Rotate ΔABC with vertices A(-1, 4), B(2, 1), and C(3, -3) about the origin by 90°.

What are the coordinates of A'?

We will have the following:

From the polynomial we will have that:

*It falls to the left and rises to the right.

This can be seeing as follows:

three angles= 180

180/3

60

The probability that at least one ball of each color is chosen is 105/8568.

Given that:-

Number of red balls in the urn = 5

Number of white balls in the urn = 6

Number of blue balls in the urn = 7

We have to find the probability that at least one ball of each color is chosen.

Let us consider the that 1 ball of each color has been chosen.

Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.

Now we have to choose 2 balls from them.

Hence,

Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = \(^{15}C_2=105\)

Total number of ways in which we can choose 5 balls from 18 balls =

\(^{18}C_5=8568\)

Hence,

Probability that at least one ball of each color is chosen = 105/8568

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Answer:

Step-by-step explanation:

a. 1+(-8)

b. 1+8

The response is calculated by taking the Laplace transform of the input, multiplying it with the transfer function G(s), and then applying the inverse Laplace transform to obtain the time-domain response.

To calculate the response of the system G(s) to the given input u(t), we first need to find the Laplace transform of the input function u(t). The input function u(t) consists of multiple sinusoidal components, which can be represented in the Laplace domain using complex exponential functions.

Taking the Laplace transform of u(t), we get U(s) = 2/(s^2 + 1) + (-4)/(s^2 + 9) + 2/(s^2 + 25). Now, we multiply U(s) with the transfer function G(s) = (s + 1)/(s^2 + 2s + 2). Multiplying these two expressions, we obtain the product G(s)U(s).

Next, we need to apply the inverse Laplace transform to obtain the time-domain response. By using partial fraction decomposition and considering the inverse Laplace transforms of individual terms, we can calculate the inverse Laplace transform of G(s)U(s).

The final result will be the time-domain response of the system G(s) to the given input u(t). The response will contain the combined effect of the system dynamics and the input signal.

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Answer:

100

tvtvtvtcxtexxxtuncd,d,w

Answer:

100

Step-by-step explanation:

because 50 + 50 = 100

Answer:

The value of a₁₀ is -1158

Step-by-step explanation:

a₃ = 18

a₆ = - 486

Now,

a₃ = 18 can be written as

a + 2d = 18 ...(1) and

a₆ = - 486 can be written as

a + 5d = - 486 ...(2)

Now, from equation (2) we get,

a + 5d = - 486

a + 2d + 3d = - 486

18 + 3d = - 486 (.°. a + 2d = 18)

3d = - 486 - 18

3d = - 504

d = - 504 ÷ 3

d = - 168

Now, for the value of a put the value of d = -168 in equation (1)

a + 2d = 18

a + 2(-168) = 18

a - 336 = 18

a = 18 + 336

a = 354

Now, For a₁₀

a₁₀ = a + 9d

a₁₀ = 354 + 9(-168)

a₁₀ = 354 - 1512

a₁₀ = -1158

Thus, The value of a₁₀ is -1158

-TheUnknownScientist

1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

In this question,

a small pool hold 1500 gallons of water.

When there's is 5 gallons of water in the pool, the person decided

that not to stand outside and watch the pool fill.

This means, from the time he had decided, the amount of water in the pool = 5 gallons.

the water was filling the pool at a rate of 2.

Let t be the time in minutes.

So, the amount of water in the pool after 't' minutes would be,

f(t) = 2t + 5

We get an mathematical model for given situation,

f(t) = 2t + 5, where t is the time in minutes

We need to find the amount of water in the pool after 50 minutes

For t = 50 minutes

f(50) = 2(50) + 5

f(50) = 100 + 5

f(50) = 105 gallons

Also, we need to find the amount of time required to fill the pool.

1500 = 2t + 5

1495 = 2t

t = 747.5 minutes

t = 12 hours 46 minutes

Therefore, 1) the mathematical model for given situation is f(t) = 2t + t, where t is the time in minutes

2) the amount of water in the pool after 50 minutes = 105 gallons

3) and the amount of time required to fill the pool =  12 hours 46 minutes

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Answer:

y = -3x + 15

Step-by-step explanation:

The equation of the line parallel to the given line that contains point is:

3x + y - 15 = 0 (General form)

y = -3x + 15 (Slope y-intercept form)

Step 1: The slope of a given line is. m = -3

Step 2: Parallel lines have the same slope, so the slope of the unknown line (m1 ) will also be -3. So, the parallel line will have a slope of m1 = -3

Step 3: Now we have a point and the slope so we can use point-slope form, which is: y - y0 = m1 (x - x0)

In this example we have: m1 = -3 , x0 = 4  and y0 = 3 . After substitution we have:

y - y0= m1(x-x0)

y - 3 = -3(x - 4)

y - 3 = -3x + 12

y = -3x + 12 + 3

y = -3x + 15

heres a picture if you don't understand the steps I wrote

Answer:

Maximun of welcome baskets is 4.

There will be 6 muffins, 4 breakfast bars and 3 bottle of juices in each basket

Step-by-step explanation:

Answer:

4 baskets

Step-by-step explanation:

3 juice 6 muffin 4 bars

The range of the function on the graph is all the real numbers greater than or equal to 0. Option B is the correct answer.

The graph of the function is a parabola that opens upwards, which means that the range of the function is all the real numbers greater than or equal to 0. The function can never take on a value less than 0, because the parabola never touches or crosses the x-axis.

The other answer choices are incorrect because they do not include all the possible values of the function. For example, the answer choice O. all the real numbers is incorrect because the function can never take on a negative value.

The answer choice O. all the real numbers greater than or equal to 2 is incorrect because the function can take on values greater than 2, such as 3, 4, and so on.

The answer choice O. all the real numbers greater than or equal to -3 is incorrect because the function can take on values greater than -3, such as 0, 1, and so on.

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Answer:

8

Step-by-step explanation:

ABCD is a parallelogram.

Measures of the opposite sides of a parallelogram are equal.

Therefore, x = 8

Answer: x=8

Step-by-step explanation:

They are parallel which means that they with be the same length

Answer:

B

Step-by-step explanation:

Great circles are the largest possible circles that can be drawn around a sphere and are the lines called in Riemann's spherical geometry.

Answer:

27

Step-by-step explanation:

4.5*3*2 = 27

hi,

You just have to multiply the three measures.  

So :  

2*3*4.5 =  27 cm³

Easy, is it not ?  

There are 8 different trips that can be made from City X to City Z, passing through City Y.

To find the number of different trips that can be made from City X to City Z, passing through City Y, we can use the multiplication principle of counting.

First, we need to choose one of the 2 major roads from City X to City Y. Then, for each of these roads, there are 4 major roads from City Y to City Z, and we need to choose one of these roads.

By the multiplication principle of counting, the total number of different trips from City X to City Z, passing through City Y, is the product of the number of choices at each stage. Thus, we get:

Number of different trips = Number of roads from City X to City Y x Number of roads from City Y to City Z

= 2 x 4

= 8

This calculation shows how the multiplication principle of counting can be used to find the total number of possible outcomes in a multi-stage process where the number of choices at each stage is known.

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Complete question is:

Automobile Trips. There Are 2 Major Roads From City X To City Y And 4 Major Roads From City Y To City Z. How Many Different trips can be made from City X to City Z, passing through City Y?

Answer:

50% decrease

Step-by-step explanation:

it would be a 50% decrease because half of 8 is 4 and 1/2 is 50 %.

Answer:It is 19.7,??

Step-by-step explanation:

Answer:

$21

Step-by-step explanation:

(a) The revenue if 600 coats are sold is $66,000. (b) 500 coats must be sold to have a revenue of $55,000. (c) The y-intercept of the graph of the equation is (0,0). (d) The slope of the graph of the equation is 110.

(a) The revenue if 600 coats are sold is $66,000.

To find the revenue if 600 coats are sold, we simply plug in 600 for x in the given formula:

y = 110x
y = 110(600)
y = 66,000

Therefore, the revenue from the sale of 600 coats is $66,000.

(b) To find how many coats must be sold to have a revenue of $55,000, we set the revenue formula equal to 55,000 and solve for x:

y = 110x
55,000 = 110x
x = 500

Therefore, 500 coats must be sold to have a revenue of $55,000.

(c) The y-intercept of the graph of the equation is (0,0). This means that when no coats are sold, there is no revenue generated.

(d) The slope of the graph of the equation is 110. This means that for every additional coat sold, the revenue increases by $110. In other words, the slope represents the rate of change of revenue with respect to the number of coats sold.

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Answer:

a square + b square = c square

Answer:

Since the calculated Z= -1.886 lies within the Z∝ = ± 1.96 we fail to reject our null hypothesis  that population mean is 31.8 oz. and not 32 ounces. There is evidence that Mill Valley Brewery is cheating customers by under-filling their bottles.

Step-by-step explanation:

Let the null hypothesis be

H0 : u = 31.8 oz    against  Ha: u ≠ 31.8 oz  two tailed test

For a two tailed test and alpha = 0.05 the z∝ = ± 1.96

The rejection region is Z ≥  ± 1.96

Here n = 50  

sample mean = x= 31.8 oz

and  sample standard deviation= s= 0.75

Population mean= u= 32

Test statistics to be used is

Z= x- u / s/ √n  which is approximately normal

Z= 31.8-32/0.75/ √50

z= -1.886

Since the calculated Z= -1.886 lies within the Z∝ = ± 1.96 we fail to reject our null hypothesis  that population mean is 31.8 oz. and not 32 ounces. There is evidence that Mill Valley Brewery is cheating customers by under-filling their bottles.

The solution to the logarithm equation is log5(2x-7) = 0 is x = 4.

What is logarithm ?

A logarithm is a mathematical function that represents the exponent to which a fixed number, called the base, must be raised to produce a given value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we have the equation \(10^3 = 1000\), the logarithm of 1000 with base 10 is 3, because \(10^3 = 1000\). Similarly, the logarithm of 8 with base 2 is 3, because \(2^3 = 8.\)

According to the question:

To solve for x in the equation:

log5(2x-7) = 0

We can use the definition of logarithms which states that log_b(x) = y is equivalent to \(b^y = x.\)

Applying this to the given equation, we get:

\(5^0 = 2x - 7\)

\(1 = 2x - 7\)

\(2x = 8\)

\(x = 4\)

Therefore, the solution to the equation is log5(2x-7) = 0 is x = 4.

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The solution of the given linear inequality will be y ≥ 18.

What are linear inequalities, exactly?

Linear inequalities are mathematical expressions that involve linear functions and the symbols "<", ">", "<=", ">=", or "≠". They are used to describe a range of possible values that a variable can take.

For example, the inequality 3x + 2 > 10 is a linear inequality, where x is a variable. It means that the possible values of x that satisfy the inequality are those that make the expression 3x + 2 greater than 10. The solution set for this inequality is x > 2.

Now,

To solve the inequality y - 6 ≥ 12, we need to isolate y on one side of the inequality sign. We can do this by adding 6 to both sides of the inequality:

y - 6 + 6 ≥ 12 + 6

Simplifying the left side, we get:

y ≥ 18

So the solution set for this inequality is all values of y that are greater than or equal to 18. We can represent this graphically on a number line by shading all values to the right of and including 18:

---|================================>

  18

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Answer:

y = 2/3x - 2

y = 8/3x - 4

Step-by-step explanation:

If you graph it you will intersect at (1 , -1 1/3)

Answer:

6 yards 4 feet 1 inch

Step-by-step explanation:

First, we have the equation:

4 yards 2 feet 7 inches + 2 yards 1 foot 6 inches

Now, let's add each:

6 yards

3 feet

13 inches

But 13 inches would be 1 foot and 1 inch, so now we have plus 1 foot and replace the inches with just 1 inch:

6 yards

4 feet

1 inch

There you have it!

Happy learning!

--Applepi101

Answer:

7 yds  1 ft 1 inch

Step-by-step explanation:

 4 yards 2 feet 7 inches

+ 2 yards 1 foot 6 inches

------------------------------------------

 6 yards  3 feet  13 inches

13 inches is more than 12 inches (  =1  ft) so subtract 12 inches and add 1 ft

6 yards  3 feet  13 inches

             =1 ft      - 12 inches

-----------------------------------------

6 yds   4 ft    1 inches

4 ft is more than  3f which is 1 yd  ( subtract 3 ft and add 1 yd)

6 yds   4 ft    1 inches

+1 yd  - 3ft

------------------------

7 yds  1 ft 1 inch

Main Answer: A normalized binary number typically consists of three parts:

Supporting Question and Answer:

What is a sign bit in a normalized binary number?

The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.

Body of the Solution: A normalized binary number typically consists of  the following three parts:

Final Answer: A normalized binary number typically consists of three parts:

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The solution to the system is approximately x = 1.58, y = 1.95.

We can substitute y from the first equation into the second one:

2x + 3(5/2x - 1) = 12,

which simplifies to:

2x + 7.5x - 3 = 12,

and further simplifies to:

9.5x = 15.

Solving for x, we get:

x = 15/9.5 ≈ 1.58.

Substituting x = 1.58 back into the first equation y = 5/2x - 1, we find:

y = 5/2*1.58 - 1 ≈ 1.95.

Therefore, the solution to the system is approximately x = 1.58, y = 1.95.

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Solve the following system using substitution.

y = 5/2 x -1

2x + 3y = 12.

6x+2y=-10

move 6x to the other side

2y=-10-6x

divide 2 on both sides

y = -3x - 5