The perimeter of a triangular park shown on the right is 11x-6.
What is the missing length?

To find the other 2 sides of the right triangle with the given hypotenuse using Pythagorean theorem we use A² = B² + C²

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where

BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation. It should be remembered that a right-angled triangle's hypotenuse is its longest side.

The formula for the Pythagoras theorem is written as c² = a² + b², where c is the hypotenuse of the right triangle and a and b are its other two legs. As a result, the Pythagoras equation can be used to any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

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The three methods are used to select a sample from a larger population in order to make inferences about the population as a whole.

Probability-proportional-to-size sampling is a method where the probability of an item being selected is proportional to its size. In this case, the size is represented by the dollar amount of the sale.

Systematic selection involves selecting items at regular intervals. In this case, the starting point is 13 and the interval is 30. Every 30th item is selected, starting from the 13th item.

The starting dollar is $17,240 and the interval is $220,000. Every item with a sales amount that falls within the interval is selected with a probability proportional to its size.

The random-number table selection technique involves using a random number table to select items. The last four digits of the invoice number are used to determine which item is selected.

The selection process starts at row (0004) and column (01) and continues across the row and then down to the next row.

The probability of an item being selected in each method differs and is important in ensuring a representative sample is obtained.

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Answer:Yes

because there were at least 10 "successes" and at least 10 "failures" in the sample

Step-by-step explanation:

Answer:

20% or 0.2

Step-by-step explanation:

→ 32 ÷ 160

common factor

→ = ⅕

convert the number

→ = 20% or 0.2

hope this helps!

The value of function f' (x)=28 and G' (x)=63

    x           f(x)       g(x)      f' (x)       g' (x)
      1            3           2          4            6

      2            1           3          5             7
      3             2          1          7             9        


                                       
F(X)=f(f(x))

F' (X)=(F' (f(x)) x F' (x)⇒ (chain rule)

F' (1)=F' (F(1)x f' (1))

=f' (3) x f' (1)   (( ∵  f(1)=3))

=7 x 4        (∵f' (3)=7, f' (1)=4))

=28

G(x)=g(g(x))

G' (x)=g' (g(x) X  g' (x) ⇒   (chain rule)

G' (2)=g' (g(2) x g' (2)

=g' (3) x g' (2)     (∵g(2)=3))

=9x7        ((∵g' (3)=9, g' (2)=7))

=63


The chain rule is a formula in calculus that expresses the derivative of the composition of two differentiable functions f and g in terms of f and g's derivatives.
d/dx(f(g(x)=f'(g(x)g'(x).


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Answer:

0.00576

Step-by-step explanation:

Answer: 2.49

Step-by-step explanation:

$2.00 is an automatic fee, so this is our y-intercept.

$4.98 for every two meals, so if we divide that by two, we get the price for one meal, which is $2.49.

The correct option is (D). On average, the number of breakdowns per day varies from the mean by about 0.28.

Because standard deviation represents the typical distance between each data point and the mean.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.

So, the correct answer is On average, the number of breakdowns per day varies from the mean by about 0.28.

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Answer:

To find the probability that both a randomly selected male student and a randomly selected female student are smokers, we can use the formula for conditional probability: P(A and B) = P(A) * P(B|A), where A is the event that the male student is a smoker and B is the event that the female student is a smoker.

First, we need to find the probability that a randomly selected male student is a smoker:

P(A) = (number of male smokers) / (total number of male students) = 63 / (63 + 147) = 63/210

Next, we need to find the probability that a randomly selected female student is a smoker, given that the male student is a smoker:

P(B|A) = (number of female smokers and male smokers) / (number of male smokers) = 70 / 63

Finally, we can find the probability that both students are smokers by multiplying these two probabilities together:

P(A and B) = P(A) * P(B|A) = (63/210) * (70/63) = 0.09

So the probability that both a randomly selected male student and a randomly selected female student are smokers is 0.09 or 9%.

Step-by-step explanation:

Answer:

$5

Step-by-step explanation:

Let the cost of a children's ticket be x.

The cost of an adults ticket would be x + 3. (adult ticket costs $3 more than a children's ticket.)

200 adult tickets would cost 200(x+3), and 100 children's ticket would cost 100x.

The combined costs of children's ticket and adult would be 200(x+3) + 100x.

Using these information, the equation: 200(x+3) + 100x = 2100 can be formed.

200(x+3) + 100x = 2100

200x + 600 + 100x = 2100

300x = 1500

x = 5

The children's ticket cost $5.

Double check.

200*8 + 100*5 = 2100.

Answer: g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.

Step-by-step explanation: The expression g(x) - h(x) can be found by subtracting h(x) from g(x).

g(x) = -3x^2 + 2x - 6

h(x) = -4 - x

So,

g(x) - h(x) = (-3x^2 + 2x - 6) - (-4 - x) = -3x^2 + 3x - 2.

Answer:

  f'(-3.5) ≈ 0.8292

  f'(2) ≈ 5.277

  f'(4) ≈ 10.34

Step-by-step explanation:

You want the approximate derivative of f(x) = 8·1.4^x using h=0.001 at x = {-3.5, 2, 4}.

The derivative is approximated by the formula ...

  [tex]f'(x)\approx\dfrac{f(x+h)-f(x)}{h}\\\\f'(x)\approx\dfrac{f(x+0.001)-f(x)}{0.001}\qquad\text{for $h=0.001$}\\\\f'(x)\approx\dfrac{8\cdot1.4^{x+0.001}-8\cdot1.4^x}{0.001}\qquad\text{using the given $f(x)$}[/tex]

The calculation for different values of x is tedious, but not difficult.

For example, ...

  f'(-3.5) = (8·1.4^-3.499 -8·1.4^-3.5)/0.001 = (2.4648358 -2.4640066)/0.001

  = 0.0008292/0.001

  f'(-3.5) = 0.8292

The remaining f'(x) values are shown in the attached table in the column f₁(x₂).

__

Additional comment

When function evaluation is repeated for different values, it is usually convenient to let a calculator or spreadsheet do the math. You can enter the formula once and have it evaluated as many times as you need.

The formula shown can be simplified to f'(x) ≈ 8000(1.4^(x+.001) -1.4^x), reducing the tedium by a small amount. The second attachment shows a different calculator using this formula.

Answer:

Step-by-step explanation:

The equation 25d^3 + 210d^2 - 640 = 0 can be reduced to a quadratic equation by using the factor theorem:

(d - 8)(25d^2 + 182d + 80) = 0

So, one root of the equation is d = 8. To find the other two roots, you can solve the quadratic equation:

25d^2 + 182d + 80 = 0

Using the quadratic formula, the roots can be calculated as:

d = (-b ± √(b^2 - 4ac)) / 2a

Where a = 25, b = 182, and c = 80.

So,

d = (-182 ± √(182^2 - 4 * 25 * 80)) / 2 * 25

d = (-182 ± √(33124 - 8000)) / 50

d = (-182 ± √(25124)) / 50

d = (-182 ± 158) / 50

Therefore, the roots of the equation are:

d = (-340 + 158) / 50 = (-182 + 158) / 50 = (-24) / 50 = -0.48

d = (-340 - 158) / 50 = (-182 - 158) / 50 = -340 / 50 = -6.8

So, the solutions to the equation are d = 8, -0.48, and -6.8.

The correct answer is  [78.2, 82.3].

It is a statistical quantity that provides information about how far the individual values in a data set deviate from the mean (average) value.

The standard deviation is calculated by finding the square root of the variance, which is the average of the squares of the deviations of each value in the data set from the mean. The formula for standard deviation is:

σ = [tex]\sqrt{ \frac{1}{n}[/tex] × Σ ([tex]x_{i}[/tex] - μ)²

where:

σ is the standard deviation,

n is the number of values in the data set,

[tex]x_{i}[/tex] is each value in the data set,

μ is the mean of the data set,

Σ ([tex]x_{i}[/tex] - μ)² is the sum of the squares of the deviations of each value from the mean.

To calculate the 95% confidence interval for the population mean, we need to know the population standard deviation. Since we don't have that information, we will use the sample standard deviation as an estimate.

Using the sample data, the sample mean is 80.25 and the sample standard deviation is 2.83.

The 95% confidence interval for the population mean is calculated as follows:

CI = [tex]\bar x[/tex] ± t×[tex]\frac{s}{\sqrt{n} }[/tex]

where:

[tex]\bar x[/tex] = sample mean = 80.25

s = sample standard deviation = 2.83

t = t-statistic for a 95% confidence level with 11 degrees of freedom (n-1)

n = sample size = 12

Using a t-table, the t-statistic for a 95% confidence level with 11 degrees of freedom is 2.201.

CI = 80.25 ± 2.201 × [tex]\frac{2.83}{\sqrt{12} }[/tex]

CI = 80.25 ± 2.201 × 0.913

CI = 80.25 ± 2.006

CI = (78.24, 82.26)

Rounding off to the nearest tenth, the 95% confidence interval for the population mean is [78.2, 82.3].

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The complete question is:

Answer:

13

Step-by-step explanation:

26/2

Answer:

Jake and Sam each can pick 13 presents

Step-by-step explanation:

Since they have 26 presents and they want to spilt them evenly we can use the Average

Mean = 26/2 = 13

Jake and Sam each can pick 13 presents

The number of bystanders would be least likely to affect your decision about the number of additional resources needed at the scene.

The number of injured persons, evidence of any hazards, and the nature of the illness are all factors that should be taken into consideration when determining the additional resources needed.

Probability and statistics are two closely related branches of mathematics that are used to analyze and make predictions about the behavior of random phenomena.

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Answer:

The answer is 24 inches

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

Step 1: Substitute the a as 6.

Step2: 5*(a) =5*6, which equals 30

Step 3: 5(6) - 30= 0

The number line that best represents all the possible numbers of games in which Jana scored 2 goals this season is given by the

Second number line.

To obtain the number line, we must first obtain the inequality that represents the problem.

This hockey season, she scored 0 goals in 22 games, 1 goal in each of 16 games, and 2 goals in each of the remaining games, hence her total number of goals is given as follows:

16 + 2x.

In which x is the number of games that she scored 2 goals.

She scored less than 29 goals, hence the inequality is given as follows:

16 + 2x < 29

2x < 13.

x < 6.5.

The number of games is a discrete amount, meaning that the possible amounts are given as follows:

x = 0, 1, 2, 3, 4, 5 and 6.

Thus the second number line is the correct number line.

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Step-by-step explanation:

We know that the water level in the tank is 15 cm initially, and after 2 days it has dropped to 14 cm. Therefore, the water level is dropping by 1 cm per day. To find out when the water will run out, we need to know how many days it will take for the water level to drop to 0 cm.

To find this out, we can use the following formula:

Days = (Initial water level - Final water level) / Rate of evaporation per day

Plugging in the values, we get:

Days = (15 - 0) / 1 = 15 days

So, the water will run out in 15 days.

By algebra properties and trigonometric formulas, the trigonometric equation sin α + cos α is equal to √7 / 2.

In this problem we find the definition of trigonometric equation, whose value must be found by means of algebra properties and trigonometric formulas. First, write the entire formula:

sin α + cos α

Second, square the formula:

(sin α + cos α)² = sin² α + 2 · sin α · cos α + cos² α

Third, simplify the formula and clear sin α + cos α:

(sin α + cos α)² = 1 + 2 · sin α · cos α

sin α + cos α = √(1 + 2 · sin α · cos α)

Fourth, find the value of the resulting trigonometric equation:

sin α + cos α = √[1 + 2 · (3 / 8)]

sin α + cos α = √7 / 2

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Answer: The quotient when 18f^2+45f is divided by 9f is 2f+5.

To find the quotient when 18f^2+45f is divided by 9f, we use the rule for long division of polynomials. We divide the first term of the dividend (18f^2) by the first term of the divisor (9f). This gives us a quotient of 2f.

We then multiply the divisor (9f) by the quotient (2f) and subtract it from the dividend (18f^2+45f). This leaves us with 45f.

Next, we bring down the next term of the dividend (45f) to get 45f + 45f.

Now we divide the new dividend (45f + 45f) by the divisor (9f) to get a quotient of 5.

So the final quotient is 2f + 5.

Step-by-step explanation:

The explicit formula for aₙ is a formula for the nth term of this sequence aₙ = 8n + 17.

What is the explicit formula?

The explicit formulae for L-functions are relations between sums over the complex number zeroes of an L-function and sums over prime powers, introduced by Riemann for the Riemann zeta function.

The formula for the nth term of this sequence is a_n = 8n + 17.

This means that each term in the sequence is equal to 8 multiplied by the position of the term (n) plus 17.

For example, the first term (n = 1) is 25, which can be calculated as 8 * 1 + 17 = 25.

The second term (n = 2) is 33, which can be calculated as 8 * 2 + 17 = 33, and so on.

hence, the explicit formula for aₙ is a formula for the nth term of this sequence is aₙ = 8n + 17.

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Answer:

(9-1) · 3 ÷ 7 + 5

Step-by-step explanation:

(9-1) · 3 ÷ 7 + 5

8 · 3  ÷ 7 + 5

24 ÷ 7 + 5

[tex]\frac{24}{7}[/tex] + 5

[tex]\frac{24}{7}[/tex] + [tex]\frac{35}{7}[/tex]

[tex]\frac{59}{7}[/tex]

The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales."

Establish the markdown. Subtract the actual selling price from the difference in pricing. After that, multiply this outcome by 100. The outcome is a percentage markdown.

Here,

The "Markdown%" is defined by RICS and the majority of the retail business as "Markdown dollars divided by Sales." The dollar discount is divided by the NET retail sales price to determine the markdown percentage (times 100). As an illustration, a

=>  $30 item is reduced to $24 and sold.

=> The markdown percentage is 25% ($6/$24).

=> Original Sales Price X (100% minus Markdown Percentage)

=>  New Sales Price Paid Percentage=  Discount Percent is 10%

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If a variable needs to be eliminated, to solve -7x - 10y = -83 4x - 10y = 16, the correct first step is to:

Subtract to eliminate y.

In order to solve a system of linear equations, we can use elimination method. The goal of elimination method is to simplify the system of equations by making one of the variables disappear or equal to zero.

Here, the system of equations is:

To eliminate one of the variables, we can add or subtract the equations so that one of the coefficients cancels out.

In this case, we want to eliminate y. We can do that by subtracting the first equation from the second equation.

When we subtract the first equation from the second equation, the y-term will cancel out because the coefficients are the same:

--------- (subtract the two equations)

11x = 99

Now, we only have one variable, x, and we can easily solve for it:

x = 9

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The solution to the system of equations is x = (y + 2) / 3 and y = 2.5.

Equations are mathematical statements that express the relationship between two or more variables. An equation typically consists of an equal sign, two expressions containing the variables, and the equals sign is used to show that the two expressions on either side of it are equal in value. Equations are used to solve problems, make predictions, and describe patterns.

Let's start by solving for x in the first equation:

y = 3x - 2

Add 2 to both sides of the equation:

y + 2 = 3x

Divide both sides of the equation by 3:

(y + 2) / 3 = x

Now that we've solved for x, we can substitute x into the second equation.

y = x + 2

Substitute (y + 2) / 3 for x:

y = (y + 2) / 3 + 2

Simplify the left side of the equation:

y = (y + 2 + 3) / 3

Multiply both sides of the equation by 3:

3y = (y + 5)

Subtract y from both sides of the equation:

2y = 5

Divide both sides of the equation by 2:

y = 5 / 2

y = 2.5

Therefore, the solution to the system of equations is x = (y + 2) / 3 and y = 2.5.

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Answer:

The equation need to solve this problem is y=a(b)^x

a= the starting value

b= the rate of change

x= the time

to get the rate of change do the following:

add 1 to the percentage of change (only if value is growing)

subtract the percentage from one (only if value is decaying)

Since the printer is depreciating it is a decay.

The rate of change for this problem is showed below.

1-0.05

0.95 is the rate of change.

Below is the equation for the problem.

y=35000(0.95)^4 Work the problem.

Y=35000(0.814506250

Y=28507.71875 Since we are working with money we round to two decimal places.

The printer's value after four years is $28,507.72.

Answer:

The time value, at the end of the fifth year, of a 5-year annuity that pays $200 every month, starting from the beginning of the second month, when the continuously compounded interest rate is 9.959%, is $11,828. To calculate this, we can use the formula A = PMT x [((1 + r)n - 1) / r], where PMT is the payment amount, r is the continuously compounded interest rate, and n is the number of payments. In this case, PMT = $200, r = 0.09959, and n = 60. Plugging these values into the formula, we get A = $200 x [((1 + 0.09959)60 - 1) / 0.09959] = $11,828.

The value of angle A and C is 14° and 121° respectively

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

The sum of angle in a triangle is 180°

Therefore 45+6x-5+x-7 = 180

collect like terms

45-5-7+6x+x =180

33+7x = 180

7x = 180 - 33

7x = 147

x = 147/7

x= 21

therefore the value of angle A = ( 21-7) = 14°

and angle C = 6(21) - 5

C = 126-5

C = 121°

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Answer:

  (a) 5.78%

  (b) $10,594.63

  (c) 5.95%

Step-by-step explanation:

You want the annual rate, the 1-year balance, and the effective yield on an account in which $10,000 is deposited, and the value doubles in 12 years.

The compound interest formula is ...

  A = Pe^(rt)

where P is the amount invested at annual rate r for t years, and A is the account balance.

Solving for r, we have ...

  ln(A/P)/t = r

The account value will have doubled when A/P = 2, so the rate is ...

  r = ln(2)/12 ≈ 0.057762 ≈ 5.78%

The annual rate is about 5.78%.

The balance after 1 year is ...

  A = 10000·e^(ln(2)/12·1) = 10000·2^(1/12) = 10594.63

The balance after 1 year will be $10,594.63.

The APR (r) will be ...

  A = P(1 +r)^t

  10594.63 = 10000(1 +r)¹

  r = 10594.63/10000 -1 = 0.059463 ≈ 5.95%

The effective yield is about 5.95%.