A Chemist has 100g of 25% acid solution. How much of these solution he needs to drain and replaced with 70% acid solution to obtain 100g of 60% acid solution?

Answer:

B. Division

Step-by-step explanation:

We have been given an expression [tex]175-(8+\frac{45}{3})*7[/tex]. We are asked to determine which operation will we use first to simplify our given expression.

Using order of operations PEMDAS, we will remove parenthesis first. To remove parenthesis, we need to simplify [tex]\frac{45}{3}[/tex].

Therefore, we will use division first to simplify our given expression.

The flavors are in the ratio 5 to 4 which is Peach to plum .

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that  box contains 16 cherry fruit chews, 15 peach fruit chews, and 12 plum fruit chews.

Therefore, we have

15 divided by 3

15/3 = 5

12 divided by 3

12/3 = 4

The ratio 5 to 4 is Peach to plum .

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She used 84 pompoms and 105 beads for the wooden penguins

How many pompoms and beads did she use for the wooden penguins in all.

From the question, we have the following parameters that can be used in our computation:

wooden penguins = 21

Also, we have

Pompoms = 4 and Beads = 4 for each wooden penguins

Using the above as a guide, we have the following:

Total pompoms = 4 * 21 = 84

Total beads = 5 * 21 = 105

Hence, she used 84 pompoms and 105 beads

Sydney used a total of 189 pompoms and beads for all 21 wooden penguins.

To find the total number of pompoms and beads Sydney used for all the wooden penguins, we first need to determine how many decorations she used for one penguin.

She used 5 pompoms and 4 beads for each penguin.

So, for each penguin, the total number of decorations = 5 (pompoms) + 4 (beads) = 9 decorations.

Now, to find the total number of decorations for all 21 wooden penguins, we multiply the number of decorations for one penguin by the total number of penguins:

Total decorations = 9 decorations/penguin × 21 penguins

= 189 decorations.

Therefore, Sydney used a total of 189 pompoms and beads for all the wooden penguins.

Answer is provided in the image attached.

Step-by-step explanation:

Speed with which the players throw a small hard ball is 188 miles per hour. We need to convert the speed of the ball in kilometers per hour.

Firstly we can see the conversion from mile per hour to kilometer per hour as :

1 miles = 1609.34 meters

Also, 1 mile per hour = 1.60934 kilometer per hour

To convert 188 mph to km/h we can use the unitary method as :

188 mile per hour = 1.60934 × 188 kilometer per hour

188 mile per hour = 302.557 kilometer per hour

So, the speed of the ball is 188 miles per hour or 302.557 kilometer per hour. Hence, this is the required solution.

10 times greater is the product 4x300 than the product 4x30 after taking the ratio of the number, the answer is 10.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The two numbers are 4x30 and 4x300

To find how many times greater the other number.

Let x time greater the product of 4x300 than the product 4x30

4×300 = 4×30x

x = 4×300/4×30

x = 10

Thus, 10 times greater is the product 4x300 than the product 4x30 after taking the ratio of the number, the answer is 10.

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Answer

Find out the  ratio represented  the number of yellow balls to red balls .

To proof

Let us assume that the number of yellow balls be x.

As given

There are 20 balls in a bag.

Ten of the balls are red, 4 are green, and the rest are yellow.

than the equation becomes

x + 10 + 4 = 20

x = 20 - 14

x = 6

therefore the number of yellow balls be 6 .

Now find out the ratio between the the number of yellow balls to red balls .

the number of yellow balls be 6 .

the number of red balls be 10 .

[tex]\frac{Number\ of\ yellow\ balls}{Number\ of\ red\ balls} = \frac{6}{10}[/tex]

solving

[tex]\frac{Number\ of\ yellow\ balls}{Number\ of\ red\ balls} = \frac{3}{5}[/tex]

Therefore the ratio of the the number of yellow balls to red balls is 3 :5 .

Option (d) is correct .

Hence proved

Answer:

$4

Step-by-step explanation:

36/9=4

36 is the number of oranges.

We know that 9 oranges is $1.

If 36 goes into 9, 4 times, that means 36 oranges costs $4.

Hope this helps :)

Using partial quotients for division is helpful as it simplifies division into easier to manage multiplication and subtraction problems, enhances intuitive and mental math skills, and allows students to verify their answers easily.

Using partial quotients when dividing can be helpful because this method turns a complex division problem into a series of simpler multiplication and subtraction problems. Unlike traditional long division that requires more complex, multiple-digit calculations, partial quotients approach the division process by allowing the student to subtract multiples of the divisor from the dividend in parts. This can be intuitive and less intimidating for students as they can work with smaller, more manageable numbers.

Partial quotients also allow for flexible thinking in mathematics. One can use estimates and adjust them in subsequent steps if necessary. This builds a deeper understanding of the division process instead of just rote procedure-following, and develops estimation and mental math skills over time. Moreover, it provides a clear pathway to check the work by adding the partial quotients, enhancing the student's ability to verify their own answers, and reinforcing the relationship between multiplication and division.

In practice, breaking down a division problem into smaller parts makes solving complex calculations more accessible and can be considered a shortcut that streamlines the division process. As such, this technique can be especially useful when dealing with larger numbers where traditional methods could become cumbersome. It introduces students to the concept of approximation, which is a valuable skill in both mathematics and real-life problem-solving scenarios.

The fraction [tex]\frac{7}{35}[/tex] represents how many games Krista's softball team lost out of the 35 games Krista's team played.

To find the percent of games that Krista's team lost, we need to turn the fraction [tex]\frac{7}{35}[/tex] into a percent.

We can reduce [tex]\frac{7}{35}[/tex] by dividing both the numerator and denominator by the Greatest Common Factor of 7 and 35 using 7.

7 ÷ 7 = 1

35 ÷ 7 = 5

Now, we have our reduced fraction.

1 ÷ 5 = 0.2

0.2 × 100 = 20%

Therefore, Krista's softball team lost 20% of their games.

To calculate the remaining travel time to reach a destination, subtract the distance already driven from the total trip distance, then divide the remaining distance by the average speed. For this question, after driving 145 miles out of 345, and traveling at an average speed of 50 miles per hour, it will take 4 more hours to reach the destination.

The student's question involves calculating the remaining time needed to reach a destination when driving at a constant speed, a typical problem in motion related to average speed and distance. We are given that the total distance is 345 miles, the average speed is 50 miles per hour, and the student has already driven 145 miles. To find the remaining time, we subtract the distance already covered from the total distance and then divide by the average speed.

First, we calculate the remaining distance to be covered by subtracting the distance already driven from the total distance: 345 miles - 145 miles = 200 miles. Next, we determine the time it would take to travel the remaining 200 miles at the average speed of 50 miles per hour. Time is calculated by dividing the remaining distance by the average speed.

Using the formula Time = Distance ÷ Speed, we have Time = 200 miles ÷ 50 miles/hour. This simplifies to 4 hours. Therefore, it will take 4 more hours for the student to reach their destination if they continue to drive at the same average rate of speed.

It will take 4 additional hours to reach the destination by driving the remaining 200 miles at an average speed of 50 miles per hour.

To calculate the time it will take to reach the destination, we can use the formula for time which is:

Time = Distance / Speed.

You have already driven 145 miles, so you have 345 miles - 145 miles = 200 miles left to travel. Given that you are driving at an average rate of 50 miles per hour, the remaining travel time can be calculated as follows:

Time = 200 miles / 50 miles per hour = 4 hours.

Therefore, it will take 4 more hours to reach your destination.

To find the time it will take to reach your destination, you need to divide the remaining distance by the average speed. So, if you have already driven 145 miles, you have 345 - 145 = 200 miles left to drive. Using the formula: time = distance / speed, the time it will take to reach your destination is 200 miles / 50 miles per hour = 4 hours.

The value of k in the expression is -8.

We have,

2 - (3/4)k = (1/8)k + 9

Combine like terms on one side.

-(3/4)k - (1/8)k = 9 - 2

Simplify.

-k (3/4 + 1/8) = 7

-k (6 + 1)/8 = 7

-(7/8)k = 7

Multiply 8 on both sides.

-(7/8)k x 8 = 8 x 7

-7k = 56

Divide -7 on both sides.

k = -56/7

k = -8

Thus,

The value of k in the expression is -8.

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