556 multiplied by 34

Therefore, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

What is the equation?

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here given that,

A car is traveling at a speed of [tex]75[/tex] km/h.

As we know,

[tex]1km=1000m[/tex]

[tex]1h=60s[/tex]

So,

[tex]75[/tex] km/h=[tex]\frac{75(1000)}{3600}[/tex] m/s

[tex]=\frac{75000}{3600}\\\\[/tex]

Hence, the speed of the car in m/s is [tex]\frac{75000}{3600}[/tex] m/s i.e., option (B) is correct.

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Answer:

Sure, I'd be happy to show you how to simplify this expression. Here are the steps:

1. In this expression, we have three numbers that are being multiplied together, 2, x^2, and y, and the entire product is raised to the power of 3.

2. Let's take each part of the product individually and raise them to the power of 3.

  For the first part, 2 raised to the power of 3: this gives us 8, since 2 * 2 * 2 equals 8.

3. The next part is [tex]x^2[/tex] raised to the power of 3. When raising a power to another power, we multiply the powers together. Therefore, (x^2)^3 becomes x^(2*3), which can be simplified to x^6.

4. Finally, y raised to the power of 3 remains as y^3.

5. So, when we put together all three parts, we obtain the simplified expression, and (2x^2y)^3 simplifies to 8x^6y^3.

So, the simplified expression for (2x^2y) ^3 is 8x^6y^3.

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To determine how much hardener is required for 16 containers of resin, multiply 55 mL by 16 to get 880 mL, and then convert this to liters by dividing by 1,000, resulting in 0.88 liters of hardener needed.

To determine how much hardener should be added to 16 containers of resin, we must multiply the amount needed for one container by the number of containers. The formula given states that 55 mL of hardener is required for each container of resin. To find the total amount for 16 containers, we perform the following multiplication:

Therefore, 0.88 liters of hardener should be added to 16 containers of resin.

Final answer:

To determine the amount of hardener needed for 16 containers of resin, multiply 55 mL by 16 to get 880 mL and then convert that to liters, resulting in 0.88 liters of hardener.

Explanation:

To find out how much hardener should be added to 16 containers of resin, where each container requires 55 mL of hardener, you need to do a simple multiplication operation. Multiply the amount of hardener needed for one container by the number of containers:

Therefore, you should add 0.88 liters of hardener to the 16 containers of resin.

The linear function that represents this graph is given by:

y = 300 - 0.6667x.

A linear function is modeled by:

y = mx + b

In which:

From the graph, when x = 0, y = 300, hence the y-intercept is of b = 300. The amount decays to 0 when the x-intercept is of x = 450, hence the slope is given by:

m = -300/450 = -0.6667.

Which means that the equation is:

y = 300 - 0.6667x.

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Answer:

C

Step-by-step explanation:

[tex] p\%=\dfrac{p}{100}\to 75\%=\dfrac{75}{100}=0.75\\\\n-the\ number\\\\the\ equation:\\\\n+0.75n=80\\\\1.75n=80\ \ \ \ |:1.75\\\\n=\dfrac{80\cdot100}{1.75\cdot100}\\\\n=\dfrac{8000}{175}\\\\n=\dfrac{8000:25}{175:25}\\\\n=\dfrac{320}{7}\\\\n=45\dfrac{5}{7} [/tex]

Final answer:

The student can fill up their gas tank up to 4 times within their $108 budget for gasoline. The inequality used to determine this is 27n ≤ 108, solved by dividing both sides by 27.

Explanation:

To solve the student's question regarding how many times they can fill up their gas tank within a $108 budget, we need to set up an inequality and solve it. Let's define the variable n as the number of times they can fill up their tank.

Step A: Write the Inequality

Since it costs $27 to fill up one tank, and the student has budgeted no more than $108 for gas, the inequality will be:

27n ≤ 108

Step B: Solve the Inequality

To find out how many times the student can fill up the tank, we divide both sides of the inequality by 27:

n ≤ [tex]\frac{108}{ 27}[/tex]

n ≤ 4

Therefore, the student can fill up their gas tank up to 4 times within their budget.

Answer:

The value of x is 12 in

Step-by-step explanation:

Given the right angled triangle having sides 5 in , 13 in and x in

We have to find the value of x.

By applying Pythagoras theorem, we get

[tex]Hypotenuse^{2} = Base^{2} + Perpendicular^{2}[/tex]

⇒ [tex]13^{2}=x^{2}+5^{2}[/tex]

⇒  [tex]169=25+x^{2}[/tex]

⇒  [tex]x^{2} = 144[/tex] ⇒ x=12 in

Hence, length of base is x in i.e 12 in