rectangles beneath a semicircle a rectangle is constructed with its base on the diameter of a semicircle with radius 5 and its two other vertices on the semicircle. what are the dimensions of the rectangle with maximum area

Answer:

900,000

Step-by-step explanation:

From the given table, we are told that the honeybee beats its wings at a rate of:

There are 60 seconds in a minute, and 60 minutes in an hour.

Therefore, there are:

To find how many times a honeybee can beat its wings in an hour, multiply the number of times it beats its wings per second by 3600:

⇒ 250 × 3600 = 900,000

Therefore, a honeybee beats its wings 900,000 beat per hour.

Based on the calculations, the distance between points (-5, -5) and (-9, -2) on a coordinate plane is equal to: A. 5 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given the following points:

Substituting the given points into the formula, we have;

Distance = √[(-2 - (-5))² + (-9 - (-5))²]

Distance = √[(-2 + 5)² + (-9 + 5)²]

Distance = √[3² + 4²]

Distance = √[9 + 16]

Distance = √25

Distance = 5 units.

In conclusion, we can logically deduce that the distance between the given points on a coordinate plane is 5 units.

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Complete Question:

What is the distance between (-5, -5) and (-9, -2?

Choose 1 answer:

A. 5

B. 7

C. √12

D. √29

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

Explanation:

gradient = slope

Pick any two points on the diagonal line and use the slope formula.

I'll pick the two points (0,4) and (4,10)

[tex](x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (4,10)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{10 - 4}{4 - 0}\\\\m = \frac{6}{4}\\\\m = \frac{3}{2}\\\\[/tex]

The slope is 3/2.

Meaning we go up 3 and to the right 2.

The solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

Given;

To evaluate the value of a given integral;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex]

Let;

[tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex]

Now, assume u = x² + 4

→ [tex]2\cdot \int \left(x^2+4\right)^3xdx[/tex] = [tex]2\cdot \int \frac{u^3}{2}du[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→ [tex]2\cdot \frac{1}{2}\cdot \frac{u^4}{4}[/tex]

→  [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

By adding constant C;

[tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]+ C

Hence, the solution of the given integral [tex]\int \left(x^2+4\right)^3\cdot \:2xdx[/tex] = [tex]\frac{1}{4}\left(x^2+4\right)^4[/tex]

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Answer:

Step-by-step explanation:

First solve the equation:

-11y-9=2

-11y=11

y=-1.

We then take this and plug it back into the original equation:

8(-1)+3

-8+3

-5.

So your answer is -5.

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

The given coordinate points are {(1, 2), (-2, 2), (5, 2), (4, 2)}.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

A) {(1, 2), (-2, 2), (5, 2), (4, 2)}

It is a function as every input has a single output.

So, 1, -2, 5 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 5, 4} and range ={2}

B) {(7, 8), (7, 9), (7, 10), (7, 11)}

Since the element 7 corresponds to four different images i.e., 8, 9, 10 and 11. So, this relation is not a function.

C) {(0,0)}

It is a function as every input has a single output.

So, 0 is the element of the domain of the given relation.

Here domain ={0} and range ={0}

D) {(1, 4), (-2, 8), (2, 2), (4, 9)}

It is a function as every input has a unique output.

So, 1, -2, 2 and 4 are the elements of the domain of the given relation.

Here domain ={1, -2, 2, 4} and range ={4, 8, 2, 9}

{(1, 4), (-2, 8), (2, 2), (4, 9)} it is a function as every input has a unique output. Therefore, option B is not a function.

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Answer:

4p-5/7=a

Step-by-step explanation:

4p=12a+5-5a

4p-5=12-5a

4p-5=7a

4p-5/7=a

Answer:

Step-by-step explanation:

one over the six raised to the third power = 0.00462962962

Answer:

1/216 ≅ 0.00462963

Step-by-step explanation:

Don't know if you need decimal or fraction so I put both

1/6 X 1/6 X 1/6 = 1/216

Answer: 8

[tex]m^{2} = 9+55\\m^{2} = 64\\m=8[/tex]

Answer: m = 8

9 + 55 = 64

[tex]\sqrt{64}[/tex] = 8

[tex]8^{2}[/tex] = 64

The representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

In this question, we have been given an equation y = 3x + 1

We need to find the correct representation  of given equation.

For x = 0,

y = 3(0) + 1

y = 1

For x = 2,

y = 3(2) + 1

y = 7

for x = -1,

y = 3(-1) + 1

y = -2

This means, the options A, B and C are incorrect.

Therefore, the representation of equation y = 3x + 1 is as shown below.

The correct answer is option (D)

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Answer:

1) 112°

3) 55°

4) 51°, complementary angles

Step-by-step explanation (question one):

3x +10 +2x = 180

3x +10 +2x -10 = 180 -10

3x + 2x = 170

5x = 170

x = 34

3(x)+10 = angle ABD

3(34)+10 = angle ABD

102+10 = angle ABD

angle ABD = 112°

Step-by-step explanation (question two):

180 -70 = 2x

110 = 2x

55 = x

angle SQT = 55°

Step-by-step explanation (question three):

Since it's a right angle, we can simply subtract.

90 -39 = 51

angle b = 51°

I wish you luck on your homework!

Using the theories of archaeology, we got that date on the coin represents

a terminus post quem if a coin with a date on it is found in a sealed archaeological deposit.

Potassium-argon dating: This absolute dating method was actually developed by the A.E. Douglass, an American astronomer, chiefly from work he conducted at the Pueblos of American Southwest tree-ring dating Layers of the sediments resulting from the melting of ice sheets and deposited in the lakes on an annual basis are known as varves

Hence, if a coin with a date on it is found in a sealed archaeological deposit, and we know that the deposit can be no older than the date on the coin. in that situation the date on the coin represents a terminus post quem.

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Answer:

x=8

No it’s not an equilateral

Step-by-step explanation:

Since side AB is about the same length as BC we can set them equal to each other

x-1=7

 +1 +1

x=8

This is not an equilateral because if you fill in X for the third side you will get 5

8-3=5

The coordinates of the image of reflecting (3, -2) across the line y = 5 are (3, 12)

When we reflect a point (x, y) across a horizontal line of the form:

y = a

The coordinates of the image after the reflection are:

(x, 2a - y)

In this case we have the point (3, -2), and we reflect this across the line y = 5, then the new coordinates are:

(3, 2*5 - (-2))

(3, 10 + 2)

(3, 12)

The coordinates after the image are (3, 12)

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Answer:

-0.16

Step-by-step explanation:

Divide the answer :)

A linear function in slope-intercept form that only corresponds with this table is y = 2x + 8.

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + b

Where:

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following parameters:

Point (x, y) = (-1, 6)

Point (x, y) =  (0, 8)

Substituting the given points into the formula, we have;

Slope, m = (8 - 6)/(0 - (-1))

Slope, m = (2)/(0 + 1)

Slope, m = 2/1

Slope, m = 2.

In Mathematics, the y-intercept of a graph occurs at the point where the x-value is equal to zero (0), which is 8 in the table shown above.

Therefore, the slope-intercept form is given by:

y = mx + b

y = 2x + 8

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The probability that no two ants will reach the same vertex is 5/256.

Plane, point B and attention. Ants that move to D can come from either E or C. Ants moving to E can come from either B or D of points A and F of the octahedron. Therefore, there are 2 degrees of freedom to decide which ants move to D, 2 degrees of freedom to decide which ants move to E, and 2 degrees of freedom to decide which ants move to A.

So there are 2× 2× 2=8 ways an ant can move to different points.

There are 8 ways for ants to move to different points.

Points B, there are a total of 8 + 4 + 8 = 16 ways Ant can move to her different points. Aligned the square so that point B is defined as point where the ant moved from point A.

An ant can actually move from point A to 4 different points, so there are a total of 4×20=80 ways an ant can move to different points.

Each ant acts independently and has 4 different points to choose from.

So each ant has a 1/4 chance of moving to the desired location. Since he has 6 ants, the probability of appearance is

= 1/4096

So, the desired answer is 80/4096

= 5/256

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Answer:

24

Step-by-step explanation:

let the starting number be x

she sold 1/2 x and has 1/2 x remaining with her

she bought 13 and has 25 now

so, 1/2x + 13 = 25

1/2 x= 25-13 = 12

hence x= 24

Answer:

    24

Step-by-step explanation:

now Mei has 25 stamp collections after adding 13 more to what she remained with after selling; this means that after selling she was left with (25_13)=12

this is the half of what she had initially

this means that she initially had (12*2)=24

this gives means that she started with 24 as a stamp of her collection

Answer:

Step-by-step explanation:

The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5. For 800 ml of salad:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml = 300 ml

The amount of yoghurt that Karolina used when making 800 ml of salad is 300 ml.

Answer:

 (a)

  [tex]\left[\begin{array}{cc}20&80\\32&3\end{array}\right][/tex]

Step-by-step explanation:

You want the product of the given 2×2 matrices.

The value at any given (row, column) of the result matrix is the dot product of the corresponding row of the first matrix with the corresponding column of the second matrix.

For example, row 2 column 1 of the result will be the dot product of row 2 of the left matrix with column 1 of the right matrix:

  [-2, 3]·[-4, 8] = (-2)(-4) +(3)(8) = 8 +24  = 32

This is sufficient to identify the first answer choice as the correct one.

__

Additional comment

A suitable calculator can compute the entire product for you, as in the attachment.

The probability of a type I error is 0.022.

Given,

In the question;

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

Hence, The probability of a type I error is 0.022.

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The equation of the exponential function represented by the table y = 0.12x + 0.01

From the table choose two points

The first point = (1, 0.04)

The second point = (2, 0.16)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation

The slope of the line = (0.16 - 0.04) / (2-1)

= 0.12/1

= 0.12

From the table we can see that at x = 0 the value of y = 0.01, then the value of y intercept is 0.01

The slope intercept form is

y = mx + b

Substitute the values in the equation

y = 0.12x + 0.01

Hence, the equation of the exponential function represented by the table y = 0.12x + 0.01

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Answer:

1.5 minutes (or 1 minute and 30 seconds)

Step-by-step explanation:

5 : 40 = x : 12

x = (5 * 12)/40

x = 12/8

x = 1.5 minutes

Answer: 1 min and 50 seconds

Step-by-step explanation:

first, you have to find the unit rate of how many papers the printer can make in a min which is 40 divided by 5 which gets you a unit rate of 8 for every minute then you take your 12 paper and divide it by your unit rate of 8 per minute which gets you how long it would take to print 12 papers which equal 1.5

Answer:

the answer is c, 6 3/4.

Step-by-step explanation:

An algebraic representation which best describes this transformation is: C. (x, y) → (5x/2, 5y/2).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

By critically observing the graph, we can logically deduce the following vertices:

In this scenario, the transformation rule is given by this algebraic representation:

Q (x, y)                      →               Q' (x, y)

Coordinate Q = (2, 0)   →  Coordinate Q' = ((5/2 × 2), (5/2 × 0)) = Coordinate Q' = (5, 0).

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Answer: B

Step-by-step explanation:

Answer:

Your answer is B

Step-by-step explanation:

From the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

As given in the question,

Total pounds of hamburger need to be made = 1 / 4 pounds

Total pounds of ground beef is used to make hamburger = 2 1 / 2 pounds

Let us consider 'n' be the total number of hamburger to be made each of

1 / 4 pound .

Required equation to show the given relation is given by:

n × ( 1 / 4) = 2  1/ 2

Convert mixed fraction into proper fraction we get,

⇒ n × ( 1 / 4) = 5 /2

⇒ n = ( 5/ 2) × ( 4 /1)

⇒ n = 5 × 2

⇒ n = 10 hamburgers

Therefore, from the given data, total number of hamburgers of (1/4) pounds each using 2 1/2 pounds of ground beef is equal to 10.

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Answer: $56.25

Step-by-step explanation:

First, I'm going to assume that she makes 25% profit on the selling price.

Set the cost of the shirt as x. Profit is calculated as selling price - cost. Profit is stated to be 25% or [tex]\frac{1}{4}[/tex], so an equation can be set up as:

[tex]\frac{1}{4} *75=75-cost\\\\cost = 75-\frac{1}{4} *75=56.25[/tex]

The linear equation is equal to

y = -3x + 8

m = slope

x = input variable

c = 8

The given equation is linear function or linear equation

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables to suit the problem to be solved

y = output variable

m = slope

x = input variable

c = y intercept

In comparison, to the linear equation given as equal to

y = -3x + 8

m = -3

x = input variable

c = 8

putting the input variables gives out put accordingly

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It will take 11 years for the canyon floor to have an elevation of −31 feet.

A mathematical statement known as an equation makes two expressions' values equal. It is a mathematical statement that says "this is equivalent to that," in other words. The left side appears to be a mathematical expression, the centre appears to be an equal sign, and the right side is another mathematical expression. The right side of the equation frequently has a value of zero.

Given,

The first step in this situation is to define the variables.

So, we have:

x: the age in years

y: height in feet

The equation used to model the issue is then written.

So, we have:

y = 1.5x - 14.5

Then, at a -31 foot elevation, we have:

-31 = 1.5x - 14.5

For years,

x = -16.5/1.5

x = 11

In 11 years it will take for the canyon floor to have an elevation of −31 feet.

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