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The function that represent the number of transactions per month is aₙ=10×2ⁿ⁻¹.

Given that,

Month, n       Number of Transactions, f(n)

   1                                 10

   2                                 20

   3                                 40

   4                                 80

Here, in the number of transactions 10, 20, 40, 80.

First term =a=10, common ratio = r = 20/10 =2, 40/20 =2 and 80/40 =2.

Use the formula aₙ=arⁿ⁻¹. Where, a = first term of the sequence, r= common ratio and n = number of terms.

Now, aₙ=10×2ⁿ⁻¹

Therefore, the function that represent the number of transactions per month is aₙ=10×2ⁿ⁻¹.

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They have to sell D. 75 shirts to make a profit of $300.

The total cost of buying and printing the shirts was $600.

In order to make a profit of $300, they would therefore have to raise:

= Cost + profit

= 600 + 300

= $900

As they are selling each shirt $12, the number of shirts they would have to sell to get to $900 is:

= 900 / 12

= 75 shirts

They would therefore have to sell 75 shirts in order to make a profit of $300.

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$16,000 was invested in the account earning 6% interest and

$10,500 was invested in the account earning 5% interest.

Given that, Ngoc invests a total of $26,500 in two accounts. The first account earned an annual interest rate of 6% and the second account earned an annual interest of 5%. At the end of one year, the total amount of money gained was $1485.

We need to find how much was invested into each account.

A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.

Now,

Let x be the amount of money invested at 6% interest.

Let y be the amount of money invested at 5% interest.

Thus, x +y = 26,500-----(1) and 0.06X + 0.05Y = 1485-----(2)

Multiply 0.06 to the equation x +y = 26,500, so we get 0.06x+0.06y=1,590-----(3)

By subtracting equation (2) from (3), we get

0.01y=105

⇒y=10,500

Substituting y=$10500 in equation (1), we get x=$16,000

Therefore, $16,000 was invested in the account earning 6% interest and

$10,500 was invested in the account earning 5% interest.

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Answer:

70°

Step-by-step explanation:

RSTU is a kite,

Sum of 4 internal angles= 360°

m∠U=m∠S=80

m∠T= 360° - (130°+80°+80°)= 70°

Answer:

Step-by-step explanation:

Answer:

the formula for the area of a trapezoid is area =(top + bottom)/2 x height

using the given information we can solve

for x:

234 = (20+32)/2 X

234 = 52/2 X

234 = 26 X

X=234/26

X= 9 units

Area:

Approximately 211.24 square feet

Explanation:

Im going to assume you are asking for the surface area of a sphere with a diameter of 8.2ft. The equation to find this is: \(A = 4\pi r^2\)

Firstly, we need to convert the diameter to the radius. The diameter is always twice the length of the radius, so the radius must be 4.1ft

Plug this value in:

\(A = 4\pi (4.1)^2\\A = 4\pi(16.81)\\A = 211.24\)

Answer:

127.24

Step-by-step explanation:

A= 3.14(pie) r^2

A=3.14(pie) 9^2

A=254.47 ÷2

A= 127.24

It is a horizontal line as there is no y-axis in its equation.

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.

Correct answer will be a. 0.007

The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.

Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.

Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.

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Answer:

3:1

Step-by-step explanation:

It’s three times the original

Answer:

28.25

Step-by-step explanation:

simple addition
6.35 + 10.2 + 5.85 + 5.85 = 28.25

The height of the frame will remain the same.

The height of the frame is 6 inch

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

A frame:

The frame can be considered as a rectangle.

Wide = 9 inch

Height = 6 inch

_______

|               |

|               | 6-inch (height)

|               |

|_______|

  9-inch (wide)

If wide = 3 inches the height remains the same.

Thus,

The height of the frame will remain the same.

The height of the frame is 6 inch

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Answer:

not enough information

Step-by-step explanation:

There are no options

The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

What is the fraction?

A fraction is a part of a whole or a ratio of two numbers expressed with a horizontal line between them.

Part A: The shaded part of the figure in choice B

is divided into three equal parts

there are three kinds of activities

Part B: According to the choice B of part A. there are 12 equal parts in total so each activity takes up 1/12.

figure in all the parts of the choice up to B of part A, get 12 equal parts

Hence, The shaded part of the figure in choice B is divided into three equal parts

There are 12 equal parts in total so each activity takes up 1/12.

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Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.

Here,

Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.

Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.

The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.

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5.

6.

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A sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion.

To calculate the required sample size, we can use the formula:

n = (\(z^2\) * p * q) /\(e^2\)

where n is the sample size, z is the z-score corresponding to the desired level of confidence (in this case, 2.576 for 99% confidence), p is the estimated population proportion (0.165, based on the NWBC's finding), q is 1-p, and e is the maximum error we want to tolerate (in this case, 0.06 or 6 percentage points).

Substituting the values, we get:

n = (2.576^2 * 0.165 * 0.835) / \(0.06^2\)

Solving for n, we get:

n ≈ 329

Therefore, a sample size of 329 would be required to be 99% confident that the estimated proportion of women-owned businesses not providing employee benefits is within 6 percentage points of the true population proportion. Note that this assumes a simple random sample and that the population size is much larger than the sample size, so the finite population correction is not needed.

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Answer:

Q2)

We have food for 400 people, and it will last for 23 days.

Then we have an inverse relation, where the number of days decreases as the number of people increases, this means that we have a relationship like:

23 days = K/400 people.

Then we get:

(23 days)*(400 people) = K = 9200 days*people.

Now if we increase the number of people by 60, we get.

people = 460

Then the number of days that this will last is:

D = (9200 days*people)/460 people = 20 days.

The food will last for 20 days.

Q3) We have a proportional relationship (y = k*x) such that y = 40 when x = 200, then we get:

40 = k*200

With this, we can find the value of k

40/200 = k = 0.2

Then the proportional relationship is:

y = 0.2*x

a) We need to replace x by 15.

y = 0.2*15 = 3

y = 3

b) We need to replace y by 8.

8 = 0.2*x

8/0.2 = x = 40

x = 40

Q3) y is inversely proportional to x (y = k/x), and y = 8 when x = 30.

Then we get:

8 = k/30

Then the value of k is:

8*30 = k = 240

then the relationship is:

y = 240/x

a) we need to replace x by 4

y = 240/4 = 60

y = 60

b) we need to replace y by 360

360 = 240/x

360*x = 240

x = 240/360 = 0.666...

x = 0.666...

The weight of the fat, sinew, and trimming to be taken out from the whole tenderloin is given to be 1.65 pounds.  Therefore, the total edible tenderloin in pounds is 3.86155 pounds.

The total weight of the whole tenderloin is given to be 2.5 kg.The weight of the fat, sinew, and trimming to be taken out from the whole tenderloin is given to be 1.65 pounds.

To calculate the total edible tenderloin in pounds, we need to convert the weight of whole tenderloin from kg to pounds.

1 kilogram (kg) = 2.20462 pounds (lbs)

Therefore,2.5 kg = 2.5 x 2.20462 = 5.51155 lbs We are given that 1.65 pounds of fat, sinew, and trimming need to be taken out from the whole tenderloin.

So, the total edible tenderloin in pounds = 5.51155 - 1.65= 3.86155 pounds

Therefore, the total edible tenderloin in pounds is 3.86155 pounds.

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Answer:

Step-by-step explanation:

P(t) = K / (1 + (K/P0 - 1) * e^(-rt))

In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).

To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.

To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.

To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.

To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).

I hope this helps! Let me know if you have any further questions.

A variable that can only take on specific numeric values is called  A discrete random variable.

According to the statement

A variable which is used to select a specific numeric value and we have to find a those variable

A discrete random variable is one which may take on only a countable number of distinct values.

So, A variable that can only take on specific numeric values is called  A discrete random variable.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

The complex plane, also known as the Argand plane, is a graphical representation of complex numbers in mathematics. It is a two-dimensional plane with the real axis representing the real part of a complex number and the imaginary axis representing its imaginary part.

1. The set of points in the complex plane that satisfy the relation |z-z1| = |z-z2| forms a circle with its center at the midpoint of z1 and z2, and with a radius equal to half the distance between z1 and z2.

2. The set of points in the complex plane that satisfies the relation 1/z = z forms a pair of lines that intersect at the origin, with slopes equal to 1 and -1. These lines divide the complex plane into four quadrants, and the set of points consists of the complex numbers that lie on the unit circle.

3. The set of points in the complex plane that satisfies the relation Re(z) = 3 forms a vertical line at x=3. All points on this line have the same real part, equal to 3.

4. The set of points in the complex plane that satisfies the relation Re(z) > c (respectively, >=c) forms a half-plane to the right (respectively, including) of the vertical line x=c. All points in this region have real parts greater than (respectively, greater than or equal to) c.

5. The set of points in the complex plane that satisfies the relation Re(az + b) > 0 forms a line that is the image of the real axis under the transformation az + b. The set of points consists of those complex numbers that lie to one side of this line.

6. The set of points in the complex plane that satisfy the relation |z| = Re(z) + 1 forms a hyperbola. The foci of the hyperbola are on the real axis, at x = -1 and x = 1.

7. The set of points in the complex plane that satisfies the relation Im(z) = c forms a horizontal line at y=c. All points on this line have the same imaginary part, equal to c.

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Answer:

The girl is 2.5 meters below sea level

Step-by-step explanation:

We are told in the question that:

A girl is snorkeling 1 meter below sea level

Hence, her elevation in meters below the sea level = -1m

We are told in the question that:

She then dives down another 1.5 meters

Once again: Her elevation in meters below the sea level = -1.5m

How far below sea level is the girl?

This is calculated as:

-1 m + -1.5m

= -1m - 1.5m

= -2.5m

Therefore, the girl is 2.5 meters below sea level

Answer:

(7×X)+5

Step-by-step explanation:

Answer:

(7×x) +5

Step-by-step explanation:

product of 7 and a number means 7x. increase by 5 means + 5

Answer:

9/5

Step-by-step explanation:

First we have to find the constant k

m = k/(p-1)^2  (p-1)^ goes on the bottom of the fraction because of the inverse.

5 = k/(4-1)^2

5 = k/3^2

5 = k/9  Multiply both side by 9

45 = k  We know can use this constant to solve our problem

m = 45/(6-1)^2

m = 45/5^

m = 45/24

m = 9/5