Please help me with this

A scientist has two solutions, which she has labeled Solutuion A and Solution B. Each contains salt. She knows that Solutuion A

ratelena [41]

a = amount (in oz) of solution A

b = amount of solution B

The scientist wants a mixture of 110 oz, so

a + b = 110

Solution A consists of 65% salt, so each ounce of solution A contributes 0.65 oz of salt; similarly, each ounce of B contributes 0.9 oz. The mixture is supposed to consist of 75% salt, which amounts to 0.75 * (110 oz) = 82.5 oz of salt. So

0.65 a + 0.9 b = 82.5

Solve for a and b:

b = 110 - a

0.65 a + 0.9 (110 - a) = 82.5

0.65 a + 99 - 0.9 a = 82.5

0.25 a = 16.5

a = 66 ==> b = 44

5 0

3 years ago

65.25=7.25h-10.25 if you solve what would you get?

Ksivusya [100]

Answer:

h=10.4137931 ..

Explanation: 10.25 +65.25=75.5 . 75.5 divided by 7.25=10.4137931

3 0

3 years ago

A large cable company reports the following.

Oduvanchick [21]

Answer:

Step-by-step explanation:

Let n(U) be total amount or customers = 100%

n(C) = 80% of its customers subscribe to its cable TV service.

n(I) = 41% of its customers subscribe to its Internet service.

n(T) = 31% of its customers subscribe to its telephone service.

n(CnI) = 25% of its customers subscribe to both its cable TV and Internet service.

n(CnT) = 20% of its customers subscribe to both its cable TV and phone service.

n(InT) = 22% of its customers subscribe to both its Internet and phone service.

n(CnInT) = 15% of its customers subscribe to all three services

number of those that subscribed to TV only = n(C) - (n(CnInT')+(n(CnI'nT)+(n(CnInT))

= 80-[(25-15)+(20-15)+15]

= 80-{10+5+15)

= 80-30

= 50

Hence 50% read cable TV only

Pr(cable TV only) = 50/100 = 1/2

2) number of people that read internet and cable TV = 25%

Pr(internet and cable) = 25/100 = 1/4

3) number of people that had exactly two services are;

n(cable and internet only)+n(internet and phone only)+(cable and phone only)

= (25-15)+(22-15)+(20-15)

= 10+7+4

= 21%

Hence 21℅ read exactly two services

pr(exactly 2 services) = 21/100

4) number of people that read internet and cable only = n(CnI) - n(CnInP)

= 25-15 = 10%

Pr(Internet and cable only) = 10/100 = 1/10

8 0

3 years ago

· The volume of a box in the shape of a cube<br>is 2197 cm3. Find the area of one side of the box.

Yuliya22 [10]

Answer:

Let the side of the cube be x.

Volume = length × width × height

For a cube:

Length = width = height

Now volume = x × x × x = x³

This equals 2197

Therefore :

X³ = 2197

X = ∛2197

= 13

The side of the cube = 13cm

Area = length × width

Length = width = 13cm

Area = 13 × 13 = 169

= 169 cm²

I hope this helps!

4 0

4 years ago

Consider the sequence of numbers: 3/8, 3/4, 1 /18, 1 1/2, 1 7/8

vredina [299]

Question:

Consider the sequence of numbers: $\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Which statement is a description of the sequence?

(A) The sequence is recursive, where each term is 1/4 greater than its preceding term.

(B) The sequence is recursive and can be represented by the function

f(n + 1) = f(n) + 3/8 .

(C) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4 .

(D) The sequence is arithmetic and can be represented by the function

f(n + 1) = f(n)3/8.

Answer:

Option B:

The sequence is recursive and can be represented by the function

$f(n + 1) = f(n) + \frac{3}{8} .$

Explanation:

A sequence of numbers are

$\frac{3}{8}, \frac{3}{4}, 1\frac{1}{8}, 1\frac{1}{2}, 1\frac{7}{8}$

Let us first change mixed fraction into improper fraction.

$\frac{3}{8}, \frac{3}{4}, \frac{9}{8}, \frac{3}{2}, \frac{15}{8}$

To find the pattern of the sequence.

To find the common difference between the sequence of numbers.

$\frac{3}{4}-\frac{3}{8}=\frac{6}{8}-\frac{3}{8}= \frac{3}{8}$

$\frac{9}{8}-\frac{3}{4}=\frac{9}{8}-\frac{6}{8}= \frac{3}{8}$

$\frac{3}{2}-\frac{9}{8}=\frac{12}{8}-\frac{9}{8}= \frac{3}{8}$

$\frac{15}{8}-\frac{3}{2}=\frac{15}{8}-\frac{12}{8}= \frac{3}{8}$

Therefore, the common difference of the sequence is 3.

That means each term is obtained by adding $\frac{3}{8}$ to the previous term.

Hence, the sequence is recursive and can be represented by the function $f(n + 1) = f(n) + \frac{3}{8} .$

3 0

3 years ago