Without multiplying, determine the sign of the product (356,864)(−194,758).

The sign of the product is positive because a positive multiplied by a negative is a positive.
The sign of the product is negative because a positive multiplied by a negative is a negative.
The sign of the product is negative because the second number is negative.
The sign of the product is positive because the first number is positive.

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.

Final answer:

The constant of proportionality of 1/3 means that for every unit increase in one variable, the other variable increases by 1/3 of that unit. It is a number that relates two quantities that are directly proportional to each other.

Explanation:

The question 'what is the constant of proportionality of 1/3' can be related to various contexts in Mathematics and Science. In mathematics, a constant of proportionality is a number that relates two quantities that are proportional to each other. If one quantity is always the product of the other quantity and a constant, this constant is called the constant of proportionality.

For example, if you have an equation y = (1/3)x, then the constant of proportionality between x and y is 1/3. This means for every unit increase in x, y increases by 1/3 of that unit. It can also appear in a science context, such as in Ohm's Law, where V = IR, and 'R' can be considered the constant of proportionality that relates voltage (V) and current (I), or in the specific heat equation, where the specific heat serves as the constant.

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.

Learn more about expressions here:

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A real world problem reflected in the expression 5x + 10 can involve calculating the total cost of books plus a membership fee in a bookstore. The quadratic formula is used for solving quadratic equations, which have significant applications in various fields.

An example of a real world problem represented by the expression 5x + 10 is calculating the total cost of purchasing multiple items. Imagine you are at a bookstore, and each book costs $5. There is also a one-time membership fee to join the bookstore's readers club, which is $10. If x represents the number of books you decide to purchase, then 5x would represent the total cost of the books, and when you add the $10 membership fee, the expression for calculating your total cost would be 5x + 10.

Additionally, the concept of quadratic formula is significant in mathematics as it helps in finding solutions for quadratic equations, such as t² + 10t - 2000 = 0. This equation can be solved by rearranging to have 0 on one side and then applying the quadratic formula. Understanding quadratic equations is crucial not just in theoretical math but also practical real world applications like physics or economics.

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.

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 :)

Answer: 2 x 40 = 80

Step-by-step explanation: there are two baskets of apple fruit labelled basket X and basket Y, each basket consists 150 green apple fruit.

You were asked to select 40 green apple fruit from each of the basket and put it together in basket Z.

40 green apples from both baskets X and Y equals 80 green apples in basket Z.

2 x 40 =80

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

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.

The X and Y intercepts of the given equation can be found by setting variables to zero in turn and solving for the other. The X intercept is -3 and the Y intercept is 6.

To find the X and Y intercepts of -8x + 4y =24, we should set each variable equal to zero in turn to solve for the other. The X intercept occurs when Y is zero, and the Y intercept happens where X is zero.

For finding X-intercept, place Y equal to zero in the equation, so we get -8x +4(0) = 24. Solving it leads us to X = -3.

For the Y-intercept, let’s place X equal to zero in the equation. Here we get -8(0) + 4y = 24. Solving this yields Y = 6. So, the X intercept is -3, and the Y intercept is 6.

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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.