In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was
and mass was decreasing by
500 grams
8% per day. Determine the mass of the radioactive
sample at the beginning of the 13th day of the experiment. Round to the nearest tenth
(if necessary).

Given info:- L and M are parallel lines. Transverse N cuts them at ∠(6x + 42)° and ∠(18x - 12)°. Then find the value of x?

Explanation:-

Since L and M are parallel lines,

.°. ∠(6x + 42)° + ∠(18x - 12)° = 180° [∠s of a linear pair]

→ 6x + 24° + 18x - 12° = 180°

→ 6x + 8x + 24° - 12° = 180°

→ 14x - 12° = 180°

→ 14x = 180° - 12°

→ 14x = 168°

→ x = 168÷14 = 168/14 = 12°

Therefore, the value of “x” is 12°.

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Lines l, m, and n are parallel. What is the value of x?Lines l, m, and n are parallel. Parallel lines labeled, top to bottom, l, m, and n. A transversal forms a...

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Answer:

XY = 13 cm

Step-by-step explanation:

Area of a triangle formula:

area = base × height / 2

a = bh / 2

Plug numbers into equation:

32.5 = b × 5 / 2

Multiply both sides by 2 to isolate the variable

65 = b × 5

Divide both sides by 5 to isolate the variable

13 = b

Check your work:

32.5 = 13 × 5 / 2

32.5 = 65 / 2

32.5 = 32.5

Correct

Answer:

13

Step-by-step explanation:

Area=½×b×h

32.5=½×b×5

32.5=5/2b

To get be multiply each side by reciprocal of 5/2 which is 2/5

b =13

Using Scientific notation, the expression (6.1 * 10⁴) + (5.2 * 10⁴) can be written as;  11.3 * 10⁴

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 × 10⁸.

Now, we want to use scientific notation to simplify;

(6.1 * 10⁴) + (5.2 * 10⁴)

Using distributive property of equality, we can say that the expression can be broken down as;

10⁴(6.1 + 5.2)

= 11.3 * 10⁴

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a. 44.4% of the time each service desk is idle.

b. The probability that both service clerks are busy is 0.22 or 22%.

c. The probability that both service clerks are idle is 11.1%.

d. On average, 0.67 customers are waiting in line in front of each service desk.

e. A customer takes, on average, 5.33 minutes to get serviced from the moment they join the queue (i.e., waiting plus service time).

a) The arrival rate is 1 customer every 6 minutes. Therefore, 10 customers arrive at each service desk every hour. The service rate is 1 customer every 4 minutes, which means that a service desk can handle 15 customers every hour.

The utilization rate of each service desk = arrival rate/service rate = (10/60) ÷ (15/60) = 2/3 Average number of customers in the system at any time (queue + service) = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2

Therefore, the average number of customers in the queue is the average number of customers in the system minus the average number of customers in service:Average number of customers in the queue = 2 - 2 = 0

Therefore, each service desk is idle for 60% - 15.6% = 44.4% of the time.

b) The probability of a service desk being busy is equal to its utilization rate = 2/3.

Therefore, the probability of both service clerks being busy is:P(both busy) = (2/3)² = 4/9 = 0.44

c) The probability of a service desk being idle is equal to 1 - utilization rate = 1 - 2/3 = 1/3.

Therefore, the probability of both service clerks being idle is:P(both idle) = (1/3)² = 1/9 = 0.11 or 11%.

d) We can use Little's Law to calculate the average number of customers in the queue:

Average number of customers in the queue = arrival rate x average waiting time in queue Average waiting time in queue = average number of customers in queue / arrival rate = 0 / (10/60) = 0 Average number of customers in the queue = 0 Therefore, on average, 0.67 customers are waiting in line in front of each service desk.

e) The average time a customer spends in the system (waiting + service) is equal to the average number of customers in the system divided by the arrival rate:

Average time in system = average number of customers in system / arrival rate Average number of customers in system = utilization/(1 - utilization) = (2/3)/(1 - 2/3) = 2 Average time in system = 2 / (10/60) = 12/10 = 1.2 minutes = 72 seconds The service time is 4 minutes. Therefore, the average waiting time is:

Average waiting time = average time in system - service time = 1.2 - 4 = -2.8 minutes We can't have negative waiting time, so the actual waiting time is 0.

Therefore, a customer takes, on average, 5.33 minutes (4 minutes of service + 1.33 minutes of waiting) to get serviced from the moment they join the queue.

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Answer:

your answer is 8

hope this helped

Answer:

8

Step-by-step explanation:

|-7 - 1|

=> |-8|

=> 8

' | | ' represents absolute value

Absolute value of -ve number is +ve

Absolute value of +ve number is + ve

When the base of the ladder is 12 feet from the wall, the base is moving away from the wall at a rate of approximately 4.125 ft/s.

When the base of the ladder is 9 feet from the wall, the base is moving away from the wall at a rate of approximately 5.5 ft/s.

To solve this related rates problem, we can use the Pythagorean theorem to relate the lengths of the ladder, the distance of the base from the wall, and the height on the wall.

Given:

Ladder length: 15 feet

Rate of change of the ladder height:

dh/dt = -5.5 ft/s (negative because the height is decreasing)

Distance from the wall: x

We can use the Pythagorean theorem to relate the lengths:

x^2 + h^2 = 15^2

Differentiating both sides with respect to time t:

2x(dx/dt) + 2h(dh/dt) = 0

We want to find dx/dt when x = 12 ft and x = 9 ft.

When x = 12 ft:

Plugging in the values:

2(12)(dx/dt) + 2h(-5.5) = 0

24(dx/dt) - 11h = 0

To find the value of h, we can substitute the values into the Pythagorean theorem equation:

12^2 + h^2 = 15^2

h^2 = 225 - 144

h^2 = 81

h = 9 ft

Substituting h = 9 ft into the equation:

24(dx/dt) - 11(9) = 0

24(dx/dt) = 99

dx/dt = 99/24

dx/dt ≈ 4.125 ft/s

Therefore, when the base of the ladder is 12 feet from the wall, the base is moving away from the wall at a rate of approximately 4.125 ft/s.

When x = 9 ft:

Using a similar process, we find h = 12 ft.

Substituting h = 12 ft into the equation:

24(dx/dt) - 11(12) = 0

24(dx/dt) = 132

dx/dt = 132/24

dx/dt ≈ 5.5 ft/s

Therefore, when the base of the ladder is 9 feet from the wall, the base is moving away from the wall at a rate of approximately 5.5 ft/s.

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Answer:

a) 1/10

b) 110

Step-by-step explanation:

A) we start by getting the total number of rolls

That would be;

11 + 22 + 7 + 8 + 13 + 19 = 80

The frequency of getting a 4 is 8

The probability that the next roll will be a 4 is;

8/80 = 1/10

b) Firstly, we get the probability of getting a 2

We have this as:

22/80

So for 400 rolls, the number of 2’s will be;

22/80 * 400

= 22 * 5 = 110

Answer:

Step-by-step explanation:

9 padlocks cost $25.20

Let the cost of a padlock be x

Then

A padlock costs $2.8

Answer: Rational

Explanation:

Any number that can be written as a fraction or mixed number is rational.

57.63004 can be written as \(57\frac{63004}{100000}\) , therefore it is rational.

Step-by-step explanation:

A can do 1/(t+2) of the task in 1 hour.

B can do 1/(t+18) of the task in 1 hour.

t×1/(t+2) + t×1/(t+18) = t/t = 1 (the full task is done)

t + t×(t+2)/(t+18) = t+2

t×(t+18) + t×(t+2) = (t+2)(t+18)

t² + 18t + t² + 2t = t² + 20t + 36

2t² + 20t = t² + 20t + 36

2t² = t² + 36

t² = 36

t = 6

Answer:

uumm

Step-by-step explanation:

Go faster 50 for insurance And 40 per hour

Blaster Jet Ski 70 for insurance and 30 per hour

50 + 40x = 70 + 30x

x is the hours

10 x = 20

x = 2

after 2 hours both will charge the same amount of money .

The value of the line integral is 65π/2

To use Green's Theorem, we need to express the given line integral as a double integral over the region enclosed by the curve C.

Let's start by finding the curl of the vector field F = (1 - y^3, x^3 + e^y^2).

∂F₂/∂x = 3x^2
∂F₁/∂y = -3y^2

So the curl of F is given by:

curl(F) = ∂F₂/∂x - ∂F₁/∂y = 3x^2 + 3y^2

Now, using Green's Theorem, we have:

∫ C (1 - y^3) dx + (x^3 + e^y^2) dy = ∬ R (3x^2 + 3y^2) dA

where R is the region enclosed by C.

To find the limits of integration, we need to find the equations of the circles. They are:

x^2 + y^2 = 4 and x^2 + y^2 = 9

The first circle has radius 2 and the second circle has radius 3. We can convert to polar coordinates to integrate over the region R:

∫ from 0 to 2π ∫ from 2 to 3 (3r^2)r dr dθ

Simplifying the integrand, we have:

∫ from 0 to 2π ∫ from 2 to 3 3r^3 dr dθ

Evaluating the inner integral first, we get:

∫ from 0 to 2π [3/4 (3^4 - 2^4)] dθ

= (3/4) (81 - 16) ∫ from 0 to 2π dθ

= 65π/2

Therefore, the value of the line integral is 65π/2

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The possible values of ∠H in the triangle ΔHIJ are 18.38° and 161.62° to the nearest tenth of a degree.

Given:In ΔHIJ, h = 9.2 inches, j = 9 inches, and ∠J = 19°.

We need to find all possible values of ∠H, to the nearest 10th of a degree

Solution:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let ∠H = xBy applying the angle sum property of the triangle, we get

∠H + ∠I + ∠J = 180°

⇒ x + ∠I + 19° = 180°

⇒ ∠I = 180° - x - 19°

⇒ ∠I = 161° - x

Using the sine rule, we get

sin x/sin 19° = h/jsin x/sin 19°

= 9.2/9sin x

= sin 19° × 9.2/9sin x

= 0.3184x

= sin⁻¹ 0.3184

∴ x = 18.38° or

x = 161.62°

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In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

Answer:

f(4) = 6

Step-by-step explanation:

Given the rule f(n) = 4f (n - 1) + 2 where f(1) = 3, f(n) is just a fancy way to name the variable y. As you've seen before, there are equations that are usually y equals x and something. For example:

y = mx + b

is the same thing as

f(n) = y = mn + b.

It might be that you have multiple of the same equation where f(n) and f(x) have two different outcomes.

The f(n) part (bolded) is the "x variable" in this equation. So in f(1), n = 1.

f(n) = 4f (n - 1) + 2

f(n) = (4fn - 4f) + 2

f(n) = (n) + 2

f(1) = 1 +2

3 = 3

Now do the same thing for f(4):

f(n) = 4f (n - 1) + 2

f(n) = (4fn - 4f) + 2

f(n) = (n) + 2

f(4) = 4 + 2

f(4) = 6

Therefore, the truth value of Proposition 2A is False.

To determine the truth value of Proposition 2A, let's substitute the given truth values for the variables:

A = True

B = True

X = False

Y = False

Now let's evaluate the truth value of each component of the proposition:

(X ⊃ A) • (B ⊃ ∼ Y):

(False ⊃ True) • (True ⊃ ∼ False)

(True ⊃ True) • (True ⊃ True)

True • True

True

(B ∨ Y) • (A ⊃ X):

(True ∨ False) • (True ⊃ False)

True • False

False

[(X ⊃ A) • (B ⊃ ∼ Y)] ⊃ [(B ∨ Y) • (A ⊃ X)]:

True ⊃ False

False

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Answer: The one on the bottom right.

Step-by-step explanation:

Symmetry is basically like a mirror. The line of symmetry is the exact point where it starts to reflect.

A symmetrical shape can also be folded onto itself equally.

Looking at the photo, the picture on the bottom right is the left part of the figure.

Answer:

Refer to the attached file

Hope it helps..

Reason:

There's a 30% chance they buy the popcorn, which means there's a 70% chance they don't buy it.

100% - 30% = 70%

Then convert the 70% to 0.7

Answer:

0.7 or 70%

Step-by-step explanation:

0.3 * 100 = 30%

100%-30% = 70%

You either buy or not. If 30% you don't then 70% you do.

A "place value" is just a number containing a decimal point whereby each digit place value equals ten times every place value to its right

In mathematics, every digit in an integer does have a place value.

Thus, a "place value" is just a number containing a decimal point whereby each digit place value equals ten times every place value to its right

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Answer: 98*

Alternate exterior angles are equal

Answer: 98 degrees

Step-by-step explanation:

98 degrees and x are alternate exterior angles.

Answer:

Step-by-step explanation:

If you are implying that the equation is "6x = 60"

Divide both sides by 6 to get just x by itself, then you'd have your answer.

X  = 10

Answer:

y= 3x + 5

Step-by-step explanation:

Some examples

(1,8)

8= 3 (1) + 5

8 = 3 + 5

8= 8

(2,11)

11= 3 (2) + 5

11= 6 + 5

11= 11

Answer:

The shaded segment  = The arc area - The triangle

The arc area = pi x radius^2 x angle/360

                     = pi x 9^2 x (360-270)/360 = 63.61 (m2)

The triangle area = 9 x 9/2 = 41.5 (m2)

(because this is right triangle)

=> The shaded segment = 63.61 - 41.5 = 22.11 (m2)

If the stream narrows from 30 feet to 20 feet, the width of the stream has narrowed, and the velocity should increase. The correct answer is b.

According to the principle of conservation of mass, when the width of a stream narrows, the volume flow rate (the amount of water passing through a given point per unit time) must remain constant if there are no other factors involved.

The volume flow rate (Q) can be calculated as the product of the cross-sectional area (A) and the velocity (v): Q = A * v.

When the width of the stream narrows from 30 feet to 20 feet while the volume flow rate remains constant, the cross-sectional area decreases. To maintain a constant volume flow rate, the velocity must increase.

This is because the same amount of water is passing through a smaller cross-sectional area, requiring an increase in velocity to compensate for the reduced width.

Therefore, the correct statement is that the width of the stream has narrowed, and the velocity should increase.

The correct answer is b.

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The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.

To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.

The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.

Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.

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