a rock dropped into a pond causes a circular wave of ripples whose radius increases at 4 inches per second. how fast is the area of the circle of ripples expanding at the instant that the radius of the circle is 24 inches?

Question is incomplete. Answering in a general way;

The side CA has a length of  [tex]\sqrt{c^{2}-b^{2} }[/tex] and Angle C is of 28 degrees.

Given,

Right angled triangle ABC

Length of side AB = b

Length of side BC = c

Angle B = 62°

Angle A = 90°

We have to find the length of side CA and Angle C;

Here,

According to Pythagorean theorem,

Hypotenuse = [tex]\sqrt{base^{2}+altitude^{2} }[/tex]

Here,

Altitude = [tex]\sqrt{Hypotenuse^{2} -Base^{2} }[/tex]

CA = [tex]\sqrt{c^{2} -b^{2} }[/tex]

Now,

Sum of interior angles of a triangle is 180°

Then,

∠A + ∠B + ∠C = 180°

So,

90° + 62° + ∠C = 180°

∠C = 180° - 152°

∠C = 28°

That is,

The length of side CA is [tex]\sqrt{c^{2}-b^{2} }[/tex] and Angle C is 28°

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Answer: C. x ≥ 3

Step-by-step explanation:

5x−10≥−3x+14

Step 1: Add 3x to both sides.

5x−10+3x≥−3x+14+3x

8x−10≥14

Step 2: Add 10 to both sides.

8x−10+10≥14+10

8x≥24

Step 3: Divide both sides by 8.

8x/8 ≥ 24/8

x ≥ 3

Hope this helps!!

Answer:

Your question choices are messed up fix and I can help

Step-by-step explanation:

:)

Therefore the solution for this question is  the unit price of each pair of gloves is $7.99.

One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.

Here,

The cost of 6 pairs of gloves  = $47.94

Now, the unit price = Price per unit of the given item

Let x be the unit price of the glove

thus

x=47.94/6

x=7.99

or it can be written as price of glove=$7.99

Therefore, Unit price of the glove = $7.99

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The equation the represent the event of taking Mrs. Evans taking 9 students to an amusement park and Mr. Sanchez is taking 14 students to a water park is

The problem is solved using simultaneous equation, the equations required is derived as follows:

Amusement park

Admission: $2x per student

Ride Fee: $3.00

Mrs. Evans is taking 9 students to an amusement park

9($2x + $3.00)

Water park

Admission: $x per student

Ride Fee: $4.50

Mr. Sanchez is taking 14 students to a water park

14($x + $4.50)

The total cost is the same for both groups of students

9($2x + $3.00) = 14($x + $4.50)

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1)  An expression for the amount of fabric needed to make 13 pairs of wings is; 3/4 * $8 = $6 each

2) An expression of the total cost is; 3/4 * $8 * 13 = $78

3) The way we will use  associative and commutative properties is to start by treating 1 yard of fabric like the fraction 4/4.

4) Simplifying equals $78

We are told that each pair of wings is made with 3/4 yard of fabric. Since the fabric costs $8 per yard. Thus;

1) 3/4 * $8 will give us the cost of the amount required for 3/4 yard of fabric.  3/4 * $8 = $6 each

2) Now, we are told that Mr. Townsend needs to make 13 pairs of butterfly wings and as such;

Amount needed to make 13 pairs is expressed as; 3/4 * $8 * 13 = $78

3) Treat 1 yard of fabric like the fraction 4/4.

Now, if this 1 fabric is equal to $8, then it means that 3/4 of the fabric will be $6. That is for one pair of butterfly wings, there's 13 of those so multiply $6 by 13.

This pattern is easier  because we know how much 1 fabric costs, but we don't know what 3/4 of it does, so we treat 1 yard of fabric as the fraction 4/4.

4) Simplifying the expression gives; $78

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The unit rate of the first employee is $29 an hour and the second is $22 an hour.

What is the rate?

Rates are a special type of ratio that incorporates the dimension of time into the denominator. Familiar examples include measurements of speed (miles per hour) or water flow (gallons per minute). Example #1: If a car travels 24 miles in 2 hours, its average speed is a rate of 24 miles/ 2 hours = 12 miles/hr.

We have,

given the two graphs, which show the earnings on the x-axis and time(hr) on the y-axis of both employees working at the same company.

Both earn money at constant rates.

and the points on the graphs are

points on the graph of employee 1 earnings:-

(2, 58) and (3, 87)

the rate of earnings

58/2 = 29

87/3 = 29

points on the graph of employee 2 earnings:-

(1, 22)

the rate of earnings

22/1 = 22

Hence, the unit rate of the first employee is $29 an hour and the second is $22 an hour.

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The speed when the train travels 440 kilometers in 4 hours is 110 km per hour.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

In this case, the train leaves the station at time t=0. Traveling at a constant speed, the train travels 440 kilometers in 4 hours.

The speed will be:

= Distance / Time

= 440 / 4

= 110 km per hour.

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Complete question

A train leaves the station at time t=0. Traveling at a constant speed, the train travels 440 kilometers in 4 hours. Calculate the speed.

Required equation of points plotted on graph relating range gain(k) and charging time(t) is k=4t.

A two-variable linear equation is one in which both variables have exponent 1.

An object in geometry known as a line is simply one that is described as being straight, thin, one-dimensional, zero width, and extending on both sides to infinity.

In essence, a straight line is just a line devoid of any bends.

Additionally, we can state that any line that crosses two certain points on the same plane will be singular.

Straight line form

m= y 2. – y 1/x 2-x 1

y-y 1=m (x-x 2)

A (0,0) and B (5,20)

([tex]x_{1}[/tex],[tex]y_{1}[/tex]  ) = (0,0) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) = (5,20)

m = 20-0/5-0

   = 20/5

   = 4

([tex]x_{1}[/tex],[tex]y_{1}[/tex]  ) =(0,0)

y-0=4(x-0)

y=4x

Replace y with k and x with t

k=4t

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The verb that corresponds to laugh based on the option is D. mock.

A verb is a word that denotes an action that is physical. Verbs are words that describe an action, an occurrence, or a state of being (exist). There must be a verb in almost every sentence. The infinitive is a verb's fundamental form.

It should be noted that mock simply means to laugh at or make fun of (someone or something) especially by copying an action or a way of behaving or speaking.

Therefore, based on the information, the correct option is D.

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Complete question

The verb corresponding to laugh

attend

drink

prophesy

mock

theorize

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The population has increased by 51.56% from last year to this year.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of population last year = 2,639,000,000

Number of population this year = 3,999,635,444

The best estimate of the total population of last year and this year.

= [ (3,999,635,444 - 2,639,000,000) / 2,639,000,000 ] x 100

= ( 1360635444 / 2,639,000,000 ) x 100

= 51.56 %

Thus,

The population has increased by 51.56% from last year to this year.

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Answer:

None? Are you sure you copied the question right?

Step-by-step explanation:

x^2 - 3x - 4 = | x+3 | -2

Substitute

(-4)^2 - 3(-4) - 4 = | (-4)+3 | -2

16 + 12 -4 = 1-2

Not equal

(−3)^2 - 3(−3) - 4 = | (−3)+3 | -2

9+9-4 = -2

Not equal

(−1)^2 - 3(−1) - 4 = | (−1)+3 | -2

1 -3 -4 = 2-2

Not equal

4^2 - 3(4) - 4 = | 4+3 | -2

16 - 12-4 = 7-2

The equation that shows that the total number of markers Mrs. Larsen gets y depends on the number of boxes she buys x, will be;

⇒ y = 8x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Mrs. Larsen wants to get some markers for her class.

She notices that they come in boxes of 8.

Now,

Let total number of markers = y

And, Number of boxes = x

Here, She notices that they come in boxes of 8.

So, We can formulate;

⇒ y = 8x

Thus, The equation that shows that the total number of markers Mrs. Larsen gets y depends on the number of boxes she buys x, will be;

⇒ y = 8x

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it has one solution

.............................

Answer:

b

Step-by-step explanation:

Answer:

47.5%

Step-by-step explanation:

Given that μ = 144, σ = 27:

For x = 144: z= 144-144/27=0

For x = 198: = 198-144/27 = 2

Therefore, From the normal distribution table: gives  0.5000 and 2 gives .97725

So the required percentage = 0.97725- 0.5000 = 0.47725= 47.5%

Hence, 47.5% of the population would be between 144 and 198

Answer:

3 down from p and 6 left

I hope this helps, sorry if it wrong. it should be right

The conjugate of the expression (-3 + 8i) is (-3 - 8i)

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

(-3 + 8i)

The above expression is a complex number

A complex number is represented as

a + bi

Such that its conjugate is a - bi

This means that we simply negate the imaginary part

So, we have

Expression = (-3 + 8i)

Conjugate = (-3 - 8i)

Hence, the conjugate is (-3 - 8i)

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38/53 is as simplest form.

As 53 is a prime no. and they do not have a common factor 38/53 can not be simplified further.

A fraction is written in the form of p/q, where .

Fractions are of two types. They are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, a fraction 38/53.

Now 38 = 2×19 but 53 is a prime number 53 = 1×53 so they do no have any common factor to simplify.

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[tex]30=2.5x \\ \\ 60=5x \\ \\ x=\boxed{12}[/tex]

Answer:

28512cm cubed

Step-by-step explanation:

22/7×4.5 squared ×4squared×28

Answer:

(x + 8)^2 + y^2 = (x - 8)^2

Step-by-step explanation:

Answer:

a) yes

b) yes

c) no

d) yes

Step-by-step explanation:

-2 + 5 = 3

5-2 = 3

-2 - (-5) = -2 + 5 = 3

-2 - 5 = -7

5 + (-2) = 5-2 = 3

Answer:

[tex]1\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{2}{4}+\frac{2}{3} +\frac{2}{6}[/tex]

[tex]\frac{6}{12}+\frac{8}{12} +\frac{4}{12}[/tex]

[tex]\frac{6 + 8 + 4}{12}[/tex]

[tex]\frac{18}{12}[/tex]

[tex]1\frac{1}{2}[/tex]

Answer:

[tex]\begin{gathered} \sf \frac{2}{4} + \frac{2}{3} + \frac{2}{6} = \\ \\ \sf\frac{12 \div 4 \times 2 + 12 \div 3 \times 2 + 12 \div 6 \times 2}{12} = \sf \\ \\ \sf\frac{6 + 8 + 4}{12} = \\ \\ \sf\frac{18}{12} = \frac{ 6}{4} = \\ \ \\ \sf\frac{3}{2} = \boxed { \sf1 \frac{1}{2}} \end{gathered}[/tex]

How to add heterogeneous fractions:

Heterogeneous fractions are fractions that have different denominators.

To add heterogeneous fractions, follow these steps:

The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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Answer:

-4[tex]p^{4}[/tex] + [tex]12p^{3}[/tex] - 5[tex]p^{2}[/tex]

Step-by-step explanation:

[tex]-8p^{4}[/tex] + [tex]12p^{3}[/tex] + [tex]4p^{4}[/tex] - [tex]8p^{2}[/tex] + [tex]3p^{2}[/tex]  Combine the terms with the same exponents

([tex]-8p^{4}[/tex] + [tex]4p^{4[/tex]) + [tex]12p^{3}[/tex] + ([tex]-8p^{2}[/tex] + [tex]3p^{2}[/tex])

[tex]-4p^{4}[/tex] + [tex]12p^{3}[/tex] - [tex]5p^{2}[/tex]

Answer: 28 and 7

7 x 4 = 28

28 + 7= 35

Since the random sample of 200 patients are classified irrespective of their health conditions , as to whether or not they took an omega-3 fish oil tablet daily

The most basic random sample gives each unit in the population an equal probability of being chosen.

calculation

The study in question is an observational one. No treatments were used in the study because there were none.

b) Since the 200 patients who made up the random sample were divided into groups without regard to their physical health.

When patients are divided into groups at random, it may be discovered that one group's patients are in better health than the other. The results then might become skewed. Therefore, our study's conclusion might be false.

c) The outcomes of this study cannot be generalized.

We cannot determine the actual cause of the elevated cholesterol level because the study is observational. The conclusions of an observational study cannot therefore be generalized.

d) No, we are unable to evaluate cause and effect in an observational study. There's a possibility that another factor could be working without the dependent.

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Answer:

Step-by-step explanation:

Use the given functions to set up and simplify 6/8.

4 =

6/8 = 3/4

1/5 mi/hr mulitplied by 1 hr = 1/5 mi

Answer: Dimension of pool are length = 12 feet, width = 54 feet and depth = 6 feet.