Iodine-125 has a half-life of about 60 days.

How many milligrams of a 500 mg sample will remain after 300 days?

Answer:

Part A: The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.

Part B: No, the point (-4,6) is not included in the solution area for the system.

Step-by-step explanation:

System of inequalities:

(1) y > 2x + 3

(2) y < -(3/2)x - 4

Part A

1) The first inequality represents the region over the line:

y=2x+3

This is a linear equation and its graph is a right line. We must graph the right line, and then shadow the area above this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:

x=0→y=2(0)+3→y=0+3→y=3; Point=(x,y)→Point=(0,3)

x=1→y=2(1)+3→y=2+3→y=5; Point=(x,y)→Point=(1,5)

1) The second inequality represents the region below the line:

y= -(3/2)x - 4

This is a linear equation and its graph isaright line. We must graph the right line, and then shadow the area below this right line. To graph this right line we need two points, because through two points only goes one right line. Giving two arbitrary values to x, for example:

x=0→y=-(3/2)(0)-4→y=0-4→y=-4; Point=(x,y)→Point=(0,-4)

x=2→y=-(3/2)(2)-4→y=-3-4→y=-7; Point=(x,y)→Point=(2,-7)

The two lines intersect at the point (-2,-1). The solution area is to the left of x=-2, over the right line y=2x+3 and below the right line y=-(3/2)x-4.

Part B

No, the point (-4,6) is not included in the solution area for the system, because this point is not below the right line y=-(3/2)x-4

Part A: The purple region in the graph attached below is the solution to the given inequalities.

Part B: (-1,-1) is not included in the solution area for the system of inequalities.

In mathematics, inequalities specify the connection between two non-equal expressions.

Given the following information:

1) y > −4x − 1

2) y is less than 3 over 2 times x minus 1, this can be expressed in inequality as follows:

[tex]y < \dfrac{3}{2}x-1[/tex]

Part A:

Attaching image to describe the graph of the system with shaded area.

The red colored region corresponds to the solution of inequality of line 1)

The blue colored region corresponds to the solution of inequality of line 2)

Thus, purple colored region corresponds to the common region due to the 2 lines.

Part B:

To check whether (-1,-1) is included in the solution area for the system:

Mathematical justification:

Substituting (-1,-1) in eq1)

-1>-4(-1)-1

-1>3

This is false as -1 is less than 3.

Substituting (-1,-1) in eq2)

-1<3(-1)/2-1

-1<-3/2-1

-1<-5/2

-1<-2.5

This is also false as -1 is greater than -2.5

Thus, it is justified that (-1,-1) is not included in the solution.

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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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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:

I need help with this problem.

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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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?

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.

A unit rate means a rate for one of something.

The distance of the state park from their house is 42 miles.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. 

We have,

Time taken to reach state park from house = 4 hours

First two hours, speed = 12 miles per hour

This can be written as:

1 hour = 12 miles

2 hours = 2 x 12 miles = 24 miles. ______(1)

The last two hours = 9 miles per hour

This can be written as:

1 hour = 9 miles

2 hours = 2 x 9 miles

2 hours = 18 miles ______(2)

From (1) and (2) we get,

24 + 18 = 42 miles

Thus,

The distance of the state park from their house is 42 miles.

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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

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.

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.

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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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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