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stira [4]
2 years ago
10

The ratio of cups of sugar to gallons of lemonade is 3 cups to 2 gallons. How many cups of sugar are needed to make 15 gallons o

f lemonade? Set up a proportion in the work area to represent this situation.
Mathematics
1 answer:
stepan [7]2 years ago
6 0

Answer:

The ratio of cups of sugar to gallons of lemonade is 3 cups to 1 gallon. How many cups of sugar are needed to make 5 gallons of lemonade?

Step-by-step explanation:

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What is the 38th term of 459,450,441,..
galina1969 [7]

Answer:

The 38th term of 459,450,441,.. will be:

a_{13}=351

Step-by-step explanation:

Given the sequence

459,450,441,..

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

computing the differences of all the adjacent terms

450-459=-9,\:\quad \:441-450=-9

so

d=-9

The first element of the sequence is

a_1=459

so the nth term will be

a_n=-9\left(n-1\right)+459

a_n=-9n+468

Putting n=38 to find the 38th term

a_n=-9n+468

a_{13}=-9\left(13\right)+468

a_{13}=-117+468

a_{13}=351

Therefore, the 38th term of 459,450,441,.. will be:

a_{13}=351

3 0
3 years ago
Find the difference for the subtraction 7.211- 5.24
Serhud [2]

Answer:

1.971

Step-by-step explanation:

7.211 - 5.24 = 1.971

4 0
2 years ago
Read 2 more answers
A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch
ivolga24 [154]

Answer:

(a) 0.9412

(b) 0.9996 ≈ 1

Step-by-step explanation:

Denote the events a follows:

P = a person passes the security system

H = a person is a security hazard

Given:

P (H) = 0.04,\ P(P^{c}|H^{c})=0.02\ and\ P(P|H)=0.01

Then,

P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\

(a)

Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})

The value of P (P) is:

P(P)=P(P|H)P(H)+P(P|H^{c})P(H^{c})\\=(0.01\times0.04)+(0.98\times0.96)\\=0.9412

Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

7 0
3 years ago
Find the GCF<br> 50x^4, -10x^5, 2x^6
shtirl [24]

Answer:

2 x^4

Step-by-step explanation:

Recall that the GCF is the greatest of the product of factors that are common to all these three expressions

then for the pure numerical part, the factor common to 50, -10 , and 2 is "2"

and for the variable part x^4 is the largest common to all three expressions.

Therefore the GCF is: 2 x^4

7 0
2 years ago
Read 2 more answers
Area is 180,length is 1 1/4,what is the width
rusak2 [61]
180 is the area and the length is 1.25 so we need to find the width. We need to divide 180/1.25 which is 144.
144*1.25 is 180
The width is 
144
7 0
2 years ago
Read 2 more answers
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