The venn diagram shows sports played by 10 students let event A= The student play basketball let event B= the student plays soccer

The solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.

The solution to the initial value problem can be obtained by using the substitution method. We first substitute the given function into the differential equation, which gives us the linear differential equation in y:

y' + 2y = 5x

We can then solve this linear differential equation by integrating both sides and applying the initial condition. This gives us the solution in y:

y = 5x/2 + C

where C is an arbitrary constant. To calculate the value of C, we plug in the initial condition y(0) = 2 into the equation. This gives us C = -2, so the solution to the initial value problem is given by:

y = 5x/2 - 2.

To illustrate this, let's consider the initial condition y(0) = 2. Plugging this into the solution equation gives us y = 5x/2 - 2, so when x = 0, we get y = -2, which matches the initial condition.

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The percent change for each year is given as follows:

The percent change is obtained applying the proportions in the context of this problem.

The equation that defines the percent change is the change in the year divided by the initial population during the year.

Hence the percent change for each year during the period is given as follows:

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A common aspect ratio for computer screens is 16:9, which means that for every 16 units of width, there are 9 units of height. This aspect ratio is also used on many televisions and mobile devices.

If a screen has an aspect ratio of 16:9, the width and height will be similar on all screens with this aspect ratio. However, the diagonal measurement will vary depending on the size of the screen.

Congruent screens are two or more screens that have the same dimensions. Two screens are congruent if and only if corresponding sides are equal and corresponding angles are equal. This can be proven using the postulates of congruence, such as the SSS (Side-Side-Side) postulate or the SAS (Side-Angle-Side) postulate.

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The 10% condition when constructing a confidence interval for a population proportion states that the sample size should be less than 10% of the population size.

This is expressed mathematically as follows:

n/N < 0.10

Where n is the sample size and N is the population size. For example, if the population size is 500, then we must ensure that the sample size is less than 50 (500 x 0.10 = 50). This is because if the sample size is larger than 10% of the population size, then the confidence interval will not be reliable. In other words, the results of the confidence interval may be inaccurate and biased.

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a) The ecosystem is in the sea. Option D

b) The ecological level is population. option D

c) The factors in the study are pressure, and temperature

d) The common limiting factor in biomes is lack of water

e) The carrying capacity is the highest population an environment can support over a long period. Option A

We have to note that the ecosystem has to do with the part of the habitat that is composed of the living and the non living parts. The non living parts of the ecosystem are called the abiotic factors while the living parts of the ecosystem are called the biotic factors.

In the ecosystem, we have the producers, the consumers and the decomposers and these are called the trophic or the feeding levels in the system.

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No, we cannot conclude that pedestrians are safer in San Francisco than in Los Angeles based on the data provided. The number of pedestrian fatalities in a given county is only one factor in determining the safety of pedestrians in that county.

Other factors, such as the number of pedestrians in each county, the number of vehicles in each county, the number of traffic laws in each county, and the number of traffic enforcement officers in each county, all play a role in determining the safety of pedestrians in a given county.

We would also need to consider other factors such as the number of pedestrian-friendly infrastructure in each county, the number of pedestrian-friendly policies in each county, and the number of pedestrian-friendly initiatives in each county. With this additional data, we would be able to make a more informed conclusion about which county is safer for pedestrians.

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Answer:

Step-by-step explanation:

Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Expected values are = 150/7 .Ci-square distribution is Day of the week observed count Expected Chi-square = O E (O -E )2/E

testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Statistical hypothesis: A statement about the nature of a population. It is often stated in terms of a population parameter.

Null hypothesis: A statistical hypothesis that is to be tested. : The alternative to the null hypothesis.

Test statistic: A function of the sample data.

The critical value for the chi-square statistic is determined by the level of significance (typically . 05) and the degrees of freedom. The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns.

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Answer:

4

Step-by-step explanation:

because its the factor

The scale factor of the dilation of triangles is k = 4/3

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the scale factor of the dilation be represented as k

Now , the measure of leg of the first triangle is a = 3 units

The measure of leg of the second triangle is b = 4 units

So , the dilated triangle is given by

3 k = 4

Divide by 3 on both sides , we get

k = 4/3

Hence , the dilation factor is k = 4/3

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There are 2100 workers in​ the company

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since 85​% of the workers are women, we can say:

The percentage of worker that aren't women = 100% - 85​% = 15​%

Let N represent the number of all workers. If 315 people work for the company who​ aren't women. We can say:

15​% of N = 315

15/100 × N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

Method 2:

We can write:

N - 0.85N = 315

0.15N = 315

N = 315/0.15

N = 2100 workers

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Answer:

The height of the building is 43.7 feet.

Step-by-step explanation:

Attached is a sketch of the problem.

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the height of the building by using the TAN function.

So we can say the tangent of angle x is the opposite side divided by the adjacent side.

[tex]tan(x)=\frac{O}{A}[/tex]

Lets solve for [tex]O[/tex].

Multiply both sides by [tex]A[/tex].

[tex]tan(x)*A=\frac{O}{A}*A[/tex]

Simplify the right side by cancelling the common factor of [tex]A[/tex].

[tex]tan(x)*A=O\\O=A*tan(x)[/tex]

Now lets evaluate the height of the building.

In this example we are given

[tex]x=17\\A=143[/tex]

[tex]O=143*tan(17)[/tex]

[tex]O=43.7195[/tex]

The correct answer is, the figure is a line segment.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

from the given figure,

we get,

AB is a line segment.

Hence, The correct answer is, the figure is a line segment.

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now, the assumption being that your granpa's are depositing the money at the beginning of the month.

[tex]~~~~~~~~~~~~\stackrel{\textit{deposits at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic deposits}\dotfill & 100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.03}{12} \right)^{12 \cdot 18}-1}{\frac{0.03}{12}} \right]\left(1+\frac{0.03}{12}\right) \\\\\\ A=100\left[ \cfrac{(1.0025)^{216}-1}{0.0025} \right](1.0025) \implies \boxed{A \approx 28665.52}[/tex]

An equation of a line, in slope-intercept form, for the total fee y for any number of hours x is y = 15x + 60.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Since the total fee that is being charged by this construction company is denoted by y and it charges $15 per hour for debris removal, plus a one time fee, an equation that models this situation is given by;

y = 15x + c

Next, we would determine the y-intercept as follows;

195 = 15(9) + c

y-intercept, c = 195 − 135

y-intercept, c = 60.

Therefore, the required equation is y = 15x + 60.

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The best way to improve the running speed of the game is to use an algorithm which can quickly evaluate potential moves and select the best one.

For example, alpha-beta pruning is an algorithm which is used for game tree search. It prunes the search tree and eliminates the branches which are not likely to contain the optimal solution. Alpha-beta pruning uses the following formula to evaluate positions:

Max(α, Min(β, v))

Where α is the best value that the maximizing player can guarantee at the current branch of the tree, β is the best value that the minimizing player can guarantee at the current branch of the tree and v is the value of the current position. The evaluation of the position helps to quickly identify the best move. This reduces the time taken to evaluate the potential moves and thus improves the running speed of the game.

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The exponential model for the population can be written as P(t) = 11,000(1.163)t, where P(t) represents the population size in t years and 1.163 is the growth rate.

We can calculate the population size at any time t by multiplying the initial population size (11,000) by the growth rate (1.163) raised to the power of t. For example, after 10 years the population size would be P(10) = 11,000(1.163)10 = 22,906.7. We can also use the model to predict the population size in future years. For example, the population size in 20 years will be P(20) = 11,000(1.163)20 = 40,803.7. For example, if the population is measured after 10 years, the equation would be P(10) = 11,000(1.163)^10. Solving for P(10) yields a population of 21,945 organisms. Thus, the population has grown by 16.3% per year over the 10-year period and has increased by 10,945 organisms.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &12 \end{cases} \\\\\\ A = 500[1+(0.04)(12)] \implies A = 740[/tex]

x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

What is the root of the equation?

A root of an equation is a value of the variable that makes the equation true. An equation is a statement that asserts the equality of two expressions. A root of an equation is also known as a solution or a zero of the equation.

The two values of x that are roots of the equation x^2 + 3x - 6 = 0 are x = -2 and x = -3.

To find the roots of the equation, we can use the factoring method, which consists of factoring the polynomial on the left side of the equation.

x^2 + 3x - 6 = 0

(x-2)(x+3) = 0

So, x - 2 = 0, x = 2 and x + 3 = 0, x = -3

Alternatively, we can use the Quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the roots are given by:

x = (-b ± √(b^2 - 4ac))/ 2a

So, by plugging in the values of a, b and c we have:

x = (-3 ± √(3^2 - 41-6))/ 2*1 = (-3 ± √(9+24))/2 = (-3 ± √33)/2 = (-3 ± √33)/2 = -2, -3

Hence, x = -2 and x = -3 are the two values of x that are roots of the equation x^2 + 3x - 6 = 0

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Answer:

We dissect each statement from the problem above to fully understand it.

the sum of a number and 7 is (x + 7)

3 times this is 3(x + 7)

is means the equal sign here 3(x + 7) =

Two less then 5 times the number is 5x - 2.

Therefore, the answer is B, 3(x + 7) = 5x - 2

The list of items that shows what Elena could buy is the list for which the sum of all prices is at most 10.

The maximum amount that Elena can spend is given as follows:

$10.

Hence, for each list, the sum is calculated for the prices of all the items, giving the total price.

The list with a sum of at most $10 is the list that shows what Elena can buy.

The problem is incomplete, hence the general procedure needed to solve it is presented.

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Answer:

The statement that is true is:

All the equal parts must have the same area.

This is true because when a rectangle is divided into equal parts, it means that the area of each part is the same. The lines dividing the shape can be drawn in any direction (top to bottom, left to right, diagonal, etc.) and the shape of the parts can also be different( rectangles, squares or any shape).

Answer:

The answer to your questionis 3.65

Answer:

3.25, 3.50, 3.50, 3.50, 3.65, 4.00, 4.00, 7.50, 7.99

3.65 is the median.

Step-by-step explanation:

You're welcome.

The value of  PQ / BD of given parallelogram where Diagonal BD intersects line CM and line CN at P and Q, respectively  = 1/3

Let's consider the two triangles BMP and DCP.
Here,
∠DPC = ∠BPM (because they are vertically opposite angles)
∠DCP = ∠BMP (because they are alternate interior angles of transversal CM with DC // BM)
∴△BMP∼△DCP (By AA theorem)
Thus,
ABCD is a parallelogram. Therefore AB = DC and AD = BC.
It is given that M is the midpoint of AB
BD  = DQ  + BQ                BD = BP  + PD

BD = 2BQ  + BQ               BD = 2PD + PD

BD  = 3BQ                        BD = 3PD

therefore

BQ  = PD And

Since DQ  = 2BQ  then  DQ  = 2PD and

PD + PQ = 2PD   subtract PD from each side

PQ  = PD

so BQ = PD  = PQ

BD = PD + PQ + BQ

BD  = PQ  + PQ  + PQ

BD  = 3PQ

Therefore the value of  PQ / BD of given parallelogram is PQ / BD  = 1/3.

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The amount of work that the laborer has done, given the weight of the bricks and the laborer is 4, 577 Joules .

To calculate the amount of work done by the laborer, we can use the formula:

work = force x distance x

where:

force is the force applied,

distance is the distance moved,

The force applied by the laborer is the combined weight of the laborer and the bricks:

= 895N + 575N

= 1, 470N

Therefore, the work done by the laborer is:

Work = 1, 470N x 3.1m

= 4577 Nm or Joules (J)

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Answer:

Step-by-step explanation:

1/2 is your answer

The average rate of change on the interval [2, 2 + h] is r = 2.

Wewant to find the average rate of change of p(x) = 2x + 5 on the interval [2, 2 + h]

Remember that the average rate of change on an interval [a, b] is:

r = ( p(b) - p(a))/(b - a)

So on this case, we have:

r = ( p(h + 2) - p(2))/(2 + h - 2)

r = ( 2*(x + h) + 5 - 2*x - 5)/h

r = (2h)/h

r = 2

The average rate of change is 2.

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Answer:

10

Step-by-step explanation:

120/a = 12

120=12a

120/12 = a

a = 10

Answer:

1,440

Step-by-step explanation:

120 x 12 = 1,440

120 / 1,440 = 12

The solution to the system of equations include the following: B. (6, 3).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the system of equations, we can reasonably infer and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-axis and y-axis, which is given by the ordered pair (6, 3).

In conclusion, the ordered pair (6, 3) is a solution to the system of equations represented by the given graph.

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The factorised for. of the given Polynomial expression using the greatest common factor is; 2 (14x - 1).

It follows from the task content that the factorised form of the given Polynomial expression is to be determined using the greatest common factor.

Since the given expression is; 28x - 2.

By careful observation of the two terms (28x and -2) in the polynomial expression; the greatest common factor is; 2.

Hence, the factorised form of the polynomial expression as required is; 2 (14x - 1).

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