To begin a bacteria study, a petri dish had 2700 bacteria cells. Each hour since, the number of cells has increased by 5. 2%.



Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.



Write an exponential function showing the relationship between y and t.

Answer:

Exact weight of quarters now in circulation in the United States  (continuous random variable )

Shoe sizes of humans (discrete random variable)

Political party affiliations of adults in the United States ( random variable)

Step-by-step explanation:

continuous random variable: this is a random experiment where the data usually assume an infinite mode. meaning it is continuous.

discrete random variable: this is the assigning of values based on the outcome of a radom experiment.

random variable: a random variable is a set of possible outcomes from a random experiment

The minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.

Total surface area = Area of 2 similar trapeziums + Area of rectangles of 4 different rectangles

area of a triangle = 1/2 ×Base×Height and area of a rectangle is Length×Breadth.

= 2×1/2(7+3)×3+8×5+8×3+8×3+8×7

= 174 square inches

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Using ratio and proportion, Louie is correct.

Ratio is defined as the relationship between two quantities. On the other hand, proportion is defined as the equality between two or more ratios.

From the given graph (see attached photo), the coordinates of Point F and Point G is (4, 8) and (-6, -7).

If the ratio of FP to PG is 4 to 1, then the ratio of the horizontal distance and vertical distance between the two endpoints is also 4 to 1.

FP : PG = 4 : 1

FP/PG = 4/1 = 4

x-coordinate of P

(4 - x)/(x - -6) = 4

(4 - x) = 4(x + 6)

4 - x = 4x + 24

-5x = 20

x = -4

y-coordinate of P

(8 - y)/(y - -7) = 4

(8 - y) = 4(y + 7)

8 - y = 4y + 28

-5y = 20

y = -4

Hence, the coordinates of Point P is (-4, -4).

Therefore, Louie is correct, while Nicky is mistaken probably while setting up the proportion and solving for the coordinates.

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We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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Answer:

230 g

Step-by-step explanation:

4.3 x molar mass of NH4Cl

Molar Mass of NH4Cl = 14.0067 + 4x1.0079 + 35.453 = 53.491

4.3 x 53.491 = 230 g

The probability that the conveyor belt will function for a month without a breakdown is approximately 0.061 (accurate to 3 decimal places after the decimal point).

To find the probability that the conveyor belt will function for a month without a breakdown, given that the number of monthly breakdowns follows a Poisson distribution with λ = 2.8, we will use the Poisson probability formula:

P(X = k) = (e^(-λ) * (λ^k)) / k!

In this case, k = 0 (no breakdowns) and λ = 2.8. Plug these values into the formula:

P(X = 0) = (e^(-2.8) * (2.8^0)) / 0!

P(X = 0) = (e^(-2.8) * 1) / 1

Now, use a calculator or software to compute e^(-2.8) and multiply it by 1:

P(X = 0) ≈ 0.06078

So, the required probability is approximately 0.061 (accurate to 3 decimal places after the decimal point).

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For the construction of an inscribed circle the required construction that must be known is the angle bisector. The correct option is (A).

The angle bisector is a line that divides an angle into two equal parts. For a circle inscribed in a triangle the line joining the center to the vertex is the angular bisector of the interior angle.

The diagram for the given case can be drawn as follows,

For the circle inscribed in the circle, all the sides are tangents.

By the property of tangents to a circle ∠ODB and ∠OFB are right angles.

Now, in ΔODB and ΔOFB the relation is obtained as,

∠ODB = ∠OFB  (right angles)

OB = OB           (Common sides)

And, OD = OF  (radius of the circle)

⇒ ΔODB ≅ ΔOFB (by RHS criteria)

This implies that ∠ODB ≅ ∠OFB.

Thus, the line joining the centre and the vertex of triangle bisects its angles.

Hence, for the given case the required construction to be known is the angle bisector of triangle.

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By choosing the annual contract and breaking it after 5 months, your parents would lose $574.00.

If you enter into an annual contract at $467.00/month and break it after 5 months, you would have paid:

= $467.00 x 5

= $2,335.00

Since breaking the annual contract incurs a penalty of 2 months' rent, your parents would need to pay an additional of:

= $467.00 x 2

= $934.00

If parents opted for the month-to-month contract at $539.00/month, the total cost for 5 months would be:

= $539.00 * 5 month

=  $2,695.00.

So, by choosing the annual contract and breaking it after 5 months, your parents would lose:

= $3,269.00 - $2,695.00

= $574.00.

Full question "Your parents are considering renting you an apartment instead of paying room and board at your college. The month-to-month contract is $539.00/month and the annual contract is $467.00/month. If you break the annual contract, there is a 2-month penalty. If you enter into an annual contract but decide to leave after 5 months, how much do your parents lose by not doing the month-to-month contract."

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None of the given options (i.e. a, b, c, or d) is correct.

Given the prices of consumer items, we can find the estimate of the current CPI.

The percentage change in the price of the consumer item over time can be given as:

Percentage change = (Current Price − Price in 1983)/Price in 1983 × 100%

Now, using the percentage change we can find the average percentage change (increase or decrease) in prices. We calculate the average percentage change by finding the sum of the percentage change in prices of all items and then dividing it by the number of items.

Thus, we have:

Average percentage change = [(126.85−67.45)/67.45 + (29.95−15.25)/15.25 + (2.25−1.15)/1.15 + (44.25−22.85)/22.85]/4Average percentage change = 4.4188%

Now, the current CPI can be found using the following formula:

Current CPI = CPI in 1983 × [1 + (Average percentage change)/100]Current CPI = 100 × [1 + 4.4188/100] ≈ 104.42 ≈ 104

Therefore, the reasonable estimate of the current CPI is 104.

None of the given options (i.e. a, b, c, or d) is correct.

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By solving the given equation and then substituting solution in original equation we found out that x=3 and x=-7 are extraneous solution.

The extraneous solutions are the solutions that does not work in the original equation.

Original equation

\($\log _{4}(x)+\log _{4}(x-3)=\log _{4}(-7x+21)$\)

Now we will simplify this

\(\log _{4}(x(x-3))=\log _{4}(-7 x+21)$\\\\x(x-3)=-7 x+21\\\\&x^{2}-3 x=-7 x+21 \\\\\\&x^{2}-3 x+7 x-21 =0\\\\&x^{2}+4 x-21=0\\\\\\&x^{2}-3 x+7x-21=0\\\\\\(x-3)(x+7)=0\\x=3,-7\)

Now, we will determine the extraneous solution, by substituting  x=3 and x=-7 in the originally given equation.

Substituting  x=3,

\(\log _{4}(3)+\log _{4}(3-3)=\log _{4}(-21+21) \\\\\log _{4}(3)+\log _{4}(0)=\log _{4}(0)\)

As we know log(0)  is undefined , Hence x=3 is extraneous solution

Now Substituting  x=-7

\(\log _{4}(-7)+\log _{4}(-7-3)=\log _{4}(-7(-7)+21)\\\\\log _{4}(-7)+\log _{4}(-10)=\log _{4}(-28)\)

As we know log is not defined for negative numbers hence x=-7 is extraneous solution

By solving the given equation and then substituting solution in original equation we found out that x=3 and x=-7 are extraneous solution

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Answer:

30.84 cm

Step-by-step explanation:

Formula for perimeter of semi-circle = πr + 2r

Radius (r) = 6 cm

π = 3.14

Perimeter

= πr + 2r

= 3.14(6) + 2(6)

= 3.14(6) + 12

= 18.84 + 12

= 30.84 cm

_________

Hope it helps ⚜

Answer:

30.85 cm to 2 d.p.

Step-by-step explanation:

The perimeter is made up of the diameter ( = 2*radius) and half a full circle

= 6*2 + 1/2 * π* 6

= 12 + 3π

= 30.849

Answer:.

Step-by-step explanation:

Answer:

n = 23

Step-by-step explanation:

Let Sara's number be n.  Then -3(n - 11) = -36

Solve for n - 11 by dividing both sides by -3:  n - 11 = 12.

Adding 11 to both sides yields n = 23

Answer:

i believe that the correct answer is -1

Answer:

Step-by-step explanation:

Think of it as a triangle.

They give you the length of the bottom side and the location of the tops of the buildings.

You need to find the hypotenuse ( the longest side or the length of the rope)

Use the pythagorean theorem

\(a^{2} + b^{2} = c^{2}\)

10 ^2 + 4^2= c^2

100 + 16 = c^2

116 = c^2

c is about 10.77

The length of the rope is 10.77 m

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the length of the rope be = H

Let the distance between the two buildings be L = 10 m

Let the height of the first building be A = 8 m

Let the height of the second building B = 4 m

Now ,

The expressions form a right angled triangle with the base of the triangle has a length of 10 m and the height of the triangle is 4m

Height of the triangle = A / 2 = 4m

So , the hypotenuse of the triangle will be the length of the rope

From the Pythagoras Theorem , The hypotenuse² = base² + height²

So , H² = ( A / 2 )² + L²

Substituting the values , we get

H² = 4² + 10²

H² = 16 + 100

H² = 116

Taking square roots on both sides , we get

H = √116

H ≈ 10.77 m

Therefore , the value of H is 10.77 m

Hence , The length of the rope is 10.77 m

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it's true because it gives interset or compensation amount to the individuals or organizations which motivates people to save their money in a saving account

fourty four percent hope this helps !

Answer

24 frames per second

Step-by-step explanation:

Total frames=86,400

Total time=1 hour

Find frame per second

1 hour= 60 minutes*60 seconds

1 hour=3600 seconds

Frame per second=Total frames/Total number of seconds

=86,400/3600

=24 frames per second

Effective annual interest rates: 12.6825% for the first 14 years, 19.56182% thereafter.

Balance in present value: $444,117.28.

Balance in future value: $6,903,087.93.

   The effective annual interest rates for the given operations are 12.6825% for the first 14 years and 19.56182% thereafter. These rates take into account compounding on a monthly basis and reflect the actual annual return on the investments.

To calculate the effective annual interest rate for the first 14 years, we can use the formula: (1+monthly interest rate)12−1(1+monthly interest rate)12−1. Plugging in the monthly interest rate of 1%, we find that the effective annual interest rate is 12.6825%.

For the period after 14 years, the effective annual interest rate can be calculated using the same formula, but with the monthly interest rate of 1.5%. Substituting this value, we obtain an effective annual interest rate of 19.56182%.

   The balance in present value can be calculated as the sum of the present values of the contributions and withdrawals. The present value of a cash flow can be calculated using the formula: FV(1+r)n(1+r)nFV​, where FV is the future value, r is the interest rate, and n is the number of periods.

To calculate the balance in present value, we need to determine the present value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in present value is $444,117.28.

   The balance in future value can be calculated as the sum of the future values of the contributions and withdrawals. The future value of a cash flow can be calculated using the formula: PV×(1+r)nPV×(1+r)n, where PV is the present value, r is the interest rate, and n is the number of periods.

To calculate the balance in future value, we need to determine the future value of the contributions, withdrawals, and future contributions. Applying the formula for each cash flow and summing them up, we find that the balance in future value is $6,903,087.93.

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Answer:

425.39

Step-by-step explanation:

The problem says you need a simple interest bridge loan.

You need to finance $73,000.

The interest rate is 6% (0.06)

You need the loan for 9 months.

The formula for simple interest rate is the following:

Where SI is the simple interest. P is the principal or money borrowed. r is the interest rate in decimal form. t is the time in years.

As you need the loan for 9 months, we need to convert it to years, as follows:

Now, replace the known values and solve for SI:

You will pay $3,285 interest for the loan.

Answer: C

Step-by-step explanation:

The area of the domain enclosed by the curve with parametric equations x = tsin t, y = cost, t ∈ [0, 2π] is 2π + 2.

The parametric equations given are:

x = t sin t
y = cos t

To find the area of the domain enclosed by the curve, we can use the formula for the area of a region bounded by a curve given in parametric form:

A = ∫[a,b] y dx

where a and b are the limits of the parameter t that describe the domain of the curve.

In this case, we have:

a = 0
b = 2π

So, we need to compute:

A = ∫[0,2π] cos(t) (t sin(t)) dt

Using integration by parts with u = t and dv = sin(t) dt, we get:

A = [t cos(t)]|[0,2π] - ∫[0,2π] cos(t) dt + ∫[0,2π] sin(t) dt

The first integral evaluates to:

[t cos(t)]|[0,2π] = 2π

The second integral evaluates to:

∫[0,2π] cos(t) dt = [sin(t)]|[0,2π] = 0

The third integral evaluates to:

∫[0,2π] sin(t) dt = [-cos(t)]|[0,2π] = 2

Therefore, the area of the domain enclosed by the curve is:

A = 2π - 0 + 2 = 2π + 2

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Answer:

576 cm squared

Step-by-step explanation:

The method for determining the similar relationship between the parameters of two equations has been explained below.

The relationship between parameters in two equations depends on the specific equations and parameters involved. In general, parameters are constants or variables that are used to define or modify the behavior of a mathematical or physical system.

If two equations have the same parameters, then changes in those parameters will affect the behavior of both equations in the same way and if they have different parameters, then changes in those parameters may affect the behavior of the equations differently. In general, to determine the relationship between parameters in two equations, you would need to analyze the equations and their specific parameters to understand how they are related.

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Both are vertical angles (opposite)

So, they are congruent ( equal)

6a +11 = 2a+83

Solve for a:

6a -2a = 83-11

4a= 72

a= 72/4

a= 18

Value of the angles:

6a+11 = 6(18)+11 = 108+11 = 119°

2a+83 = 2(18)+83 =

Doug passed the matt as they both finished their sixth lap. If both boys ran at a constant speed, with doug running 2 miles an hour faster than matt, the speed of the matt is 10 miles per hour.

Doug ran 2 miles an hour faster than Matt, so let Matt’s speed equal x miles per hour. Then  the Doug’s speed equals to  x + 2 miles per hr. Each of the lap is one-quarter of a mile, so  the Doug runs 1.5 miles the time it takes Matt to run  1.25 miles. Place this information in a chart:

                                Rate                        Time

Doug                      x+2                             1.5/x+2

Matt                         x                                   1.25/x

 Doug and Matt took the same amount of time from the time as Doug started, lets make an equation by setting the two times in the equation equal to each other, and then solve for x:      

 1.5/x+2 = 1.25/x

 1.5x = 1.25(x+2)

 1.5x = 1.25x+2.5

 0.25x =  2.5

  x = 10

The Matt ran at 10 miles per hour.      

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Answer:

The hand moved \(\bf \frac{3}{4}\) of a complete turn.

Step-by-step explanation:

The hand moved from 3 to 12, that is, it moved:

12 - 3 = 9 hours

In a clock, 12 hours represent a complete turn.

∴ Using the unitary method:

12 hours    ⇒     1 turn

1 hour        ⇒     \(\frac{1}{12}\) turns

9 hours     ⇒     \(\frac{1}{12}\)  × 9 = \(\frac{9}{12}\)

                                     = \(\bf \frac{3}{4}\) turns    (simplified)

∴ The hand moved \(\bf \frac{3}{4}\) of a complete turn.

The answer is  \(\boxed{\frac{3}{4}}\).

To find the fraction of a complete turn it moved in this case, take the ratio between hours covered between 3 and 12, and the hours covered in a complete turn.