Find the sum of the first 36 terms of the following series, to the nearest integer. 13, 19, 25, ...​

9514 1404 393

Answer:

  a) ∆RLG ~ ∆NCP; SF: 3/2 (smaller to larger)

  b) no; different angles

Step-by-step explanation:

a) The triangles will be similar if their angles are congruent. The scale factor will be the ratio of any side to its corresponding side.

The third angle in ∆RLG is 180° -79° -67° = 34°. So, the two angles 34° and 67° in ∆RLG match the corresponding angles in ∆NCP. The triangles are similar by the AA postulate.

Working clockwise around each figure, the sequence of angles from lower left is 34°, 79°, 67°. So, we can write the similarity statement by naming the vertices in the same order: ∆RLG ~ ∆NCP.

The scale factor relating the second triangle to the first is ...

  NC/RL = 45/30 = 3/2

__

b) In order for the angles of one triangle to be congruent to the angles of the other triangle, at least one member of a list of two of the angles must match for the two triangles. Neither of the numbers 57°, 85° match either of the numbers 38°, 54°, so we know the two triangles have different angle measures. They cannot be similar.

Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

Answer: 207

I hope you get it right

Answer:

  9x +y = 12

Step-by-step explanation:

You want the standard form equation for the line with slope -9 through the point (2, -6).

The point-slope form equation is a good place to start when given a point and a slope. That equation is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y -(-6) = -9(x -2) . . . . line with slope -9 through point (2, -6)

This can be rearranged to the desired form:

  y +6 = -9x +18 . . . . . . eliminate parentheses

  9x +y = 12 . . . . . . . . add 9x -6

The length of the rectangle is (10+x) cm and the width of the rectangle is x cm.

According to the question,

We have the following information:

The width of the rectangle = x cm

Now, the length of the rectangle is given to be 10 cm more than the width of the rectangle.

So, this can be converted in the following mathematical expression:

Length of the rectangle = 10+x cm

(More to know: the area of the rectangle is given by the formula l*b where l is the length and b is the breadth of width of the rectangle.)

Hence, the length of the rectangle is (10+x) cm and the width of the rectangle is x cm.

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The weight of the radioactive substance will be 30 grams after 4.15 years.

Given that,

Initial weight of the substance = 250 grams

The equation which is used to determine the amount of the substance remaining after t years is,

S = 250 (0.60)^t

The amount of the substance will be 30 grams, when,

250 (0.60)^t = 30

(0.60)^t = 30/250

(0.60)^t = 0.12

㏒ ((0.60)^t = ㏒ 0.12

t ㏒ ((0.60) = ㏒ 0.12

t = ㏒ 0.12 / ㏒ ((0.60)

t = 4.15

Hence the amount of the substance will be 30 grams after 4.15 years.

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The minimum value of y is -1. This can be answered by the concept from equation of a circle.

To find the minimum value of y, we need to rewrite the given equation in terms of y. Completing the square, we have:

x² - 14x + y² - 48y = 0
(x² - 14x + 49) + (y² - 48y + 576) = 49 + 576
(x - 7)² + (y - 24)² = 625

This is the equation of a circle with center (7,24) and radius 25. The minimum value of y occurs at the bottom of the circle, which is the point (7,24-25).

Therefore, the minimum value of y is -1.

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EXPLANATION

To derive the answer to the question, we would have to draw some diagrams.

The above diagram shows the triangle formed from the height of the building and the shadow

We will also draw another triangle

The above diagram shows the triangle formed from the height of the woman and the shadow

This is simply a case of similar triangles.

Therefore we can find the height by taking the ratio of the sides.

Therefore, the height of the building is 80 feet

The earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

a. The earnings per share for Company XYZ can be calculated by dividing the closing price by the P/E ratio. In this case, the closing price is $100.76 and the P/E ratio is 1525. Therefore, the earnings per share can be calculated as $0.066 per share (rounded to the nearest cent).

b. Based on the historical P/E ratio range of 12-14, the stock price of Company XYZ seems overpriced. The P/E ratio indicates the price investors are willing to pay for each dollar of earnings generated by the company. A higher P/E ratio suggests that investors have higher expectations for future earnings growth. In this case, the P/E ratio of 1525 is significantly higher than the historical range of 12-14, indicating that the stock is being valued at a much higher premium relative to its earnings. This suggests that the stock price may be inflated and not in line with the company's historical valuation metrics, indicating an overpriced condition.

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Answer:

Answer: -7

Step-by-step explanation:

The roots at which the graph of f(x) =(x + 4\()^6\)(x + 7\()^5\) cross the x axis are -4 and -7.

In mathematics, a root is a solution to an equation that is usually stated as a number or an algebraic formula.

A quadratic equation's roots are the variable values that fulfil the equation. They are also referred to as "solutions" or "zeroes" of the quadratic equation.

We have If(x) = (x + 4\()^6\)(x + 7\()^5\) cross the x-axis then y = f(x) = 0.

Now, if f(x) = 0

then (x + 4\()^6\)(x + 7\()^5\) = 0

Now, calculating in separate the value of x as

x +4 =0 and x+ 7= 0

x = -4 and x = -7

Thus, the roots cross x axis at -4 and -7.

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Answer:

f = 19

Step-by-step explanation:

8 = f - (13 - 2)

f - (13 - 2) = 8

f - 11 = 8

f - 11 + 11 = 8 + 11

f = 19

Answer:

i think the answer is f=19

Answer:

b. 1 foot 5 inches

Step-by-step explanation:

because one foot is 12 inches

The two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

What are the binomials expression ?

The expression x(x − 8) − 9(x − 8) can be simplified as follows:

x(x − 8) − 9(x − 8) = x² - 8x - 9x + 72

= x² - 17x + 72

To find the two binomials, we need to factor the expression \(x^2 - 17x + 72\). We can do this by finding two numbers that multiply to 72 and add to -17. Those numbers are -8 and -9. Therefore, we can write:

\(x^2 - 17x + 72 = (x - 8)(x - 9)\)

Hence, the two binomials for the expression x(x − 8) − 9(x − 8) are (x - 8) and (x - 9).

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There are 35 unique ways to select 4 A students from 7 A students. This can be calculated using the formula: 7C4 = 7! / (4! * (7 - 4)!)

This is a permutation and combination problem that involves finding the number of unique arrangements possible for 4 students out of 7 students who have received grades A.

The formula for permutation of n items taken r at a time is given by P(n,r) = n! / (n-r)! where n is the total number of items and r is the number of items taken at a time.

In this case, we have to find P(7,4) = 7! / (7-4)! = 5040/3! = 840. This means there are 840 different ways in which 4 A students can be uniquely selected from a class of 7 students who received grades A.

This concept is important in many areas of mathematics and science, particularly in the field of statistics where it is used in hypothesis testing, estimation and prediction.

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Answer:

32.87°

Step-by-step explanation:

It is asking for the measure of angle B.

\(tanB=\frac{opposite}{adjacent}\)

\(tanB=\frac{4.2}{6.5}\)

Now you need to find the arctan because you want the angle. (make sure your calculator is in degree mode)

B= arctan(4.2/6.5)

angle B= 32.86867893°

Answer:

x=6

Step-by-step explanation:

Because they are vertical angles, they are equal to one another, so the equation you have to set up would Be 5x=30 and you divide both sides by 5 and yopu get x=6 :)

Answer:

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} ) \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(2,-5); B(6,1)

So we have

\(M = ( \frac{2 + 6}{2} \: , \: \frac{ - 5 + 1}{2} ) \\ = ( \frac{8}{2} \: , \: - \frac{4}{2} )\)

We have the final answer as

Hope this helps you

Using the concept of equations, 1552 people attended the festival last year.

Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.

An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.

Let the number of people who attended the festival last year =x

Then, we can write an equation as

1785=1.15 × x

x = 1785/1.15

=1552 people

So, last year's attendance = 1552

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After rounded to the nearest thousandth, the probability of getting at most 2 heads in 8 coin tosses is 0.109.

Now, The probability of getting at most 2 heads in 8 coin tosses can be calculated using the binomial distribution formula.

Since, The formula is

P(X ≤ 2) = Σ C(n, x) pˣ (1-p)ⁿ⁻ˣ,

where n is the number of trials (in this case, 8), x is the number of successful events (heads), p is the probability of a successful event (0.5 for a fair coin), and Σ means to add up the values of the expression for all values of k from 0 to 2.

Hence, Using this formula, we get

P(X ≤ 2) = C(8,0) 0.5 0.5 + C(8,1) 0.5 0.5 + C(8,2) 0.5 0.5

             ≈ 0.109.

Therefore, After rounded to the nearest thousandth, the probability of getting at most 2 heads in 8 coin tosses is 0.109.

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In order to find the number of distinguishable permutations of the group of letters A, A, G, E, E, E, M, we can use the following formula:

The number of permutations = n! / (n1! n2! ... nk!), where n is the total number of objects to be arranged, and n1, n2, ..., nk are the numbers of objects that are identical to one another.

For this problem, we have 7 letters with 2 A's, 3 E's, and 1 G and 1 M letter.

Using the formula above, we can find the number of distinguishable permutations: 7! / (2! 3! 1! 1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (3 × 2 × 1) × (1 × 1) × (1 × 1)] = 2520

Therefore, there are 2520 distinguishable permutations of the group of letters A, A, G, E, E, E, M.

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Answer:

A. 21...............

Answer: x = 21

Step-by-step explanation:

first, move the constant to the right.

(x + 6)^1/3 = -2 + 5

then, rewrite and calculate.

(again, square root symbols on the computer don't work.)

next, simplify the equation.

x + 6 = 27.

then. move the constant to the right.

x = 27 - 6

finally, finish the calculations.

x = 21

The optimal dimensions for the garden to maximize the area are 30 feet by 18 feet, with fencing costing $2 per foot on three sides and $3 per foot on the fourth side.

To determine these dimensions, we start by setting up the equation based on the given information. The cost of fencing for three sides is equal to 2 times the sum of the length and width of the garden, while the cost of fencing for the fourth side is 3 times the length of the garden. Since the total cost of fencing should not exceed $120, we can set up the equation:

2(l + w) + 3l = 120

Simplifying this equation, we get:

5l + 2w = 120

Next, we aim to maximize the area of the garden, which is given by the formula A = lw. We can solve for one variable in terms of the other using the equation obtained above. Substituting the value of w in terms of l into the area equation, we have:

A = (120 - 2w)/5 * w

A = (120w - 2w^2)/5

To find the maximum area, we can take the derivative of the area equation with respect to w and set it equal to zero. Solving this equation, we find w = 30. Substituting the value back into the equation, we get l = 18.

Therefore, the optimal dimensions for the garden are 30 feet by 18 feet to maximize the area, with the given cost of fencing.

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Answer:

80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

i did 12*6 then i did 2*4 then i add the products

Answer:

\(f(a) = 4(a + 4) - 3 = 4a + 16 - 3 \\ f(x) = 4a + 13 \\ f(5) = 4(5) + 13 = 20 + 13 \\ \boxed{f(5) = 33}\)

Answer:

V=lwh=5 x 9 x 3=135cm+33=4

Step-by-step explanation:

Answer:

.04

Step-by-step explanation:

The total present value of these payments at the time the first payment is made is 1,735.85 (747.26 + 988.59).

To calculate the present value of these payments, we need to use the formula for the present value of an annuity:

\(PV = (P/i) x [1 - (1+i)^-n]\)

Where:
P = payment amount
i = annual effective rate
n = number of payments

Using this formula, we can calculate the present value of the first 10 payments:

\(PV = (100/0.07) x [1 - (1+0.07)^-10] = 747.26\)

To calculate the present value of the remaining 10 payments, we need to first calculate the payment amounts. To do

this, we can use the following formula:

\(Pn = P1 x (1 + g)^n\)

Where:
Pn = payment in year n
P1 = first payment amount
g = growth rate
n = number of years since first payment

For the 11th payment:

\(P11 = 105 x (1 + 0.05)^1 = 110.25\)

For the 12th payment:

\(P12 = 110.25 x (1 + 0.05)^1 = 115.76\)

And so on, until the 20th payment:

\(P20 = 163.32 x (1 - 0.05)^8 = 79.24\)

Now we can calculate the present value of these payments:

PV = \((110.25/0.07) x [1 - (1+0.07)^-10] + (115.76/0.07) x [1 - (1+0.07)^-9] + ... + (79.24/0.07) x [1 - (1+0.07)^-1]\)

PV = 988.59

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Answer:

The maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels further  

Also the distance of the maximum height of first pluck from the player is less than the distance of the second pluck from the player hence the second pluck travels further

Step-by-step explanation:

From the question we are told that

  The maximum height of the first pluck is  \(h_1 = 3 \ ft\)

   The height of the second height is mathematically represented as

              \($y=x\left(0.15-0.001x\right)\)

=>           \(y=0.15x -0.001x^2\)

Generally at maximum height  \(y' = 0\)

So

      \(y'=0.15 -0.002 x = 0\)

=>    \(x =  75 \  ft \)

Here 75 ft is the horizontal distance the second pluck traveled at maximum height

   So the maximum height of the second pluck is mathematically represented as

       \(y=0.15(75) -0.001(75)^2\)

=>     \(y=  5.625 \  ft \)  

So comparing the maximum height  of the first and the second pluck we see that the maximum height of the second pluck is greater than that of the first pluck, hence the second pluck travels father