In using induction to prove that is divisible by 10, what statement can be represented by Sk + 1?

The Power e is to which a number should be raised to get the specified number is called the logarithm of that specific number. For example, the logarithm to the base of 10 of 1000 is 3 because 10 raised to the power 3 is 1000.

The logarithmic function is the reverse of the Mathematical function of the exponential function. The logarithmic function is log ax = y is equal to x = ay.

There are mainly two types of logarithms normally used in Mathematics. They are one is common logarithms and second natural logarithms.

The log number ‘e’ is an irrational Mathematical constant and is mostly used as the base of natural logarithms. The number ‘e’ is the only unique number in mathematics whose value of natural logarithm is equal to unity.

The value of log ‘e’ was calculated in 1683 by Jacob Bernoulli.

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Answer:

k=6.5

Step-by-step explanation:

by the graph, when x=0, y=-3

y = 2x+c

-3=2(0)+c

then,

c=-3

for y = 10,

10=2(k)-3

k=6.5

Answer:

760

Step-by-step explanation:

25%= 190

100 = 25 × 4

100% (total number of people) = 190 × 4 = 760

The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

f(x) = √(2x + 6) - 3

The parent function is given as,

f(x) = √x

Multiply by 4, then we have

f(x) = 4√x

f(x) = √2x

Shift the function 3 units downwards and 6 units left.

f(x) = √(2x + 6) - 3

The transformations that were applied to obtain the graph will be Multiply by 4 and Shift the function 3 units downwards and 6 units left.

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The complete question is given below.

The length of the hypotenuse is \(36\sqrt{2}\).

Given that

Consider triangle DEF.

The legs have a length of 36 units each.

Triangle DEF is shown.

Angle DFE is 90 degrees and angles FDE and DEF are 45 degrees.

The lengths of sides DF and FE are 36 units.

We have to determine

What is the length of the hypotenuse of the triangle?

According to the question

The length of the hypotenuse is determined by using the Pythagoras theorem following all the steps given below.

The length of the hypotenuse is determined by;

\(\rm (Hypotenuse)^2= (Base)^2+(Perpendicular)^2\\\\ (Hypotenuse)^2= (36)^2+(36)^2\\\\ (Hypotenuse)^2= 1296+1296\\\\ (Hypotenuse)^2= 2592\\\\ Hypotenuse = \sqrt{2592}\\\\ Hypotenuse = \sqrt{2\times 4 \times 4\times 9\times 9}\\\\ Hypotenuse= 9 \times 4 \times \sqrt{2}\\\\ Hypotenuse= 36 \sqrt{2}\\\)

Hence, the length of the hypotenuse is \(36\sqrt{2}\).

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Answer:

D. 36/2

Step-by-step explanation:

In quantitative research, data collection from the same respondents at 2 or more points (waves) in time is referring to "longitudinal."

A method for gathering and interpreting numerical data is known as quantitative research. It can be used to discover patterns and averages, to make predictions, to verify causal linkages, and to generalize results to larger groups.

Some features regarding quantitative research are-

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Using probability of independent events, it is found that the probability that it will purchase the mineral rights to exactly one of the two mountains is given by:

c. 0.51

If two events, A and B, are independent, the probability of both happening is the multiplication of the probability of each happening, that is:

\(P(A \cap B) = P(A)P(B)\)

In this problem, these following two events result in the rights of exactly one of the two mountains being bought:

Hence:

\(p = 0.55(0.6) + 0.45(0.4) = 0.51\)

Thus, option c is correct.

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Answer:

25>x-5 = x anything less than 30

Step-by-step explanation:

first add 5 to both sides

then u get 30.

30-5 is 25

so, you know that x must be any number less than 30 that is not 0

Answer:

x < 30

Step-by-step explanation:

\(25>x-5\\\\25+5>x-5+5\\\\{30>x}\\\\\boxed{x<30}\)

Hope this helps.

Answer:

Yellow White And Orange I pretty Sure!! Im sorry if this is not what you want! I can change it if so.

Step-by-step explanation:

A quotient of a number and 6

Explanation: Quotient means that you divide something by another. Let's let n be the "number". Therefore, "a quotient of a number and 6" refers to n6 or n÷6 .

To find the number of tickets bought at the theater, we simply subtract the total online and fundraiser sales from the overall ticket count: 4025 - 2415 = 1610 tickets. So, 1610 tickets were bought at the theater.

We need to figure out how many tickets were bought online and in the fundraiser. If 2/5 of the tickets were bought online, that means 3/5 of the tickets were bought in other ways (since 2/5 + 3/5 = 1). So, if 1/5 of the tickets were bought in a fundraiser, that means 2/5 of the tickets were bought at the theater (since 1/5 + 2/5 = 3/5). Now we just need to use this information to find out how many tickets were bought at the theater.

If there are tickets for 4025 people and 2/5 were bought online and 1/5 were bought in a fundraiser, that means:
4025 x 2/5 = 1610 tickets were bought online
4025 x 1/5 = 805 tickets were bought in a fundraiser
Now we can subtract those two numbers from the total number of tickets to find out how many were bought at the theater: 4025 - 1610 - 805 = 1610 tickets were bought at the theater.

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We have X and Y variables the value as follows,

A. Notice that X can only be -1 and 1. Y can also only be -1 or 1.

So, P{X=1} = 1-P{X=-1} and P{Y=1} = 1 - P{Y=-1}

Let's use this fact along with some simple algebra:

\(p(1,1)= P[X=1, Y=1]\\p(1,1)= P[X=1]*P[Y=1]\\p(1,1)= (1-P[X=-1])*(1-P[Y=-1])\\p(1,1)= 1-P[Y=-1]-P[X=-1]+P[X=-1]*P[Y=-1]\\p(1,1)= 1-P[Y=-1]-P[X=-1]+p(-1,-1)\)

But we can also observe that P{Y=-1}=P{Y=-1}=0.5 (This comes from the assumption E[X]=E[Y]=0)

So:

p(1,1) = 1 - 0.5 - 0.5 + p(-1,-1)

Therefore:

p(1,1) = p(-1,-1), QED

B. We can basically do the same thing as part A.

\(p(1,-1)=P(X=1,Y=-1)\\p(1,-1)=P(X=1)*P(Y=-1)\\p(1,-1)=[1-P(X=-1)]*(1-P[Y=1])\\p(1,-1)=1-P(Y=1)-P(X=-1)+P(X=-1)*P{Y=1}\\p(1,-1)=1-P(Y=1)-P(X=-1)+p(-1,1)\)

And we can observe P{Y=1}=P{X=-1}=0.5 (This comes from the assumption E[X]=E[Y]=0)

So:

p(1,-1) = 1 - 0.5 - 0.5 + p(-1,1)

Therefore:

p(1,-1) = p(-1,1)

You can use any statistical calculator for C-E.

C.4/3

D.4/3

E. 0

The sentence "p=2p(1,1)" may cause some misunderstanding. The issue is that the statement is meaningless. p can be either variable notation or probability notation. If we consider p to be a variable and p(1,1) to be a probability, then p=2p(1,1)=2*.25=.5. Yet, this would be ineffective for addressing questions C, D, and E. Perhaps the questioner is referring to the fact that p(1,1) appears twice as frequently as the other combinations in the data. If it were the case, the following would be the answers:

C.6/5

D.6/5

E. 4/25

However, this would violate the assumption made earlier that

E[X] = E[Y] = 0

If (1,1) occurs twice as often in the sample, then E[X] = E[Y] = 1/5.

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Answer:From 141.748 to 148.835 when you convert them using a conversion chart

Step-by-step explanation:.

Answer:

112.765789 ect

Step-by-step explanation:

Answer:

x = 7°

Step-by-step explanation:

(8x + 6)° + 118° = 180°

8x = 56°

x = 7°

by the inverse function definition, we will have that:

Remember that, by definition, for an invertible function f(x) we have that:

f(x) = y

then:

f⁻¹(y) = x

Where f⁻¹(x) is the inverse function of f(x).

Now, we want to find:

f⁻¹(-2)  and f⁻¹(1)

If you look at the given table, we can see that we have the points (3, -2) and (0, 1), which means that:

f(3)= -2

f(0) = 1

Then, by the inverse function definition, we will have that:

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The z-score for a raw score of 6 is 0.5.A z-score indicates how many standard deviations a raw score is away from the mean.

To calculate the z-score for a raw score of 6 given a mean of 4 and a standard deviation of 4, we can use the formula:

z = (raw score - mean) / standard deviation

Substituting the values into the formula, we get:

z = (6 - 4) / 4

z = 0.5

Therefore, the z-score for a raw score of 6 is 0.5.

In this case, a z-score of 0.5 indicates that the raw score of 6 is half a standard deviation above the mean of 4.

Z-scores are useful because they allow us to compare scores from different distributions. For example, if we have two sets of data with different means and standard deviations, we can convert them into z-scores to compare them directly. A positive z-score means that the raw score is above the mean, while a negative z-score means that the raw score is below the mean. The magnitude of the z-score indicates how far the raw score is from the mean in terms of standard deviations.

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The cross of a red oval with a purple oval will produce approximately 44.4% red long, 22.2% red oval, 22.2% purple long, and 11.1% purple oval offspring.

Based on the information given, we can represent the pure-breeding colors and shapes as follows:

Red color (RR) is dominant over white color (rr)

Long shape (LL) is dominant over round shape (ll)

We can also represent the hybrids as:

Purple color (Rr) is a result of a cross between red and white pure-breeding colors

Oval shape (Ll) is a result of a cross between long and round pure-breeding shapes

Given that we are crossing a red oval (RrLl) with a purple oval (RrLl), we can set up a Punnett square to determine the possible genotypes and phenotypes of their offspring:

RL Rl rL rl

RL RRLl RRll rRLL rRlL

Rl RRLl RRll rRLL rRlL

rL RrLL RrLl rrLL rrLl

rl RrLl Rrll rrLl rrll

From the Punnett square, we can see that there are nine possible phenotypes, which can be grouped by color and shape:

Red long (RRLL, RRLl, RrLL, RrLl): 4/9 or about 44.4% chance

Red oval (RRll, Rrll): 2/9 or about 22.2% chance

Purple long (rRLL, rRlL): 2/9 or about 22.2% chance

Purple oval (rrLL, rrLl, rrll): 1/9 or about 11.1% chance

Therefore, the cross of a red oval with a purple oval will produce approximately 44.4% red long, 22.2% red oval, 22.2% purple long, and 11.1% purple oval offspring.

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Answer: It will be 9378.94

Step-by-step explanation: You have to divide 16200 by 14.25% to get 1136.84211. Then multiply 1136.84211 by 6 to get 6821.05266. Finally you subtract 6821.05266 from 16200 to get your answer, 9378.94

Answer:

y= -2x - 1

Step-by-step explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

Substitute these points into this formula to find the slope of this linear function.

Simplify and solve for the slope m.

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

Substitute m = -2 and the point (1, -3) into this equation.

Simplify this equation and put it into slope-intercept form: \(y=mx+b\).

The equation of the linear function represented by the table is y = -2x - 1.

Answer:

y= -2x - 1

Step-by-step explanation:

Take two of the points given by the data in the table.

Using the x-values 1 and 2, they have a y-value of -3 and -5, respectively.

Therefore, we can write these out as coordinate points: (1, -3) and (2, -5).

The equation to find the slope of a line is:

Substitute these points into this formula to find the slope of this linear function.

Simplify and solve for the slope m.

The slope of this linear function is -2. Now, we can use this slope and substitute it into the point-slope equation along with another one of the points on the function.

Point-slope equation:

Substitute m = -2 and the point (1, -3) into this equation.

Simplify this equation and put it into slope-intercept form: .

The equation of the linear function represented by the table is y = -2x - 1.

The statement "The constraint x₁ ≤ x₂ in a BIP problem means that alternative 2 cannot be selected unless alternative 1 is also selected" is false because the constraint allows for the possibility of alternative 2 not being selected even if alternative 1 is selected, but it does require that if alternative 2 is selected, then alternative 1 must also be selected.

In binary integer programming, the constraint x₁ ≤ x₂ indicates a relationship between two binary decision variables, x₁ and x₂. Specifically, it means that if x₁ is set to 1 (i.e., selected), then x₂ must also be set to 1 in order to satisfy the constraint.

However, if x₁ is set to 0 (i.e., not selected), then x₂ can be either 0 or 1, as long as it does not violate any other constraints in the problem. In other words, the constraint ensures that if alternative 2 is selected, it can only be selected if alternative 1 is also selected, but it is possible for neither alternative to be selected.

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In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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Answer: 5 units

Step-by-step explanation:

5/2 = 2.5

they are 2.5 away on each side of 0 therefore the points are 5 units away from each other

False. There is no strong evidence to support the claim that the temporal pattern of super-eruptions (M>8 eruptions) is random.

The statement claims that the temporal pattern of super-eruptions is random, implying that there is no specific pattern or correlation between the occurrences of these large volcanic eruptions. However, scientific studies and research suggest otherwise. While it is challenging to study and predict rare events like super-eruptions, researchers have analyzed geological records and evidence to understand the temporal patterns associated with these events.

Studies have shown that super-eruptions do not occur randomly but tend to follow certain patterns and cycles. For example, researchers have identified clusters of super-eruptions that occurred in specific geological time periods, such as the Yellowstone hotspot eruptions in the United States. These eruptions are believed to have occurred in cycles with intervals of several hundred thousand years.

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The description of the route of the limousine is

First, the limousine drives 18 blocks right and 8 blocks down and then it drives 17 blocks left and 2 blocks up

From the question, we have the following parameters that can be used in our computation:

T<18, -8> o T<-17, 2>

The above parameters represent the transformation and the positions of the limousine

The above statement represents the direction in words

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Let me see.

Row 1 = 10 bricks

Row 2 = 10 bricks

On top of each row there are 6 bricks.

Two rows times 6 bricks per row is 12 bricks.

Total = 20 + 12 or 32 bricks.

Answer:

data given

Universal set 40people

people who can sew 14

people who can knit 12

people who can do both 5

Step-by-step explanation:

•people who can sew only

=14-5

=9

•people who can knit only

=12-9

=7

Union of people who can sew and the one who can knit

=9+7+5

=21

who do neither

=40-21

=19

: .people neither sew or knit are 19

Answer:

x = 11/3 = 3 2/3

y = 13/3 = 4 1/3

Step-by-step explanation:

Here, we want to solve the system of equations simultaneously

x + y = 8

2x -3 = y

From the second equation, we have an equation for y

we can simply proceed to substitute this into the first equation

x + 2x - 3 = 8

3x - 3 = 8

3x = 8 + 3

3x = 11

x = 11/3

Recall;

y = 2x - 3

y = 2(11/3) - 3

y = 22/3 - 3

y = (22-3(3))/3

y = (22-9)/3 = 13/3

Answer:

33

Step-by-step explanation:

Answer:

The angle that says it is 120 degrees looks wrong. That is an acute angle

Step-by-step explanation: