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max2010maxim [7]
3 years ago
14

Pam budgets $164 for fitness training. She buys a pair of hand weights for $12.65 and pays $10 per fitness class. Which inequali

ty represents the number of fitness classes, c, that Pam can take and stay within her budget?
A. 164 ≥ 12.65 + 10c
B. 164 ≤ 12.65 + 10c
C. 164 ≥ 12.65c + 10
D. 164 ≤ 12.65c + 10
Mathematics
1 answer:
NARA [144]3 years ago
7 0

Answer:

A

Step-by-step explanation:

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Use the circle to solve for the missing measures. Assume lines that appear tangent are tangent. Do NOT round any answers.
wlad13 [49]

The given circle having two external tangents, according to circle

theorem, have the following values;

  • r = 3
  • m∠1  = 82°
  • m∠2 = 49°
  • x = 82°

<h3>How can the radial  length and angles be found?</h3>

r² + 1.6² = (0.4 + r)²

(0.4 + r)² - (r² + 1.6²) = 0

0.8·r - 2.4 = 0

0.8·r = 2.4

r = 2.4 ÷ 0.8 = 3

  • <u>r = 3</u>

y = 49°

From the two tangent angle theorem, we have;

m∠1 = ((82 + 98 + 82) - (360 - ((82 + 98 + 82)))) ÷ 2 = 82

  • <u>m∠1  = 82°</u>

According to circle theorems, angle at the center is twice angle

subtended at the circumference.

m∠2 = (360 - (82 + 98 + 82)) ÷ 2 = 49°

  • <u>m∠2 = 49°</u>

The length of the chord subtended by the arc <em>x</em> is equal to the length of

the chord subtended by 89°, which gives;

  • <u>x = 82°</u>

Learn more about circle theorems applications here:

brainly.com/question/16879446

4 0
2 years ago
Sam decides to build a square garden. If the area of the garden is 25x2 + 30x + 9 square feet, what is the length of one side of
seropon [69]
The correct answer is C. (5x+3) feet, and here is how I got it.
This is the equation you need to use:
(a+b)^2 = (a+b) (a+b)
So, let us plug in 5x and 3 here:
(5x+3)^2 = (5x+3)(5x+3) = 25x^2 + 15x + 15x + 9 = 25x^2 + 30x + 9 which is the area of the garden. 
5 0
3 years ago
8. Madison uses 54 beads to make one necklace. If Madison has 2,185 beads, how many necklaces can she make and how many beads wo
hram777 [196]

Answer:

B) 40 necklaces with 25 left over

Step-by-step explanation:

7 0
2 years ago
PLS HELP ASAP, WILL MARK YOU BRAINLIEST!!!!
GuDViN [60]

Answer:

Try looking at each angle and add the sides

Step-by-step explanation:

4 0
2 years ago
If 20% of the people in a community use the emergency room at a hospital in one year, find
Pie

Answer:

a) 87.91% probability that at most three used the emergency room

b) 20.13% probability that exactly three used the emergency room.

c) 3.28% probability that at least five used the emergency room​

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Sample of 10 people:

This means that n = 10

20% of the people in a community use the emergency room at a hospital in one year

This means that p = 0.2

a) At most three used the emergency room

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074

P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684

P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020

P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791

87.91% probability that at most three used the emergency room

b) Exactly three used the emergency room

P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013

20.13% probability that exactly three used the emergency room.

c) At least five used the emergency room​

P(X \geq 5) = 1 - P(X < 5)

In which

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

From 0 to 3, we already have in a).

P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672

P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328

3.28% probability that at least five used the emergency room​

4 0
3 years ago
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