What’s the converse of the Pythagorean theorem

Answer:

\(p = 0.7204\)

Step-by-step explanation:

The missing parameters are:

\(n = 4135\) --- sample size

\(w = 2979\) --- those worried about robots and computers doing human jobs

Required

The point estimate

To do this, we simply divide the number of worried people by the sample size

\(p = \frac{w}{n}\)

\(p = \frac{2979}{4135}\)

\(p = 0.7204\)

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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Answer:

I think it's 40 . I'm not sure

Answer:

0.6 liter per kilo

Step-by-step explanation:

Answer:

y = 4x + 3

Step-by-step explanation:

Step 1: Write the general equation

y = mx + b

Step 2: Identify b, the Y intercept (x = 0)

b is the value of y when x = 0.

From the graph, when x = 0, y = 3.

Therefore, b = 3

Step 3: The second point from graph (x, y):

P = (1, 7)

Step 4: Define m as ratio of rise / run:

\( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Step 5: Put coordinates into ratio:

Using the two coordinates, (0, 3) and (1, 7), we would have,

\( m = \frac{7 - 3}{1 - 0} \)

Step 6: Perform subtraction to get slope:

\( m = \frac{4}{1} \)

m = 4

Step 7: Substitute values into y = mx + b:

Thus, plug in the values of m and b into the slope-intercept equation.

b = 3, m = 4, therefore:

y = (4)x + (3)

Step 8: Write answer:

y = 4x + 3

Answer:

6-18y-9x

Step-by-step explanation:

Answer:

5+n(-4)

Step-by-step explanation:

this is the equation if that helps??

Answer:

5*N-4 five times a number n minus four

When it comes to interest, most Certificates of Deposit (CDs) will allow periodic interest payouts. So, correct option is B.

A CD is a type of savings account that allows you to earn a fixed interest rate on your deposit for a specific period of time, called the term. Typically, the longer the term of the CD, the higher the interest rate offered.

However, during the term of the CD, the funds are locked in, meaning that you cannot withdraw the principal without incurring a penalty.

While some CDs may allow for unlimited withdrawals of interest, this is not common, and may still come with restrictions or penalties. Loans against principal are also not typically allowed with CDs, as the funds are meant to be held for a set term.

Therefore, the most common option available for CD holders is to receive periodic interest payouts, which can be monthly, quarterly, or annually, depending on the terms of the CD. This allows the CD holder to earn interest on their deposit while still receiving some income during the term of the CD.

So, correct option is B.

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Answer:

The laplace transform is \(\frac{2}{(s+6)^3}\)

Step-by-step explanation:

We will solve this problem by applying the laplace transform properties (their proofs are beyond the scope of this explanation).

Consider first the function f(t) = 1. By definition of the laplace transform, we have

\(F(s) = \int_{0}^{\infty}f(t)e^{-st}dt\)

when f(t) = 1 we get

\(F(s) = \int_{0}^{\infty}e^{-st}dt = \left.\frac{-e^{-st}}{s}\right|_{0}^{\infty} = \frac{1}{s}\)

We will apply the following properties: Define L(f) as applying the laplace transform

\(L(e^{at}f(t)) = F(s-a)\) (this means, multiplying by an exponential corresponds to a shift in the s parameter of the transform of f)

\(L(t^nf(t)) = (-1)^n\frac{d^n F}{ds^n}\) (this is, multypling by \(t^n\) is equivalent to taking the n-th derivative of the transform.

We are given the function \(g(t) = t^2e^{-6t}\cdot 1 \). Since the transform of the constant function 1 is 1/s, by applying the first property we get

\(L(e^{-6t}\cdot 1 ) = \frac{1}{s+6}\)

By applying the second property we get

\(L(g(t)) = L(t^2 e^{-6t} \cdot 1) = (-1)^2\frac{d^2}{ds^2}(\frac{1}{s+6}) = \frac{2}{(s+6)^3}\)

Answer:

Step-by-step explanation:

4s + 8 + s - 3 + 9s + 7 + 4s + 8 = 18s + 20

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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Reason:

See the screenshot below. I used GeoGebra to plot the points.

The sub group of points D, E, F form a bowl shaped region. Imagine a small parabola passing through these points. Point E is either the local min or very close to it. This is because point E is at the bottom of the bowl shape.

Answer:

i) \( 3y^2 -4y +1=0\)

We can divide both sides of the equation by 3 and we got:

\( y^2 -\frac{4}{3}y +\frac{1}{3}=0\)

Now we can complete the square and we got:

\( (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0\)

\( (y- \frac{2}{3})^2 =\frac{1}{9}\)

We take square root on both sides and we got:

\( y-\frac{2}{3}= \pm \frac{1}{3}\)

And the solutions for y are:

\( y_1 = \frac{1}{3} +\frac{2}{3}=1\)

\( y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}\)

ii) \( y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

And with \( a = 3, b=-4 and c =1\) we got:

\( y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}\)

And we got:

\( y_1 = 1 , y_2 =\frac{1}{3}\)

Step-by-step explanation:

Part i

For this case we have the following function given:

\( 3y^2 -4y +1=0\)

We can divide both sides of the equation by 3 and we got:

\( y^2 -\frac{4}{3}y +\frac{1}{3}=0\)

Now we can complete the square and we got:

\( (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0\)

\( (y- \frac{2}{3})^2 =\frac{1}{9}\)

We take square root on both sides and we got:

\( y-\frac{2}{3}= \pm \frac{1}{3}\)

And the solutions for y are:

\( y_1 = \frac{1}{3} +\frac{2}{3}=1\)

\( y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}\)

Part ii

We can use the quadratic formula:

\( y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}\)

And with \( a = 3, b=-4 and c =1\) we got:

\( y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}\)

And we got:

\( y_1 = 1 , y_2 =\frac{1}{3}\)

The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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Answer:

50

Step-by-step explanation:

difference of ratio=7-3=4

sum of ratio=3+7=10

if difference 4 total=10

if difference 20 total=10/4×20=50

Answer:

r = -39

Step-by-step explanation:

So we are trying to solve the equation for r.

-6(2r + 8) = -10(r - 3)

Divide both sides by -2. (This will make distributing much easier.)

3(2r + 8) = 5(r - 3)

Distribute the 3 on the left side and the 5 on the right side,

6r + 24 = 5r - 15

Subtract 24 from both sides.

6r = 5r - 39

Subtract 5r from both sides.

r = -39

So now we have solve the equation.

I hope you find my answer and explanation to be helpful. Happy studying. :)

Answer:

Ok its -39

Step-by-step explanation:

https://www.tiger-algebra.com/en/solution/linear-equation-one-unknown/-6(2r+8)=-10(r-3)/

Answer:

the first one

Step-by-step explanation:

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

-235+84i

Step-by-step explanation:

I hope this is what you were looking for.

The equation for g (x) is,

⇒ g(x) = x² -3

Since, The function is,

⇒ f (x) = x²

when x = 0, f(x) = 0

hence it has vertex at (0,0)

Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),

Then, g(x) must be shifted along y axis.

So, We get;

g(x)= x²+c

when x = - 1, g(x)= 4

4 = (-1)² + c

4 = 1 + c

c = 3

Thus, The equation for g (x) is,

g(x) = x² -3

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Answer:

Step-by-step explanation:

7). x + y = 4 ⇒ y = 4 - x -----> xy = - 96

x(4 - x) = - 96 ⇔ x² - 4x - 96 = 0

D = ( - 4)² - 4(1)(- 96) = 400 = (20)²

\(x_{1}\) = (- ( - 4) - 20) ÷ 2(1) = - 8

\(x_{2}\) = ( - ( - 4) + 20) ÷ 2 = 12

Numbers are - 8 and 12

8). It's your turn now. You can do it

9). x² - 5x + 3 = 0

0 < \(x_{1}\) < 1

4 < \(x_{2}\) < 5

10). - x² + 3x + 1 = 0

-1 < \(x_{1}\) < 0

3 < \(x_{2}\) < 4

11). x² + 2x - 2 = 0

- 3 < \(x_{1}\) < - 2

0 < \(x_{2}\) < 1

Answer:

1 3/8   D

Step-by-step explanation:

The first and most obvious part of the answer is that the paper clip is at least 1 inch long. The question is how much longer?

It is between 1/4 of an inch and 1/2 of an inch. In fact it is exactly half way between them.

So that resembles an average.

(1/4 + 1/2)/2 = (1/4 + 2/4) / 2 = (3/4)/2

\(\frac{\frac{3}{4} }{2} = \frac{\frac{3}{4} }{\frac{2}{1} }\)

Now the trick is to invert the denominator (make it 1/2) and multiply

3/4 * 1/2 = 3/8

To solve the problem we must know about Force.

A force is given as the product of mass and acceleration.

\(\rm{Force = mass\times acceleration\)

Acceleration is the rate of change of velocity per unit time. It is given as,

\(\rm{ Acceleration = \dfrac{v-u}{t}\)

The mass of the child is 33 kg.

Explanation

Given to us

\(\rm{Force = mass\times acceleration\)

\(66\ N = mass \times 2\\\dfrac{66}{2}= mass\\mass =\dfrac{66}{2}\\\\mass= 33\ kg\)

Hence, the mass of the child is 33 kg.

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Answer:

\(11x^{2} -5x+5\)

Step-by-step explanation:

\(3x^{2}-4x-1+8x^{2} -x+6\)

\(3x^{2}+8x^{2}-4x-x-1+6\)

Combine like terms

\(11x^{2}-5x +5\)

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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Answer:

1 y=3x 2 y=38x 3 y=202x 4 y=2x 5 y=16x

Step-by-step explanation:

Answer:do yo use I’ll need help

Step-by-step explanation:

Answer:

3/8

(B)

Step-by-step explanation:

3+2+3=8.

There are 3 orange, so 3/8

Answer:

7/8

Step-by-step explanation:

3+3+2=8 but it said probability she selected AN orange marble

Answer:

-72 y^4

Step-by-step explanation:

(8y^2)(-9y^2)​

Multiply the coefficients

8*-9 = -72

Add the exponents since the bases are the same

y^2 * y^2 = y^(2+2) = y^4

(8y^2)(-9y^2)​ = -72 y^4

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.