Find and even number between 20 and 50 that is a multiple of 5 and 8

Answer:

B

Step-by-step explanation:

By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².

In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:

(a · cos A + b · sin A)² + (a · sin A - b · cos A)²

Second, expand the expression by algebra properties:

a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A

(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A

(a² + b²) · (cos² A + sin² A)

Third, use the fundamental trigonometric formula:

a² + b²

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Answer:

\(y=-\frac{2}{5} x+\frac{36}{5}\)

Step-by-step explanation:

→ Find the gradient

\(\frac{4-6}{8-3}= \frac{-2}{5} =-\frac{2}{5}\)

→ Write into y = mx + c format

\(y=-\frac{2}{5} x+c\)

→ Substitute in ( 3 , 6 )

\(6 = -\frac{6}{5} +c\)  ∴ \(c = 6+\frac{6}{5} =\frac{36}{5}\)

→ Rewrite into y = mx + c format

\(y=-\frac{2}{5} x+\frac{36}{5}\)

Answer:

? = 900

Step-by-step explanation:

lets change ? to x

(100 + x) / 100 = 10

we will substitute /100

(100 + x) /100 · 100 = 10 · 100

100 + x = 1000

we substitute +100

100 + x -100 = 1000 - 100

x = 900

hope this helps =D happy learning!!

Answer:

To find the answer, we can use the formula:

number of won games / total number of games played = percentage won

Let x be the total number of games played. We know that the percentage won is 65%, or 0.65 as a decimal. So we can set up the equation:

number of won games / x = 0.65

To solve for x, we can cross-multiply:

number of won games = 0.65x

We want to find a whole number value for x that makes sense. One way to do this is to try each answer choice and see if it gives a whole number value for the number of won games. Let's start with choice A:

If the team played 22 games, then the number of won games is:

number of won games = 0.65 * 22 = 14.3

This is not a whole number value, so we can rule out choice A.

We can repeat this process for each answer choice. When we try choice C, we get:

number of won games = 0.65 * 18 = 11.7

This is also not a whole number value, so we can rule out choice C.

When we try choice D, we get:

number of won games = 0.65 * 14 = 9.1

This is also not a whole number value, so we can rule out choice D.

Therefore, the only remaining answer choice is B, which gives us:

number of won games = 0.65 * 20 = 13

This is a whole number value, so the team could have played 20 games in total last season.

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

b = 8

Step-by-step explanation:

7b-20=3b+12

7b - 3b - 20 = 3b -3b + 12

4b - 20 = 12

4b - 20 + 20 = 12 +20

4b = 32

b = 8

According to the information, the maximum infection rate is:  k * 2500 * (5000 - 2500) = 6250k = 40

To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:

where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:

To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:

This implies that 5000 - 2x = 0, and therefore:

Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.

However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:

If the infection rate is 40 new cases per day, we have:

which implies that:

Therefore, the maximum infection rate is:

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The lines through the sides of the triangle tell you all 3 sides are the same. A triangle that has all 3 sides the same have interior angles of 60 degrees.

2x - 10 = 60

Add 10 to both sides

2x = 70

Divide both sides by 2:

X = 35

Answer: 35

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Question 24 :

P594.65 : 35 days

P594.65/7 : 35/7 days

P84.95 : 5 days

⇒ A. P84.95

Question 25 :

88.75 + 85.5 + 90.5 + 87.25 / 4

352/4

88

⇒ B. 88

Question 26 :

I = P × r × t

I = 580.00 × 0.065 × 1

I = P37.70

⇒ B. P37.70

Answer:

The points that are 17 units from P(-97,2) are:

(-105,-13) and (-105,17)

Step-by-step explanation:

Distance between two points

The distance between points A(x,y) B(w,z) can be calculated with the formula:

\(d=\sqrt{(w-x)^2+(z-y)^2}\)

One point is (-105,y) and the other is (-97,2). Computing the distance between them:

\(d=\sqrt{(-97-(-105))^2+(2-y)^2}=\sqrt{8^2+(2-y)^2}=\sqrt{64+(2-y)^2}\)

This distance is 17, thus:

\(\sqrt{64+(2-y)^2}=17\)

Squaring on both sides:

\(64+(2-y)^2=289\)

Operating:

\((2-y)^2=289-64=225\)

Taking the square root:

\((2-y)=\pm 15\)

There are two possible solutions:

\(2-y=15\Rightarrow y=-13\)

\(2-y=-15\Rightarrow y=17\)

The points that are 17 units from P(-97,2) are:

(-105,-13) and (-105,17)

The Avery had a case against the state of Georgia for not giving him a “trial of his peers"  that the jury's final pick does not correspond to its real likelihood, and events occurred arbitrarily more frequently.

1)Black Americans make up 165814.

population is 691797.

691797 - 165814 = 525983

if you are not Black American.

Probability is =\(\frac{ C_{12}^{525983} }{C_{12}^{691797} }\) = 0.037316709.

2)African Americans = 165814.

population is= 691797.

Probability is equal to \(\frac{165814}{691797}\)=0.23968519.

As a juror

African Americans = 111.

21624 people live there.

Probability is equal to  \(\frac{165814}{691797}\)= 0.051563078

Hence, the answer is yes, but more likely.

3)Juror probability:   \(\frac{165814}{691797}\)= 0.051563078

Hence, based on 60 x0.05, there should be about 3 African Americans, yet there are none. hence, by chance.

4)As we can see, the jury's final pick does not correspond to its real likelihood, and events occurred arbitrarily more frequently.

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Answer:

this is the solution

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer: 81.25mm or 8.125cm

Step-by-step explanation:

Numerator is actual size, denominator is the size in picture

Using the z-score formula as shown below

Calculate the z-score range from 380 miles to 420miles

The probability for the range will be

Option A is the right answer

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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Answer: 9% sales tax

Step-by-step explanation: 40.33-37=3.33

so, now we got to divide 3.33 by 37 (3.33/37) and that = 0.09. Now we got to do 0.09x100 and you get 9%. So basically, subtract, divide, and multiply by 100

Answer:

8x+12y=120

Step-by-step explanation:

i took the test

The expression is equivalent to the expression (12 + 3) ÷ 5 is (3 + 12) ÷ 5

From the question, we have the following parameters that can be used in our computation:

(12 + 3) ÷ 5

The above expression is a quotient expression

However, we can apply some algebraic properties

Take for instance;

12 + 3 can be expressed as 3 + 12

So, we have

(12 + 3) ÷ 5 = (3 + 12) ÷ 5

Hence, the expression is equivalent to the expression is (3 + 12) ÷ 5

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The Surface area of Triangular Prism is 132 cm².

We have have the dimension of prism as

Sides = 3 cm, 4 cm, 5 cm

and, l = 10 cm

and, b= 4 cm

Now, Surface area of Triangular Prism as

= (sum of sides) l + bh

= (3 + 4 + 5)10 + 4 x 3

= 12 x 10 + 12

= 120 + 12

= 132 cm²

Thus, the Surface area of Triangular Prism is 132 cm².

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Answer:

the total cost would be $20.25

Step-by-step explanation:

Answer:

I honestly have no idea

Step-by-step explanation:

good luck

Answer:

p = x² − 6x + 10

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−i is a root, then 3+i is also a root.

p = (x − (3−i)) (x − (3+i))

p = x² − (3+i)x − (3−i)x + (3−i)(3+i)

p = x² − 3x − ix − 3x + ix + (9 − i²)

p = x² − 6x + 10

You can check your answer using the quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ 6 ± √(36 − 40) ] / 2

x = (6 ± 2i) / 2

x = 3 ± i

Answer:

Slope = - 5

Step-by-step explanation:

Let,

x1 = 13

x2 = 14

y1 = 11

y2 = 6

Formula : -

Slope = ( y2 - y1 ) / ( x2 - x1 )

Slope = ( 6 - 11 ) / ( 14 - 13 )

          = - 5 / 1

Slope = - 5

Answer:

\(\boxed{\sf slope:-5}\)

Step-by-step explanation:

Slope :

\(\boxed{\sf m=\cfrac{rise}{run} =\cfrac{y_2-y_1}{x_2-x_1}}\)

\(\sf ^*m=slope\)

\(\sf (x_1, y_1): first \: coordinates\)

\(\sf (x_2, y_2): second\: coordinates\)

___________________

\(\sf \left(x_1,\:y_1\right):\left(13,\:11\right)\)

\(\sf \left(x_2,\:y_2\right):\left(14,\:6\right)\)

\(\sf slope\:(m)=\cfrac{6-11}{14-13}\)

\(\sf slope\:(m)=-5\)

____________________

Answer:

50

Step-by-step explanation:

0.8 * x = 40

40/0.8=50

The equation of the line that passes through (2,28) and is perpendicular to the line that passes through (3,7) and (-2,5) is 5x + 2y = 66.

To find the equation of the line that passes through the point (2,28) and is perpendicular to the line that passes through the points (3,7) and (-2,5).

We need to follow a few steps.

Let us first determine the slope of the line passing through the points (3,7) and (-2,5).

We use the formula for finding slope, which is given as follows:m = (y2 - y1)/(x2 - x1)

Here,

x1 = 3, y1 = 7, x2 = -2, y2 = 5.

Substituting these values, we get:m = (5 - 7)/(-2 - 3) = -2/-5 = 2/5

Therefore, the slope of the line passing through (3,7) and (-2,5) is 2/5.

Now, since the line that we are looking for is perpendicular to this line, its slope will be the negative reciprocal of this slope.

We find the negative reciprocal as fol

lows:-

1/(2/5) = -5/2

Therefore, the slope of the line we are looking for is -5/2.

Now we can use the point-slope form of the equation of a line to find its equation.

This equation is given as follows:y - y1 = m(x - x1)

Here, (x1, y1) = (2,28) and m = -5/2.

Substituting these values, we get: y - 28 = (-5/2)(x - 2)

Expanding this equation, we get: 2y - 56 = -5x + 10

Rearranging this equation, we get: 5x + 2y = 66

Therefore, the equation of the line that passes through (2,28) and is perpendicular to the line that passes through (3,7) and (-2,5) is 5x + 2y = 66.

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