Three distinct, five-sided dice are rolled, and the numbers showing are recorded. How many different outcomes are possible

There is no logarithm base provided in the expression "log 5 + 2". Therefore, we assume that the base is 10, which is the default base for logarithms when no base is specified.

Using the logarithmic identity that states

"log a + log b = log(ab)",

we can combine the terms as follows:

log 5 + 2 = log(5) + log(10^2) [Note that 10^2 = 100]

Now, using the same identity, we can simplify this further:

log(5) + log(100) = log(5 * 100) = log(500)

Therefore, the expression "log 5 + 2" can be simplified as a single logarithm of "log 500" with base 10.

there are 1,008 different computer systems possible, given the constraints provided.

what is constraints?

Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.

In the given question,

To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

So, for this problem, we have:

8 different choices for computers

7 different choices for monitors

9 different choices for printers

2 different choices for scanners

Using the multiplication principle, the total number of different computer systems possible is:

8 x 7 x 9 x 2 = 1,008

Therefore, there are 1,008 different computer systems possible, given the constraints provided.

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Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

The equatiοn has nο sοlutiοn.

An equatiοn is defined as a mathematical statement in algebra that prοves the equality οf twο mathematical expressiοns. Fοr example, the fοrmula 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the wοrd "equal."

Here the given equatiοn is ,

=> |4x-4(x+1)|=4

Nοw simplifying the equatiοn then,

=> 4x-4(x+1)=± 4

=> 4x-4x-4=±4

=>-4=±4

Hence the given equatiοn has nο sοlutiοn.

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Answer:

16

Step-by-step explanation:

Find an equivalent fraction which is 6/16.

201.5 is the smallest average of 200 different positive and odd integers.

Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.

The average of this set is (1+3+5+...+397+399+401)/200 = 201.

Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.

One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.

The new set is {1, 3, 5, ..., 397, 399, 403}.

The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.

Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.

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The equation that Sharon can use to find c is

                               300(c-0.20)= 180

The average amount the cable company charges per channel was $0.8.

An equation is a mathematical statement which can be constructed by two expressions connected by an sign which is called equal '=' sign to find out the value of unknown variable.

For example, 3x – 11 = 16 is an equation. Solving this equation, we get the value of x as x = 9.

Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.

Let us take in previous case the bill was $c for one channel.

so for 300 channels it will be $300c.

If Sharon has for $0.20 less per channel

Then price per channel will be $(c-0.20)

For 300 channels it will be $300(c-0.20)

It equals to $180

so equating both values we get the  equation and the equation will be,

          300(c-0.20)= 180

The equation that Sharon can use to find c is

                               300(c-0.20)= 180

To find the average amount we will solve c from the equation.

                                  300(c-0.20)= 180

                                ⇒ c-0.20 = 180/300 [ dividing both sides by 300 we get]

                                 ⇒ c- 0.20 =0.6

                                  ⇒ c= 0.8 [ Adding both sides 0.20 we get]

 Hence, The average amount the cable company charges per channel was $0.8.  

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Answer:

145°

Step-by-step explanation:

∠1 + ∠2 = ∠3

5x + (4x + 10) = 10x - 5

9x + 10 = 10x - 5

10x - 9x = 10 + 5

x = 15

∠3 = 10x - 5 = 10(15) - 5 = 150 - 5 = 145

The inequality that models the amount of weight the forklift can carry is: 45x + 70y ≤ 3000

An inequality is a mathematical statement that indicates a relationship between two expressions that are not equal. It uses comparison symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two expressions.

The total number of boxes that a forklift can carry is x + y.

The total weight that the forklift can carry is equal to 45x + 70y pounds, which is less than or equal to 3000 pounds.

Therefore, the inequality that models the number of boxes the forklift can carry is:

x + y ≤ 60

The inequality that models the amount of weight the forklift can carry is:

45x + 70y ≤ 3000.

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Each of the value of x in the diagram above are as follows

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.

Next, we would determine each of the missing angles denoted by x as follows with respect to the START BOX;

x = 141° (alternate interior angles theorem).

x = 39° (corresponding angles).

x + 169 = 180

x = 180 - 169 = 21°.

x = 88° (vertically opposite angles).

x = 180°- 82°

x = 98°

x + 41 = 180

x = 180 - 41 = 139°.

x + 117 = 180

x = 180 - 117 = 139°.

x = 102° (vertically opposite angles)

x + 130 = 180

x = 180 - 130 = 50°.

x + 14 = 180

x = 180 - 14 = 166°.

x + 18 = 180

x = 180 - 18 = 162°.

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The value of x using Pythagoras theorem to solve the diagram is 1.25 m.

Pythagoras theorem states that the square of the hypotenus in a right angled triangle is equal to the sum of the of the two other sides.

To solve for x we use pythagoras theorem in the diagram below.

Formula:

From the diagram,

Substitute these values into equation 1 and solve for x

Hence, x is 1.25 m.

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Answer:

I think it will be

y=1/3x+0

The probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

According to the First Principle of Probability, the outcomes of one chance occurrence have no bearing on those of succeeding chances occurrences. Thus, the chance of getting heads the second or third time you flip it stays at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.

The Bayes Theorem asserts that the likelihood of a second tournament given the first occurrence multiplied by the odds of the first event equals the conditional event's likelihood depending on the presence of another event.

The probability of rolling a number other than 1 or 5 on a fair die is 4/6 or 2/3, since there are four favorable outcomes (2, 3, 4, 6) out of six possible outcomes.

To find the probability of rolling no 1 and no 5 in five rolls, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each roll, the probability of rolling a number other than 1 or 5 is 2/3. Therefore, the probability of rolling no 1 and no 5 in five rolls is:

(2/3) * (2/3) * (2/3) * (2/3) * (2/3) = (2/3)⁵ ≈ 0.131

Rounding to three decimal places, the probability is approximately 0.131.

Therefore, the probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

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A model to find a fraction equivalent to 1/4 is found to be 0.25.

The intervals among two integers are illustrated by the display of fractions on a number line, which also reveals the basic idea behind the generation of fractional numbers.

Now, for the given fraction 1/4.

To get the model of 1/4, draw number line and mark number starting from

0 to 4.

Divide in 4 equal part.

The first part shows the fraction 1/4 = 0.25.

Thus, a model to find a fraction equivalent to 1/4 is found to be 0.25.

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The graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

What is graph?

A graph is a data structure consisting of a set of vertices (also called nodes or points) connected by edges (also called arcs or lines). It is used to represent relationships between objects or entities in a system or network. Graphs are commonly used in computer science, mathematics, and other fields where complex data structures need to be analyzed and visualized.

In a graph, each vertex may be connected to one or more other vertices by edges. The edges may be directed (pointing from one vertex to another) or undirected (connecting vertices without a specific direction). A graph can be represented mathematically as a set of vertices and a set of edges that connect them.

To find where the graph of the equation x²-x-2=y crosses the x-axis, we need to find the values of x when y=0.

So, let's set y=0 and solve for x, x²-x-2=0

We can factor this quadratic equation as (x-2)(x+1) = 0

So, the solutions are

x-2=0 or x+1=0

which give:

x=2 or x=-1

Therefore, the graph of x²-x-2=y crosses the x-axis at the points (-1,0) and (2,0).

So the answer is option D: (-1,0) and (2,0).

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Answer:

E

Step-by-step explanation:

[tex]3(p - 4) = 2(p + 1)[/tex]

Multiply every term inside the bracket by the term on the outside:

[tex]3p - 12 = 2p + 2[/tex]

Collect like-terms (also, moving the term to the other side changes its sign to the opposite of the previous one):

[tex]p = 14[/tex]

EXPLANATION

step 1. 3×p - 3×4 = 2×p + 2×1 ( brackets means × or multiplication )

step 2. 3p - 12 = 2p + 2 ( collect like terms )

step 3. -2p - 3p = 2 + 12 ( calculate the like terms and when we calculate them it would not be multiplication or division )

step 4. -1p = 14 ( answering look like this )

step 5. -1p/ 1 = 14/1 ( divided it by the number to get the variable )

step 6. p = 14 ( finally answer the question and check it all your calculate )

If you think you are brilant do not run for only the answer, but check up and understand it how it come.

ANSWER

(E) 14

The two-column proofs of the line segments are shown below

Given that

HI = 13

IJ = 13

IJ ≅ JH

The proof is as follows

Statement                                                Reason

HI = 13, IJ = 13, IJ ≅ JH                            Given

HI ≅ IJ                                                      Substitution property

HI ≅ JH                                                    Substitution property (proved)

Given that

AL = SK

The proof is as follows

Statement                                                Reason

AL = SK                                                    Given

AL + LS = AS                                            Point–line–plane postulate

LS + SK = LK                                            Point–line–plane postulate

LS + AL = LK                                            Substitution property

AS = LK                                                    Point–line–plane postulate

                                                                (proved)

Given that

DG = 11

GF = 11

GF ≅ EF

The proof is as follows

Statement                                                Reason

DG = 11, GF = 11, GF ≅ EF                        Given

DG ≅ GF                                                   Substitution property

DG ≅ EF                                                    Substitution property (proved)

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The correct answer is option 2: if Lamont's sales are $2708.33, he earns $2290.63 with Plan B.

To determine which pay structure is better for Lamont, we need to compare the total amount of money he earns under each plan for different levels of sales. We can set up a system of equations to represent the two plans:

Plan A:

Total Pay = 1775 + 0.19S

where S is Lamont's total monthly sales

Plan B:

Total Pay = 2100 + 0.07S

To find the point at which the two plans yield the same result, we can set the two equations equal to each other and solve for S:

1775 + 0.19S = 2100 + 0.07S

0.12S = 325

S = 2708.33

If Lamont's monthly sales are exactly $2,708.33, then he earns the same amount of money under both plans - this is the break-even point.

However, for sales above this amount, Plan A becomes the better option as the commission rate is higher. Option 1 is incorrect because it assumes that Plan A is always better, whereas we know from the calculations that this is not the case. Option 3 is correct for sales above $2,708.33, but not for sales below this amount. Option 4 is also incorrect as we know that Plan B yields a slightly higher payout for sales exactly equal to the break-even point.

Therefore, option 2 is the correct answer as it accounts for the break-even point and accurately reflects the difference in total pay between Plan A and Plan B for Lamont's sales of $2,708.33.

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When the slope is an integer the best answer would be a. the rise number is one.

Any number, including zero, positive numbers, and negative numbers, is an integer. An integer can never be a fraction, a decimal, or a percent, it should be observed. Integers include things like 1, 3, 4, 8, 99, 108, -43, -556, etc.

When the slope is an integer, it means that the rise over run is also an integer, and the rise and run are relatively prime. Therefore, the best answer would be:

Therefore, the correct answer is a. the rise number is one.

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Answer:

the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.

From point A, we can use tangent function to find x:

tan(5°) = (119 + h) / x

From point B, we can use tangent function again to find y:

tan(18°) = (119 + h) / y

We want to find the distance between point A and point B, which is the difference between x and y:

distance AB = y - x

We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:

h = x tan(5°) - 119

tan(18°) = (119 + x tan(5°) - 119) / y

tan(18°) = x tan(5°) / y

y = x tan(5°) / tan(18°)

distance AB = y - x = x (tan(5°) / tan(18°) - 1)

Now we can plug in the values and use a calculator to find the distance:

distance AB = x (tan(5°) / tan(18°) - 1)

distance AB = x (0.107 - 1)

distance AB = -0.893 x

Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:

x = distance AB / -0.893

Using a calculator, we get:

x ≈ 181.74 feet

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

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Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.

What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?

Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.

Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:

AW = AY (given)

AZ = AX (given)

WY = XZ (as WY and XZ bisect each other)

Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.

Since opposite sides are congruent, we have WX || YZ.

Similarly, we can show that WZ || XY.

Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.

Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."

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The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4

ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.

By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:

α + β = -c/6

And the prοduct οf the rοοts is given by:

αβ = 4/6 = 2/3

We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:

αβ = α + β + 2

Substituting the values we knοw, we get:

2/3 = -c/6 + 2 + α + β

Simplifying this expressiοn, we get:

2/3 = -c/6 + 2 - c/6

Multiplying bοth sides by 6, we get:

4 = -c + 12 - c

Simplifying, we get:

2c = 8

c = 4

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Answer:

The solid formed by rotating the two-dimensional shape (which appears to be a right-angled triangle) about the line is a cone.

Answer:

identy the solid formed by

Answer:

To find the slope of a line parallel to 5x - 2y = 2, we need to first rearrange the equation in slope-intercept form, y = mx + b, where m is the slope of the line. 5x - 2y = 2 -2y = -5x + 2 y = (5/2)x - 1 The slope of the line is 5/2. Since we are looking for a line parallel to this line, the slope of the parallel line will be the same as the slope of the original line, which is 5/2. Therefore, the slope of a line parallel to 5x - 2y = 2 is 5/2.

The value of log(27) is 1.431.

What is logarithm?

The power to which a number must be raised in order to obtain other numbers is referred to as a logarithm. The easiest method to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be expressed as multiplication and division of logarithms.

We can use the property of logarithms that states that log a (b^c) = c log a (b) to evaluate log 27 using the given approximations:

log 27 = log (3³) = 3 log 3 ≈ 3(0.477) ≈ 1.431

Therefore, log 27 ≈ 1.431.

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Answer:  4,258,375

Step-by-step explanation:

(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.

(b) The probability of all three cards being literature questions is 2.4%.

(c) 5%.

Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.

(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.

To calculate this probability, we use the formula

P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.

(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.

The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.

(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.

The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.

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Answer:

k=0 or k=1/27

Step-by-step explanation:

3k-81k^2=0

3k(1-27k) =0

3k=0 or 1-27k=0

k=0 or -27k= -1

k= 1/27