You roll a fair 6-sided die twice. Find the probability of getting the same number.

Answer:

Formula for length between coordinates is given as √(x1-x2)²+(y1-y2)², which x and y being the coordinates of the points.

Length of RS = √(9-9)²+(-9-10)²

= √0+(-19)²

= √361

= 19 units

Answer:

Step-by-step explanation:

Since both of the points have same x- coordinate of 9, the distance between the points is the absolute value of the difference of y-coordinates:

Translating the given words into algebraic expression it becomes  2v(w-u) .

In the question ,

the word phrase is given as" double the difference of w and u, and then multiply the result by v "

for translating into algebraic expression , we proceed step by step

step 1 : difference of w and u

we get , (w - u)

step 2 : double the difference of w and u ,

we get , 2(w-u)

step 3 : then multiply the result by v ,

we get , 2(w-u)*v

= 2v(w-u)

Therefore , translating the given words into algebraic expression , the expression is 2v(w-u) .

The given question is incomplete , the complete question is

Translate the following word phrase into an algebraic expression , "double the difference of w and u, then multiply the result by v "

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The length of side BC, |BC|, is 2 units. The correct option is C. 2 units

From the question, we are to determine the length of side BC

First, we will determine the length of side BD

From Pythagorean theorem, we can write that

|BD|² = |AB|² + |AD|²

From the given information,

|AB| = 1

|AD| = 1

Thus,

|BD|² = 1² + 1²

|BD|² = 1 + 1

|BD|² = 2

|BD| = √2

Also, we can write that

|BC|² = |BD|² + |DC|²

From the given information,

|BD| = |DC|

Thus,

|BC|² = (√2)² + (√2)²

|BC|² = 2 + 2

|BC|² = 4

|BC| = √4

|BC| = 2

Hence, side BC is 2 units

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The total number of lions that were surveyed is 18.

It should be noted that based on the information given in the survey, 2/3 of the lions said that they were happy to serve as King of the forest, while another 1/9 thought it was way too much responsibility and 14 lions gave one of these two answers.

The total lions that were surveyed will be illustrated thus:

Let the total number of lions be x.

Therefore, (2/3 + 1/9)x = 14

= 7x/9 = 14

Cross multiply

7x = 9 × 14

x = (9 × 14) / 7

x = 9 × 2

x = 18

Therefore, the total number of lions is 18.

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By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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The equation of parabola is  (x − 3)² = −8(y − 2).

A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax²+ bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.

Given:

Vertex = (3, 2)

Directrix, y =4

line of symmetry is the Y value in the vertex = 2

directrix, y= 2 - p

  p = -2

and, a= 1/4p = -1/8

and, focus = (3, (2-2)) = (2, 0)

Now, equation of parabola

y= -1/8 (x- 3)² + 2

-8y = (x- 3)² + 2

(x − 3)² = −8(y − 2)

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Answer:

17 miles

Step-by-step explanation:

5 1/2 + 3= 8 1/2 x 2 = 17

Answer:

Step-by-step explanation:

f(15) = F(75-2times 5)

Answer: f(15) = F(75-2times 5)

Step-by-step explanation: f(15) = F(75-2times 5)

The complement of the event is diamond, club or spade.

The complement of an event means " to not choose the mentioned one" .

That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.

In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.

Thus the complement of the event is diamond, club or spade.

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Answer: x = 3.3

Step-by-step explanation:

Based on the given conditions, formulate: 60,000 * 25% * x = 50,000

Multiply the monomials: 15000x = 50,000

Divide both sides of the equation by the coefficient of variable: x = 50,000

                                                                                                                ______

                                                                                                                  15,000

Cross out the common factor: x 10

                                                     3

Round the number: x = 3.3

Answer x = 3.3

The speed of the stream is 6 [tex]km/h[/tex]

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat

downstream = (18 + x) km/h.

The time is taken to go upstream = distance/speed

[tex]24/(18-x)[/tex] hours.

Similarly, the time is taken to go downstream =

[tex]24/(18+x)[/tex] hours.

According to the question,

[tex]24/(18-x) - 24/(18+x) = 1[/tex]

[tex]x^{2} +48x-324=0[/tex]

Using the quadratic formula, we get

[tex]x=\frac{-48+\sqrt{48^{2}+1296 } }{2}[/tex]

x = 6 or -54

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.

Hence the speed of the stream is 6 km/h.

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Answer: 26 degrees

Step-by-step explanation: Count from -15 to 11 or add them up.

Answer:

Step-by-step explanation:

y +2(y-5)=2y+2

y + 2y - 10 = 2y +2

3y - 10 = 2y +2

3y - 2y = 2 + 10

y = 12

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

check

12 + 2 * (12 - 5) = 2 * 12 + 2             (remember PEMDAS)

12 + 24 - 10 = 24 + 2

26 = 26

the answer is good

Answer:

$125

Step-by-step explanation:

Find out what the percentage increase is in ten years.

2.5%->change to decimal thingy (divide by 100) 0.025 then multiply it by the total amount of years(10): 0.025(10)= 0.25- 25%

The cost percentage in 10 years is 25%

Next multiply your new percentage by the jacket's original cost: 0.25(100)=25

So $25 is the amount that the jacket has increased over ten years

Add 25 to 100 to fin the cost of the jacket in 10 years.

Kinda a confusing explanation but the answer is right.

The researchers use inferential statistics.

Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.  

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Using the definition of the Laplace transform:

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]

Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,

[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]

or equivalently as

[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]

Then the Laplace transform is

[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]

and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.

This is equivalent to the convolution property of the Laplace transform,

[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]

where

[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]

In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].

To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:

[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],

where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].

In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:

[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].

Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:

[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].

Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.

Using a system of equations, the amounts of each coin that he has is given as follows:

The variables to the system of equations are given as follows:

Nicholas has nickels, dimes and quarters that total $12.30, hence, considering the value of each coin:

0.05x + 0.1y + 0.25z = 12.30.

The number of dimes is 3 more than twice the number of nickels, hence:

y = 2x + 3.

The number of quarters is three times the number of nickles, hence:

z = 3x.

Then we can solve for x as follows:

0.05x + 0.1y + 0.25z = 12.30.

0.05x + 0.1(2x + 3) + 0.25(3x) = 12.30.

x = 12. (nickels)

Then the other amounts are as follows:

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The equation of the line passing through point P (0,1) = y=2x-1

What is Equation of line ?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

Rise over run = (y+1)/(x-0)

                      =(y+1)/x =-2

 slope is (y+1)/(x-0) =(y+1)/x

                               =-2;

-2x=y+1, or

y+2x =-1, or

y=-2x-1

in the form of the slope intercept

The parallel line with the value of y=-2x+3 has been moved down by 4 units. The point at which this line crossed the y-axis was y=3. Now, with a 4 downshift, it crosses the y-axis at y=1.

Plugging the location (0,1) into the new equation:

y=2x-1 yields

1 = 2(0)-1

to validate the math.

Hence, the Equation of line passing through point P(0,1) is y=2x-1

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Answer:

The average change is -0.7 per hour.

Step-by-step explanation:

-2.8/4

The correct classification of DEF is a right-angled scalene triangle.

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The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.

These are the x-values when y is equal to zero.

From the graph provided, the values of x when the graph cuts the x-axis are:

Therefore, the coordinates of the x-intercepts are:

The answer type is "Two points".

The zero of a function is the value of x of the point on which the value of y is equal to zero.

You can observe in the graph the such a point is the point (1,0).

Hence, the zero of the function is x = 0

Answer:

(x - 4) (2x - 1)(3x + 2)

Step-by-step explanation:

Dividing:

x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient

        6x^3 -24x^2

                       x^2 - 6x

                       x^2 - 4x

                              -2x + 8

                              -2x + 8

6x^2 + x - 2

= 6x^2 - 3x + 4x - 2

= 3x(2x - 1) + 2(2x - 1)

= (3x + 2)(2x - 1)

The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The domain

On the graph of the function, we can see that:

The x values start from 0 and it extends indefinitely to the right

This means that the domain is x >= 0

The range

On the graph of the function, we can see that:

The y values extend indefinitely on all sides of the coordinate plane

This means that the range is -∝ < y < ∝

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Answer:

p= -8

Step-by-step explanation:

[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]

Highest possible whole number is 3.

A triangle has three sides, three angles, and three vertices, which are its characteristics. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property. Any two triangle sides can add up to a length that is longer than the third side.

Given Data

Sum of length of any two sides of a triangle is always equal to the third side.

For sides a, b and c

We must have, a + b > c

Sides of triangle are x, x +3 and 10cm

So,

x + x+ 3 > 10

2x > 10 - 3

2x> 7

x > [tex]\frac{7}{2}[/tex]

Possible values of x are 3.5, 3, and so on.

Highest possible whole number is 3.

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The estimates are used to construct the estimated regression equation:

ŷ = b0 + b1x.

Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.

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Answer: The answer is x-y = -2