In 2016, a school started its own aquarium with n’2 fish. In 2021, there were n² fish in the same aquarium. There were 81 fish in 2021. How many fish were there in 2016?
Show your work

y = 5

Solution:

7y = 5y + 10

7y - 5y = 10

2y = 10

\(\frac{2y}{2}\) = \(\frac{10}{2}\)

y = 5

Checking:

7y - 5y = 10

7(5) - 5(5) = 10

35 - 25 = 10 ✓

Answer:

5y+10=7y. (reason opposite sides of pam. are equal)

10=7y-5y

10=2y

∴y=5

The speed of the Belinda is 0.1 miles/minute.

The correct option is B.

Given

Belinda walks 2 miles to the store and it takes her 20 minutes.

The speed is defined as the ratio of distance covered and time.

The following formula is used to calculate speed;

\(\rm Speed = \dfrac{Distance}{Tiame}\)

Substitute all the values in the formula;

\(\rm Speed = \dfrac{Distance}{Tiame}\\\\\rm Speed = \dfrac{2}{20}\\\\\rm Speed = 0.1\ \text{miles per minute}\)

Hence, the speed of the Belinda is 0.11 miles/minute.

To know more about Speed click the link given below.

https://brainly.com/question/7359669

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

Learn more about angle here:

https://brainly.com/question/31818999

#SPJ11

The x-component of the normal vector is -42, the y-component is 0, and the z-component is -14.

A vector is a quantity that describes not only the magnitude of an object but also its movement or position with respect to another point or object. It is sometimes referred to as a Euclidean vector, a geometric vector, or a spatial vector.

To find the normal vector to the tangent plane of \(z = 7e^{(x^2-6y)\) at the point (12, 24, 7), we first need to find the partial derivatives of the function with respect to x and y evaluated at this point.

Taking the partial derivative with respect to x, we get:

\(∂z/∂x = 14xe^{(x^2-6y)\)

Evaluating this at the point (12, 24), we get:

\(∂z/∂x = 14(12)e^{(12^2-6(24))} = 0\)

Taking the partial derivative with respect to y, we get:

\(∂z/∂y = -42e^{(x^2-6y)\)

Evaluating this at the point (12, 24), we get:

\(∂z/∂y = -42e^{(12^2-6(24))} = -42\)

Therefore, the normal vector to the tangent plane at the point (12, 24, 7) is given by:

(0, 0, -1) x (-14, 0, 42) = (-42, 0, -14)

So, the x-component of the normal vector is -42, the y-component is 0, and the z-component is -14.

Learn more about vector on:

https://brainly.com/question/17157624

#SPJ1

Answer:

should be 12

Step-by-step explanation:

because parallel lines usually are the same size unless specified in the question so u can say "12 because BC and AD are parallel lines"

the system of equations has a solution if and only if a = 0, b = 0, and

c = 0

To determine the values of the constants a, b, and c for which the given system of equations has a solution, we can use the concept of linear dependence. A system of equations has a solution if and only if the determinant of the coefficient matrix is not zero.

The coefficient matrix for the system is:

[[0, 2, 1],

[1, -1, 1],

[1, 3, 2],

[3, -1, 1]]

To find the determinant of this matrix, we can perform row operations to simplify it:

R2 = R2 - R1 and R4 = R4 - 3R1:

[[0, 2, 1],

[1, -3, 0],

[1, 3, 2],

[0, -5, -2]]

R4 = R4 + 5R2:

[[0, 2, 1],

[1, -3, 0],

[1, 3, 2],

[0, 0, 0]]

The determinant of this simplified matrix is 0. Therefore, the system of equations has a solution if and only if the determinant is not zero.

Now, let's analyze the values of a, b, and c based on the determinant being zero:

If a = 0, b = 0, and c = 0, then the system has a solution.

For any other values of a, b, and c, the system does not have a solution.

In conclusion, the system of equations has a solution if and only if a = 0, b = 0, and c = 0.

Learn more about simplified matrix here:

https://brainly.com/question/29298249

#SPJ11

Answer:

616 cm^2

Step-by-step explanation:

using π r ^ 2

22/7 × 14^2

616 cm^2

a) The probability that a tire will be too narrow is 0.252492. b)The probability that a tire will be too wide is 0.091211. c) , the probability that a tire will be defective is 0.252492 + 0.091211 = 0.343703.

a. To calculate the probability that a tire will be too narrow, we need to find the area under the normal distribution curve that falls below the lower specification limit.

Using the Z-score formula, we calculate the Z-score for the lower specification limit as follows:

Z = (Lower specification limit - Mean) / Standard deviation

Z = (22.8 - 23) / 0.15

Z = -0.666667

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the left of Z = -0.666667 is approximately 0.252492.

b. To calculate the probability that a tire will be too wide, we need to find the area under the normal distribution curve that falls above the upper specification limit.

Using the Z-score formula, we calculate the Z-score for the upper specification limit as follows:

Z = (Upper specification limit - Mean) / Standard deviation

Z = (23.2 - 23) / 0.15

Z = 1.333333

Next, we find the corresponding area from the standard normal distribution table or using a calculator. The area to the right of Z = 1.333333 is approximately 0.091211.

c. The probability that a tire will be defective is the sum of the probabilities of it being too narrow and too wide, since being outside the specification limits indicates a defect.

Therefore, the probability that a tire will be defective is approximately 0.252492 + 0.091211 = 0.343703.

Learn more about Standard deviation visit:

brainly.com/question/13498201

#SPJ11

Answer:

Below

Step-by-step explanation:

Z score is the ± standard deviations from the mean

The value of the expression after evaluating it according to the values of c and d is 42.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Since, no expression is given, let us assume that the expression is

c + d / 4

Now we have to evaluate the value of the expression according to the values of c and d,

For that, we will simply put the given values in the expression and solved it accordingly,

Put c = 36 and d = 24 in the expression we assumed,

c + d / 4 = 36 + 24/4

= 36 + 6 = 42

Hence, the value of the expression after evaluating it according to the values of c and d is 42.

Learn more about expressions, click;

https://brainly.com/question/13947055

#SPJ1

Answer:

2x - 13

Step-by-step explanation:

If one number is 13 less than another number, we can represent the greater number as x and the smaller number as (x-13).

So, the sum of these two numbers can be represented as:

x + (x-13) = 2x - 13

Therefore, the sum of these two numbers is 2x - 13.

Answer:

74.5

Step-by-step explanation:

Answer:

3rd one

Step-by-step explanation:

Answer:    1.0057m

Step-by-step explanation:

Answer:

8, 15, 17

Step-by-step explanation:

That's a triple I remember

Answer:

The solution of this system of linear equations is \((x,y) = (-3,-2)\).

Step-by-step explanation:

Let be the following system of linear equations:

\(2\cdot x - 7\cdot y = 8\) (1)

\(-3\cdot x + 2\cdot y = 5\) (2)

From (1) we clear \(y\):

\(2\cdot x -8 = 7\cdot y\)

\(y = \frac{2\cdot x - 8}{7}\)

And we apply this variable in (2):

\(-3\cdot x+2\cdot \left(\frac{2\cdot x -8}{7} \right)= 5\)

\(-3\cdot x +\frac{4}{7} \cdot x -\frac{16}{7} = 5\)

\(-\frac{17}{7}\cdot x = \frac{51}{7}\)

\(x = -\frac{51}{17}\)

\(x = -3\)

And the value of \(y\) is:

\(y = \frac{2\cdot (-3)-8}{7}\)

\(y = -\frac{14}{7}\)

\(y = -2\)

The solution of this system of linear equations is \((x,y) = (-3,-2)\).

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

Learn more about homeostasis at: https://brainly.com/question/3888340

#SPJ4

Using the circumference of the circle, it is found that:

About 7.1 feet of railing needs to be replaced.

The circumference of a circle of radius r is given by:

\(C = 2\pi r\)

It is equivalent to 360º.

In this problem, the diameter is of 30 feet, hence the radius is 15 feet, so:

\(C = 2\pi (15) = 30\pi\)

Then, considering that the circumference is equivalent to 360º, the length to be replaced is given by:

\(L = \frac{27}{360} \times 30\pi = 7.1\)

About 7.1 feet of railing needs to be replaced.

More can be learned about the circumference of a circle at https://brainly.com/question/25846963

Answer: 7.1

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

In a group G of order 3n, where n is a positive integer not divisible by 3, if x and y are elements of order 3, it can be proven that y is conjugate to either x or x⁻¹. This result highlights the relationship between elements of order 3 in such groups.

To prove that y is conjugate to either x or x⁻¹, we need to consider the properties of groups of order 3n and elements of order 3.

First, since the order of G is 3n, by Lagrange's theorem, the order of any element in G must divide the order of the group. Therefore, the orders of x and y must be divisors of 3.

Since x has an order of 3, it means that x generates a cyclic subgroup of order 3. Similarly, y also has an order of 3 and generates another cyclic subgroup of order 3 in G.

Now, if x and y are elements of the same cyclic subgroup, then they are conjugate to each other. This is because within a cyclic subgroup, every element is conjugate to any other element. Therefore, if x and y are in the same cyclic subgroup, y is conjugate to x.

On the other hand, if x and y are in different cyclic subgroups, we can consider the cosets formed by these subgroups. Since the order of G is 3n and each subgroup has an order of 3, there are exactly n cosets. This means that each element in one subgroup is conjugate to exactly one element in the other subgroup. Therefore, if x and y are in different cyclic subgroups, y is conjugate to x⁻¹.

Hence, we have shown that in a group G of order 3n, if x and y are elements of order 3, y is conjugate to either x or x⁻¹.

Learn more about: Group theory and Conjugacy

brainly.com/question/32559990

#SPJ11

"Vary directly" is another way of saying "directly proportional".

In simple English, this just means, as one increases, the other increases too.

a = 6

b = 4

The question says find out what a is when b is 16.

First, lets find how many times larger b has gotten.

16/4 = 4

b had gotten 4 times bigger to go from b=4 to b=16

If a is varying directly, it means that it will also get 4 times bigger.

Therefore, a = 6 x 4 = 24

Using the Poisson distribution, there is a 0.8335 = 83.35% probability that 2 or fewer will be stolen.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

The probability that a rental car will be stolen is 0.0004, hence, for 3500 cars, the mean is:

\(\mu = 3500 \times 0.0004 = 1.4\)

The probability that 2 or fewer cars will be stolen is:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-1.4}1.4^{0}}{(0)!} = 0.2466\)

\(P(X = 1) = \frac{e^{-1.4}1.4^{1}}{(1)!} = 0.3452\)

\(P(X = 2) = \frac{e^{-1.4}1.4^{2}}{(2)!} = 0.2417\)

Then:

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2466 + 0.3452 + 0.2417 = 0.8335\)

0.8335 = 83.35% probability that 2 or fewer will be stolen.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530

#SPJ1

The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.

By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.

Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.

Learn more about probability:

https://brainly.com/question/31828911

#SPJ11

These instructions provide a general framework for addressing your questions. If you can provide the specific data files or any additional information, I can assist you further in performing the analyses.

To address your questions, I will need access to the specific data files mentioned in order to perform the requested analyses. As an AI text-based model, I don't have direct access to external files or the capability to process and display visual plots. However, I can still guide you through the general steps and concepts involved in solving these problems. Let's break it down:

a. Constructing a histogram:

To construct a histogram of the shopping times, you need to determine appropriate intervals or bins to group the data. Once you have chosen the bins, count the number of observations falling within each bin and create bars to represent the frequencies. The width of each bar should be proportional to the frequency.

b. Constructing a stem-and-leaf display:

A stem-and-leaf display is a way to organize and present numerical data. The stems represent the leading digits of the data values, while the leaves represent the trailing digits. This display helps to visualize the distribution and order of the data.

c. Commenting on the plots:

After constructing the histogram and stem-and-leaf display, you can analyze the patterns and characteristics of the data. Look for measures of central tendency (such as the mean or median) and measures of variability (such as the range or standard deviation) to gain insights into the shopping times.

Q2. Constructing time-series plots:

To construct time-series plots, you need to plot the values of the index against time. The index values are on the vertical axis, while the time is on the horizontal axis. Use the given vertical axis ranges to ensure the plot is properly scaled.

c. Commenting on the time-series plots:

After constructing the time-series plots, observe the trends, patterns, and fluctuations in the index values over time. Look for any significant changes, seasonal patterns, or irregularities that may help in understanding the behavior of the exchange rate.

Q3. Cross table and row percentages:

To create a cross table, you'll need the data file Stordata. The table should have days of the week as rows and the four sales quartile intervals as columns. Count the number of sales falling within each combination of day and quartile, and fill in the cells of the table accordingly.

a. Computing row percentages:

Row percentages are calculated by dividing each cell value by the corresponding row's total and multiplying by 100. This provides the percentage distribution of sales quartiles within each day of the week.

b. Major differences in sales level:

Compare the row percentages across different days of the week. Look for substantial differences in the distribution of sales quartiles. Identify the days that have notably higher or lower percentages in specific quartiles compared to others.

c. Interpretation:

Based on the row percentages, you can infer the variations in sales levels by day of the week. For example, if one day consistently has a higher percentage in the top sales quartile, it suggests that day tends to generate higher revenue. Conversely, if a day has a higher percentage in the lower sales quartiles, it implies relatively lower sales performance.

Remember, these instructions provide a general framework for addressing your questions. If you can provide the specific data files or any additional information, I can assist you further in performing the analyses and interpretation.

Learn more about standard deviation here:

https://brainly.com/question/13498201

#SPJ11

Answer:

8.5% (you can approximate that, that's the exact number and it isn't too funky)

Step-by-step explanation:

Percentage is out of 100, and over here we see that 200 is 2 times the amount of 100. So that means that if we divide 200 by 2, we get 100, which means we also divide 19/2 to get 8.5. That means, out of 100 light bulbs, 8.5 of them burned out. This is really easy to convert because the percentage is already out of 100, so you just make 8.5 into a percent which is 8.5%

Let me know if you have any questions.

Answer: 18

Step-by-step explanation:

The options are:

A. 23

B. 18

C. 14

D. 32

Since we are told that the ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16. This simply means that the ratio of flour tortillas to the total number of packages on the shelf was (16 -7 = 9) 9 to 16.

Therefore, to get the number that could represent the number of packages of flour tortillas the clerk put on the shelf we have to find the multiple of 9 in the question given . This will be:

Multiples of 9 = 9, 18, 27, 36, 45 ....

Based on the option, the answer will be 18.

The distance from point \($a\left(-1,\ 7\right)$\) to the line \($y=3x$\) is about 4.5 units, rounded to the  nearest tenth.

The distance from point \($a\left(-1,\ 7\right)$\) to the line \($y=3x$\) is equal to the length of the perpendicular line from point \($a$\) to the line\($y=3x$\). The formula to find the distance from a point \(($x_1, y_1$)\) to a line \($ax+by+c=0$\) is given by:

\($$\frac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}.$$\)

Substituting\($$\frac{|ax_1+by_1+c|}\) into the formula, we get:

\($$\frac{|-3(-1)+1(7)+0|}{\sqrt{3^2+1^2}} = \frac{20}{\sqrt{10}}.$$\)

Therefore, the distance from point \($a\left(-1,\ 7\right)$\) to the line \($y=3x$\) is about 4.5 units, rounded to the nearest tenth

Learn more about distance here :

https://brainly.com/question/11348670

#SPJ4

Answer:

x=8

Step-by-step explanation:

The angles are vertical angles so they are equal

8x+36 = 5x+60

Subtract 5x from each side

8x+36-5x = 5x+60-5x

3x+36 = 60

Subtract 36 from each side

3x+36-36 = 60-36

3x =24

Divide each side by 3

3x/3 = 24/3

x=8

Answer:

as in pic below

Step-by-step explanation: