Write down next two terms in this number pattern: 2,5,9,14,20

Answer:

r=53 degrees

______

yan po

The fraction by which the income decreased in August is given as follows:

1/5.

The total income is given by a proportional relationship of the cost per item and the number of items sold, hence:

y = kx.

In which:

For August, the parameters are given as follows:

Hence the August expression is given as follows:

y = 4k/3 x 3x/5

y = 12kx/15

y = 4kx/5.

Hence the decrease is given as follows:

1 - 4/5 = 5/5 - 4/5 = 1/5.

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a) The graph of the function, highlighting the part indicated by the given interval is shown.

b) A definite integral that represents the arc length of the curve over the indicated interval is,

L = ∫[0,4] √[(x² + y²) / x²] dx

Now, For the arc length of the curve, we can use the formula:

L = ∫[a,b] √[1 + (dy/dx)²] dx

First, let's find the derivative of x with respect to y:

dx/dy = -y / √(25 - y²)

Now, we can find the derivative of x with respect to x by using the chain rule:

dx/dx = dx/dy dy/dx = -y / √(25 - y²) (dx/dy)⁻¹

= -y / √(25 - y²) × √(25 - y²) / x

= -y / x

Substituting this into the formula for arc length, we get:

L = ∫[0,4] √[1 + (-y/x)²] dx = ∫[0,4] √[(x² + y²) / x²] dx

Unfortunately, this integral cannot be evaluated with the techniques we have studied so far.

However, we can approximate the value of the arc length using numerical methods such as the trapezoidal rule or Simpson's rule.

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Answer:

the answer is A I think it will help u

Answer:

When you combine -14 -9and3

than you actually get -20

Answer:

ANSWER, A

Step-by-step explanation:

\(\frac{x^{2} }{20} +\frac{y^{2} }{36} =1\)

The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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f(x) = √x g(x) = 1/(x - 4)

Domain of (f o g)(x) ==> 4 < x < +inf ==> x > 4

Doamain of (g o f)(x) ==> x >= 0, x different of 16

Answer:

\(\displaystyle \sin\theta=\frac{12}{13}\)

Step-by-step explanation:

We are given that:

\(\displaystyle \cos\theta =-\frac{5}{13}\text{ where $\theta$ is in QII}\)

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using the Pythagorean Theorem, solve for the opposite side (we can ignore the negative for now):

\(o=\sqrt{13^2-5^2}=12\)

And since θ is in QII, sine is positive, and cosine and tangent are both negative.

Sine is the ratio of the opposite side to the hypotenuse. Therefore:

\(\displaystyle \sin\theta=\frac{12}{13}\)

Answer: A monomial representation is a way to express a polynomial as a product of powers of its variables, where each power is a non-negative integer. For example, the polynomial 2x^3 + 4x^2 - 6x + 8 can be represented as a monomial representation of (2x^3)(x^2)(-6x)(8).

Symmetric polynomials are polynomials that are invariant under permutation of their variables. A symmetric presentation is a way of expressing a symmetric polynomial as a sum of elementary symmetric polynomials, which are defined as the sum of all possible products of variables taken i at a time, where i ranges from 1 to the number of variables. For example, the symmetric polynomial x^3 + y^3 + z^3 can be expressed as a symmetric presentation of x + y + z.

Step-by-step explanation:

The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: A certain type of bacteria doubles every hour

Now number of hours between 9-12 pm

is 15 hours

if at 9 a.m the amount of bacteria is x then we have in 15 hours

at t=1 we have the number of bacteria was

T=2×15

=30

Similarly we have for t=15 we get

T=15×2¹⁵

Hence, The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

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Answer:

is it to late now??

Step-by-step explanation:

Answer: If you are meaning for the number to be squared would be ten.

Step-by-step explanation:

49 divided by 2 equals 7, 7 plus 3 =10

The answer would be C. 10

Answer:

Answer:

Step-by-step explanation:

You graph it

The answer is log4(9x)

Answer:it’s 2100

Step-by-step explanation:

The volume of the cone is one-third of the product of its base area and its height. The volume of the cone is 2,700π units³.

The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,

\(\text{Volume of the cone}= \dfrac{1}{3} \times (\pi r^2) \times h\)

Given the radius of the circular base is 10  units and the height of the cone is 81.

\(\text{Volume of the cone}= \dfrac{1}{3} \times (\pi r^2) \times h\)

\(\text{Volume of the cone}= \dfrac{1}{3} \times (\pi \times 10^) \times 81\\\\\text{Volume of the cone}= 2,700 \pi \rm\ units^3\)

Hence, the volume of the cone is 2,700π units³.

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Step-by-step explanation:

-(3x+y=32)

3x-2y=17

-3x-y=-32

3x-2y=17

-3y=-15

y=5

3x+(5)=32

-5. -5

3x=27

x=9

Answer:

x=9

y=5

Answer:

x = 9

y = 5

Step-by-step explanation:

3x + y = 32...(1)

3x - 2y = 17....(2)

multiplying equation (1) by 2 we get,

6x + 2y = 64...(3)

Adding eq(2) and (3) we get,

6x + 2y = 64

+ 3x - 2y = 17

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

9x. = 81

therefore, x = 81/9

therefore, x = 9

substituting value of x in eq( 1)

3 * 9 + y = 32

27 + y = 32

y = 32 - 27

y = 5

The radius of the cylindrical shaped soup can is r = 3.3 cm

Given data ,

A company is designing a soup can that is in the shape of a right circular cylinder. The height of the can will be 3 times the radius of the can. The volume of the can will be 350 cubic centimeters

Now , Volume of Cylinder = πr²h

where h = 3r

On simplifying , we get

350 = πr²3r

350 = 3πr³

Divide by 3π on both sides , we get

r³ = 37.13615

Taking cube root on both sides , we get

r = 3.3 cm

Hence , the radius of soup can is r = 3.3 cm

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Answer:

5.1 × 10^7

look up scientific calculator :)

Given that a restaurant has a total of 16 tables, each of which can seat a maximum of 4 people, and if 50 people were sitting at the tables in the restaurant with no tables empty, we need to find out the greatest possible number of tables that could be occupied by just 1 person.

Here, the maximum number of people that can be seated in the restaurant = 16 tables × 4 persons per table = 64 persons.Thus, number of empty seats = 64 − 50 = 14 empty seats.Let's assume x be the greatest possible number of tables that could be occupied by just 1 person. So, number of tables occupied by more than one person = 16 − x.

As the 50 people are seated in the restaurant, the number of persons occupying more than one seat plus the number of persons occupying exactly one seat should add up to 50. So, the number of persons occupying more than one seat = 50 − number of persons occupying exactly one seat = 50 − x.So, the total number of seats occupied is:x + 2(16 − x) = 50 − x⇒ 3x = 18⇒ x = 6.Hence, the greatest possible number of tables that could be occupied by just 1 person is 6.

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For the given scenario: the Probability of making both shots are A. 0.64 and B. 0.72

a) If a player makes 80% of his foul shots, the probability of making a single foul shot is 0.8. Since the two shots are considered independent events, the probability of making both shots is the product of the individual probabilities.

Therefore, the probability of making both shots is 0.8 * 0.8 = 0.64.

To calculate the probability of making exactly one shot, we need to consider two scenarios: making the first shot and missing the second, or missing the first shot and making the second. Each scenario has a probability of 0.8 * 0.2 = 0.16.

Therefore, the probability of making exactly one shot is 0.16 + 0.16 = 0.32.

Similarly, the probability of missing both shots is 0.2 * 0.2 = 0.04.

b) In this case, the outcome of the second shot depends on the outcome of the first shot. If the player makes the first shot (with a probability of 0.8), the probability of making the second shot is 0.9.

Therefore, the probability of making both shots is 0.8 * 0.9 = 0.72.

If the player misses the first shot (with a probability of 0.2), the probability of making the second shot is 0.7.

Therefore, the probability of making exactly one shot is 0.2 * 0.7 = 0.14.

Since there are only two possible outcomes (making both shots or making exactly one shot), the probability of neither shot being made is 1 - (0.72 + 0.14) = 0.14.

Therefore, for the given scenario:

a) Probability of making both shots: 0.64

  Probability of making exactly one shot: 0.32

  Probability of missing both shots: 0.04

b) Probability of making both shots: 0.72

  Probability of making exactly one shot: 0.14

  Probability of missing both shots: 0.14

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Answer:

21/20

Step-by-step explanation:

One way to look at it:

Convert 1.05 to a percentage so it's easier to see it as fraction out of 100

fraction x 100 = %

1.05 x 100 = 105%

105% means 105/100, and reducing the fraction gives 21/20.

21/20 = 1.05

The standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

To calculate the standard deviation of the sampling distribution of sample means, we need to use the formula for the standard deviation of a sample mean. This formula states that the standard deviation of the sampling distribution (σ) is equal to the standard deviation of the population (σ) divided by the square root of the sample size (n).

Given that the population standard deviation (σ) is 5.9 pounds and the sample size (n) is 72, we can plug these values into the formula:

Standard Deviation of the Sampling Distribution (σ) = σ / √n

σ = 5.9 pounds

n = 72

Substituting these values, we get:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / √72

To find the standard deviation of the sampling distribution, we need to evaluate the square root of 72. Using a calculator or mathematical software, we find that √72 is approximately 8.49.

Now, let's calculate the standard deviation of the sampling distribution:

Standard Deviation of the Sampling Distribution (σ) = 5.9 / 8.49 ≈ 0.695 pounds (rounded to two decimal places)

Therefore, the standard deviation of the sampling distribution of sample means, based on samples of the amounts of weight lost by 72 people on this diet, is approximately 0.695 pounds.

This value represents the average amount of variation or dispersion in the means of different samples taken from the population. It indicates how much the sample means are likely to deviate from the population mean.

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The functions and their transformations are

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

f(x) = 2(x + 1)² - 3

A translation down by 5 units is represented as

f(x) - 5

So, we have

f(x) - 5 = 2(x + 1)² - 3 - 5

f(x) - 5 = 2(x + 1)² - 8

Rewrite as

h(x) = 2(x + 1)² - 8

A translation left by 5 units is represented as

f(x + 5)

So, we have

f(x + 5) = 2(x + 1 + 5)² - 3

f(x + 5) = 2(x + 6)² - 3

Rewrite as

k(x) = 2(x + 6)² - 3

A translation right by 5 units is represented as

f(x - 5)

So, we have

f(x - 5) = 2(x + 1 - 5)² - 3

f(x - 5) = 2(x - 4)² - 3

Rewrite as

g(x) = 2(x - 4)² - 3

A translation up by 5 units is represented as

f(x) + 5

So, we have

f(x) + 5 = 2(x + 1)² - 3 + 5

f(x) + 5 = 2(x + 1)² + 2

Rewrite as

j(x) = 2(x + 1)² + 2

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Answer:

8

Step-by-step explanation:

Answer: x = 0, Y = 2    

              x = 1, Y = 5

Step-by-step explanation:

Y = −3x^2 + 6x + 2

Y = 3x + 2

We can set the two equations equal to each other, since they both equal Y:

−3x^2 + 6x + 2 = 3x + 2

−3x^2 + 3x = 0

 3x(-x + 1) = 0

This gives us two possible solutions:

x = 0

x = 1

When x = 0, Y = 3(0) + 2 = 2

When x = 1, Y = 3(1) + 2 = 5

Therefore, the solutions to the system of equations are:

x = 0, Y = 2

x = 1, Y = 5

The top priority during physical activity in the classroom is the safety and well-being of the students.

Ensuring a safe environment for physical activity helps prevent injuries and promotes the overall health and engagement of the students.

1. Supervision: Adequate adult supervision should be provided to monitor the students' activities, ensuring they are engaged in safe and appropriate physical exercises.

2. Proper Warm-up and Cool-down: Encouraging students to perform warm-up exercises before engaging in more vigorous activities and cool-down exercises afterward helps prevent injuries and promotes proper muscle recovery.

3. Suitable Physical Activities: The chosen physical activities should be age-appropriate, taking into account the students' physical abilities and limitations. Activities should be designed to minimize risks and promote participation for all students.

4. Clear Instructions and Demonstration: Teachers should provide clear instructions and demonstrate proper techniques for exercises or activities to ensure students understand how to perform them safely and effectively.

5. Equipment and Environment Safety: Regular inspection of equipment and ensuring the physical environment is free from hazards (such as tripping hazards or obstacles) is essential for maintaining a safe setting.

6. Individual Needs and Modifications: Teachers should consider any individual needs or limitations of students, such as physical disabilities or health conditions, and make necessary modifications or adaptations to ensure their safety and inclusion.

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the top priority during physical activity in the classroom is?

The change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

We have,

Length of coasts along the hill = 62.2 meters,

And,

The angle car make with the ground = 28.3°,

And,

The mass of the car = 1234 kg,

Now,

We know,

From the Work Energy Theorem that,

The change in Potential energy = The work done on the mass.

And,

Work done i.e. W = F × s × CosΘ

Here,

F = Force,

s = Distance car cover,

And,

Θ = Angle car make with the ground,

And,

We know that,

Force i.e. F = mass × acceleration due to gravity = m × g

And,

g= Acceleration of gravity = 9.8 m/s²

So,

Now,

Putting values,

i.e.

F = 1234 × 9.8 = 12093.2 Newton

Now,

Using the Formula of Work done,

i.e.

W = F × s × CosΘ,

Putting values,

i.e.

W = 12093.2 × 62.2 × Cos(28.3°)

On solving we get,

W = 662,292.459 Joule

So,

Chane in potential energy = 662,292.459 Joule

Hence we can say that the change in potential energy of the car coasts along the hill will be 662,292.459 Joule.

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