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A standard number cube with the numbers 1 through 6 is rolled. Find the probability of rolling a number less than 4.



A).1/4


B).1/3


C).1/2


D).2/3

Answer:

Option A

Step-by-step explanation:

We are given the inequality 4x + 6 [tex]\leq[/tex] 18;

[tex]4x + 6 \leq 18,\\4x \leq 12,\\\\x \leq 12 / 4,\\x \leq 3,\\\\Conclusion - Option A[/tex]

As you can tell, the second step was derived through the subtraction of 6 from either side of the inequality sign. 18 - 6 is 12, which resulted in the simplified inequality [tex]4x \leq 12[/tex]. Dividing 4 on either side, we derived [tex]x \leq 3[/tex], which is Option A

Answer:

Step-by-step explanation:

[tex]\sqrt{8xyz^{3}}*\sqrt{10x^{3}y^{2}z} =\sqrt{8xyz^{3}*10x^{3}y^{2}z}\\\\ =\sqrt{2*2*2*2*5*x^{1+3}*y^{1+2}*z^{3+1}} \\\\\\=\sqrt{2^{4}*5*x^{4}*y{3}*z^{4}} \\\\=2^{2}*x^{2}*y*z^{2}\sqrt{5y} \\\\\\=4x^{2}yz^{2}\sqrt{5y}[/tex]

Answer:

[tex]=-\left(3x-1\right)\left(x-3\right)[/tex]

Step-by-step explanation:

[tex]10x-3-3x^2\\\mathrm{Factor\:out\:common\:term\:}-1\\=-\left(3x^2-10x+3\right)\\\mathrm{Factor}\:3x^2-10x+3:\quad \left(3x-1\right)\left(x-3\right)\\3x^2-10x+3\\\mathrm{Write\:in\:the\:standard\:form}\:ax^2+bx+c\\=3x^2-10x+3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(3x^2-x\right)+\left(-9x+3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}3x^2-x\mathrm{:\quad }x\left(3x-1\right)\\3x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=3xx-x[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x\\=x\left(3x-1\right)\\\mathrm{Factor\:out\:}-3\mathrm{\:from\:}-9x+3\mathrm{:\quad }-3\left(3x-1\right)\\-9x+3\\\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3\\=-3\cdot \:3x+3\\\mathrm{Factor\:out\:common\:term\:}-3\\=-3\left(3x-1\right)\\=x\left(3x-1\right)-3\left(3x-1\right)\\\mathrm{Factor\:out\:common\:term\:}3x-1\\=\left(3x-1\right)\left(x-3\right)\\=-\left(3x-1\right)\left(x-3\right)[/tex]

Answer:

[tex]802[/tex]

Step-by-step explanation:

[tex]18^3=5832[/tex]

[tex]19^3=6859[/tex]

[tex]2018+2019+2020=6057[/tex]

[tex]6859-6057=802[/tex]

Check.

[tex]6057+802=6859[/tex]

[tex]\sqrt[3]{6859} =19[/tex]

Answer:

2019.

Step-by-step explanation:

Let x = 2018, then x + 1 = 2019 and x + 2 = 2020.

x(x + 1)(x + 2)

= x(x^2 + 3x + 2)

= x^3 + 3x^2 + 2x ................(A)  

Now the perfect cube of x + 1 is:

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

If we add x + 1 to (A) we get this expression so the answer is x + 1

= 2019.

Answer:

  4 cm

Step-by-step explanation:

You want the length of the smaller of two similar pieces of cardboard when the larger has an area of 150 cm² and a length of 10 cm, while the smaller has an area of 24 cm².

The scale factor for lengths is the square root of the scale factor for areas. It will be ...

  √(24/150) = 0.4 . . . . . . = smaller / larger

The smaller cardboard has a length of ...

  0.4 × 10 cm = 4 cm

__

Additional comment

Sometimes folks like to write this as a proportion:

  [tex]\dfrac{\text{smaller length}}{\text{larger length}}=\sqrt{\dfrac{\text{smaller area}}{\text{larger area}}}[/tex]

Solving this for "smaller length" gives the expressions we used above:

  smaller length = (larger length) × √(smaller area/larger area)

Answer:

Step-by-step explanation:

If the longest side is 6.2 cm, and it is twice the length of the shortest, then we can write an equation as 2x=6.2, where x is the short side length.

Then, since a triangle has 3 sides, the medium side length is 14.5-6.2-x.

Hope that helped,

-sirswagger21

Answer:

Between 1997 and 2004, Baffin Bay’s polar bear population  

decreased

.

528 is about  

25

percent of 2074.

Step-by-step explanation:

Answer:

decreased

25

Step-by-step explanation:

Answer:

Step-by-step explanation:

A perfect square trinomial is the square of a binomial.

One of the special products and factors formulas that you should know is

(a + b)^2 = a^2 + 2ab + b^2; another is (a - b)^2 = a^2 - 2ab + b^2.

So, if you are given a trinomial and can use either of the above identities to rewrite it as the square of a binomial, you've got it.

Answer:

this is false because 5/18 is equivalent to 10/36

Answer:

zdsczsczscs

Step-by-step explanation:

Answer:

The value to be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x² is -(x + 11)

Step-by-step explanation:

By long division, we have;

[tex]{\left ({x^{3}-6x^{2}+11x+8} \right )\div 1 - 3x + x^{2}}[/tex] = x - 3

-(x³ - 3·x² + x)

     -3·x² + 10·x + 8

     -(-3·x² + 9·x -3)

                  x + 11

Therefore, -(x + 11) should be added to the polynomial x³ - 6·x² + 11·x + 8 so that it is completely divisible by 1 - 3·x + x².

That is  (x³ - 6·x² + 11·x + 8 - x - 11) ÷ (1 - 3·x + x²) = x - 3.

Answer:

Point Q is further from A than point P, therefore, they are not the same point

Step-by-step explanation:

The given information are;

Point P partitions the directed segment from A → B into the ratio of 1:3

Point Q partitions the directed segment from B → A into the ratio of 1:3

We note that the properties of a directed segment are that it has a length and direction with a defined starting or initial point.

Hence the two segments when arranged in the same direction are;

A B and B A

Hence point P is at a the point 1/(1 + 3) or 1/4 of AB or 1/4 times the length of AB from A

Point Q is at a the point  1/4 of B/A or 1/4 times the length of AB from B which is 3/4 times the length of AB from A

Therefore, point Q is further from A than point P which means they are not the same point.

Answer:

No, P is One-fourth the distance from A to B, and Q is One-fourth the distance from B to A.

Step-by-step explanation:

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

[tex]\log _{10}\left(10x-1\right)=\log _{10}\left(9x+7\right)\\\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)\\10x-1=9x+7\\\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\10x-1+1=9x+7+1\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\10x-9x=9x+8-9x\\\mathrm{Simplify}\\x=8\\[/tex]

The solution of the equation ㏒₅(10x - 1) = ㏒₅(9x + 7) is x = 8.

A logarithm is simply the opposite function of the exponentiation.

It is the exponent to which a number or value is raised to get some other number.

That is, if c = aˣ, then we can write it as x =logₐ c.

Given that,

㏒₅(10x - 1) = ㏒₅(9x + 7)

Let the value of both be n.

So, ㏒₅(10x - 1) = n and  ㏒₅(9x + 7) = n

By the definition of logarithms,

10x - 1 = 5ⁿ and 9x + 7 = 5ⁿ

So,

10x - 1 = 9x + 7

10x - 9x = 7 + 1

x = 8

Hence the value of x is 8.

Learn more about Logarithms here :

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Answer: 700

84 is 12% of What Number:

12% of 700 is 84

100% of 700 is 700, therefore 12 percent of 700 equals 84.

To check this, 12% of 700 IS 84 (Check on Calculator)

Hope this helps!!

Answer:

210

Step-by-step explanation:

There are 7 * 6 * 5 ways to finish. This is because we have 3 slots:

For 1st place, there are 7 people that could take that place, so we have 7

For 2nd place, there are 6 people, because one person already took 1st, so they cant be second as well.

For 3rd place, there are 5 people, because 2 people already took first and second place, and neither of them can be third then.

So we have:

7*6*5 = 210

Answer:

210 ways

Step-by-step explanation:

For 1 st place there are 7 different runners

Now there are only 6 options

For 2nd place there are 6 different runners

Now there are only 5 options

For 3rd place there are 5 different runners

7*6*5

Answer:

the smallest r is the 4r and the biggest r is the r^2

VERTEX (-2,-64)

Step-by-step explanation:

Answer:

smaller r = -10

larger r = 6

The ordered pair for the vertex of the parabola is [tex](-2,-64)[/tex]

Step-by-step explanation:

We have the function [tex]f(r)=r^2+4x-60[/tex]

In order to factor this quadratic equation, we need to look for two numbers that will

Add together to get 4

Multiply together to get -60

Lets look for the numbers that multiply to give us -60.

-1 and 60

1 and -60

2 and -30

-2 and 30

3 and -20

-3 and 20

4 and -15

-4 and 15

5 and -12

-5 and 12

6 and -10

-6 and 10

Now, we just need to determine which of these numbers will add together to get us 4.

Those two numbers would be -6 and 10.

This means that our factored form of this equation will be

[tex]f(r)=(r-6)(r+10)[/tex]

From this, we can find our roots, which are the solutions to the equation when it is equal to 0.

[tex](r-6)(r+10)=0\\\\r=-10, r=6[/tex]

These are our r values.

The vertex of a parabola will always be directly between the two roots.

The number that is between -10 and 6 is [tex]r=-2[/tex]

To find the y-value of the coordinate pair, we just need to plug -2 into our function.

[tex]f(-2)=(-2)^2+4(-2)-60\\\\f(-2)=4-8-60\\\\f(-2)=-64[/tex]

This means that the ordered pair for the vertex of the parabola is [tex](-2,-64)[/tex]

Answer:

C = 10 π cm

Step-by-step explanation:

Diameter is 2 x radius = 2*5.4 = 10.8 cm

radius r = 5 cm

diameter d = 10 cm

circumference C = 31.4 cm

area A = 78.5 cm2

In Terms of Pi π

circumference C = 10 π cm

area A = 25 π cm²

Formulas: Circle Formulas in terms of Pi π, radius r, and diameter d

Radius and Diameter:

r = d/2

d = 2r

Area of a circle:

A = πr2 = πd2/4

Circumference of a circle:

C = 2πr = πd

Answer:

c

Step-by-step explanation:

got it right on my test

Answer:

2 in by 3 in

Step-by-step explanation:

1 in = 4 ft Divide both sides with 4

0.25 in = 1 ft

0.25 * 8 = 2 in

0.25 * 12 = 3 in  

2 in by 3 in

Answer: 2 in by 3 in

Step-by-step explanation:

1 in = 4 ft Divide both sides with 4 0.25 in = 1 ft 0.25 * 8 = 2 in 0.25 * 12 = 3 in 2 in by 3 in

Answer:

the set of all the real values which are strictly greater than zero which is all positive real numbers

Step-by-step explanation:

In interval notation: (0, ∞)

Any exponential function with a positive base and positive multiplier will have a horizontal asymptote at y=0 and will extend to +∞. That's what this one does.

Range of a function--

The range of a function is the set of all the values that are attained by a function.

We are asked to find the range of the function f(x)

the set of all the real values which are strictly greater than zero

x > 0

please mark me brainliest :)

Answer:

9.5(2) = 19 is the diameter

Step-by-step explanation:

Answer:

19 cm

Step-by-step explanation:

Diameter is twice the radius, thus 2 x 9.5 cm = 19 cm

Answer:

I'm not sure but I think the answer is >

Step-by-step explanation:

It looks rig but if I were u I wouldn't trust me

i just did the quiz, It's > !

Answer:

the mle of P=0.833

Step-by-step explanation:

X=incorrect answer

And probability of success to be denoted as P

Here X posses a binomial distribution along with 'r' and 'p'parameter

CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLATION

Answer:

8

Step-by-step explanation:

4+4

6-6+8

Answer:

7A - 42

Step-by-step explanation:

7(A-6)

Distribute

7*A - 7*6

7A - 42

Answer:

The last one on the bottom right

Step-by-step explanation:

When we are trying to fit a line for a number of points, we can fix this line at several points on the graph. However, out of the several lines that we can fit, only one of these lines would work perfectly and it is called the line of best fit.

The reason why it is called the line of best fit is that it is drawn in a manner in which it leaves equal number of points above it as below it.

Supposed we have 15 points for our graph with the line of the slope passing thorough 5, the line of best fit in this case would leave 5 points above and another 5 below the line.

Leaving 6 and 4 is also manageable, but in case where 3 and 7 are left above and below the line, then it becomes a problem

Thus, out of all the representations we have, the one on the bottom right best works

Given That:

x - (Rebecca's share + John's share) = 24

x - (x/3 + x/4) = 24

12x/12 - (4x / 12 + 3x / 12) = 24

5x/12 = 24

5x = 24 x 12

5x = 288

x = 57 or 58

Answer:

1) -2

2) 8/7

Step-by-step explanation:

1) 10x+8=3(x-2)

  10x+8=3x-6

  10x-3x=-6-8

  7x=-14

  x=-2

2) 10x+8=3x

   10x-3x=8

   7x=8

   x=8/7

Hope it helps

Answer:

(A)[tex]128^{x/3}[/tex]

(D)[tex](4(2^{1/3}))^x[/tex]

Step-by-step explanation:

We want to determine which of the expression is equivalent to:

[tex]\sqrt[3]{128}^ x[/tex]

By the law of indices:

[tex]\sqrt[3]{128}=128^{1/3}\\$Therefore:\\\sqrt[3]{128}^ x \\=(128^{1/3})^x\\=128^{x/3}[/tex]

Similarly:

[tex]\sqrt[3]{128}^ x \\=\sqrt[3]{64*2}^ x\\=(4\sqrt[3]{2})^ x\\=(4(2^{1/3}))^x[/tex]

The expressions that are equivalent to (∛128)ˣ are; (128)^(x/3) and (4(2^(1/3))ˣ

We want to find the expression that is equivalent to (∛128)ˣ

From law of indices, we have that;

(∛128)ˣ = [(128)^(1/3)]ˣ

This can be further expressed as;

(128)^(x/3)

Similarly, we have the simplified expression at;

[(128)^(1/3)]ˣ = (64 * 2)^(x/3)

⇒ (4³ * 2)^(x/3)

⇒ (4(2^(1/3))ˣ

Read more about law of indices at; https://brainly.com/question/11761858

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