How do I prove that the square of an odd number is always one more than a multiple of 8?

a) The experimental units are the Acacia Trees.

b) The treatments carried used are; active beehives, empty beehives and no single beehive.

c) The response variable is the damage that the elephants caused to the trees.

Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.

From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.

The treatments carried out here are the active beehives, empty beehives and no single beehive.

The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.

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Work Shown:

[tex](x_1,y_1) = (-5,-3) \text{ and } (x_2,y_2) = (8,-1)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-1 - (-3)}{8 - (-5)}\\\\m = \frac{-1 + 3}{8 + 5}\\\\m = \boldsymbol{\frac{2}{13}}\\\\[/tex]

A slope of 2/13 means we go up 2 units and to the right 13 units. If starting at (-5,-3) and following this movement pattern of "up 2, right 13", then we arrive at (8,-1).

Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B

A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.

On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.

From the graph the actual heart rate=150

but calculated heart rate from best fit line=148

Difference between actual and calculated=150−148=2

Option B is correct.

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a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

The speedup of a parallel algorithm will eventually reach some limit.

What is parallel algorithm?

An algorithm is a set of instructions that takes input from the user and, after doing some calculations, generates an output. A parallel algorithm is one that can carry out multiple operations simultaneously on various processing units and then combines all of the separate outputs to get the desired outcome.

An algorithm that can execute several instructions concurrently on various processing devices and then aggregate all of the individual outputs to produce the final result is known as a parallel algorithm.

Because a parallel algorithm's speedup is never equal to the number of processors, it ultimately reaches a limit beyond which it can no longer be accelerated. At that point, the algorithm will no longer be accelerated and the speedup will stop.

Hence, the speedup of a parallel algorithm will eventually reach some limit.

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Proportional relationship for the given table is true and is define as

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

As given in the question,

Value of x and y in the given table are :

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.

y / x for all the values of x and y:

First values:

y /x = 6.4 / 25.6

      = 0.25

Second values:

y/x = 18.2/ 72.8

    = 0.25

Third values :

y /x = 19.3/ 77.2

      = 0.25

0.25 is equivalent to One fourth ( 1/4).

Constant of proportionality exist = 0.25 or One fourth.

Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.

The complete question is:

Determine if the table how a proportional relationship.

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

Yes, it is proportional because all y over x ratio are equivalent to one third.

No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.

No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

The angles in the intersected lines are as follows:

When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.

Angle a is vertically opposite to angle b.

Vertically opposite angles are congruent.

Therefore,

∠a ≅ ∠b

Hence,

x + 8 = 100(vertically opposite angles)

x = 100 - 8

x = 92

b + x + 8 = 180(sum of angles on a straight line)

b + 92 + 8 = 180

b = 180 - 100

b = 80 degrees.

Hence,

a = 80 degrees

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Answer: the student forgot to multiple by right side of equation 2 in line 2

Step-by-step explanation: your welcome :)

The expression 5(x + 7) has a sum of two terms 5x and 35.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, an expression 5(x + 7).

Now distributing 5 to x and 7 we get 5x + 35.

So, The expression 5(x + 7) has the sum of two terms.

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Answer: 34.5

Step-by-step explanation:

    To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.

517.5 / 15 = 34.5

1138.5 / 33 = 34.5

1242 / 36 = 34.5

Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good

Step-by-step explanation:

7(x-1)=3x+2

Distribute through the parentheses

7x-7=3x+2

Move the variable to the left-hand side and change its sign

7x-7-3x=2

or Move the constant to the right-hand side and change its sign

7x-7-3x=2

Collect like terms

4x=2+7

And then Add the numbers

4x=9

Divide both sides of the equation by 4

x=9/4

Mixed number is 2 1/4

The equation of the new function is g(x) = 4(2ˣ)

The exponential equation is given as

f(x) = 2ˣ

Then, we have the transformation to be:

Vertically stretch by a scale factor of 4

The scale factor can be represented as k

So, we have

k = 4

The rule of vertical stretch by a scale factor of k is represented a

g(x) = kf(x)

So, we have

g(x) = 4 * 2ˣ

This gives

g(x) = 4(2ˣ)

Hence, the equation is g(x) = 4(2ˣ)

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In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables

The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.

Looking at the options and based on the definitions above, option C adequately describes the test statistic.

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Answer:

-------------------------------

Find y:

The response variable in this study is

Yield of crop.

"Information available from the question"

In the question:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil.

Now, According to the question:

Let's know:

What is called fertilizer?

A fertiliser is a natural or artificial substance containing chemical elements (such as Nitrogen (N), Phosphorus (P) and Potassium (K)) that improve growth and productiveness of plants. Some synonyms include the terms "enrichment" or "plant nutrient".

The answer is:

Yield of crop.

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The complete question is this:

A study is conducted to determine if one can predict the yield of a crop based on the amount of fertilizer applied to the soil. The response variable in this study is

Answer:

7

Step-by-step explanation:

649-531=118

We know that there are 118 more guests per hour.

Divide 826 by 118 to get 7.

Answer: 7

Step-by-step explanation:

The first line of the table is 2 and 236 if you divide 236 by 2 you get 118

Then after that you times it by any number after 5.5 until you get 826.

The domain when the maximum number of people allowed in the movie theater is 60 people would be: B. 0 ≤ x ≤ 60.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Since the maximum number of people that are allowed in the movie theater is 60 people, we can logically deduce that the input values (x-values) for its function is less than or equal to 60. Therefore, the domain of the function on this graph is given by:

Domain = [0, 60]

Domain = 0 ≤ x ≤ 60.

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Complete Question:

The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.

40 ≤ y ≤ 160

0 ≤ x ≤ 60

40 ≤ x ≤ 160

0 ≤ y ≤ 60

Answer:

the answer is 0 is less than or equal to x which is less than or equal to 60

Step-by-step explanation:

Domain is the x value

Since the max amount of people is 60, and people is x value the answer i put above is a reasonable domain.

Hope this helps!

The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.

In this problem, the data-set is given as follows:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.

Hence the mean is of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.

After the change, the data-set is of:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.

Hence the mean will be of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.

Then the increase will be of:

1065 - 1035 = 30.

The median of a data-set is the middle element of the data-set, the value which:

The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.

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Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

Hopes this helps please mark brainliest

This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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The probability mass function (pmf) of X formally displays the likelihood of events where X=xk.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

We can list the components of RX if X is a discrete random variable since RX is a countable set. In other words, RX=x1,x2,x3,... can be written.

Note that the random variable X here has the potential values x1, x2, x3

While we typically use capital letters to designate random variables, we typically use lowercase letters like x, x1, y, and z to denote the integers in the range.

We are interested in learning the probability that a discrete random variable, X, equals a certain value, xk.

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The relations which are functions as required to be identified in the task content are;

It follows from the task content that the relations which are functions among the given answer choices are to be identified.

Since the definition of a function is such that; a function is a special kind of relation in which case only one output value is assigned to each input values.

Put simply, a function has only one output value for each input value.

Therefore, it follows from the definition above that the relations which are functions among the given answer choices are as listed above.

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Answer:

attached in the file

Answer:

Domain: {9, 13, 21}

Step-by-step explanation:

Answer:

Step-by-step explanation:

The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .

In the question ,

it is given that ,

the angle bisector of the exterior angle of a triangle is parallel to a side .

we have to prove that the triangle will be an isosceles triangle .

In the triangle ABC given below , AB is extended to AD ,

SO , the exterior angle will be angle DAC ,

let AE be the bisector of the the angle .

So , the equal angles are angle DAC and angle EAC .

it is given that AE is parallel to BC , where BC is base .

we know that ,

if any line intersects two parallel lines then every pairs of alternative  Interior angles are same and also their corresponding angles are equal .

Here AE is parallel to BC and line BD intersects them ,

So , angle ABC = angle DAE    ( corresponding angles )

angle ACB = angle EAC   ( alternate angles )

Now , as AE is the bisector of angle DAC ,

we have , angle DAC = angle EAC

So , we get , angle ABC = angle ACB .

In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal

that means , AB=AC

Hence , the given Triangle is an isosceles triangle .

Therefore , it is proved that the triangle ABC is an isosceles triangle .

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Answer:

f(x) = 3x + 4

f(4) = 3(4) + 4 = 12 + 4 = 16

Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:

y = f(0) = 1.

Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:

y = g(0) = -1.

From the information provided above, we have the following function:

g(x) = f(x) + k

g(0) = f(0) + k

Making k the subject of formula, we have:

k = g(0) - f(0)

k = -1 - 1

k = -2.

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Using polar coordinates, the result for integral is - 0.448[tex]\pi[/tex]

What is polar co-ordinates?

In arithmetic, the polar coordinate system may be a two-dimensional organization within which every purpose on a plane is set by a distance from a indicator and an angle from a reference direction.

Main body:

The most used relation for polar coordinates is:

[tex]x^{2} +y ^{2} =r^{2}[/tex]

An integral in Cartesian coordinates is converted to polar using:

[tex]\int\int{f(x,y)} \, dA = \int\int{ f(r, \beta )d\beta[/tex]

In this problem:

f(x,y) = sin [tex]x^{2} +y^{2}[/tex]

thus

f(r,[tex]\beta[/tex]) = sin[tex]r^{2}[/tex]

Region between the circles with center at the origin and radii 1 and 3, thus the inner limits of integration are r =1  and r =3.

First quadrant, thus, the outer limits of integration are: [tex]\beta[/tex] = 0,[tex]\beta[/tex] = [tex]\pi /2[/tex].

The polar integral is:

I = [tex]\int\limits^3_1 {sinr^{2} r} \, dr[/tex]

Using substitution:

u =[tex]r^{2}[/tex] ⇒ du = 2rdr⇒ dr = du /2

I = 1/2[tex]\int\ {sin u} \, du[/tex]

 = -[tex]cos r^{2[/tex] /2     where limits are 3, 1

Applying the fundamental theorem of calculus:

I = [tex]-cos 5^{2} /2[/tex][tex]-cos1^{2}/2[/tex]

I = - 0.996

Then, the outer integral is:

O =[tex]\int\limits^\pi _0 {-0.996} \, d\beta[/tex]

O=  - 0.448[tex]\pi[/tex]

Hence the result for integral is - 0.448[tex]\pi[/tex]

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