Stretch
2. A gym runs two fitness classes, spinning and circuits.
On Saturday 100 people visited the gym.
18 people attended the spinning class.
10 people attended both classes.
56 people did not attend either class.
a) Represent this information on a Venn diagram
६
S
Ic с
10
(3)
56
A person who attended the gym is selected at random. .
Find the probability that this person:
b) attended only circuits
(2)
c) attended exactly one class
(2)
d) attended spinning, given that they attended circuits
. (2)

Hey there!

Let's solve this equation.

5x+3x-4=10

add the x's

8x-4=10

add 4 to both sides

8x=10+4

8x=14

divide both sides by 8

x=14/8

Reduce the fraction;

x=7/4 (improper fraction)

x=1+3/4 (mixed number)

Hence, the equation has 1 solution.

Hope everything is clear.

Let me know if you have any questions!

#ILoveLearning

:-)

Answer:

i presume it has

Step-by-step explanation:

only 1 solution.

combine like terms & then solve

Answer:

The highest common factor of 30 and 45 is 15.

Step-by-step explanation:

factors of 30 = 1, 2, 3, 4, 5, 6, 10, 15, 30 ; factors of 45 are = 1, 3, 5, 9, 15, 45)

Greatest common factor is 15

Answer:

15.

Step-by-step explanation:

HCF is also called GCD. So, you divide both numbers with a common number that can divide both numbers at the same time without a remainder.

     3    30         45

      5    10          15

            2             3

3 × 5 = 15

Answer:

Check the last answer...

Step-by-step explanation:

Look at image above...

Answer:

Two methods both tell us the ball is at 20 feet height at 0.783 seconds going up and 1.28 seconds on the way down.

Step-by-step explanation:

The question can be answered by either calculation or by graphing.

Calculation:

Set the equation to h = 20 feet and solve with the quadratic equation.

h= 4 + 33t - 16t^2

4 + 33t - 16t^2 = 20

- 16t^2 + 33t + 4 = 20

- 16t^2 + 33t - 16 = 0

I find solutions of 0.779 and 1.28 seconds.  

Graphing:

See the attached graph.

The graph shows solutions of 0.783 and 1.28 seconds.

Both methods show the ball to be at 20 feet height at 0.783 seconds going up and 1.28 seconds on the way down.

Answer:

See below.

Step-by-step explanation:

7,824/10=782.4

782.4

 |

The 8 is in the tens place. It represents 80.

-hope it helps

Answer:

80

Step-by-step explanation:

7824÷10=782.4

Therfore the 8 is in the tens place meaning that the 8 in this is 80

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate is of [tex]\pi = 0.61[/tex], while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2[/tex]

[tex]n = 1015.5[/tex]

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:

285.6

Step-by-step explanation:

formula= I=PRT

i=?

p=102

r=5

t=36 months

5=0.05

102(1+(0.05x36)=285.6

Answer:

Step-by-step explanation: 276.9

Answer:

Ali played on his PSP longer

Step-by-step explanation:

3/4 of an hour is long than 2/3 because 3/4 of an hour is 45 minutes and 2/3 of an hour is 40 minutes and 45 > 40

Answer:

  a. a[1] = 3; a[n] = 2a[n-1]

  b. a[n] = 3·2^(n-1)

  c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

The recursive rule is ...

  a[1] = 3

  a[n] = 2×a[n-1]

__

The explicit rule is ...

  a[n] = a[1]×r^(n-1)

  a[n] = 3×2^(n-1)

__

The 15th term is ...

  a[15] = 3×2^(15-1) = 3×2^14

  a[15] = 49,152

Answer:

3.0625[tex]\pi[/tex] ft^2

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

A=[tex]\pi[/tex]1.75^2

A=3.0625[tex]\pi[/tex]

3.0625[tex]\pi[/tex] ft^2

Answer:

Step 1: 2*5 - 4y = 2

Step 2: 10 - 4y = 2

Step 3: -4y = -8

Step 4: y = 2

Step-by-step explanation:

Answer:

?????

Step-by-step explanation:

Answer:

4,650.

Step-by-step explanation: If the total number of people at the game is 12,400 and 3/8 of those people were Season ticket holders. You simply multiply 12,400 x (3/8).

Using proportions, considering the daily penalty fee paid, it is found that he will pay $50 altogether.

A proportion is a fraction of a total amount.

In this problem, since he will spend $285.00, having $277.00, he will be $8.00 in debt.

He will pay a penalty fee of $7.00 per day for 6 days, along with the $8.00, hence the total payment in dollars will be given by:

P = 6 x $7.00 + $8.00 = $50.00.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:72

Step-by-step explanation:6 x 12=72

Answer:

x - 7

Step-by-step explanation:

x + 8 - 15

Subtract 15 - 8 = 7

x  - 7

~Lenvy~

Answer:

(0, 0) : traveling 0 inches in 0 seconds

(1, 1.5) : traveling 1.5 inches in 1 second

(3, 4.5) : traveling 4.5 inches in 3 seconds

The unit rate is

1.5 inches a second

1.5 / 1 i think thats how you write it

Answer:

given ,

number of coins in bag A = 5x

number of coins in bag B = 3x

_____________________________________

According to Question ,

8 coins are taken from Bag B and put into Bag A

The ratio of coins in Bag A to Bag B is now 11 : 5

therefore ,

[tex] \frac{5x + 8}{3x - 8} = \frac{11}{5} \\ \\ 5(5x + 8) = 11(3x - 8) \\ \\ 25x + 40 = 33x - 88 \\ \\ 33x - 25x = 40 + 88 \\ \\ 8x = 128 \\ \\ x = \cancel\frac{128}{8} \\ \\ \fbox{x =16} [/tex]

now ,

[tex]no. \: of \: coins \: in \: bag \: A = 5x \\ \dashrightarrow{5 \times 16 = 80 \: coins}[/tex]

[tex]number \: of \: coins \: in \: bag \: B = 3x \\ \dashrightarrow{3 \times 16 = 48 \: coins}[/tex]

[tex]total \: number \: of \:coins = 80 + 48 \\ \dashrightarrow{ 128 \: coins}[/tex]

hope helpful :D

Step-by-step explanation:

the ratio that relates two given values in what is known as a proportional relationship.

self explainatory

Answer:

45.57

Step-by-step explanation:

We first need to multiply :)

4 x 3.00 = 12.00

15.00 x 2 = 30.00

Now we add!

12.00 + 30.00 = 42.00

And we multiply one more time to find the answer!!

42 x 0.085 = 3.57

And we now add one more time!!

42.00 + 3.57 = 45.57

The answer will be $45.57. :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

38.75

Step-by-step explanation:

Not sure what you mean by ioth but when you add up all the numbers and divide by n, you get 38.75 (hopefully you can round it to whatever you want)

Answer:

See below, please

Step-by-step explanation:

Left side

[tex] {(2x + 1)}^{2} - {(x + 1)}^{2} [/tex]

[tex] = (4 {x}^{2} + 4x + 1) - ( {x}^{2} + 2x + 1)[/tex]

[tex] = (4 {x}^{2} - {x}^{2} ) + (4x - 2x) + (1 -1 )[/tex]

[tex] = 3 {x}^{2} + 2x[/tex]

Right side

[tex]3 \times {(x + 1)}^{2} - 1[/tex]

[tex] = 3 \times ( {x}^{2} + 2x + 1) - 1[/tex]

[tex] = 3 {x}^{2} + 6x + 3 - 1[/tex]

[tex] = 3 {x}^{2} + 6x + 2[/tex]

After compared with both sides, we can make a conclusion that

This equation isn't an identity.

Answer:

4

Step-by-step explanation:

2a + 2 / a = 4

2a + 2 = 4a

4a - 2a = 2

2a = 2

a = 1

2a² + 2 / a²

a = 1

2(1²) + 2 / 1²

2 + 2 / 1

4

Answer:

x = 5

Step-by-step explanation:

-x² + 10x - 25 = 0

x = {-10±√((10²)-(4*-1*-25) / (2*-1)

x = {-10±√(100-100)} / -2

x = {-10)/-2

x = 5

Comprobación:

- (5²) + 10*5 - 25 = 0

-25 + 50 - 25 = 0

Check the picture below.

keeping in mind that the difference of the distances of d1 and d2 is always a consistent constant value, as you can see in the left-hand-side of the picture, if we keep on sliding on the hyperbolic line shrinking d2 from being slanted to be horizontal, once we put d1 and d2 on a horizontal line, as you see on the right-hand-side, if we subtract the pink line from the orange line, what's leftover is, yeap, you guessed it.

The best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

A company has an opportunity to bid on three contracts. Probability of profit and loss by all three contract is listed in the table below.

Contract profit,   (P)* of profit, (P)* to break even loss, (P)* of loss

The company which will give the maximum profit probability and minimum loss probability will be the best investment.

In the above table, the southeast contract has the maximum probability of profit, which is 50% among all the contracts. Similarly, it has the lowest probability of loss, which is 20%.

Thus, the best investment of the company is in southeast contract. The probability of profit of this contract is maximum 50% and of loss is minimum 20%.

Learn more about the probability here;

https://brainly.com/question/24756209

Answer:

It's A. Southeast

Step-by-step explanation:

t = 180 - 66 - 57 = 57°