Consider the data set on the number line. Determine the interquartile range.
A) 3
B) 6
C) 14
D) 17

The amount of Thorium-228 left after 22.8 years of decay from an initial 50 gram sample, given its half-life of 1.9 years, is 0.124 grams.

In this problem of thorium -228 decay, we apply the formula for exponential decay which is A=A0e^-kt. 'A0' represents the initial amount, which in this case is 50 grams. 'A' is the final amount after 't' years, and 'k' is the decay constant. To find the decay constant first, we note that thorium-228 decays to 50% of its initial quantity in 1.9 years. Therefore, we can write the equation 0.5=A0e^-1.9k. Solving for 'k', we get k = ln(2)/1.9, which allows us to derive the time constant for the decay.

Now we use this value of 'k' to find out the amount of thorium-228 left after 22.8 years. Plugging the values into our formula, we get: A = 50e^((ln2/1.9)*-22.8). Solving this yields a value of 0.124 grams, which means option C is correct.

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To find the amount of thorium-228 remaining after 22.8 years, we can use the formula A = A0e -kt. The correct answer is B) 30.32 grams.

To solve this problem, we can use the formula A = A0e-kt where A is the amount of the substance at a given time, A0 is the initial amount, k is the decay constant, and t is the time elapsed.

In this case, we are given that thorium-228 decays 50% every 1.9 years.

This means that the decay constant k = ln(2)/1.9. We can substitute the values into the formula and solve for A: A = 50 * e(-ln(2)/1.9)*22.8 = 30.32 grams.

Therefore, the correct answer is B) 30.32 grams.

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Answer:

oof

Step-by-step explanation:

Answer:

86°

Step-by-step explanation:

Supplementary angles add up to 180°.  So the supplementary angle of 94° is:

x + 94° = 180°

x = 86°

Answer:

P(A)= 21/36

P(B)=1/2

Step-by-step explanation:

Given:

An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is rolled twice

So the sample space of rolling two dices is:

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Total number of sets=36

1)Now Finding probability of

Event A: The sum is greater than 6

From the above sample space sets that have the sum >6 are

(6,1)

(5,2) (6,2)

(4,3) (5,3) (6,3)

(3,4) (4,4) (5,4) (6,4)

(2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

there are 21 sets

hence probability of Event A= 21/36

P(A)= 21/36

2) Now Finding probability of

Event B: The sum is an odd number

From the above sample space sets that have the sum an odd number are

(2,1)(4,1) (6,1)

(1,2)(3,2) (5,2)

(2,3) (4,3)(6,3)

(1,4) (3,4) (5,4)

(2,5) (4,5) (6,5)

(1,6) (3,6) (5,6)

there are 18 sets

hence the probability of Event B = 18/36

         P(B)= 1/2 !

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

The ratio of the areas of the difference circles:

[tex]\dfrac{A_1}{A_2}=\dfrac{\pi r_1^2}{\pi r_2^2}=\dfrac{r_1^2}{r_2^2}=\left(\dfrac{r_1}{r_2}\right)^2[/tex]

We have

Circle A: r₁ = 4ft

Circle B: r₂ = 9 ft

Substitute:

[tex]\dfrac{A_A}{A_B}=\left(\dfrac{4}{9}\right)^2=\dfrac{16}{81}[/tex]

the ratio of the area of Circle A to the area of Circle B is 16/81, which corresponds to answer choice (d).

To find the ratio of the area of Circle A to the area of Circle B, we use the formula for the area of a circle, which is A = (pi)r^2. For Circle A, with a radius of 4 feet, the area is (pi)(4 ft)^2. For Circle B, with a radius of 9 feet, the area is (pi)(9 ft)^2.

Calculating these areas:

Area of Circle A = (pi)(4 ft)^2 = 16(pi) ft^2

Area of Circle B = (pi)(9 ft)^2 = 81(pi) ft^2

Now, we take the ratio of the two areas:

Ratio = (Area of Circle A) / (Area of Circle B) = (16(pi) ft^2) / (81(pi) ft^2) = 16/81

Therefore, the ratio of the area of Circle A to the area of Circle B is 16/81, which corresponds to answer choice (d).

Answer:

0.41 per cup

Step-by-step explanation:

in 3 gallons of liquid is 48 cups so 19.68 and divide by 48 so 19.68/48=0.41

Answer:

$0.41 per cup

Step-by-step explanation:

there are 16 cups in a gallon

after that multiply 16 times 3 which would be 48

Now divide $19.68 divided by 48

check---

0.41 times 48 = 19.68

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

m - slope

b - y-intercept

We have y-intercept b = -2. Substitute:

We have the point (4, 12) → x = 4, y = 12. Put them in the equation:

12 = 4m - 2         add 2 to both sides

14 = 4m       divide both sides by 4

14/4 = m → m = 3.5

Answer:

y = 3.5x - 2

Step-by-step explanation:

We know that the y-intercept of our equation is -2, so our current equation is: y = mx - 2. Now we have to find m, which is the slope. Now, we plug in the points into the equation y = mx - 2, and we get 12 = 4m - 2. Thus, m is 3.5. Our final equation is y = 3.5x - 2.

Answer:

p > 5 and p <-8

Step-by-step explanation:

To solve this, you first need to isolate p.

First add 6 on both sides of the equation:

[tex]-6 + |2p+3| >7\\\\(+6) -6 + |2p+3| >7 +6\\\\2p + 3 > 13[/tex]

Then subtract 3 from both sides of the equation.

[tex]2p+3-3>13-3\\\\2p > 10\\[/tex]

The divide both sides by 2.

[tex]\dfrac{2p}{2}>\dfrac{10}{2}\\\\p>5[/tex]

Another solution is possible because of the absolute value.

If [tex]|2p+3|>13[/tex]

Then [tex]|2p+3|<-13[/tex]

Thus we can solve the second solution:

[tex]|2p+3|<-13[/tex]

[tex]2p+3<-13[/tex]

Isolate P again by subtracting both sides by 3

[tex]2p+3-3<-13-3[/tex]

[tex]2p<-16[/tex]

Then divide both sides by 2:

[tex]\dfrac{2p}{2}<-\dfrac{16}{2}[/tex]

[tex]p<-8[/tex]

Answer:

p > 5, p < -8

Step-by-step explanation:

We are given the following inequality and we are to find its solution:

[tex]-6+|2p+3|>7[/tex]

Adding 6 to both sides to get:

[tex]-6+6+|2p+3|>7+6[/tex]

[tex]|2p+3|>13[/tex]

We know the absolute rule that [tex]\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a[/tex].

So [tex]2p+3>13[/tex] or [tex]2p+3<-13[/tex]

[tex] 2 p > 1 3 - 3 [/tex], [tex] 2 p < - 1 3 - 3 [/tex]

[tex] 2 p > 1 0 [/tex], [tex] 2 p < - 1 6 [/tex]

[tex]p>\frac{10}{2}[/tex], [tex]p<\frac{-16}{2}[/tex]

p > 5, p < -8

Hi there! The answer you're looking for is $72.30. Simply multiply $482 by 0.05 (5%) and multiply that answer by three (three years) to get $72.30! Let me know if this helps! <3

Answer: $72.30

Step-by-step explanation: To solve this problem, first begin with the interest formula.

Formula: Interest = principal × rate × time

In this problem, we are solving for the interest.

The principal is the amount invested which in this case is $482. The rate is 5% which we can write as .05 and the time is 3 years.

Interest = (482)(.05)(3)

Interest = 72.3

This means that the interest earned is $72.30.

For this system of equation I used substitution:

Step 1: Every time you see a y in the equation y = 2x - 1 replace it with -4x - 19

-4x - 19 = 2x - 1

Step 2: Isolate x

(-4x + 4x) - 19 = (2x + 4x) - 1

-19 = 6x - 1

-19 + 1 = 6x + (- 1 + 1)

-18 = 6x

x = -3

Step 3: To solve for y replace x in the equation y = 2x - 1 with -3

y = 2(-3) - 1

y = -6 - 1

y = -7

(-3, -7)

Check:

-7 = -4(-3) - 19

-7 = 12 - 19

-7 = -7 --------------------------------> Correct!

-7 = 2(-3) - 1

-7 = -6 - 1

-7 = -7 --------------------------------> Correct!

Hope this helped!

I got you fam!

Here's what I worked out for you:

1. Answer is C (-3, -5)

2. Answers are C and D (5, -1)

3. Answers are A and B (0, 3)

I'm one Brainliest away from ranking up, so one would be super appreciated! Thanks and good luck!

For this case we have that if "y" varies directly with "x", we can propose:

[tex]y = kx[/tex]

Where "k" represents the constant of proportionality.

According to the data:

[tex]180 = kn\\n = k5[/tex]

We substitute the second equation in the first:

[tex]180 = k * k5\\180 = 5k ^ 2\\k ^ 2 = \frac {180} {5}\\k ^ 2 = 36[/tex]

We apply root:

[tex]k = \pm \sqrt {36}\\k = \pm6[/tex]

If k = 6, then[tex]n = 6 * 5 = 30[/tex]

Answer:

[tex]n = 30[/tex]

Answer:

EDGE 2020

Step-by-step explanation:

C) 30

trust me

We find out the number of lemons needed per cup by dividing the total number of lemons by the total number of cups. In this case, 18 lemons divided by 15 cups gives us the number of lemons used per cup of lemonade.

This question is asking how many lemons are required for each cup of lemonade if 18 lemons are used to make 15 cups of lemonade. This is a simple proportional math problem. To solve this, we divide the total number of lemons by the total number of cups.

Step 1: Identify the total number of lemons and cups, which are 18 and 15 respectively.

Step 2: Divide the total number of lemons by the total number of cups (18 lemons / 15 cups).

Step 3: The solution will show the number of lemons used per cup of lemonade.

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Answer:

The expression that represent the volume of the prism is  [tex]\frac{1}{2}x^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the prism is equal to

[tex]V=LWH[/tex]

In this problem we have

[tex]L=x\ units[/tex]

[tex]W=x\ units[/tex]

[tex]H=(1/2)x\ units[/tex]

substitute

[tex]V=(x)(x)(1/2)x=\frac{1}{2}x^{3}\ units^{3}[/tex]

Answer:

Its the first one

Step-by-step explanation:

Answer:

each box has 52 in it

Step-by-step explanation:

first you subtract 288 from 548  =260

this is the total number of nails minus the total 1 inch nails

then you divide 260 by 5 because he has five boxes of 2 inch names which means that you have to account for the even number of nails in each box

Answer:

There were 52 2-inch nails in each box.

Step-by-step explanation:

Let the number of nails in each 2 inch box be = x

As Tony bought 288 other nails and 5 boxes of 2 inch nails with a total purchase of 548 nails, we get the following equation;

[tex]288+5x=548[/tex]

[tex]=> 5x=548-288[/tex]

[tex]=> 5x=260[/tex]

x = 52

Hence, there were 52 2-inch nails in each box.

Answer:

12.6 units²

Step-by-step explanation:

Since PX is a tangent to the circle then OP  and PX are at right angles.

A ΔOPX = 12, thus

OP × PX = 12, that is

6OP = 12 ( divide both sides by 6)

OP = 2 ← radius of circle

Area of circle = πr² = π × 2² = 4π ≈ 12.6 units²

Answer:

ε₀= 0.035

Step-by-step explanation:

The question is on residual/ error which is the vertical distance between the actual value of y and the estimated value of y.

General formulae is;

ε₀= y₀ - y₁

From the graph attached, the point on the line y=5x+2  is (5.407,29.035)

ε₀= 29.035- 29.000

ε₀= 0.035

Answer:

KL does not name the same line.

Step-by-step explanation:

You'll recognize that if you go from KM, it stays on the same. You go from MN it stays on the same line. KN also stays on the same line. By K and L are two completely different lines. L can only be with N or J

Answer:

NL

Step-by-step explanation:

Answer:

- 10 and 60

Step-by-step explanation:

1

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = (3 × - 2) - 4 = - 6 - 4 = - 10

2

To evaluate f(8) substitute x = 8 into f(x)

f(8) = 8² - 4 = 64 - 4 = 60

Answer:

Step-by-step explanation:

[tex]1)\\f(x)=3x-4\\\\f(-2)\to\text{put x = -2 to the equation of the function}\ f(x):\\\\f(-2)=3(-2)-4=-6-4=-10\\2)\\f(x)=x^2-4\\\\f(8)\to\text{put x = 8 to the equation of the function}\ f(x):\\\\f(8)=8^2-4=64-4=60[/tex]

Answer:

7.76(x) / 4 = Total cost

$25.22

Step-by-step explanation:

Given in the question that,

number of glue sticks that cost $7.76 = 4

To find the cost of 13 glue sticks first we need to find the cost of one glue stick, for that we will need cost of 4 sticks with 4

4    ---->    $7.76

1     ---->    $7.76/4

                $1.94

Multiply the cost of 1 glue with 13

3  ----->    $1.94x13

               $25.22

Equation

where x represent number of glue sticks

Answer:

System of equations:

5r +7.50t = 127.50

r +t = 19

Answer:

t = 13 . . . number of people who ordered taco salads

Step-by-step explanation:

One equation expresses the total bill: the number of each item ordered multiplied by its price, all item subtotals added to make the order total.

The other equation expresses the total number of orders: the sum of the orders of roast beef sandwich and the orders of taco salads.

__

The solution can be found easily by substitution.

r = 19 -t

5(19 -t) +7.50t = 127.50

95 +2.50t = 127.50 . . . . . . simplify

2.50t = 32.50 . . . . . . . . . . subtract 95

t = 13 . . . . . . . . . . . . . . . . . . divide by 2.50

The number who ordered taco salads is 13.

First we must find area of a single square.

Meaning we divide total area of 80 centimetres squared by 5 since we have 5 squares in the shape.

[tex]A_{square}=\frac{A_{shape}}{5}=\underline{16}[/tex]

Now from the picture we can see that the perimeter of shape is combined by 4 times 3 times the length of side of 1 square.

So we need to find side of 1 square.

[tex]a=\sqrt{A_{square}}=\sqrt{16}=\underline{4}[/tex]

As we stated before the formula for perimeter of this shape is:

[tex]P=4(3\cdot a)=4(3\cdot4)=4\cdot12=\boxed{48}[/tex]

The perimeter of shape is 48 centimetres.

Hope this helps.

r3t40

By determining the proportion of classmates who prefer green and applying it to the entire school population, we predict that approximately 72 students at the school would choose green as their favorite color.

To predict the number of students who favor green as their favorite color, we will assume the sample of classmates is representative of the entire school.

First, we need to find out how many students in the class chose green as their favorite color. Say, for example, 4 of the 22 classmates picked green. To find the predicted number for the school, we calculate:

Number of green-favoring classmates / Total classmates = Proportion of green-favoring classmates

4 / 22 = 0.1818 (rounded to four decimal places).

Now, apply this proportion to the entire school population:

0.1818 × 396 = Predicted number of students who favor green at the school.

71.55 - Since we can't have a fraction of a student, we round to the nearest whole number, predicting that about 72 students in the school would choose green as their favorite color.

Based on the data provided, I predict that approximately 72 students in the school would choose green as their favorite color.

1. Since you surveyed 22 classmates, the percentage of classmates who prefer green can be calculated. Let's assume that [tex]\( x \)[/tex] represents the number of classmates who prefer green. Therefore, [tex]\( \frac{x}{22} \)[/tex] is the proportion of classmates who prefer green.

2. Now, we can use this proportion to estimate the total number of students in the school who prefer green. Since there are 396 students in total, the estimated number of students who prefer green would be[tex]\( \frac{x}{22} \times 396 \).[/tex]

Now, let's find [tex]\( x \):[/tex]

- Let's assume [tex]\( y \)[/tex] is the number of classmates who prefer green. Since you surveyed 22 classmates, the percentage of classmates who prefer green can be calculated as [tex]\( \frac{y}{22} \).[/tex]

- Assuming that the number of classmates who prefer green is proportional to the total number of students who prefer green in the school, we can set up a proportion: [tex]\( \frac{y}{22} = \frac{x}{396} \).[/tex]

- Cross-multiplying, we get [tex]\( 396y = 22x \).[/tex]

- Solving for [tex]\( x \),[/tex] we find [tex]\( x = \frac{396y}{22} \).[/tex]

- Since we don't know the exact number of classmates who prefer green, let's assume a hypothetical scenario where 4 of your classmates prefer green. So, [tex]\( y = 4 \).[/tex]

- Substituting [tex]\( y = 4 \)[/tex] into the equation, we get [tex]\( x = \frac{396 \times 4}{22} = \frac{1584}{22} = 72 \).[/tex]

By surveying your classmates, you get a sample proportion of those who prefer green. Extrapolating this proportion to the entire school population, you can estimate the total number of students who prefer green. However, this estimation assumes that your classmates' preferences are representative of the entire school's preferences. So, based on this calculation, approximately 72 students in the school are predicted to choose green as their favorite color.

Complete question:

You survey your 22 classmates on there favorite color. There are 396 students at your school. How many students in the school do you predict would choose green as there favorite color?

I think the answer is 3/10

The probability that we will get a lead role, given that we are chosen to be in the play is 0.5.

Probability is the ratio that shows the likelihood of an event occurring from a given set of possible events.

The probability that we will be chosen for the play is 0.4.

The probability that we will get the lead role is 0.1.

We have to find the probability that we get a lead role, given that we are already chosen to be in the play.

In this situation, the probability can be found by adding the probability of being chosen and the probability that we will get the lead role.

This can be done as shown below:

The probability that we get a lead role, given that we are already chosen to be in the play = The probability that we will be chosen for the play + The probability that we will get the lead role

= 0.4 + 0.1

= 0.5

The probability of us getting a lead role given that we have already been chosen for the play is found to be 0.5. The correct answer is option D.

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Answer:

2x + 2(3) + 5

Step-by-step explanation:

Given expression

2(x + 3) + 5

In order to solve the expressions or to simplify the expressions, basic mathematical rules are considered.

Basic mathematical rules include the BODMAS. The order is Brackets, of powers, division, multiplication, addition and then subtraction is solved at last.

For the given expression, the 2 outside the bracket (x+3) will be multiplied inside first.

=> 2(x+3) + 5

Step 1:

=> 2x + 2(3) + 5

Step 2:

=> 2x + 6 + 5

Step 3

=> 2x+11

So the first step is 2x + 2(3) + 5 ..

Answer:

2x + 2(3) + 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.  That +2 shifts this result UP by 2 units.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

We have given that function

y=1/(x+5)+2

We have to determine,

The graph of this function compares with the graph of the parent function, y=1/x.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

That +2 shifts this result UP by 2 units.

Therefore the graph of the y=1/x is given below.

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Answer:

8 laps

Step-by-step explanation:

Assuming in the equation given than n represents the number of laps run and t represents the time in minutes, when we plug in 16 in for t and simplify we get:

n=5/10*16

n=1/2*16 (Simplify the fraction by dividing top and bottom by 5)

n=16/2 (Multiply the fractions together by writing 16 as 16/1 and multiplying straight across)

n=8

Answer:

8

Step-by-step explanation:

This question is a bit of a guess. You have to assume that n is in laps and that t  is in minutes.

n = (5/10) * t Reduce 5/10 to 1/2

n = 1/2 * 16

n = 8

So if the assumptions are correct, he should be able to do 8 laps.

Answer:

$4999

Step-by-step explanation:

Let the cost of the car be x

Then considering 20% markup, the sticker price is:

Since 20% of x is 20/100x = 0.2x,

So dealer paid $4999 for the car

Answer:

a . is the right answer

trust me

Final answer:

When evaluating the expression -3x³ - 4x for x = -1, by plugging in the value and simplifying the expression, we obtain the result of 7.

Explanation:

The question at hand requires us to evaluate the expression -3x³ - 4x when x = -1. To do this, we substitute -1 for x into the expression and simplify. Here's the step-by-step calculation:

Therefore, when we evaluate the expression -3x³ - 4x for x = -1, the result is 7.