MATHEMATICS COLLEGE

A recipe requires 3/4 cups of sugar for every 14 cookies how many cups of sugar will be needed to bake 168 cookies

Answers

Answer 1

Answer:

Answer:

9 cups

Step-by-step explanation:

3/4 cups of sugar for 14 cookies

There are 168÷14 = 12 set of 14 cookies in 168

So we need 12 times 3/4 sugar

12 × 3/4 = 9 cups of sugar needed

Answer 2

Answer:

Answer:

Step-by-step explanation:

ratio problem

3/4 sugar/14 cookies = x sugar/168

126 = 14x

x = 9

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According to a recent survey of households, the poll found that 41 % of the adults watching a special event on TV enjoyed the commercials more than the event itself. Consider a random sample of nine adults who watched the special event. Complete parts a through d below.a. For this experiment, define the event that represents a "success".
i. A success is an adult who did not enjoy the commercials more than the event on TV itself.
ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b. What is the probability that less than four people enjoyed the commercials more than the event?
c. What is the probability that exactly six or seven people enjoyed the commercials more than the event?
d. What is the mean for this binomial distribution?

Answers

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) P(X < 4) = 0.4576

c) P(X=6) + P(X=7) = 0.1064

d) Mean = 3.69

Step-by-step explanation:

a) The population parameter stated in the survey is the event that represents a success. Hence, A success is an adult who enjoyed the commercials more than the event on TV itself.

b) The probability that less than four people enjoyed the commercials more than the event

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of adults sampled = 9

x = Number of successes required = number of people that enjoyed the commercial more than the event on TV = less than 4

p = probability of success = probability of enjoying the commercial more than the event = 0.41

q = probability of failure = probability of NOT enjoying the commercial more than the event = 1 - 0.41 = 0.59

P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.00866299582 + 0.05418043148 + 0.15060323326 + 0.24419846296

P(X < 4) = 0.45764512351 = 0.4576

c) The probability that exactly six or seven people enjoyed the commercials more than the event = P(X=6) + P(X=7)

Using the Binomial distribution formula

P(X=6) + P(X=7) = 0.08194801935 + 0.02440582659 = 0.106353846 = 0.1064

d) Mean = expected value of people that would enjoy the commercial more than the main event = np = 9×0.41 = 3.69

Hope this Helps!!!

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) $P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

c) $P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

d) $\mu = np =9*0.41=3.69$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=9, p=0.41)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Part a

The success on this case is:

ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

Part b

For this case we want this probability:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)$

And we can find the individual probabilities and we got:

$P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

Part c

For this case we want this probability:

$P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

Part d

For this case the mean is given by:

$\mu = np =9*0.41=3.69$

A ball is dropped from a height if 30 feet the ball bounces after each bounce the height attained by the ball is 60% of the previous height write an nth term formula to model the situation what is the maximum height attained by the ball after five bouncesA.0.12ft
B.6.40ft
C.2.33ft
D.1.40ft

Answers

This information will be modeled using the formula
thus we shall have:
Sn=ar^n
where:
a=first term
r=common ratio
from the information:
a=30 ft
r=60/100=3/5=0.6
therefore the formula will be
Sn=30(0.6)^n
where n is the number of terms:
thus when n=5 th sum will be:
S5=30(0.6)^5
S5=30(0.6)^5
S5=2.33 ft
Answer: 2.33 ft

Answer:

2.33

Step-by-step explanation:

PLEASE HELP!! (3/5) - 50 POINTS -

Answers

Answer:

infinite number of solutions

Step-by-step explanation:

A dependent system is where the two equations are the same line has has an infinite number of solutions

Answer:

$\boxed{\sf D) \ an\ infinite \ number \ of \ solutions}$

Step-by-step explanation:

A dependent system of equations has an infinite number of solutions.

When you graph the system of equations, both the equations represent the same line and have an infinite number of solutions.

What is the right option?

Answers

C. -x + 2y = 8

Hope this helped :)

A rectangular prism is 3 meters long, 4 meters wide, and has a total surface area of 94 square meters. What is its height?3 m
4 m
5 m
6 m

Answers

S = 2lw + 3lh + 2wh
94 = 2(3)(4) + 2(3)(h) + 2(4)(h)
94 = 2(12) + 2(3h) + 2(4h)
94 = 24 + 16h + 8h
94 = 24 + 14h
- 24 - 24
70 = 14h
14 14
5 = h

The answer is C.

Answer: answer is C

Step-by-step explanation:

Nikki makes $9.50 an hour working at Current Electronics She plans to buy a DVD recorder that costs $269.60. Write and solve an inequalitydescribing how many hours h Nikki will have to work to be able to buy the DVD recorder
A. 269,60 -- 29.56; 28 hours
B. 9.50h 2 269,60; 29 hours
C. 269.60 + h 29.50; 31 hours
D. 269.60 2 9,50; 30 hours

Answers

Answer:I would believe it's the first choice. I'm not great with the inequalities though so it could be wrong. If you work 29 hours making $9.50, you make like $275 or something so it is greater than the $269.60 you need. :D

Answer:

nikki should quit her job

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