 2w - 4w, or -5 w.
If, however, you meant "exponentiation" by " * " then you have w^1 - w^2 - 2w^2, which in turn equals w - 3w^2, or, in descending order by powers of w, -3w^2 + W.
-8(4+9x)=7(-2-11x)
please help me solve this i have no clue and this is my math homework
Distributive property
-8*4=-32 -8*9x=-72x
-32-72x=7(-2-11x)
7(-2)=-14 7(-11x)=-77x
-32-72x=-14-77x
Combine Like Terms
-32+14=-18 -77x+72x=-5x
-18=-5x
Divide both sides by -5 and theres your answer
Five years ago, Jay borrowed $1500 from his mother. He agreed to pay $150 in interest. What is the simple annual interest rate for this loan?
Answer:
It would be 2%
Step-by-step explanation:
Hope this helps! :D
The simple annual interest rate for this loan will be 2%.
What is the definition of simple interest?Simple interest is extra money paid by the person borrowing the money. The formula for the simple interest is;
[tex]\rm SI = \frac{P \times R \times T}{100}[/tex]
Given data;
P(Principal) =$1500
R(Rate)=?
T)TIme)=5year
SI(Simple interest)=$ 150
The simple interest is calculated as ;
[tex]\rm SI = \frac{P \times R \times T}{100} \\\\ 150 = \frac{1500 \times R \times 5 }{100} \\\\ R=2 \%[/tex]
Hence, the simple annual interest rate for this loan will be 2%.
To learn more about simple interests, refer to;
https://brainly.com/question/14031892
#SPJ2
if a prescription reads take 2 tablespoons 3 times a day for 10 days how many total tablespoons will the patient take?
Prove that the sum of the length of the diagonals of a quadrilateral is less than the perimeter, but greater than the half of the perimeter of this quadrilateral.
and
Prove that the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle. (The statement is true for the altitudes as well.)
Answer: Consider a quadrilateral ABCD such that AC ans BD are the two diagonals of ABCD.
With reference to figure 1 .
In triangle ABC and triangle ADC ,by using triangle inequality we have
AB +BC > AC .......(1)
and AD + CD >AC......(2)
adding (1) and (2) we have
AB+ BC+CD+AD>2AC....(3)
Similarly we get for diagonal BD
AB+BC+CD+AD>2BD....(4)
Adding (3) and (4) we get
2(AB+BC+CD+AD)> 2(AC+BD)
⇒(AB+BC+CD+AD)> AC+BD where (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now 2 diagonal divides quadrilateral into 4 quadrilaterals
Therefore AO+OD>AD
OD+OC>CD
OC+OB>BC
And OA+OB>AB
Adding all these conclude that
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD>1/2(AB+BC+CD+AD) where (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence,the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
Now consider a triangle ABC as given in figure (2)
As we now,the sum of two sides of a triangle is greater than twice the median bisecting the third side.
Therefore AB+BC>2BE
Similarly,
AB+AC>2AD
BC+AC>2CF
By adding all these we get ,
2(AB+BC+CA)>2(AD+CF)
⇒AB+BC+CA>AD+CF
Hence, the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle.
solve by completing the square: x^2-10x+8=0
[tex]x^2-10x+8=0\\\\x^2-10x+25-17=0\\\\(x-5)^2=17\\\\x-5=\sqrt{17} \vee x-5=-\sqrt{17}\\\\x=5+\sqrt{17} \vee x=5-\sqrt{17}[/tex]
Answer:
(x – 5)2 = 17
Step-by-step explanation:
edg
Write a compound inequality that represents each situation. Graph your solution. all real numbers at least –6 and at most 3
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x-------> the set of numbers that represent the solution of the situation
we know that
The expression " At least [tex]-6[/tex] " represent the inequality
[tex]x\geq -6[/tex] -----> all real numbers greater than or equal to [tex]-6[/tex]
The expression " At most [tex]3[/tex] " represent the inequality
[tex]x\leq 3[/tex] -----> all real numbers less than or equal to [tex]3[/tex]
The solution of the situation is equal to the interval-------> [tex][-6,3][/tex]
see the attached figure
find the mean, median, and mode of the data set round to the nearest tenth 15, 1 , 4, 4, 8, 7, 15, 4, 5
[tex]15,\ 1,\ 4,\ 4,\ 8,\ 7,\ 15,\ 4,\ 15,\ 4,\ 5\to\underbrace{1,\ 4,\ 4,\ 4,\ 4,\ 5,\ 7,\ 8,\ 15,\ 15,\ 15}_{11}\\\\mean=\dfrac{1+4+4+4+4+5+7+8+15+15+15}{11}=\dfrac{82}{11}\approx7.5\\\\median:1,\ 4,\ 4,\ 4,\ 4,\ \boxed{5},\ 7,\ 8,\ 15,\ 15,\ 15\\\\mode:1,\ \underbrace{4,\ 4,\ 4,\ 4}_{4},\ 5,\ 7,\ 8,\ 15,\ 15,\ 15[/tex]
Answer: mean = 7.5, median = 5, mode = 4Answer:
Mean = 7.5, median = 5, mode = 4
Step-by-step explanation:
Tom is trying to write 3/47 As a decimal. He used long division and divided until he got the quotient 0.638297872, at which point he stopped. Since the decimal doesn’t seem to terminate or repeat, he concluded that 3/47 is not rational. Do you agree or disagree? Why?
Answer:
3/47 is rational because it is a ratio of two integers.
What is the length of leg y of the right triangle?
A right triangle with hypotenuse 85 and legs 84 and y
Solution :
Given a right triangle with hypotenuse 85 and legs 84 and y.
Use Pythagoras theorem, to find the length of the leg y of the right triangle.
According to Pythagoras theorem,
[tex](hypotenuse)^{2} = leg_{1}^{2}+leg_{2}^{2}[/tex]
As given in the question,
[tex]hypotenuse = 85 \\\\leg_{1} = 84\\\\leg_{2} = y[/tex]
Put these values,
[tex]\Rightarrow 85^{2}=84^{2} +y^{2} \\\\\Rightarrow y^{2}=85^{2}-84^{2}\\\\\Rightarrow y =\sqrt{85^{2}-84^{2}} \\\\\Rightarrow y =\sqrt{169}\\\\\Rightarrow y =13[/tex]
Hence, the length of leg y =13.
Answer:
The length of leg y=13
Step-by-step explanation:
What is the least common denominator for the fractions 16 and 34 ?
Answer:
The answer is 4
Step-by-step explanation:
The answer is 4 because if you divide them both by 4 they come out even and they cant be divider by anything less. Therefore the common denominator is 4.
Answer:
12
Step-by-step explanation:
if you said 4 its not answer
it takes an ant farm 3 days to consume half of an Apple at that rate in how many days will the ant farm consume apples?
Answer:
From the comments below we see the missing part of the question is "in how many days will the ant farm consume 3 apples?"
The answer is 18.
Step-by-step explanation:
We will use a proportion to solve this. It takes 3 days to consume 1/2 of an apple; this gives us the ratio
3/0.5
We want to know how many days, x, it will take to consume 3 apples; this gives us the ratio
x/3
Together this gives us the proportion
3/0.5 = x/3
Cross multiply:
3(3) = 0.5(x)
9 = 0.5x
Divide both sides by 0.5:
9/0.5 = 0.5x/0.5
18 = x
The ant farm will take 18 days to consume 3 apples.
Given that,
Ant farm consumes 0.5 apple in 3 Days.We need to find days to consume 3 apples.Let number of days be X.Here we assume 3 apples.According to above information, calculation of data are as follows,
[tex]X = (3 \div 0.5) \times 3\\\\X = 6 \times 3[/tex]
X = 18
So, Total number of days required is 18 days.
Learn more: https://brainly.com/question/13609873
The total height of all three of Thumbelina’s sisters is 60 cm. If the heights of the three sisters are in the ratio 4:3:5, find the height of the shortest sister.
Answer: 15 cm
Step-by-step explanation:
Given : The total height of all three of Thumbelina’s sisters is 60 cm.
The heights of the three sisters are in the ratio 4:3:5 .
Let the heights of the three sisters are 4x , 3x and 5x.
According to the question , we have the following equation :-
[tex]4x+3x+5x=60\\\\\Rightarrow\ 12x=60\\\\\Rightarrow\ x=\dfrac{60}{12}=5[/tex]
Now, the height of the shortest sister will be :-
[tex]3x=3(5)=15\ cm[/tex]
Hence, the height of the shortest sister = 15 cm
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store. What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
the answer is 16.7 because you need to do 60/360
The answer is 16.67%
Explanation:
Number of customers who visited in the first week = 360
Number of customers who visited in the second week = 300
Number of customers decreased in the second week =
[tex]360-300=60[/tex]
So, the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week will be = [tex]\frac{60}{360}*100 =16.67[/tex]