A recipe that yields 12 cups of soup calls for 28ounces of beef broth. How many ounces of beef broth do you need to make 18 cups of the soup?

Answer:

The height of the pole is 38.5 m.

Step-by-step explanation:

Given information:

The height of stop sign is [tex]h=7\rm \; ft[/tex]

Length of shadow of stop sign is [tex]l=2\rm \; ft[/tex].

The length of shadow of pole is [tex]L=11\rm \; ft[/tex].

Now, the shadow is measured at the same time for both the cases. So, the triangles formed by stop sign and its shadow, and pole and its shadow will be similar.

For similar triangles, the sides are always in same proportion.

Solve for the length of pole as,

[tex]\dfrac{H}{h}=\dfrac{L}{l}\\\dfrac{H}{7}=\dfrac{11}{2}\\H=7\times 5.5\\H=38.5[/tex]

Therefore, the height of the pole is 38.5 m.

Refer the diagram for more clarity.

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Answer: Our numbers are: [tex]\sqrt{8/3}[/tex],  π, 3.01245 and [tex]\sqrt{17}[/tex]. Let's analyze them:

1) [tex]\sqrt{8/3}= \sqrt{16/6} =4/\sqrt{6}[/tex] and [tex]\sqrt{6} \geq\sqrt{4}= 2[/tex], so [tex]4/\sqrt{6} \leq4/2 = 2[/tex]

So [tex]\sqrt{8/3}\leq2[/tex]

2) the number pi is 3.14159265

3) this number is 3.01245, doesn't require more analyzing-

4) [tex]\sqrt{17}[/tex], we know that [tex]\sqrt{16} = 4[/tex], then [tex]\sqrt{17} \geq 4[/tex]

So the correct order from greatest to lowest is:

[tex]\sqrt{17}[/tex], π , 3.01245, [tex]\sqrt{8/3}[/tex]

You also can check it with a calculator, but it isn't the idea of the problem.

To calculate the volume in milliliters, we first convert gallons to liters (2 gallons * 3.875 liters/gallon = 7.75 liters), then convert liters to milliliters (7.75 liters * 1000 ml/liter = 7750 milliliters). So, Sarah purchased 7750 milliliters of milk.

Sarah purchased 2 gallons of milk, with each gallon approximately 3.875 liters. To convert liters to milliliters (ml), we should remember that 1 liter equals 1000 milliliters. So, to find the total amount in milliliters, we first convert gallons to liters (2 gallons * 3.875 liters/gallon = 7.75 liters), then convert liters to milliliters (7.75 liters * 1000 ml/liter = 7750 milliliters). Therefore, Sarah bought 7750 milliliters of milk.

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Final answer:

The question requires dividing the total amount borrowed by Susie by the number of weeks to obtain the weekly change in her allowance.

Explanation:

The question pertains to a simple mathematical calculation of equal division of a loan amount across a specified number of weeks to determine the weekly change in Susie's allowance. Although the exact loan amount isn't provided, the process would involve dividing the total sum borrowed by the number of weeks (5 weeks, as mentioned) to find out how much Susie's allowance will reduce each week.

For instance, if Susie borrowed $100, her weekly allowance would be reduced by $100 / 5 = $20 per week.

Final answer:

The weekly change in Susie's allowance is $20.

Explanation:

The weekly change in Susie's allowance can be calculated by dividing the total amount borrowed by the number of weeks she has to repay the loan. In this case, if Susie borrowed $100 and has five weeks to repay it, the weekly change in her allowance would be $100/5 = $20. Therefore, her allowance would decrease by $20 every week for the next five weeks.

The MOST reasonable estimate of the y-intercept for this linear graph is 0.6

Option C

The y-intercept of a linear graph is the point where the line intersects the graph on the y-axis

The slope-intercept form of the equation of a line is:

y  =  mx  +   c

where m is the slope

and c is the y-intercept

Considering the graph shown, the line intersects the y-axis on the point y = 0.6

Since the line intersects the y-axis on the point y = 0.6, the most reasonable estimate of the y-intercept of the linear graph is 0.6

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When expressing the given number 4.002 in word form, describe it as "four and two thousandths."

The given number is 4.002.

To express the number 4.002 in word form, we break it down into its individual place values and assign corresponding words to each place. Here's the breakdown:

4.002:

Now, let's express each place value in word form:

4.002 is spelled as "four and two thousandths."

Thus, when expressing 4.002 in word form, we describe it as "four and two thousandths."

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Answer:

√[tex]\frac{77}{11}[/tex]

The answer in the simplest radical form is [tex]\frac{\sqrt{77}}{11}[/tex].

A radical expression is an expression consisting of a square root or nth root.

The given expression is √7/√11.

Simplify the expression as follows:

√7/√11 × √11 / √11

√77 / 11

Hence, the answer in the simplest radical form is [tex]\frac{\sqrt{77}}{11}[/tex].

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The correct question is?

What is √7/√11 in the simplest radical form?

The distance between points (10,7) and (2,7) on a coordinate plane will be 8 units.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

It is given that, the points on the coordinate planes are (10,7) and (2,7).

(x₁,y₁) = (10,7)

(x₂,y₂) = (2,7)

The distance between points (10,7) and (2,7) on a coordinate plane is found as,

(d) = √(x₂ - x₁)² + (y₂-y₁)²

Substitute the given values as,

(d) = √(2 - 10)² + (7 - 7)²

=√(-8)² + (0)²

=√64

=8 units

Thus, the distance between points (10,7) and (2,7) on a coordinate plane will be 8 units.

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Answer:

b

Step-by-step explanation:

Interest, sales tax, and markups are all additional charges added to the original amount, but they differ in how they are calculated and when they are charged.

Interest is similar to sales tax and markups in that they all involve additional charges or fees that are added to the original amount.

Interest is the extra amount paid for borrowing money, while sales tax is the extra amount paid on the purchase of goods or services, and markups are the extra amount added to the cost price to determine the selling price. They all increase the total cost or price of the transaction.

The main difference is that interest and markups are calculated as a percentage of the original amount, while sales tax is calculated as a percentage of the purchase price. Additionally, interest and markups are typically charged over a period of time or for a specific duration, while sales tax is a one-time charge at the point of sale.

To estimate 524÷9, round 524 to 540 (a multiple of 9) and divide by 9. The estimate is 60.

To estimate 524÷9, you can use rounding. Round 524 to the nearest multiple of 9, which is 540. Then, divide 540 by 9, which equals 60. Therefore, the estimate for 524÷9 is 60.

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Final answer:

By dividing the total distance (20.25 miles) by the total time (2.5 hours), we find that the mouse has a top speed of 8.1 mph and could therefore travel 8.1 miles in one hour if it maintained this speed.

Explanation:

To find out how far a mouse can travel in an hour at its top speed, we can use the information provided that the mouse ran 20.25 miles in 2.5 hours. This question is essentially asking us to calculate the speed of the mouse in miles per hour (mph), which is a common way to express speed. We'll use a simple division to solve this problem.

First, we divide the total distance traveled by the total time taken to find the speed:

Performing the division:

Speed = 8.1 mph

Therefore, if the mouse continued to run at its top speed, it would be able to travel 8.1 miles in one hour.

To travel 200 meters at 5 m/s, it would take 40 seconds.

To travel 200 meters at 5 m/s, we can use the formula for speed:

speed = distance / time

5 m/s = 200 meters / time

time = 200 meters / 5 m/s = 40 seconds

The ratio of the amount of money Jason had to the amount of money Wilson had was 12:13, then Jason had $12x and Wilson had $13x.

Wilson spent $63, then in the end he had $(13x-63). Since in  the end Jason had 3 times as much money as Wilson, then

[tex]\dfrac{12x}{13x-63}=3.[/tex]

Solve it:

[tex]12x=3(13x-63),\\ \\12x=39x-189,\\ \\27x=189,\\ \\x=7.[/tex]

In the beginning Jason had $12·7=$84 and Wilson had $13·7=$91. In the end Jason had $84 and Wilson had $91-$63=$28.

Answer: Jason had $84, in the end altogether they had $84+$28=$112.

Answer:

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