how can you show that the ratios 10:4 abd 15:6 are equivalent

Answer:

[tex]5^4 = 625[/tex]

Step-by-step explanation:

There are 5 possible odd digits to choose from:  1,3,5,7,9.

When we chose our first digit, we have 5 choices (the possible odd digits). For every one of those 5 choices, we can chose our second digit in 5 different ways again, then we have 5*5 = 25 ways for choosing our first two digits. We can do the same again, as for every one of the 25 first two digits, we can chose our third digit in 5 different ways (again, the odd numbers). So we multiply it by 5 again. Repeating this one more time, because we have 5 different ways to chose our fourth digit. At the end we will have

[tex]5*5*5*5 = 5^4 = 625[/tex]

This is a commun counting technique.

Answer: 5.65 g/ml

Step-by-step explanation:

The density of a substance is given by :-

[tex]\text{Density}=\dfrac{\text{Mass}}{\text{Volume}}[/tex]

Given : The mass of a metal is 10.34 g. Its volume is 1.83 ml.

Then, the density of substance will be :-

[tex]\text{Density}=\dfrac{10.34\ g}{1.83\ ml}\\\\\Rightarrow\ \text{Density}= 5.65027322404\ g/ml[/tex]

Since , the significant figures depend on the dividend .

Here the dividend (10.34) is hundredth unit.

Then, the [tex]\text{Density}== 5.65027322404\approx5.65\ g/ml[/tex]

Answer:

C

Step-by-step explanation:

Took the test got it right

The angles in transverse parallel lines are related through some theorems such as vertical angles, corresponding angles, etc. the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]

Given the attached diagram

First, we solve for x using the corresponding angle theorem

[tex]5x + 55 = 2x + 100[/tex] ---- corresponding angles are equal

Collect like terms

[tex]5x - 2x = 100 - 55[/tex]

[tex]3x = 45[/tex]

Divide both sides by 3

[tex]x = 15[/tex]

We then  solve for [tex]\angle 2[/tex] using the straight line theorem

[tex]\angle 2 + 5x + 55 = 180[/tex] ---- sum of angles on a straight line

Substitute 15 for x

[tex]\angle 2 + 5 \times 15 + 55 = 180[/tex]

[tex]\angle 2 + 75 + 55 = 180[/tex]

Collect like terms

[tex]\angle 2 =- 75 - 55 + 180[/tex]

[tex]\angle 2 =50[/tex]

Hence, the measure of [tex]\angle 2[/tex] is [tex]50^o[/tex]

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Answer: About 111 of moons could be lined up in a row between Earth and the moon .

Step-by-step explanation:

Given : The diameter of the moon is about 3,476 kilometers.

The distance from Earth to the moon is about 384,400 kilometers.

Then , the number of moons could be lined up in a row between Earth and the moon will be :-

[tex]384,400\div3,476\\\\=110.586881473\approx111\text{ Rounded to the nearest whole number }[/tex]

Hence, about 111 of moons could be lined up in a row between Earth and the moon .

The number 13/16 is a rational number because it can be expressed as a ratio of two integers.

The number 13/16 is a rational number. A rational number is any number that can be expressed as a ratio of two integers, where the denominator (the number below the division line) is not zero. In this case, the number 13/16 can be expressed as a ratio of two integers: 13 and 16. Therefore, 13/16 is considered to be a rational number, not an irrational number. In contrast, an irrational number cannot be stated as a ratio of two integers. Examples of irrational numbers include the square root of two and pi.

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The pizza bot will take approximately 22.5 minutes to make the delivery and return to the restaurant.

To calculate the time it will take the pizza bot to make the delivery and return to the restaurant, we can use the formula:

Time = Distance / Speed

In this case, the distance is 1.5 miles (one way), and the speed is 4 mph. So, the time it will take for the pizza bot to make the delivery and return to the restaurant is:

Therefore, it will take the pizza bot approximately 0.375 hours, or 22.5 minutes, to make the delivery and return to the restaurant each time.

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The average speed for the entire trip is 38.06 mph

What is Average Speed?

The total distance traveled divided by the total time spent traveling. This will give you your average speed.

                                            S = d₁ + d₂ ... + dₙ / t₁ + t₂... + tₙ

Given data ,

d₁ = 130 miles

d₂ = 200 miles

S₁ = 65 mph

S₂ = 30 mph

t₁ = d₁ / S₁

t₂ = d₂ / S₂

And , t₁ = 130 / 65 = 2 hours

t₂ = 200 / 30 = 6.67 hours

Therefore , Average Speed = Total distance travelled / Total time taken

                                              =d₁ + d₂ / t₁ + t₂

                                              = 330 / 8.67  mph

                                              = 38.06 mph

Hence , the average speed for the entire trip is 38.06 mph

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The side length of the square rug is 10 feet and it is a rational number since it can be written as a ratio of two integers.

The area of a square is computed by squaring the length of one of its sides. The area of the rug is given as 100 square feet. Therefore, we can set up the following equation to find the side length:

S^2 = 100

Where 'S' represents the side length. To solve for 'S', we take the square root of both sides of the equation.

Therefore, S = √100

The square root of 100 is 10, so the side length of the rug is 10 feet.

Therefore, the rug has a side length of 10 ft. Since '10' can be expressed as a ratio of two integers, it is a rational number.

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Answer:

There can be many example for this equation like:

1. There are three friends and all have the same amount of money. Together they give $25 in a restaurant and they are left with $125. How much money did each have?

We can solve this like:

Let each friend had 'x' money so three friends had 3x money.

They gave out $25, means 3x-25 and are left with $125.

So, complete equation becomes :

[tex]3x-25=125[/tex]

Solving for x we get;

[tex]3x=125+25[/tex]

[tex]3x=150[/tex]

x = 50

So, each friend had $50.

Final answer:

The value of k for the equation kx^2 + x + 25k = 0 to have a repeated solution can be found by setting the discriminant to zero. Solving for k, we find that k = 0.1 and k = -0.1 are the values that yield a repeated solution for this quadratic equation.

Explanation:

To find the value of k such that the equation kx^2 + x + 25k = 0 has a repeated solution, we need to use the discriminant of a quadratic equation. The discriminant D is given by D = b^2 - 4ac. For a quadratic equation to have a repeated solution, its discriminant must be zero (D = 0). In this equation, a = k, b = 1, and c = 25k. Plugging these values into the discriminant formula gives us:

D = 1^2 - 4(k)(25k)

Setting D to zero and solving for k will give us the value(s) of k for which the equation has a repeated solution:

0 = 1 - 100k^2

k = ± 0.1

Therefore, there are two values of k that make the original equation have a repeated solution: k = 0.1 and k = -0.1.

x/6 = 12/9

x = 12/9 * 6

x = 8

check:

8/6 = 1.3333

12/9 = 1.3333

Answer:

The number 1 is common factor between any set of numbers, but, sometimes is the only common factor.

Step-by-step explanation:

This happens when the numbers do not have common prime factors, like 5 and 7.

Since 1 is a prime number, you can consider it the common primer factor of every set of numbers.

Remember:

If 'a' is a number, a prime factor of it would be 1, since a*1=a

2 parts per second so 2 x 60 = 120 parts per minute

120*60 = 7200 parts per hour

7200 x 10 = 72,000 parts per 10 hour shift

Answer:

The unit cost for cherries is greater because the slope is greater than the slope for apples.

Explanation:

Slope is the rate of change of a line.  The slope of the graph for cherries is greater; we can see this because the line is steeper.

Since the slope is greater, the unit cost is greater.

The statement that represents the unit cost in the graph is that the unit cost for cherries should be more as the slope is more than the slope for apples.

The following information should be considered:

Therefore we can conclude that the first option is correct.

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