A radioactive isotope has a half-life of 1,920 years. Let f(t)
be the amount of isotope, in milligrams, that is present after t years. If the sample originally contained 21 milligrams, write an equation modeling this situation.
F(t)=

Based on the image, we can infer that the router cannot cover the kitchen area.

To calculate if the router covers the living room and kitchen area, we must identify the area that the router can cover. In this case, the router covers an area of 850 square feet. However, we must take into account that this area is counted around the router.

From the above, we can infer that the router has signal coverage of 14 meters around it, so it would only cover the living room area.

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Answer:

Step-by-step explanation:

Answer:    x=a/3      x=a/5

Step-by-step explanation:

15x²-2ax = a²          subtract a² from both sides

15x²- 2ax - a² = 0

You would solve this like you would any quadratic.  Factor.

Start my multiplying the first and last coefficients

15(-a²)  = -15a²    =>find 2 numbers that multiply to this but add to middle

                                term (-2a)

-5a   and   +3a     multiply to -15a² and adds to -2a

Substitute the middle term with the numbers we just found, keeping the x

15x²- 2ax - a² = 0

15x²- 5ax+3ax - a² = 0         > group the first 2 terms and last 2

(15x²- 5ax)(+3ax - a²)= 0      > this is not your factors, you need to take

                                                 GCF out of each grouping

5x(3x-a)+a(3x-a)=0              >if the parenthesis is same, you did good

                                                now the parenthesis is your GCF and one of

                                                your factors, whatever is left is your other

                                                factor

(3x-a)(5x-a)=0                        > set each factor = 0 and solve for x

(3x-a)=0         and             (5x-a)=0  

x=a/3                                    x=a/5

a. The slopes of the lines are:

Slope of line 1 = -5/2

Slope of line 2 = 7/5

Slope of line 3 = -5/2

b.

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (2 - 7) / (-2 - (-4))

m = (-5) / (2)

m = -5/2

m = (-8 - (-1)) / (-5 - 0)

m = (-7) / (-5)

m = 7/5

m = (-2 - 8) / (2 - (-2))

m = (-10) / (4)

m = -5/2

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Neither

Line 1 and Line 3 : Parallel

Line 2 and Line 3 : Neither

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Ilana ran a total distance of 23.725 miles during her first week of training for a half marathon.

Distance refers to the amount of space or physical separation between two points or objects. It is a measure of how far apart two objects or points are from each other.

Ilana will run 4.125 miles each day for the first three days, which gives a total distance of:

4.125 miles/day × 3 days = 12.375 miles

For the next two days, she will run 5.675 miles per day, which gives a total distance of:

5.675 miles/day × 2 days = 11.35 miles

To find the total distance that Ilana ran during her first training week, we simply add the distances from the first three days and the next two days:

12.375 miles + 11.35 miles = 23.725 miles

Therefore, Ilana ran a total of 23.725 miles during her first week of training.

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The exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].

The function B(t) can be represented by an exponential function of the form:

B(t) = a[tex]b^t[/tex]

where 'a' is the initial number of bacteria and 'b' is the growth factor or rate at which the number of bacteria quadruples.

Given that the initial number of bacteria is 15 and the number of bacteria quadruples every hour, we can express 'b' as:

b = 4¹ = 4

Substituting the values of 'a' and 'b' in the general form of exponential function, we get:

B(t) = 15 (4[tex])^t[/tex]

Therefore, the exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].

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The simplified expression based on tej values given is 3a⁴b + 4a³b³.

An expression is a combination of variables, constants, and operators that can be evaluated to produce a single value. In programming languages, expressions are used to represent computations and are often used to assign values to variables, compare values, or perform mathematical operations. Expressions can be simple, such as a single variable or constant, or complex, involving multiple operations and variables.

It should be noted that to simplify the expression a²b(3a² +4ab²), we can distribute the a²b term to the terms inside the parentheses using the distributive property of multiplication:

a²b(3a² +4ab²) = 3a⁴b + 4a³b³

Therefore, the simplified expression is 3a⁴b + 4a³b³.

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You would need an additional $3.88 to buy the skateboard.

We need to calculate the total cost, including sales tax.

The sales tax rate is 6%, so the tax on a skateboard costing $98 would be as follows:

tax = 0.06 x $98 = $5.88

Consequently, the skateboard would have a total cost of:

total cost = $98 + $5.88 = $103.88

Since you have $100 to spend, you do not have enough money to buy the skateboard. You would need:

additional money = $103.88 - $100 = $3.88

Therefore, you would need an additional $3.88 to buy the skateboard.

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Answer: 53 ft

Step-by-step explanation:

The perimeter of a polygon is the sum of all sides. In this example, the sides are 4 ft, 20 ft, 18 ft, and 11 ft, so the perimeter is

4+20+18+11=53 ft

Answer:

x = 3,

y = -2

Step-by-step explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2

Therefore , the solution of the given problem of unitary method  comes out to be  a 95% degree of certainty that the genuine average commute time falls within this range.

To complete the work, the well-known straightforward strategy, actual variables, and any essential components from the very first and specialised inquiries can all be utilised. In response, customers might be given another opportunity to sample the product. Otherwise, important advancements in our comprehension of algorithms will be lost.

Here,

We may use the following calculation to determine the 95% confidence interval for the actual average commute time:

=> CI = x' ± t*(s/√n)

Finding the essential t-value is the first step. We can apply a two-tailed t-test with a significance level of = 0.05/2 = 0.025 because we have 16 useable findings (sample size: n = 16) and

we require a 95% confidence interval. The crucial t-value, which we determine using a t-distribution table or calculator, is roughly 2.131.

=> CI = 21.4 ± 2.131*(1.8/√16)

=>  21.4 ± 0.95

The genuine average commute time has a 95% confidence interval of 20.45 to 22.35 minutes.

Based on our sample of 16 travel times, we can thus say with a 95% degree of certainty that the genuine average commute time falls within this range.

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If a vehicle uses 2 gallons of gasoline to travel 18¹/₂ miles, at this rate, the vehicle can travel 9¹/₄ miles per gallon of gasoline.

The rate refers to the average speed of the vehicle.

The rate also describes the unit rate or the rate expressed as a percentage or in terms of speed.

The number of gallons of gasoline used to travel 18¹/₂ miles = 2 gallons

The total distance traveled using two gallons of gasoline = 18¹/₂ miles

The average distance traveled per gallon of gasoline = 9¹/₄ miles (18¹/₂ ÷ 2)

Thus, on the average, the vehicle can travel 9¹/₄ miles miles per gallon of gasoline.

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A vehicle uses 2 gallons of gasoline to travel 18 1⁄2 miles. At this rate, how many miles can the vehicle travel per gallon of gasoline?

Answer:w = 74.66 mph

d = 19.92 degrees

Step-by-step explanation:

Let's call the speed of the wind "w" and the direction angle of the wind "d". We can use vector addition to solve for these unknowns.

First, let's find the direction of the plane. The bearing of N * 65 deg * E can be represented as a vector with an initial point at the North pole and a terminal point 65 degrees east of due north. Since the plane is flying on this bearing, its direction vector is the same as the bearing vector. We can find the components of this vector as follows:

cos(65) = x / 1

x = cos(65)

y = sin(65)

So the direction vector of the plane is <cos(65), sin(65)>.

Next, let's find the ground speed vector. We can represent this vector as the sum of the plane's airspeed vector and the wind vector:

ground speed = airspeed + wind speed

We know that the magnitude of the ground speed vector is 390 mph, and we know the direction angle of the ground speed vector is 30 degrees. We can use this information to set up two equations:

|airspeed + wind speed| = 390

tan(d) = (wind speed)_y / (wind speed)_x

Since we know the direction vector of the plane, we can express the airspeed vector in terms of this vector as follows:

airspeed = 360 <cos(65), sin(65)>

Now we can substitute the airspeed vector and the wind speed vector into the equation for the ground speed vector, and use the fact that the magnitude of the ground speed vector is 390 to solve for the components of the wind speed vector:

|360 <cos(65), sin(65)> + <(wind speed)_x, (wind speed)_y>| = 390

Squaring both sides and using the fact that cos^2(x) + sin^2(x) = 1, we get:

129600 cos^2(65) + 129600 sin^2(65) + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100

Simplifying, we get:

51840 + 720(wind speed)_x cos(65) + 720(wind speed)_y sin(65) + (wind speed)_x^2 + (wind speed)_y^2 = 152100

Substituting the equation for the direction angle of the wind and simplifying, we get:

51840 + 720w cos(65 - d) + w^2 = 152100 tan^2(d)

We now have two equations and two unknowns: w and d. We can solve for them using algebra or a numerical solver. Using a numerical solver, we find:

w = 74.66 mph

d = 19.92 degrees

Therefore, the speed of the wind is 74.66 mph, and its direction angle is 19.92 degrees.

Answer:

9ft

Step-by-step explanation:

From the left side, you know one length is 4ft abd the one below is 5ft, when you add them together its the answer of 9ft, which is the missing side.

it's 9ft

its 9ft because when you add 4 +5 you get 9. two rectangles a present in the diagram. the 4ft and 5ft are apart of the rectangle where the missing side is, adding those two together would give you 9 and in a rectangle sides facing each other are epual therefore the missing side is 9

Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.

The rate at which an object's velocity varies with respect to time is known as its acceleration. It is a vector quantity whose definition is the product of the velocity change and the time period during which the change takes place. Depending on the direction and size of the velocity change, acceleration may be positive, negative, or zero. Acceleration in physics is frequently represented by the letter "a," and its SI unit is metres per second squared (m/s2).

To find when the bullet will hit the ground, we need to find the time at which y = 0.

y = vo sin(a) t - (1/2)g[tex]t^2[/tex], where g is the acceleration due to gravity (9.8 m/s^2).

Setting y = 0, we get:

0 = vo sin(a) t - (1/2)g[tex]t^2[/tex]

Solving for t using the quadratic formula, we get:

Since we want the time when the bullet hits the ground, we take the positive root:

t = (vo sin(a) + √((vo sin(a))^2 + 2gy)) / g

Plugging in the values given, we get:

t = (550 m/s * sin(a) + √((550 m/s * sin(a))^2 + 2 * 9.8 m/s^2 * 0)) / 9.8 m/s^2

Simplifying, we get:

t = (550 m/s * sin(a)) / 9.8 m/s^2

t = 35.27 seconds (rounded to two decimal places)

To find how far from the gun the bullet will hit the ground, we need to find the value of x at this time:

x = vo cos(a) t

Plugging in the values given, we get:

x = 550 m/s * cos(a) * 35.27 s

x = 18602.57 meters

Rounding to the nearest meter, we get that the bullet will hit the ground 18603 meters away from the gun.

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The probability that both events A and B will occur is 1/3 or approximately 0.3333.

To find the probability of both events A and B occurring, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is a 4 or less.

In a standard six-sided die, there are four outcomes (1, 2, 3, 4) that satisfy this condition. Out of the six possible outcomes, four are favorable, so the probability of event A is 4/6 or 2/3.

Event B: The second die is even.

In a standard six-sided die, there are three even outcomes (2, 4, 6) out of the six possible outcomes.

Therefore, the probability of event B is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the probabilities of each event:

[tex]P(A and B) = P(A) \times P(B) = (2/3) \times (1/2) = 1/3[/tex]

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Answer:

x2+10x+25

Step-by-step explanation:

It goes like this:

X2+2*1x*5+5*5

Step-by-step explanation:

58 g = 660 g * ( 1/2)^n

58 / 660 = (1/2) ^n       LOG both sides

-1.056 = n log 1/2

n = 3.508 half lives  

     3. 508  x 10 min = ~ 35.1 min

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]

[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]

Hi! To determine if two lines are parallel given their equations, follow these steps:

1. Identify the slopes of the lines from their equations.

If the equations are in the slope-intercept form (y = mx + b), the slope is the coefficient of x (m). If the equations are in standard form (Ax + By = C), you can find the slope by rearranging the equation to the slope-intercept form.

2. Compare the slopes of both lines. If the slopes are equal, the lines are parallel.

In summary, given their math equations, you need to describe their slopes and check if they are equal to determine if the lines are parallel.

Hi to confirm that two lines are parallel lines given their equation you the gradient which is the value of x in the equation y=mx + c. Where m is the gradient

The value of x if the line BD is the perpendicular bisector of AC is 11.5

From the question, we have the following parameters that can be used in our computation:

The figure where the line BD is the perpendicular bisector of AC.

To calculate the value of x, we use the following equation by setting the line segments equal to each other

3(2x - 8) = 45

Divide both sides of the above equation by 3

2x - 8 = 15

So, we have the following equation

2x = 23

Divide both sides of the above equation by 2

x = 11.5

Hence, the calculated value of x is 11.5

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Answer:

17/x = x/8

x^2 = 136, so x = 2√34

The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.

There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.

Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.

Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:

P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)

= (1/3) x (1/3)

= 1/9

Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.

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The type of pay modeled in the given image is c. Commission pay.

Commission pay is a form of variable pay where the employee is paid based on the percentage of sales that they make. In this case, the y-axis represents the pay earned and the x-axis represents the sales made.

The straight line represents the commission rate, which is constant at 15%. The more sales the employee makes, the more pay they will earn.

Therefore the correct option is C.

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An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (50.25 - 2)/(5 - 0)

Slope (m) = 48.25/5

Slope (m) = 9.65.

At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 9.65(x - 0)

y = 9.65x + 2

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The equation is true based on the model is B) (-3) + 5 = 2.

If we consider the circles on the left as negative units and the circles on the right as positive units.

Then we can see that there are 5 positive units and 3 negative units, so the sum is

= 5 - 3

= 2.

Therefore, the correct equation is: B) (-3) + 5 = 2.

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Answer:

Step-by-step explanation:

The present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

The formula for the present value of a future amount under quarterly compounding is:

PV = FV / (1 + r/4)⁴ⁿ

where PV is the present value,

FV is the future value, r is the interest rate per year, and n is the number of years.

In this case, FV = $100, r = 0.09 (9%), n = 3 years, and the interest is compounded quarterly

so the interest rate per quarter is r/4 = 0.0225.

Plugging these values into the formula, we get:

PV = $100 / (1 + 0.0225)¹² = $73.67

Therefore, the present value of $100 to be received after 3 years at 9% compounded quarterly is $73.67.

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The wrong formula was used. The correct method is: area of sector = 115/360 * 255 ≈ 81.46 square feet.

The area of a sector is calculated by using the formula:

Area of sector = ∅/360 * πr², where:

r is the radius of the circle

∅ is the central angle measure.

The error made was that a wrong method/formula was used in finding the area of sector.

Given the following:

Area of circle = 255 square feet (πr²)

∅ = 115°

Note that πr² represents the area of a circle, therefore, substituting the values into the formula, we have:

Area of sector = 115/360 * 255

Area of sector ≈ 81.46 square feet

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Answer:

surface area=bh+2ls+lb

Step-by-step explanation:

If you think it is too long to remember, just find the area of each of the shapes on it and add them together.

Hope this helps :)

From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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Answer:

distance = rate x time

where distance is 300 kilometers and time is t hours. Rearranging this formula to solve for rate, we get:

rate = distance / time

Substituting the given values, we get:

r = 300 / t

Therefore, the equation that represents the train's rate in kilometers per hour based on how many hours the trip takes is r = 300/t.

Step-by-step explanation: