Question 1-1
Determine the coordinates of A” when CASH is reflected over x=2 followed by (x,y) → (x-1, y-5).

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

3/6

Step-by-step explanation:

1 2 and 3 are less than 4 so only 3 numbers

Answer: D) 1/5

Step-by-step explanation:

Format for point-slope form:  y-y₁=m(x-x₁)

x1, y1 is a point on the line

m is the slope

So in this equation, m = 1/5

so, the slope is 1/5

hope this helps!

Answer:

Step-by-step explanation:

The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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The measure of angle A in the triangle ABC with measure a = 10.7 cm, b = 9.0cm and ∠B=55° is 76.9°

An equation is an expression that shows the relationship between two or more variables and numbers.

Sine rule is used to show the relationship between the sides and angles of a triangle.

Using sine rule:

a /sin(A) = b/sin(B)

Hence:

10.7/ sin(A) = 9 / sin(55)

A = 76.9°

The measure of angle A in the triangle ABC with measure a = 10.7 cm, b = 9.0cm and ∠B=55° is 76.9°

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The type of sample being used in this scenario is a cluster sample, where the municipality surveys all households in 149 randomly-selected neighborhoods door-to-door to gather residents' opinions on the proposed property tax increase.

In a cluster sample, the population is divided into groups or clusters, and a subset of clusters is selected for data collection. In this case, the neighborhoods are considered the clusters, and 149 randomly-selected neighborhoods are surveyed.

The advantage of using a cluster sample is that it simplifies the sampling process by grouping individuals together based on their proximity. By visiting homes door-to-door within each selected neighborhood, the municipality can efficiently gather information from a diverse range of households without the need to individually select households from the entire population.

However, it's important to note that the use of a cluster sample introduces a potential for clustering effects, where individuals within the same cluster may have similar opinions or characteristics. This clustering effect needs to be taken into account during data analysis to ensure accurate representation of the entire population.

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Answer:

12 ^ 1/2 or \(\sqrt{12}\)

Step-by-step explanation:

12^2

We want to do the inverse operation, which is the square root

We can write the square root as

^ 1/2  or as \(\sqrt{ }\)

So the inverse of squaring 12 is

12 ^ 1/2 or \(\sqrt{12}\)

=======================================================

Explanation:

Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write

\(\sqrt{x} = x^{1/2}\)

The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.

The more general rule is

\(\sqrt[n]{x} = x^{1/n}\)

which says the nth root of x is the same as x^(1/n).

Using the half-angle identity for tangent, we have: tan(157.5°) = ±sqrt((1 - cos(315°))/(1 + cos(315°))). cos(3πt) = ±sqrt((1 + cos(6πt))/2)

To find the exact values of the trigonometric functions using the half-angle identities, we can use the formulas:

tan(x/2) = ±sqrt((1 - cos(x))/(1 + cos(x)))

cos(x/2) = ±sqrt((1 + cos(x))/2)

sin(x/2) = ±sqrt((1 - cos(x))/2)

Let's apply these formulas to find the exact values for the given trigonometric functions:

tan(157.5°)

We can rewrite 157.5° as (315°/2) since it is half of 315°.

Using the half-angle identity for tangent, we have:

tan(157.5°) = ±sqrt((1 - cos(315°))/(1 + cos(315°)))

cos(3πt)

We can rewrite 3πt as (6πt/2) since it is half of 6πt.

Using the half-angle identity for cosine, we have:

cos(3πt) = ±sqrt((1 + cos(6πt))/2)

(No given function)

The exact values for the trigonometric functions using the half-angle identities can be obtained by substituting the values into the formulas and simplifying the expressions. However, since there is no specific function provided in question 8, we cannot determine its exact value using the half-angle identities.

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Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.

The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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Answer:

x/6   = 3/2

Step-by-step explanation:

Answer:

(0, 1), (1, 2)

Step-by-step explanation:

We have to find solution of system of equation, we have

\(x^2 + 1 = x + 1\)

\(x^2 - x = 0\)

\(x (x - 1) = 0\)

hence we have x = 1 or x = 0

hence ordered pairs are (x, f(x)) for x = 0 and x = 1

(0, 0 + 1) and (1, 1 + 1)

(0, 1) and (1, 2)

Hopefully this answer helped you!!

Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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Answer: 6.79

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer: 99m

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

45?

Step-by-step explanation:

Answer:

0.083333333

is the answer

Answer:

12

Step-by-step explanation:

It is likely to spin a number greater than 25 than to spin a number less than 9.

Let's assume the spinner has 'n' equally likely sections.

Given that probability of spinning a number greater than 25 is 0.45, we can represent it as \(P(Number > 25) = 0.45\)

Since the spinner has 'n' equally likely sections, the probability of spinning a number less than 9 can be represented as: \(P(Number < 9)\) (Number of sections labeled less than 9) / n

We are given the odds of spinning a number less than 9 as 2:3. \(P(Number < 9) / P(Number > = 9) = 2/3\)

Simplifying this, we get

P(Number < 9) = (2/3) * P(Number >= 9)

Since P(Number >= 9) = 1 - P(Number < 9), we will substitute it into the equation

P(Number < 9) = (2/3) * (1 - P(Number < 9))

(3/5) * P(Number < 9) = 2/3

P(Number < 9) = (2/3) * (5/3)

P(Number < 9) = 10/9.

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Answer:

1

Step-by-step explanation:

the first one because if you take the expression that you want, and expanding it out, you will get the first one.

Answer:

A

Step-by-step explanation:

(a^2)^3 (b^5)^3

The powers multiply when written like this. They don't add.

a^6 b^15

A

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

Answer:

4x + 2.5y = 184

x = y - 6

Step-by-step explanation:

Let the number of smoothies sold by stand = x

And number of cones sold = y

If the selling price of each cone = $2.5

Selling price of the 'y' cones = $2.5y

Selling price of each smoothies = $4

Then sales of smoothies = $4x

If the total sales of one day = $184

Equation for this situation will be,

4x + 2.5y = 184 -------(1)

If the stand sold 6 less smoothies than the cones,

x = y - 6 -----(2)

Therefore, system of equations contains two equations (1) and (2).

Answer:

eg;-3302/1000

Step-by-step explanation:

no because it can be written in p/q form

Here is the full question.

In order for a vaccine to be effective, it should reduce a person's chance of acquiring a disease. Consider a hypothetical vaccine for malaria‚- a tropical disease that kills between 1.5 and 2.7 million people every year.1 Suppose the vaccine is tested with 700 volunteers in a village who are malaria-free at the beginning of the trial. Three hundred of the volunteers will get the experimental vaccine and the rest will not be vaccinated. Suppose that the chance of contracting malaria is 10% for those who are not vaccinated.

Construct a two-way table to show the results of the experiments if:

(a) The vaccine has no effect

(b) The vaccine cuts the risk of contracting malaria in half

Answer:

Step-by-step explanation:

From the given information above:

Suppose, there is no effect from the vaccine, the risk of having malaria for vaccine & no vaccine is equal to 0.1

Now, the Probability of not having malaria if vaccinated or no vaccinated = 1 - 0.1 = 0.9

Therefore: the table is shown below as follows:

                             Malaria              No Malaria                Total

Vaccinated          300 × 0.1 = 30     300 × 0.9 = 270    300

No Vaccine          400 × 0.1 = 40    400 × 0.9 = 360      700-300 = 400

Total                     40 + 30 = 70      270 + 360 = 630       700

(b)

The risk of malaria for vaccinated if the vaccine cuts the risk of contracting malaria in half are equal to 0.1/2 = 0.05

Thus; the probability of not getting malaria if vaccinated = 1 - 0.05 = 0.95

The table can then be computed as follows:

                             Malaria                No Malaria                 Total

Vaccinated       300 × 0.05 = 15     300 × 0.95 = 285       300

No Vaccine      400 × 0.1 = 40         400 × 0.9 = 360         700-300 = 400

Total                 40 + 15 = 55             285 + 360 = 645       700

It will take Jamal's robot 8 seconds to catch up to Kate's robot.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let's t represent the time it takes for Jamal's robot to catch up to Kate's robot (in seconds).

During this time, Kate's robot will have traveled a distance of 2t + 8 feet.

Jamal's robot will have traveled a distance of 3t feet.

When Jamal's robot catches up to Kate's robot, these two distances will be equal:

2t + 8 = 3t

Solving for t:

3t -2t = 8

t = 8 seconds.

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Answer: number= 5.5; equation: 4x+8=30

Step-by-step explanation:

Take x for the unknown number. Then just follow the words and turn them into mathematical symbols. Easy.