A rectangular classroom is 10m long and 4.6m wide. Make a scale drawing of the classroom using the following scales.

Answer:

x = 6

Step-by-step explanation:

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Answer:

  (x -4)² +(y +3)³ = 4

Step-by-step explanation:

Each circle is centered on (h, k) = (4, -3). Each circle has a radius 1 unit smaller than the circle just outside of it. The innermost circle shown has a radius of 3, so the next in the pattern of smaller circles will have a radius of 2. The equation for a circle centered at (h, k) with radius r is ...

  (x -h)² +(y -k)² = r²

The next circle in the pattern is centered at (4, -3) and has radius 2, so its equation is ...

  (x -4)² +(y +3)² = 4

Answer:

790

Step-by-step explanation:

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Answer:

Step 1: Read the entire problem. Students will find themselves reading the story numerous times. Each time will have a different purpose in the model drawing process. Step 2: Turn the question into a sentence with a space for the answer.

The expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is that a movie website offers one free movie viewing to anyone that registers. The total number of people that register can be modeled by the function f(x) = - 27x³ - 135x² - 72x + 220, where x is the number of months passed since starting the website. The number of free movies available to choose from can be modeled as 3x + 11.

The expression that can be used to determine the average number of people that watch each free movie can be written as -

y = (- 27x³ - 135x² - 72x + 220)(3x + 11)

y = 3x(- 27x³ - 135x² - 72x + 220) + 11(- 27x³ - 135x² - 72x + 220)

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

Therefore, the expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

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Answer:

1.5

Step-by-step explanation:

To determine the scale factor used to create the image, we can compare the distances between corresponding vertices of the two triangles.

Let's start by finding the distance between A and B in triangle ABC:

distance AB = sqrt[(x_B - x_A)^2 + (y_B - y_A)^2]

= sqrt[(-2 - (-6))^2 + (-4 - (-4))^2]

= sqrt[16 + 0]

= 4

Now let's find the distance between A' and B' in triangle A'B'C':

distance A'B' = sqrt[(x_B' - x_A')^2 + (y_B' - y_A')^2]

= sqrt[(-3 - (-9))^2 + (-6 - (-6))^2]

= sqrt[36 + 0]

= 6

To find the scale factor, we can divide the distance between corresponding vertices in the image triangle by the distance between the corresponding vertices in the original triangle:

scale factor = distance A'B' / distance AB

= 6 / 4

= 1.5

Therefore, the scale factor used to create the image is 1.5.

To find the scale factor of a dilation, one can divide a side length of the enlarged shape by the corresponding side length of the original shape. In this case, the scale factor from triangle ABC to A'B'C' is 6/4 = 1.5.

In Mathematics, we can find the scale factor of a dilation by comparing corresponding distances in the original shape and its image. The scale factor can be found by dividing a side length of the enlarged shape (triangle A′B′C′) by the corresponding side length of the original shape (triangle ABC).

For example, the distance between points A and B in the original triangle ABC is 4 units (-2 - (-6) = 4), and the distance between points A′ and B′ in the enlarged triangle A′B′C′ is 6 units (-3 - (-9) = 6). So, the scale factor from ABC to A'B'C' is 6/4 = 1.5.

Therefore, the scale factor used to create the image of triangle A'B'C' from triangle ABC is 1.5.

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Answer:

Step-by-step explanation:

The formula for the area of a circle is A=πr²

r=6cm in this case

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

Answer:

2x + 3y = -13

Step-by-step explanation:

We can first find the equation of the line in point-slope form. The slope of the line is given by \((y_2-y_1)/(x_2-x_1)\), which is (-5-(-3))/(1-(-2)), or -2/3. The equation for a line in point-slope form is \(y-y_1=m(x-x_1)\) where \(m\) is the slope and \((x_1,y_1)\) is a point on the line -- in this case, we may use (1, -5). Therefore, the equation for the line is y + 5 = -2/3 (x-1).

The question asks for the equation of the line in standard form -- which is \(Ax+By=C\). We can get this by simplifying the equation above to get\(2x+3y=-13\).

Answer:

Explanation:

In a regular hexagon, we have 6 equila

He invested in each account as follows:

First account ----->  31,000

Second account ----->  10,000

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

gained - lost = 1670

0.07x - 0.05(41000 - x) = 1670

Find x :

0.07x - 0.05(41000 - x) = 1670

0.07x - 2050 + 0.05x = 1670

0.12x = 1670  + 2050

x = 31,000

41000 - 31,000 = 10,000

He invested in each account as follows:

First account ----->  31,000

Second account ----->  10,000

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Answer:

please mark as brainliest!!!!

Step-by-step explanation:

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The function g(x) is \(g(x) = (x + 7)^3\)

The function f(x) is given as:

\(f(x) = \sqrt[3]{x} - 7\)

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

\(f(x) = \sqrt[3]{x} - 7\)

Rewrite as:

\(y = \sqrt[3]{x} - 7\)

Swap x and y

\(x = \sqrt[3]{y} - 7\)

Add 7 to both sides

\(x + 7 = \sqrt[3]{y}\)

Take the cube of both sides

\(y = (x + 7)^3\)

This implies that

\(g(x) = (x + 7)^3\)

Hence, the function g(x) is \(g(x) = (x + 7)^3\)

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Answer:

Step-by-step explanation: [-2.19] = -3

[3.67] = 3

[-0.83] = -1

The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.

This can be generalized as given below:

[x] = -2, -2 ≤ x < -1

[x] = -1, -1 ≤ x < 0

[x] = 0, 0 ≤ x < 1

[x] = 1, 1 ≤ x < 2

Answer:

y = - \(\frac{3}{2}\) x

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 )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line

m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then

y = - \(\frac{3}{2}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 )

0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so

c = 0

y = - \(\frac{3}{2}\) x + 0 , that is

y = - \(\frac{3}{2}\) x

The computed values f(-3)+f(1) is 64 and f(-3)-f(1) is 52

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=3x²-7x+10.

we need to find the values of f(-3)+f(1) and f(-3)-f(1)

First let us compute the values of f(-3) and f(1)

f(-3)=3(-3)²-7(-3)+10

=27+21+10

f(-3)=58

f(1)=3(1)-7(1)+10

=3-7+10

f(1)=6

f(-3)+f(1)=58+6

=64

f(-3)-f(1)=58-6

=52

Hence, the values of f(-3)+f(1) is 64 and f(-3)-f(1) is 52

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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Answer:

For option A she would receive $1,690. For house B, she would receive $2,070 for a weeks worth of pay.

Step-by-step explanation:

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Given:

Events A and B are independent.

P(A)=

P(not B)=

Required:

P(A and B).

Answer:

We have given that P(A)=

P(not B)=

Then P(B)=

Hence, P(A and B)=

Final Answer:

P(A and B)=

Answer:

Depends on what sequence it is. For geometric it's 7/5 and for arithmetic - 2

Step-by-step explanation:

For n = 3:
a, = 1*2*3 - 1 = 5
For n = 4:
a, = 8 - 1 = 7

These are the terms for n = 3 and n = 4 but the thing is, this could be both geometric sequence and arithmetic sequence, since you didn't specify, here are the possible answers:

For geometric sequence, the rate of change is equal to An / An-1 therefore:
r = 7 /5

For arithmetic sequence, it's equal to A2 - A1 = 7 - 5 = 2

The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

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Answer:

A.), C.), D.) are true

Step-by-step explanation:

Use the properties of exponents.

Answer:

We will first find out average time of each student.

Student 1 = 60 / 12 = 5

Student 2 = 60 / 10 = 6

Student 3 = 60 / 8 = 7.5

Student 4 = 60 / 6 = 10

Student 5 = 60 / 4 = 15

Now we will take the arithmatic mean of all students average time.

A = (5+6+7.5+10+15)/5 = 43.5/5 = 8.7 minutes per problem

The solution to the equation (y)/(a) - b = (y)/(b) - a is y= ab

The equation is given as

(y)/(a) - b = (y)/(b) - a

Such that the variables a and b do not have the same value

Take the LCM

So, the equation becomes

(y - ab)/(a) = (y - ab)/(b)

Cross multiply the equation above

So, we have

by - ab² = ay - a²b

Collect the like terms

So, we have

ab + ay = ab² + a²b

Factor out a + b

y(b + a) = ab² + a²b

So, we have

y(b + a) = ab(b + a)

Divide both sides by b + a

y = ab

Hence, the solution is ab

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It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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Answer:

\(\frac{x+7}{3}\) (the second option)

Step-by-step explanation:

Hope this helps!

Given the function D(x) is defined as shown in the table

Part 1: Find D(0)

So, from the table, we will choose the value of D when x = 0

So,

Part 2: Evaluate D(5)

We will choose the value of D when x = 5

Part 3: Determine D(0) - D(5)

So, we will subtract the values of part1 and part2

a² = b² + c²

a² = 40² + 50²

a² = 1600 + 2500

a² = 4100

a = √4100

a = 64.03