A card is picked from a standard deck of 52 cards. determine the odds against and the odds in favor of selecting a 10

Answers

Answer 1

You are given a card is picked from a standard deck of 52 cards. You are asked to determine the odds against and the odds in favor of selecting a 10. There are a total of 52 cards in a deck. In selecting a 10 of any card, you get four 10's in all kinds of cards (spade, clover, heart, diamond). So to solve for the probability of the odds in favor of selecting a 10, divide four by 52 and you get 10/52 or 5/26. To solve for the probability of the odds against selecting a 10, subtract four from 52 and you will get 48 and then divide it by 52 so 48/52 or 12/13.

Answer 2

Final answer:

The odds in favor of drawing a '10' from a standard 52-card deck are 1 to 12, and the odds against are 12 to 1.

Explanation:

In a standard deck of 52 cards, there are four '10' cards - one each of hearts, diamonds, clubs, and spades. Hence the probability of drawing a '10' is 4 out of 52, or simplified, 1 out of 13.

Therefore, the odds in favor of selecting a '10' (i.e., the probability of selecting a '10' versus not selecting a '10') are 1 to 12 because for each '10' card there are 12 others that are not '10s'.

The odds against selecting a '10' are simply the inverse of the odds in favor. That is, for every one time you may draw a '10', there are 12 other times when you would draw something else, hence the odds against drawing a '10' are 12 to 1.

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Related Questions

what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\ % function transformations for trigonometric functions \begin{array}{rllll} % left side templates f(x)=&{{ A}}sin({{ B}}x+{{ C}})+{{ D}} \\\\ f(x)=&{{ A}}cos({{ B}}x+{{ C}})+{{ D}}\\\\ f(x)=&{{ A}}tan({{ B}}x+{{ C}})+{{ D}} \end{array} \\\\ -------------------\\\\[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ [/tex]

[tex]\bf \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]

with that template in mind, let's see

[tex]\bf \begin{array}{llll} y=&-4sin(&\frac{2\pi }{3}x)\\ &A&B \end{array}\qquad period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{2\pi }{3}}\implies \cfrac{\frac{2\pi }{1}}{\frac{2\pi }{3}} \\\\\\ \cfrac{2\pi }{1}\cdot \cfrac{3}{2\pi }\implies 3[/tex]

Answer:

The answer is 3 for A P E X

Step-by-step explanation:

Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.

options for the first blank are: 20.22, 35.08, 50.07, or 100.11

options for the second blank are: 2, 4, 6 or 8

Answers

The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

Given :

Flask can be modeled as a combination of a sphere and a cylinder.

The volume of Sphere is given by the:

[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]

Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.

Now, the volume of sphere of radius 2.25 inches will be:

[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]

[tex]\rm V_s = 47.71\; inches^3[/tex]

The volume of Cylinder is given by the:

[tex]V_c = \pi r^2h[/tex]

Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.

Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:

[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]

[tex]\rm V_c = 2.35\; inches^3[/tex]

Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].

Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:

Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches

Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch

Height of cylinder = [tex]3\times 2[/tex] = 6 inches

Now, the volume of sphere when radius is 4.5 inches will be:

[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]

[tex]\rm V_s' = 381.70\; inches ^3[/tex]

And the volume of cylinder when radius is 1 inch and height is 6 inches will be:

[tex]V_c' = \pi \times (1)^2\times 6[/tex]

[tex]\rm V_c'=18.85\;inches^3[/tex]

Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].

Now, divide volume with dilation by theorginal volume of the flask.

[tex]\dfrac{400.55}{50.06}=8[/tex]

Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.

For more information, refer the link given below:

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How could the relationship of the data be classified?

scatter plot with points loosely scattered going down to the right

A positive correlation
A causation
A negative correlation
No correlation

Answers

It would be C. A negative correlation. Think of it as a line. If a line goes to the right and is dipped downward just a little bit, it would have a negative slope.

Answer: A negative correlation

Step-by-step explanation:

If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.

With the increase of one quantity or variable there is decrease in the other quantity or variable.

Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.

A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.

Answers

Hello : let A(2,-1) B(8,4)
the slope is : (YB - YA)/(XB -XA)
(4+1)/(8-2) = 5/6

an equation for the line in point-slope form is : y-(-1) =( 5/6)(x-2)
y+1 = (5/6)x -5/3
6y+6 = 5x -10
the equation in standard form is : 5x-6y = 16

Answer: Equation of line in point slope form,

[tex]y + 1 = 5 ( x - 2 )[/tex]

And, Equation of line in standard form,

[tex]5 x - 6 y = 16[/tex]

Step-by-step explanation:

Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,

Then the equation of line,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]

Thus, the equation of the given line,

[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]

⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]

⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)

⇒ [tex]6(y+1)= 5(x-2)[/tex]

⇒ 6 y + 6 = 5 x - 10

⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )

⇒ 6 + 10 = 5x - 6y ( By adding 10 on both sides )

⇒ 16 = 5x - 6y

⇒ 5 x - 6 y = 16 ------(2)

Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]

Thus, equation (1) shows the in slope form of the line.

And, standard form of the line is ax + by = c where a, b and c are the integers.

Thus, equation (2) shows the standard form of the given line.

What percentage is the fraction 2/4 equal to?

Answers

Is it equal to 50% because 2/4 is .5 and to make a fraction you move the decimal over two places to the right

It is equal to 50%.
When 2/4 is simplified, it becomes 1/2, which is equal to 0.5.

What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?

Answers

find inersection first

both equal y so
2x-5=-x+1
3x-5=1
3x=6
x=2
sub back

y=2x-5
y=2(2)-5
y=4-5
y=-1
intersection is (2,-1)

paralell to a line is having same slope
y=mx+b, m is slope
given
y=1/2x+4
slope is 1/2
so
y=1/2x+b
find b
given the point (2,-1) that it must pass through
(x,y) so x=2 and y=-1
-1=1/2(2)+b
-1=1+b
-2=b

the equation is y=1/2x-2

y = 2x - 5
y = -x + 1

2x - 5 = -x + 1
2x + x = 1 + 5
3x = 6
x = 6/3
x = 2

y = -x + 1
y = -2 + 1
y = -1

solution is (2,-1)...point of intersection between the 2 lines given.

y = 1/2x + 4....slope here is 1/2. A parallel line will have the same slope.

y = mx + b
slope(m) = 1/2
(2,-1)...x = 2 and y = -1
sub and find b
-1 = 1/2(2) + b
-1 = 1 + b
-1 -1 = b
-2 = b

so ur parallel equation is : y = 1/2x - 2 <==

SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!

Answers

93. [tex]g(n) = n - 4[/tex]
[tex]f(n) = 2n^2 - 5n[/tex]

then [tex]g(n) +f(n) = (n-4) + (2n^2 - 5n)[/tex]
                                [tex]= n - 4 + 2n^2 - 5n[/tex]
                                [tex]= 2n^2 -5n + n - 4[/tex]
                                [tex]= 2n^2 - 4n -4[/tex]

95. [tex]f(n) = -n+3[/tex]
      [tex]g(n) = n^3 + 3n[/tex]
Then [tex]f(n) . g(n) = (-n+3) . (n^3 + 3n)[/tex]
                                 [tex]= -n^4 + 3n^3 - 3n^2 + 9n [/tex]

97. [tex]f(x) = 3x+1[/tex]
[tex]g(x) = 2x[/tex]
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
[tex]f(g(x)) = 3*(2x) + 1[/tex]
                  [tex]= 6x + 1[/tex]

99. [tex]f(n) = n - 3[/tex]
[tex]g(n) = 2n^2 - 3n[/tex]

[tex]g(-7) = 2*(-7)^2 - 3 * (-7) = 2* 49 + 21 = 98 + 21 = 119[/tex]
[tex]f(g(-7)) = 119 - 3 = 116[/tex]

Answer:

97.

For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).

99.

Step-by-step explanation:

A video game club charges a fixed annual membership fee of $18 and $3 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $20 the next year?

Answers

Since there is a flat membership fee of $18, the y intercept is 18. And since there is a $3 fee per number of video games rented, n, the slope or rate of change of the linear equation is 3. The slope-intercept form of a line is:

f(x)=mx+b, where m=slope and b=y-intercept so in terms of n, games rented, the cost, f(n) is:

f(n)=3n+18

Answer:

The correct answer is f(n)=3n+38

Step-by-step explanation:

Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.

Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
a. 3in, 4in, 5 in

b. 5in, 6in, 7in

c. 8in, 9in, 12in

Answers

Let "a", "b" and "с" be sides of the triangle ("с" is the longest side).
The triangle will be:

right if a² + b² = c²
аcute if    a² + b² > c²
obtuse if   a² + b² < c²

a.
a=3, b=4 and c=5

a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25 ⇒ right triangle.

b.
a=5, b=6 and c=7

a² + b² = 5² + 6² = 25 + 36 = 61   and c² = 7² = 49

61 > 49 ⇒ аcute triangle.

c.
a=8, b=9 and c=12

a² + b² = 8² + 9² = 64 + 81 = 145   and c² = 12² = 144

145 > 144 ⇒ аcute triangle.

From the information, A is a right angle, B is an acute triangle and C is an acute angle.

How to solve the triangle

It will be a right triangle if a² + b² = c². It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².

For the first one,

a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25

25 = 25

This is a right triangle.

For the second one,

a² + b² = 5² + 6²

= 25 + 36 = 61

c² = 7² = 49

61 > 49 = аcute triangle.

For the third one,

a² + b² = 8² + 9²

= 64 + 81 = 145

c² = 12² = 144

145 > 144 = аcute triangle.

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I need all the answers for question 2 and please explain each step to get the answer, thanks

Answers

a) check the picture below

b)

hmm where is that point A anyway? sounds like it's asking the same thing as in part a)

c)

well, where's M, the midpoint of BC, let's check.

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) B&({{ 1}}\quad ,&{{ 4}})\quad % (c,d) C&({{ 9}}\quad ,&{{ 10}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ M=\left( \cfrac{9+1}{2}~,~\cfrac{10+4}{2} \right)\implies M=(5,7)[/tex]

now, the coordinator says that the midpoint of MC is at 6,8, let's check.

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) M&({{ 5}}\quad ,&{{ 7}})\quad % (c,d) C&({{ 9}}\quad ,&{{ 10}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ N=\left( \cfrac{9+5}{2}~,~\cfrac{10+7}{2} \right)\implies N=\left(7~,~\frac{17}{2} \right)\implies N=\left(7~,~8\frac{1}{2} \right)[/tex]

this the picture for my question

Answers

3 is (x-3)(x-9) as when you use FOIL, you get -12x when adding -3x and -9x and also 27 when you multiply -3 times -9.

So, we know that the quadratic formula is x=-b+- the square root of b^2-4ac and all of this divided by 2a. You might be like "wow, where did all of these come from?" It is actually really easy. So, let's take your first equation: 2x^2-19x+24=0. So, let us look at the standard form for a quadratic formula: a^2+b+c=0. Now, If you look at the normal equation and the standard form for a quadratic, you will see that they are alike. Now, just match the letter with the number: a=2, b=-19, and c=24. Now that you know what each letter represents, you can plug everything into the equation x=-b+- the square root of b^2-4ac and all of this divided by 2a.

Use complete sentences to describe the range of the sine function.

Answers

The Range of a function is the set of all values that that function can take.

Given the sine function f(x)=sinx,

This function is the function which calculates the sine of the values of x.

According to the definition of the sine of an angle x in the unit circle,

[tex]-1 \leq sinx \leq 1[/tex],

so the sine of an angle is always larger or equal to -1, and smaller or equal to 1.

This means that the values that the sine function takes are any values between -1 and 1, inclusive.

This determines the Range of the sine function.

So the Range of the sine function is [-1, 1]

Which linear inequality is represented by the graph? y ≥ 1/3x – 4 y ≤ 1/3x – 4 y ≤ 1/3x + 4 y ≥ 1/3x + 4

Answers

solid line...means equal sign is present.....shading below the line means less then....u have a y int at (0,-4)...u have a positive slope of 1/3

thats gonna be 2nd answer choice

Answer:

[tex]y\leq \frac{1}{3}x-4[/tex]

Step-by-step explanation:

we know that

The solution of the inequality is the shaded area below the solid line

The slope of the line is positive

The y-intercept of the solid line is equal to [tex]-4[/tex]

therefore

The inequality must be

[tex]y\leq \frac{1}{3}x-4[/tex]

The sum of four consecutive whole numbers is 54, what are the four numbers

Answers

Let the four consecutive numbers be x, x+1, x+2, and x+3.

The sum of the four numbers is 54, therefore
x + (x+1) + (x+2) + (x+3) = 54
4x + 6 = 54
4x = 54 - 6 = 48
x = 12

Answer:
The four numbers are 12, 13, 14, and 15

A giraffe can run 40 meters per second what is its speed in miles per hour

Answers

bearing in mind that, there are

60 seconds in 1 minute,
60 minutes in 1 hr,
1000 meters in 1 km,
and 1.609 km in 1 mile

[tex]\bf \cfrac{40\underline{m}}{\underline{s}}\cdot \cfrac{60\underline{s}}{\underline{min}}\cdot \cfrac{60\underline{min}}{hr}\cdot \cfrac{\underline{km}}{1000\underline{m}}\cdot \cfrac{mi}{1.609\underline{km}}\implies \cfrac{40\cdot 60\cdot 60\cdot mi}{hr\cdot 1000\cdot 1.609} \\\\\\ \cfrac{144000mi}{1609hr}\approx 89.496581\frac{mi}{hr}[/tex]

Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.

Answers

We need to find the number of possible combinations of r objects from a set of n objects.
Jean has 5 different colors which means that n=5 and 2 colors are used to make a sign, which means r=2.
The number of combinations can be calculated with the formula:
C=n!/((n-r)!r!)
C=5!/(5-2)!*2!
C=5*4*3!/3!*2*1
C=20/2=10
The possible combinations are:
1.red blue
2.red green
3.red orange
4.red purple
5. blue green
6. blue orange
7. blue purple
8. green orange
9. green purple
10. orange purple

Determine whether the sequence is arithmetic or geometric. Sequence 1: –10, 20, – 40, 80, ... Sequence 2: 15, – 5, – 25, – 45, ... Which of the following statements are true regarding Sequence 1 and Sequence 2.

Answers

Sequence one is geometric since you are multiplying each number by a certain value (-2). Sequaence 2 is arithmetic since you are ADDING each number by -20

Answer:

Sequence 1 is arithmetic and Sequence 2 is geometric.

85 is 20% of what number? Enter your answer in the box.

Answers

20% = 20/100 = 0.2

85/0.2 = 425 ← answer

Can you square both sides of an inequality

Answers

Technically you can, if both sides of the inequality have no negative integers.

Squaring both sides of an inequality can be valid if you know both sides are non-negative, but it can introduce extraneous solutions. Therefore, it's important to check any solutions against the original inequality to ensure their validity, especially in cases involving negative numbers or functions with restricted domains.

When you're working with inequalities, you have to be careful when performing operations like squaring both sides. Unlike equalities, where multiplication or division by the same number on both sides does not change equality, with inequalities, the effect can be more complex due to the direction of the inequality sign and the possibility of dealing with negative numbers.

For instance, squaring both sides of an inequality is not always a valid operation because if one or both sides of the inequality are negative, squaring could lead to incorrect results. When you square a negative number, it becomes positive, which could potentially reverse the inequality's direction. However, if you know that both sides of the inequality are non-negative, then squaring both sides is permissible. This concept is similar to solving quadratic constraints without introducing square roots, using identities like |(1 + ix)²|² = ([1 + ix|²)².

To avoid introducing solutions that were not there originally (extraneous solutions), it is important to check the solutions obtained after squaring against the original inequality. An example where squaring both sides might be questioned is when solving trigonometric inequalities, where a common mistake is to square both sides without considering the domain of the original function.

system of equations with different slopes and different y-intercepts have one solution.

A. Always
B. Sometimes
C. Never
I think it is A but I am not sure and it is impossible for system of equations with different slopes and different y-intercepts to be parallel or infinite.

Answers

The answer is :
A. Always

Also
If two equations have different slopes but equivalent y-intercepts, they will have one solution and that will be the point where the y-intercept is. If two equations have different slopes and different y-intercepts, then there will be one solution where those two lines meet. If two equations have the same slope but different y-intercepts, the lines will be parallel, and there is no possible intersection point. And if two equations have equal slopes and equal y-intercepts, these lines will have an infinite amount of solutions, because if the equations are one the same line, every single point on that line is a solution to the system.

Always. The only time you have 0 solutions is when you have two parallel lines, meaning same slope. The only time you have more than 1 is when you have the SAME line, because every point is a answer. Therefore, when you have two completely different lines, then they MUST only have 1 solution always.

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Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent

Answers

They represent that the 2 lines are perpendicular because, the slopes of two perpendicular lines are always negative reciprocals of one another.

Answer:

Perpendicular lines.

Step-by-step explanation:

We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.

We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].

Let us find the product of slopes of both lines.

[tex]2\times \frac{-1}{2}[/tex]

Upon cancelling 2 with 2 we will get,

[tex]=-1[/tex]

Therefore, the given two equations represent equations of two perpendicular lines.

Solve the system of equations: 2x + 9y = 0 and 3x + 5y = 17.

Answers

2x + 9y = 0 (1st)
3x + 5y = 17 (2nd)

multiply (st) by 3 and (2nd) by 2

6x + 27y = 0 (1st)
6x + 10y = 34 (2nd)
----------------------------subtract
17y = -34
y = -2

2x + 9y = 0
2x +9(-2) = 0
2x = 18
x = 9

answer
(9, -2)

Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?

Answers

1+3=4. 2+2=4. 3+1=4.
3/6 or 1/2 if only addition
5-1=4. 6-2=4.
2/6 or 1/3 if only subtraction
if both 5/6

Answer:

[tex]\frac{1}{12}[/tex].

Step-by-step explanation:

Given : Two 6-sided dice are rolled.

To find : what is the probability the sum of the two numbers on the die will be 4.

Solution : We have given

Two 6-sided dice are rolled.

Dice have number { 1,2,3,4,5,6} { 1,2,3,4,5,6} .

[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].

sum of the two numbers on the die will be 4.

Case (1) : first dice rolled 3 and second dice rolled 1.

{3,1}

3 +1 = 4 .

Case (2) : first dice rolled 1 and second dice rolled 3 .

{1,3}

1 + 3 = 4 .

Case (3) : first dice rolled 2 and second dice rolled 2.

{2,2}

2 + 2 = 4.

Then there are 3 possible outcomes where the sum of the two dice is equal to 4.

The number of total possible outcomes = 36.

[tex]Probability =\frac{3}{36}[/tex].

[tex]Probability =\frac{1}{12}[/tex].

Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].

Therefore, [tex]\frac{1}{12}[/tex].

What is the factorization of the polynomial below?

x²+12x+27

A. (x+3)(x+9)
B. (x+9)(2x+9)
C. (12x+1)(x+2)
D. (3x+3)(x+9)

Answers

The answer is A.

(x + 3)(x + 9) = x^2 + 3x + 9x + 27, which simplifies to x^2 + 12x + 27

traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu

Answers

divide total miles by speed

125/65 = 1.923 hours

there are 60 minutes per hour

multiply 1.923*60 = 115.384 minutes

rounded off to nearest whole number = 115 minutes

how to write 314,207 in word form

Answers

three hundred fourteen thousand two hundred seven

Answer: three hundred fourteen thousand, two hundred seven

explanation for the comma after thousand: I’m used to putting one there because it says 314, not just 314 so I added one. Hope I helped !

Josh has 40 minutes to complete a government exam. There are 15 multiple-choice questions worth 3 points each. There are also 5 short-answer questions worth 11 points each. It takes about 2 minutes for Josh to answer the multiple-choice questions m and about 8 minutes to complete the short-answer questions s. The system of inequalities that represents this problem is graphed below. Which ordered pair is not a vertex of the feasible region?

Answers

The feasible vertices of the system representing Josh's exam are (0,0), (12,5), and (15,1.25). The non-feasible vertices are (15,0), (0,5), and (20,0). Therefore, the ordered pair (15,0) is not a vertex of the feasible region.

1. System of Inequalities:

- Time constraint: [tex]$2m + 8s \leq 40$[/tex]

- Number of multiple-choice questions: [tex]$m \leq 15$[/tex]

- Number of short-answer questions: [tex]$s \leq 5$[/tex]

2. Feasible Vertices:

- (0,0), (12,5), (15,1.25)

3. Non-feasible Vertices:

- (15,0), (0,5), (20,0)

So, the ordered pair (15,0) is not a vertex of the feasible region.

The sum of two rational numbers will always be

Answers

that would always be rational

Use the given graph to determine the limit, if it exists. A

Find limit as x approaches three from the left of f of x..

Answers

check the picture below.

Are rational numbers always, sometimes or never natural numbers?

Answers

Rational numbers are sometimes natural numbers. For example, the number 1 is both a rational and natural number. Remember that natural numbers are 1, 2, 3, 4.. etc. Rational numbers are any number that can be expressed as a ratio of 2 integers. 1/1 is rational.

Most rational numbers, however, are not natural. For example, 3/4, 89/88, and so on.

Answer:

SOMETIMES

Step-by-step explanation:

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