Three dice are going to be rolled. What is the probability that the first die rolled is a 1, the second die rolled is a 2, and the third die rolled is a 3? (If necessary, round to the nearest tenth)

Answer:

Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.

8 goes into 40 five times

3/8= (3*5)/40 = 15/40

10 goes into 40 four times

7/10= (7*4)/40= 28/40

ANSWER: A) 15/40 and 28/40

Hope this helps! :)

Step-by-step explanation:

Answer:

square

Step-by-step explanation:

i got it right in edge

Equation of parabola with focus at (0,-4) and directrix is y=4 .

As we know parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.

The parabola is opening downwards.

Let any point on parabola is (x,y).

Distance from focus(0,-4) to (x,y) = [tex]\sqrt{(x-0)^{2} +(y+4) ^{2}}=\sqrt{x^{2}+ (y+4)^{2}}[/tex]

Distance from (x,y) to directrix, y=4 is =[tex]\left | y-4 \right |[/tex]

As these distances are equal.

[tex]\sqrt{x^{2}+ (y+4)^{2}}=\left | y-4 \right |\\{x^{2}+ (y+4)^{2}=(y-4)^{2}[/tex]

→x²+y²+8 y +16 = y² - 8 y+16

→ x² = -8 y - 8 y= -16 y   [ Cancelling y² and 16 from L.H.S and R.H.S ]

So , equation of parabola is , x²= - 16 y or f(x)= -x²/16

The Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]

Equation of parabola with focus at [tex](0,-4)[/tex] and directrix is [tex]y=4[/tex] .

Parabola is the locus of all the points such that distance from fixed point on the parabola to fixed line directrix is same.

The parabola is opening downwards.

Let any point on parabola is [tex](x,y)[/tex].

Distance from focus [tex](0,-4)[/tex] to [tex](x,y)[/tex] = [tex]\sqrt{(x-0)^2+(y+4)^2[/tex]

[tex]d=\sqrt{x^2+(y+4)^2[/tex]

Distance from [tex](x,y)[/tex] to directrix, [tex]y=4[/tex] is =[tex]\left | y-4 \right |[/tex]

As these distances are equal.

[tex]\sqrt{x^2+(y+4)^2}=\left | y-4 \right |[/tex]

[tex]d={x^2+(y+4)^2=(y-4)^2[/tex]

[tex]x^2+y^2+8y+16=y^2-8y+16[/tex]

[tex]x^2=-8y-8y[/tex]

[tex]x^2=-16y[/tex]

[tex]y=\dfrac{-x^2}{16}[/tex]

So, the Equation of parabola is [tex]f(x)=-\dfrac{x^2}{16}[/tex]

Learn more about parabola here:

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Answer:

the answer is 137.1

Step-by-step explanation:

Divide the figure into recognizable shapes. Find the area of each shape and add them together.

Answer: D)  [tex]y=-5(x-5)^2+1125[/tex]

Step-by-step explanation:

Let x be the number of $2 increases in price and y be the revenue.

By using the given table , lets check all the options

A) [tex]y=(x+5)^2-1125[/tex]

For x=1, y=1045

[tex]y=(1+5)^2-1125=36-1125=-1089\\\\But\ 1045\neq-1089[/tex]

B)  [tex]y=(x-5)^2+1125[/tex]

For x=1, y=1045

[tex]y=(1-5)^2+1125=14+1125=1139\\\But\ 1045\neq1139[/tex]

C)   [tex]y=-5(x+5)^2-1125[/tex]

[tex]y=-5(1+5)^2-1125=-5(36)-1125=-1305\\\\But\ 1045\neq-1305[/tex]

D) [tex]y=-5(x-5)^2+1125[/tex]

[tex]y=-5(1-5)^2+1125=-5(16)+1125=1045[/tex]

Hence, this is the quadratic equation that models the data.

Based on the table of values, an equation of the quadratic that models the data is: D. [tex]y = -5(x-5 ) ^2+ 1125[/tex]

In Mathematics and Euclidean Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

[tex]y = a(x - h)^2 + k[/tex]

Where:

In order to determine an equation for the line of best fit or quadratic regression line that models the data points contained in the table of values, we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the number of $2 increase in price (in dollars), x and revenue, y, the quadratic regression is given by:

[tex]y =-5x^2 + 50x + 1000\\\\y = -5(x^2 - 10x) + 1000\\\\y = -5(x^2 - 10x + (\frac{10}{2})^2 ) + 1000+ (\frac{10}{2})^2\\\\y = -5(x^2 - 10x + 25 ) + 1000+25\\\\y = -5(x-5 ) ^2+ 1125[/tex]

Answer:

[tex]\angle ABC \cong \angle XYZ[/tex]

[tex]CA \cong ZX[/tex]

Step-by-step explanation:

According to the given figures:

[tex]\angle ABC \cong \angle XYZ[/tex]

Also,

[tex]CA \cong ZX[/tex]

Therefore, the answer to the first question is Angle XYZ, and the answer to the second question is ZX.

You can deduct these answers by observing the number of line that match each pair of congruent elements.

Final answer:

The area of the inscribed circle within a square with an area of 900 in² is 225π in².

Explanation:

The subject here is circle geometry, which is a part of Mathematics. Given that the area of the square is 900 in², we want to find the area of the inscribed circle. The side length a of the square can be found by taking the square root of the area, so a = √{900} = 30 inches. The diameter of the circle is the same as the side of the square, which means the radius r is half of that, so r = 30 / 2 = 15 inches. The formula for the area of a circle is A = πr², and substituting in our value of r, we get:

A = π * (15 in)² = 225π in²

Answer:

x = 26° is the answer.

Step-by-step explanation:

We have to find the value of x from the given equation.

sin 64° = cos x

since sin 64° = 0.8987

Therefore cos x = 0.8987

[tex]x = cos^{-1}(0.8987) = 26[/tex]

x = 26°

Answer:

The required relative minimum is -5

Step-by-step explanation:

Relative minimum is the point where the graph shows its minimum point or the lowest point of the graph.

Like here, we have been given a parabolic shape so, the minimum of this parabola is the coordinate of y in its vertex point.

So, its relative minimum is -5.

Option: A is the correct answer.

The value of cos P is:

             A)   [tex]\dfrac{9}{41}[/tex]

We know that if two angles A and B are complementary then,

[tex]A+B=90[/tex]

i.e.

[tex]B=90-A[/tex]

Here we have angle P and angle Q are complementary i.e.

[tex]P=90-Q[/tex]

Also, we are given,

[tex]\sin Q=\dfrac{9}{41}[/tex]

We are asked to find:

[tex]\cos P[/tex]

It could also be written as:

[tex]\cos P=\cos (90-Q)\\\\i.e.\\\\\cos P=\sin Q\\\\i.e.\\\\\cos P=\dfrac{9}{41}[/tex]

If the radius of the circle will be 5, then the diameter of the circle is 10 m. Then the correct option is C.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

Marisha plots her flower garden on a computer.

She determines that the circle that defines the part of the garden that gets watered by the sprinkler is (x − 8)² + (y + 10)² = 25.

Then the equation can be written as

(x − 8)² + (y + 10)² = 5²

The radius of the circle will be 5

Then the diameter of the circle is given as

d = 2r

d = 2 x 5

d = 10 m

Learn more about the equation of a circle here:

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[tex]\text{The formula of a distance between two points:}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\text{We have the points}\ (3,\ -4)\ \text{and}\ (3,\ -17).\ \text{Substitute:}\\\\d=\sqrt{(3-3)^2+(-17-(-4))^2}=\sqrt{0^2+(-13)^2}=\sqrt{(-13)^2}=13\\\\Answer:\ \boxed{13\ units}[/tex]

Answer:

Step-by-step explanation:

We are given expression [tex](6.3 \times 10^{-2})(9.9\times 10^{-3})[/tex].

In order to multiply above given expression, we need to multiply 6.3 by 9.9 first.

On multiplying 6.3 by 9.9 , we get 62.37.

Now we would multiply  [tex]10^{-2} \ by \ 10^{-3}.[/tex]

Therefore,

[tex]10^{-2} \times 10^{-3}= 10^{-2-3}= 10^{-2-3} = 10^{-5}.[/tex]  

Therefore,

[tex](6.3 \times 10^{-2})(9.9\times 10^{-3}) =62.37 \times 10^{-5}[/tex]

Again [tex]62.37 \times 10^{-5}[/tex] could be written as [tex]6.237 \times 10^{-4}[/tex].

Now, [tex]6.237 \times 10^{-4}[/tex] could be round to [tex]6 \times 10^{-4}.[/tex]

Therefore, correct answer is  [tex]6 \times 10^{-4}.[/tex]

Final answer:

The probability of rolling a 1 first and then rolling a 5 with two 6-sided number cubes is 1/36.

Explanation:

To find the probability of rolling a 1 first and then rolling a 5 with the second cube, we need to consider the probabilities of each event separately. The probability of rolling a 1 on the first cube is 1/6, since there is only one face with a 1 out of six possible outcomes.

The probability of rolling a 5 on the second cube is also 1/6. Since these events are independent, we can multiply their probabilities to find the overall probability:

Probability of rolling a 1 first and then rolling a 5 = (1/6) * (1/6) = 1/36