5x - 2y = 12 solve for y

The time 'x' that both Harper and Liam are running for is 0.25 hours. This is calculated by setting the total distance covered by both runners equal to each other and solving for 'x'.

The subject of your question is Mathematics, specifically dealing with concepts of race pacing and distance calculations. Here's an answer to your question:

Let's denote the time it takes for both Harper and Liam to finish the race as 'x' hours. Given that Liam runs at 4 miles per hour and has a 0.25-mile head start, the total distance he runs is 4x + 0.25 miles. Harper, on the other hand, runs at 4.5 miles per hour (0.5 mile per hour faster than Liam) for 'x' hours, so Harper runs a total of 4.5x miles.

Since both runners run the same total distance, we can set these two equations equal to each other and solve for 'x':

4x + 0.25 = 4.5x

Solving this equation gives x = 0.25 hours.

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The ratio of 3 scoops of hot cocoa mix  to 10 miniature marshmallows and 8 ounces of water.  is 3:10

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

Given :-

amount of cocoa scoops = 3

amount of miniature marshmallows used = 10

We have to find out the Ratio of scoops of hot cocoa to miniature marshmallows:

First  we will simplify the term if there is any

Scoops of hot cocoa / miniature marshmallows = 3/10

Since, the simplification is already been done

Thus, the ratio will be:
                                      3 : 10

Hence, The ratio of scoops of hot cocoa to miniature marshmallows is 3:10

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Answer:  The required value of x is 2.5.

Step-by-step explanation:  We are given to find the value of x in the following equation :

[tex]-7.5(x-3)=3.75~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the value of x, we need to solve the given equation (i).

The solution of equation (i) is as follows :

[tex]-7.5(x-3)=3.75\\\\\\\Rightarrow x-3=\dfrac{3.75}{-7.5}\\\\\\\Rightarrow x-3=-0.5\\\\\Rightarrow x=3-0.5\\\\\Rightarrow x=2.5.[/tex]

Thus, the required value of x is 2.5.

Final answer:

To calculate the percent decrease in viewership, subtract the final number of viewers from the original number, divide that by the original number, and multiply by 100, rounding to the nearest percent. The viewership decreased from 5.1 million to 3.5 million, a 31% decrease.

Explanation:

The subject of this question is Mathematics, specifically relating to percentages. To find the percent decrease in viewership from 5.1 million to 3.5 million:

Calculate the decrease in viewers: 5.1 million - 3.5 million = 1.6 million.

Find the percentage: (1.6 million / 5.1 million) × 100 = 31.37%.

Round to the nearest percent: 31.37% ≈ 31%.

Therefore, the viewership has decreased by approximately 31%.

The Kendras error is that she doesn't know multiplication.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

Given that Kendra buy 40 bouquets for $120

So each bouquet cost 120/40  = $3 so each bouquet cost $3.

By the second option, she will get bouquets at $2.50 only it is an error of Kendra.

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The product of 22 times 26 is 572.

To find the product of two numbers, one multiplies the first number by the second number. In this case, we multiply 22 by 26:

\[ 22 \times 26 = 572 \]

This is a straightforward multiplication of two two-digit numbers. The result is 572, which is the answer to the question.

Answer:   Kate's score is 65.

Step-by-step explanation:  Given that Kate's golf score was 1 less than three fourths of Greg's golf score and the sum of their scores was 153.

We are to find Kate's score.

Let x and y represents Greg's score and Kate's score respectively.

Then, according to the given information, we have

[tex]y=\dfrac{3}{4}x-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

and

[tex]x+y=153\\\\\Rightarrow x+\dfrac{3}{4}x-1=153\\\\\\\Rightarrow \dfrac{7}{4}x=154\\\\\Rightarrow \dfrac{x}{4}=22\\\\\Rightarrow x=22\times4\\\\\Rightarrow x=88.[/tex]

From equation (i), we get

[tex]y=\dfrac{3}{4}\times88-1=66-1=65.[/tex]

Thus, Kate's score is 65.

The value of the temperature -10°C is equivalent to 14°F.

The process of changing a quantity's unit of measurement to another one that reflects the same physical amount is known as unit conversion.

To convert -10°C to Fahrenheit using the formula F = 1.8C + 32, follow these steps:

Start with the given temperature in Celsius, which is -10°C. Plug in -10 for C in the formula:

F = 1.8(-10) + 32.

Simplify the equation: F = -18 + 32.

Combine like terms:

F = 14.

Therefore, -10°C is equivalent to 14°F.

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The number which can be written from 1 hundred, 2 tens and 18 ones is 138

The sum of the place value numbers can be obtained thus :

Therefore, the number which can be obtained from the place value digits given is 138

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Answer:

480 people

Step-by-step explanation:

First you would divide 180 by 37.5,

180 divided by 37.5 = 4.8

Then you multiply 4.8 with 100

4.8 times 100 =480

Therefore, Annette surveyed 480 people

We want to find the total number of people that Annette surveyed given that we know a percentage and the number that the percentage represents.

We will find that the number of people that Annette survey is 480.

To get the solution:

Let's assume that she surveyed a total of X people.

Then we can write the equivalence:

100% = X

We know that the 37.5% is equivalent to 180 people, then we can write:

37.5% = 180

The two equations are:

100% = X

37.5% = 180

Now we can take the quotient between these two equations to get:

(100%/37.5%) = X/180

Solving for X we get:

(100%/37.5%)*180 = X = 480

So the total number of people surveyed is 480.

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