xp+yp=z. (ignore the period, any answers)

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 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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Answer:

150 short-sleeved shirts and 100 long-sleeved shirts.

Step-by-step explanation:

We will use elimination to solve this system of equations.  We will make the coefficients of x the same in order to eliminate them; to do this, we must multiply the bottom equation by 15 (1/3 of 15 is 5, so 15(1/3) = 5):

[tex]\left \{ {{5x+10y=1750} \atop {15(\frac{1}{3}x+\frac{1}{2}y=100)} \right. \\\\\left \{ {{5x+10y=1750} \atop {5x+7.5y=1500}} \right.[/tex]

Subtract the second equation from the first one:

[tex]\left \{ {{5x+10y=1750} \atop {-(5x+7.5y=1500)}} \right. \\\\2.5y=250[/tex]

Divide both sides by 2.5:

2.5y/2.5 = 250/2.5

y = 100

Substitute 100 in for y in the first equation:

5x+10(100) = 1750

5x+1000 = 1750

Subtract 1000 from both sides:

5x+1000 - 1000 = 1750 - 1000

5x = 750

Divide both sides by 5:

5x/5 = 750/5

x = 150

Final answer:

To find the number of sugar packets from 40 pounds, divide by the weight per packet (1/16 pound). The calculation is 40 divided by 1/16, resulting in 640 packets.

Explanation:

To determine how many packets of sugar you can make from 40 pounds of sugar when each packet is 1/16 pounds, you would divide the total amount of sugar by the amount each packet contains. This is a basic math problem involving division.

Here's the calculation:

First, we establish that there are 40 pounds of sugar that need to be divided into packets.

Next, since each packet will contain 1/16 of a pound of sugar, we divide the total pounds of sugar by the weight of each packet.

The calculation is 40 pounds \/ (1/16) pounds per packet, which simplifies to 40 × 16 packets.

After performing the multiplication, the result is 640 packets of sugar.

Therefore, you would have a total of 640 packets of sugar if you repackage 40 pounds of sugar into 1/16 pound packets.

Answer:

are you sure it is that large number and not 3 1/2

Step-by-step explanation:

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.

Step-by-step explanation:

A card is drawn from a standard deck. A standard deck of cards has 52 cards. Its been asked if it is a king. There are 4 kings in a deck, so probability is = [tex]\frac{4}{52}[/tex] or [tex]\frac{1}{13}[/tex]

Simultaneously, a word is chosen from 'incredible' that has 10 letters. We have been asked if the letter is 'i'. In the given word, we have 2 'i's. So, probability is [tex]\frac{2}{10}[/tex] or [tex]\frac{1}{5}[/tex]

pretty simple

compares two amounts like 4:5 is a ratio

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.

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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