find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for X and y.) midpoint (3,9), endpoint (10,15)
The other endpoint is?

Given that,

Total number of snails shells and shark teeth = 60

The ratio of snail shells to shark teeth is 5:1

To find,

Total no of snail shells used by the Jeweler.

Solution,

Let there are 5x snail shells and x shark shells.

According to question,

5x+x = 60

6x = 60

x = 10

Snail shell = 5x

= 5(10)

= 50

Hence, he uses 50 snail shells.

The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.

To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.

Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is

20,18,16,14,12

In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.

The width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.

An area is a unit of measurement used to describe the size of a region on a planar or curved surface. While a plane region or area refers to the area of a shape or planar lamina, a surface region or plane area refers to the area of an open surface or the boundary of a three-dimensional object.

Given:

The initial length of the image, l = 6 inches,

The initial width of the image, w = 4 inches,

The reduced length of the image, L = 4 inches,

The area of the initial image = The area of the reduced image,

l × w = L × W

Here W is the reduced width.

Substitute the values,

6 × 4 = 4 × W

W = 6 inches,

Therefore, the width of the image which was photocopied by Jackie and has an initial length of 6 inches and width of 4 inches is 6 inches.

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Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

Answer:

K

Step-by-step explanation:

(1*500 * 5) + (10 * 3*500)

Answer:

33 1/4 or 33.25

Step-by-step explanation:

Answer:

\(-5i-41\)

Step-by-step explanation:

Hi there!

\((5-4i) (-3 - 4i) - (10-3i)\)

Open up the parentheses

\(= -15-20i+12i+16i^2- 10+3i\)

i² = -1

\(= -15-20i+12i-16- 10+3i\)

Combine like terms

\(= -5i-41\)

I hope this helps!

Answer:

The correct number line that shows the solutions to x+8 > 15 is option B.

Step-by-step explanation:

The correct number line that shows the solutions to x+8 > 15 is option B.

On this number line, you can see that the values of x that make the inequality true are greater than 7. Therefore, the solution set for this inequality is x > 7.

Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

The equation of the straight line parallel to 2x + 4y = 1 and passing through the point (1, 1) is y = (-1/2)x + 3/2.

To determine the equation of a straight line that is parallel to the line 2x + 4y = 1 and passes through the point (1, 1), we can use the fact that parallel lines have the same slope.

First, let's rearrange the given equation 2x + 4y = 1 into slope-intercept form, y = mx + b,

where m is the slope and b is the y-intercept.

2x + 4y = 1

4y = -2x + 1

y = (-2/4)x + 1/4

y = (-1/2)x + 1/4

From this equation, we can see that the slope of the given line is -1/2.

Since the parallel line we want to find has the same slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1),

where (x1, y1) is the given point.

Plugging in the values (1, 1) and the slope -1/2 into the equation, we have:

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

To simplify, we distribute the -1/2:

y - 1 = (-1/2)x + 1/2

Next, we isolate y by adding 1 to both sides of the equation:

y = (-1/2)x + 1/2 + 1

y = (-1/2)x + 3/2.

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Answer:

Fraction : 3/9

Decimal : 0.33333333 (the .3 continues)

Percent : 33.33333%

Step-by-step explanation:

Dividing 3 by 9 will give you a continous set of 3.

The relationship representing the amount of water remaining in the pool when using the large hose to pump out is

a. 1200 - 60x = y

The amount of water to be pumped out = 1200 gallons

The rate of pumping out using the small hose 20 gallons of water per minute. = -20x

let each minute be x, hence every minute 20x volume of water leaves the pond

The equation is represented as

water remaining = 1200 - 20x

in 2 hours, we have  120 minutes, when will the water finish

water remaining = 0 = 1200 - 20x

20x = 1200

x = 1200 / 20

x = 60 minutes hence 1 hour

For the large hose the rate of pumping out is tripled hence

water remaining = 1200 - 60x

y = 1200 - 60x

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Answer:it might be A

The volume of the cube with side length 8 inches is 512 inches cube.

The cube with side length s has volume s³. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides.

The volume of the cube can be calculated as follows:

A cube has all side length equal to each other.

Therefore,

volume of the cube = s³

where

Therefore,

s = 8 inches

Hence,

volume of the cube = 8³

volume of the cube = 8 × 8 × 8

volume of the cube = 512 inches cube

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The Medals are as follows:

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A + B + C = 119

Country B won 9 more than Country C so:

B = C + 9

Also, Country A won 39 more than the other two combined so:

A = B + C + 39

  = (C + 9) + C + 39

  = 2C + 48

Now we substitute into the equation:

A + B + C = 129

(2C + 48) + (C + 9) + C = 129

4C + 57 = 129

4C = 72

C = 18

So, if B = C + 9  then B = 27

and, A = 2C + 48 = 36+ 48 = 84

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Answer: 300

Step-by-step explanation:

15x+350=4850

15x=4500

x=300

Answer:

Step-by-step explanation:

The formula for calculating the time it takes to reach a target amount with a constant periodic deposit is given by

Time = ln(Target Amount / (Periodic Deposit x (1 + Interest Rate)^0)) / ln(1 + Interest Rate)

In this case, we have Target Amount = 500,000, Periodic Deposit = 500, and Interest rate = 7.8%. Plugging the values into the formula gives

Time = ln(500,000 / (500 x (1 + 0.078)^0)) / ln(1 + 0.078)

Time = ln(500,000 / 500) / ln(1.078)

Time = ln(1,000) / ln(1.078)

Time = 8.98 years

Rounding to the nearest tenth of a year, the answer is 8.9 years.

The factored representation of the quadratic function 2x² - 10x - 48 is given as follows:

2(x - 8)(x + 3).

The quadratic function for this problem is defined as follows:

2x² - 10x - 48

The leading coefficient of 2 is common to all the terms of the expression, hence the expression can be simplified as follows:

2x² - 10x - 48 = 2(x² - 5x - 24).

The term with the square of x can be simplified as follows:

x² - 5x - 24 = (x - 8)(x + 3).

Meaning that x = 8 and x = -3 are the roots of the quadratic function, hence, considering the leading coefficients and the linear factors, the simplified expression is given as follows:

2x² - 10x - 48 = 2(x - 8)(x + 3).

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The factorization of the quadratic equation is:

y = 2*(x + 3)*(x - 8)

Here we have the quadratic equation:

2x^2 - 10x - 48

To factorize it, we need to find the roots of the quadratic, to do so we need to solve the equation:

y = 2*x^2 - 10*x - 48 = 0

2x^2 -10x - 48 = 0

Dividing by 2 in both sides we will get:

(2x^2 - 10x - 48)/2 = 0/2

x^2 - 5x - 24 = 0

Now we can use the quadratic formula to get the roots:

\(x = \frac{5 \pm \sqrt{(-5)^2 - 4*1*-24} }{2} \\\\x = \frac{5 \pm 11}{2}\)

The roots are:

x = (5 + 11)/2 =8

x = (5 - 11)/2 = -3

Then the factorization will be:

y = 2*(x - (-3))*(x - 8)

y = 2*(x + 3)*(x - 8)

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Multiplying each outcome by it's respective probability, and adding them, it is found that the expected value of the game is -€0.25.

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

The probabilities of each outcome are:

The expected earnings are:

\(E = 0.5(2) + 0.25(4) + 0.125(14) + 0.125(8) = 4.75\)

Subtracting the cost to play:

\(4.75 - 5 = -0.25\)

The expected value of this game is of -€0.25.

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Answer:person up top is right it’s B

Step-by-step explanation: on edg 2020

Answer:

The answer is B

Step-by-step explanation:

lol yw guys

Answer:

\(\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x\)

Step-by-step explanation:

This derivative consist in the sum of three functions: \(f(x) = 81\cdot \sin^{-1} x^{9}\), \(g(x) = - x^{81}\) and \(h(x) = - x^{2}\). According to differentiation rules, the derivative of a sum of functions is the same as the sum of the derivatives of each function. That is:

\(\frac{d}{dx} [f(x)+g(x) + h(x)] = \frac{d}{dx} [f(x)]+\frac{d}{dx} [g(x)] +\frac{d}{dx} [h(x)]\)

Now, each derivative is found by applying the derivative rules when appropriate:

\(f(x) = 81\cdot \sin^{-1} x^{9}\) Given

\(f'(x) = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}}\) (Derivative of a arcsine function/Chain rule)

\(g(x) = - x^{81}\) Given

\(g'(x) = -81\cdot x^{80}\) (Derivative of a power function)

\(h(x) = - x^{2}\) Given

\(h'(x) = -2\cdot x\) (Derivative of a power function)

\(\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x\) (Derivative for a sum of functions/Result)

Consider that a rotation of 90° consists:

T(x,y) = > T'(y,-x)

you can notice that the rotation X(9,8) => X'(8,-9) is preciselly a rotation of 90°.

90°

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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Step-by-step explanation:

you just have to put that value in place of x in the function.

don't be so lazy you a hole do it yourself

9514 1404 393

Answer:

  28,728.15 g

Step-by-step explanation:

(11.5 gal) × (3.785 L/gal) × (1000 mL/L) × (0.66 g/mL) = 28,728.15 g

_____

That's 28,700 g rounded to 3 significant figures.

Given :

Area of rectangle.

To Find :

The dimensions of a rectangle (in m) with area 1,728 m2 whose perimeter is as small as possible.

Solution :

Let, the dimensions of rectangle is x and y.

Area, A = xy.

x = A/y.              ....1)

Perimeter, P = 2( x + y )

Putting value of x in above equation, we get :

\(P = 2( y + \dfrac{A}{y})\)

For minimum P,

\(\dfrac{dP}{dx}=2( 1 - \dfrac{A}{x^2})=0\\\\A = x^2\)

SO, it is a square.

\(x=\sqrt{A}\\\\x=\sqrt{1728\ m^2}\\\\x=24\sqrt{3}\ m\)

Therefore, the dimensions are \((24\sqrt{3},24\sqrt{3})\).24\sqrt{3}

Hence, this is the required solution.

The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are 41.6, 41.6

The area is given as:

\(\mathbf{A = 1728}\)

Let the dimension be x and y.

So, we have:

\(\mathbf{A = xy = 1728}\)

Make x the subject

\(\mathbf{x = \frac{1728}{y}}\)

The perimeter is calculated as:

\(\mathbf{P = 2(x + y)}\)

Substitute \(\mathbf{x = \frac{1728}{y}}\)

\(\mathbf{P = 2(\frac{1728}{y} + y)}\)

Expand

\(\mathbf{P = \frac{3456}{y} + 2y}\)

Differentiate

\(\mathbf{P' = -\frac{3456}{y^2} + 2}\)

Set to 0

\(\mathbf{ -\frac{3456}{y^2} + 2 = 0}\)

Rewrite as:

\(\mathbf{ -\frac{3456}{y^2} = -2}\)

Divide both sides by -1

\(\mathbf{\frac{3456}{y^2} = 2}\)

Multiply y^2

\(\mathbf{3456= 2y^2}\)

Divide by 2

\(\mathbf{1728= y^2}\)

Take square roots of both sides

\(\mathbf{y = \sqrt{1728}}\)

\(\mathbf{y = 41.6}\)

Substitute \(\mathbf{y = \sqrt{1728}}\) in \(\mathbf{x = \frac{1728}{y}}\)

\(\mathbf{x = \frac{1728}{\sqrt{1728}}}\)

\(\mathbf{x = \sqrt{1728}}\)

\(\mathbf{x = 41.6}\)

Hence, the dimensions that minimize the perimeter are 41.6, 41.6

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