Write 2^100 as a power with the following base.
4

The equation in slope-intercept form would be; y = 5x + 33

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given that line passes through points (-8, – 7) and (-6, – 3).

Now we will write in slope-intercept form,

y = m x + b .

Now to find m, we use the formula;

m = y₂ - y₁ / x₂ - x₁

Then,

m = { -3 - (-7)} / { 6 - (-8)}

m = 4 / 14

m = 2/7

Thus, y = 5x +33

Therefore,  its equation in slope-intercept form would be; y = 5x + 33

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Answer:

  -1

Step-by-step explanation:

You want to evaluate (8x -5) for x = 1/2.

Put the value where x is in the expression, then do the arithmetic.

  8x -5 = 8(1/2) -5

  = 4 -5

  = -1

The value of the expression is -1.

The formula for calculating it is perimeter of the rectangle = 2(length + width), meaning that it is equal to twice the sum of its length and width.

Given that,

We have to find which equation perfectly describes the ABCD rectangle's perimeter? How do you determine a rectangle's length and width given its perimeter?

We know that,

The total length of a rectangle's outer boundary is known as its perimeter. The formula for calculating it is perimeter = 2(length + width), meaning that it is equal to twice the sum of its length and width.

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in metres, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

A rectangle has four 90° angles.

The diagonals of a rectangle are all of the same length.

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Not agree with the Mr. Chin's conjecture, because there may be space for the desk in the room but Mr. Chin not have the actual measurement, it may or may not fit the  desk in room of given length and width.

A good guess or an idea about a pattern is a conjecture. Speculate (about something) We can only speculate about the killer's thoughts. speculate that... He speculated that the population might double within a decade. speculate about something She speculated about the existence of a brand-new species.

A mathematical assertion that has not yet been thoroughly established is known as a conjecture. When one observes a pattern that is consistent across many cases, speculations result. However, just because a pattern applies to a lot of cases does not mean that it applies to all of them. To fully accept the mathematical observation, conjectures must be demonstrated. A theorem is formed when a conjecture is thoroughly demonstrated.

A crucial step in solving a problem is making a guess; It's more than just a tool for professionals in math. It is extremely uncommon for a problem's solution to be immediately apparent in everyday problem solving. Instead, the process of solving problems involves looking at the problem structure, looking at the cases, making a guess about the solution, and then proving that guess.

Hence, not agree with Mr. Chin's conjecture.

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Answer:

A

Step-by-step explanation:

The use of analysis of variance rather than a t-test for the null hypothesis claims more than two populations.

Analysis of Variance (ANOVA) is a statistical component used to evaluate variances throughout the method (or average) of various groups. A variety of eventualities use to decide if there's any distinction among the method of various groups. Student's t-test is used to compare means between two His groups and ANOVA is used to compare means between three or more His groups. ANOVA first obtains the common t-test. A significant t-test for the ANOVA test indicates at least one pair for which the mean difference was statistically significant.

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Answer: (x + 1)^2 + (y - 3)^2 = 65

Step-by-step explanation:

Answer: (x+1)²+(y-3)²=89

Step-by-step explanation:

An equation of a circle: (x-a)²+(y-b)=R²

The center of a circle is (-1,3), hence a=-1    b=3

(x-(-1))²+(y-3)=R²

(x+1)²+(y-3)²=R²    (1)

Substitute the coordinate (7,-2) belonging to the circle into equation (1):

(7+1)²+(-2-3)²=R²

8²+(-5)²=R²

64+25=R²

89=R²

Thus, R²=89

Hence,

(x+1)²+(y-3)²=89

Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3 and Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3

a) To calculate the volume of the cylinder, we need to use the equation for the volume of a cylinder, which is πr^2h, where π is pi, r is the radius, and h is the height. In this case, the radius is 5 cm and the height is 10 cm, so the equation becomes π(5 cm)^2(10 cm) = 785.398 cm^3.

b) To calculate the volume of the hemispherical top, we need to use the equation for the volume of a hemisphere, which is 2/3πr^3, where π is pi and r is the radius. In this case, the radius is 5 cm, so the equation becomes 2/3π(5 cm)^3 = 523.598 cm^3.

Cylinder's volume = πr^2h = π(5 cm)^2(10 cm) = 785.398 cm^3

Hemispherical top's volume = 2/3πr^3 = 2/3π(5 cm)^3 = 523.598 cm^3

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The average value of the trigonometric equation f(x) = - 2 · sin x + 5 · cos x over the interval [π, 2π] is equal to 2 / π.

In this question we find the definition of a trigonometric equation consisting in the sum of two trigonometric functions on a given interval [a, b], of which we must determine its average value by means of the following integral equation:

[tex]m = \frac{1}{b - a} \cdot \int\limits^b_a {f(x)} \, dx[/tex]

Where:

First, write the entire trigonometric equation and the bounds of the interval:

f(x) = - 2 · sin x + 5 · cos x, a = π, b = 2π

Second, obtain the result of the integral equation:

[tex]m = -\frac{2}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\sin x} \, dx + \frac{5}{2\pi - \pi}\cdot \int\limits^{2\pi}_\pi {\cos x} \, dx[/tex]

[tex]m = \frac{2}{\pi}\cdot \cos x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex] + [tex]\frac{5}{\pi}\cdot \sin x[/tex] [tex]|\limits_{\pi}^{2\pi}[/tex]  

m = (2 / π) · (cos 2π - cos π) + (5 / π) · (sin 2π - sin π)

m = (2 / π) · (1 - (- 1)) + (5 / π) · (0 - 0)

m = 2 / π

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The given number on the left can be matched with the correct description of the number on the right as :

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

logical quantity is A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers. The number "0" is also a rational number because there are various ways to express it, including 0/1, 0/2, and 0/3.

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The answer is (i)Yes the given relation is a function ,

(ii) the domain is Z and range is 2Z ,

(iii) the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 }

In the question ,

it is given that ,

the relation is S₁ = {(x,y) | x,y∈ Z : y = 2x }

Part(i)  ,

We can say that Yes , the given relation is a function because for each

x ∈ Z , there exists a unique y ∈ Z .

Part(ii)

since the variable  x , y ∈ Z , the input variable is x ,

so , the domain of the function will be Z , and

the Range of the function will be = 2Z .

Part(iii) ,

Since the given function is bijective function ,

the function will have an inverse .

given y = 2x ,

the inverse ⇒ x = y/2 .

so , the inverse function is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .

There fore , the relation is a function whose domain is Z and range is 2Z n and the inverse is S₁⁻¹ = {(x,y) | x,y∈ Z : x = y/2 } .

The given question is incomplete , the complete question is

For given relation , please answer the following questions (briefly justify your answers).

(i) Is the relation a function ?

(ii) If the relation is a function, what are its domain and image ?

(iii) Is the inverse a function ? If so, what is the inverse function ?

The relation is given as : S₁ = {(x,y) | x,y∈ Z : y = 2x }

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Answer:

$1.25

Step-by-step explanation:

150 / 120

Answer:

$1.25

Step-by-step explanation:

You can find the average cost per coconut by dividing the total price by the number of coconuts. 150 divided by 120 is $1.25. Therefore, each coconut costs $1.25.

The probability mass function of the sample mean of x1, ... , xn, then the

Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).

var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function PX(x) of X.

Given that,

The probability mass function of the sample mean of x1, ... , xn,

p{x = 0} = 0.2, p{x = 1} = 0.3, p{x = 3} = 0.5

when (a) n = 2; (a) n = 3

Expectation is defined as

[tex]E[X][/tex] = ∑ˣ [tex]x P(X =x)[/tex]

We have

[tex]E[X][/tex] = ∑   [tex]x P(X =x)[/tex]

           [tex]x[/tex]∈(2,3)

[tex]E[X][/tex] = [tex]P(X =0)+2P(X=1)+3P(X=3)[/tex]

[tex]E[X][/tex] = 0.2 + 0.3 + 0.5

[tex]E[X][/tex] = 1

Variance is defined as

[tex]Var[X][/tex] = E[(X-[tex]E[X]^{2}[/tex]]

[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]

We get

[tex]E[X]^{2}[/tex] = [tex]1^{2} P[X=0]+2^{2} P[X=1]+3^{2} P[X=2][/tex]

[tex]E[X]^{2}[/tex] = 0.2 + 4(0.3) + 9(0.5)

[tex]E[X]^{2}[/tex] = 0.2 + 1.2 + 4.5

[tex]E[X]^{2}[/tex] = 5.9

Variance is defined as

[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]

[tex]Var[X][/tex] = 5.9 - [tex]1^{2}[/tex]

[tex]Var[X][/tex] = 5.9 - 1

[tex]Var[X][/tex] = 4.9

Therefore,

The probability mass function of the sample mean of x1, ... , xn, then the

Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9

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The maclaurin expansion for function eˣ  is 1 + x + x²/2 + x³/6 + x⁴/24 + .....

A function's expansion series, which provides the function's derivatives' sum, is known as a Maclaurin series.

Series [f, x, 0, n] can be used to find a function's Maclaurin series up to order n.

When x = 0, it is a specific example of the Taylor series. The series of Maclaurin is provided by

[tex]f(x) = f(x_0) + f(x_0)(x - x_0) + \frac{f"(x_0)}{2!}(x - x_0)^2 + . . .[/tex]

The formula for maclurin series is :

[tex]f(x) = \sum^{\infty}_{n=0} \frac{f^n (x_0)}{n!} (x-x_0)[/tex]

Where,

f(xo), f’(xo), f’‘(xo)……. are the successive differentials when xo = 0.

Maclaurin expansion for the function eˣ

Firstly , We will derivate the function

f(x) = eˣ

=> f'(x) = e⁰ = 1

=>  f''(x) = e⁰ = 1

=> f'''(x) = e⁰ = 1

and so on

Upon evaluation of all derivatives at x = 0, we obtain the value 1.

Moreover, f(0)=1, so we can deduce that the expansion of the Maclaurin Series as

=> eˣ = 1 + x + x²/2 + x³/6 + x⁴/24 + .....

The given question is incomplete , I answered the question in general according to the knowledge

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By simplifying the equation we can get 5y²+2y+0.4.

An equation is said to be a formula that express the equality of two expressions. These two expressions on either side of the equal sign are called the "left side" and "right side" of the equation. We usually assume that the right-hand side of the expression is zero. This can be compensated for by subtracting the right side formula from the two side formulas, so there is no loss of generality.

The equation is representing direct proportion is, by the commenting them with equal sign.

4y²+4.1+7y-3.7-5y+y²

Reorder and gather like terms-

(1.4y²+y²)+(4.1-3.7)-(7y-5y)

Collect coefficients of likes terms

(1.4+1)y²+(4.1-3.7)-(7y-5y)×y

Calculate the sum or difference we can get

2.4y²+0.4+2y

Rewrite the expression

2.4y²+2y+0.4

Thus this is the correct answer .

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Answer:

Below

Step-by-step explanation:

The probability of Z    given Y  would be

      7  out of (15+7) = 7/22

The expression that is the same as sin⁻¹ x is (b) arcsin x

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

sin^-1 x

When this expression is rewritten, we have the following representation

sin⁻¹ x

The above expression is pronounced as arc-sin of x

And it can be represented as

arcsin x

This means that the equivalent expression of the given expression is (b) arcsin x

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(a) The total score of Jesse's card is 1

(b) The value of each of the two cards can either be 0 or cards with different signs

In the question,

(a) Jesse's card are 3 , -5 , 9 and -6

We have to find the total

You should know that,

Adding a positive integer is like addition but adding a negative integer is like subtraction

So, Total score = 3 + (-5) + 9 + (-6)

=> 3 - 5 + 9 - 6

=> 1

Jesse's total score is 1

(b) Jesse has picked two cards which are not affecting her total score

So, either he got two zeroes or two cards with opposite signs with same magnitudes

Like 1 and -1 etc.

The two doesn't affect his score because their effect got cancelled out

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Abby will choose $2,400 every quarter for 4 years.

Abby will have $30455.65  if she invests at 6% compounded quarterly

What is interest rates?

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

The formula of compounded quarterly is

A = P ( 1 + r/n)^(4t)

P = Principal =  $24,000

n = 4

r = rate of interest = 6% = 0.06

t = time = 4 years

Putting the value of P, r, t in the formula of compounded quarterly:

A = 24000 ( 1 + 0.06/4)^(4×4)

A = 30455.65.

Future Value of an Ordinary Annuity

[tex]S = R[\frac{(1+i)^n-1}{i} ][/tex]

Where

S is the future value;

R is the periodic payment;

i is the interest rate per period;

n is the number of periods.

The value of R is $2,400, i = 0.06/4 = 0.015

n = (4 × 4) = 16

[tex]S = 2400[\frac{(1+0.015)^{16}-1}{0.015} ][/tex]

S = 43037.69

Abby choose: $2,400 every quarter for 4 years.

Abby will have $30455.65  if she invests at 6% compounded quarterly.

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The Remainder in the Synthetic division is three, for given problem

1 |__1___2__-3__3 is 3.

So, the correct option is option(c).

The Synthetic Division:

It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.

We have given that the synthetic division is

1 |__1___2__-3__3

We find out the remainder in the synthetic division :

Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:

1 | 1 2 -3 3

|______________

1

Add down the column( 2+1 = 3) :

1 | 1 2 -3 3

|____1_________

1 3

Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:

1 | 1 2 -3 3

|____1____3____

1 3 0

1 | 1 2 -3 3

|____1____3___0_

1 3 0 3

three, last carry-down value is the remainder.

Therefore, the remainder is 3. The option c is correct.

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Complete question:

What is the remainder in the synthetic division problem below?

a. 6

b. 4

c. 3

d. 5

Points (0,200) and (200,0) fall outside of the feasible region hence they cannot be the optimal solution.

For the given condition,

Points are (48,84), (0,120), (0,0), (90,0)

The objective function is,

maximize 4X + 10Y

Take point (48, 84), here X = 48 and Y = 84

Substitute values in the objective function equation as shown below;

Z = 4 * 48 + 10 * 84

  = 1032

For point (0,120)

Z = 4 * 0 + 10 * 120

  = 1200

For point (0,0)

Z = 4 * 0 + 10 * 0 =0

For point (90,0)

Z = 4 * 90 + 10 * 0

  = 360

The value of the objective function is maximum at point (0,120). Its value is 1,200.

The viable region does not include points (0,200) and (200,0), hence they cannot be the best option.

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Answer: -6

Step-by-step explanation:

(0,y)

at y intercept, x is 0. therefore sub x with 0 and solve

y= 3(0)-12/0+2

= -12/2

=-6

Answer:

x≈33.36

Step-by-step explanation:

The marks on the lines mean they are the same lenth, that means the other two angles are both 29 degrees. Because triangle angles add up to 360, we can add the two 29 degree angles and subtract them from 360 to get the angle of the equation. From here we can solve to find x.

[tex]29+29=58[/tex]

[tex]360-58=302[/tex]

[tex]11x-65=302\\[/tex]

[tex]11x=367[/tex] (add 65 on both sides)
[tex]x[/tex]≅[tex]33.36[/tex] (divide 11 on both sides)

The additional information is required in order that the triangles are congruent for the SSS congruent theorem is IW = IH

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

Triangles = IWO, and IHO

Given theorem = SSS

The SSS congruent theorem implies that the corresponding sides of the triangles in question are congruent

From the question, we can see that the following corresponding sides on the triangles have the same mark

W O and H O

A O and A O

This implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

IW must be congruent to IH

Hence, the additional information on the congruency of the triangles is IW = IH

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josh is 3 years older than 4 times kim's age. the sum of their ages is less than 43. inequality for the situation, then the oldest age kim could be.

4k + 3 < 43

k < 10

We are given that Josh is 3 years older than 4 times Kim's age. We can express this as 4k + 3, where k represents Kim's age. We are told that the sum of their ages is less than 43, so we can write this as an inequality: 4k + 3 < 43. To find the oldest age Kim could be, we can solve this inequality for k. To do this, we subtract 3 from both sides, giving us 4k < 40. Finally, we divide both sides by 4, giving us k < 10. Therefore, the oldest age Kim could be is 10.

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$2256000 is the top rate paid the previous year.

percentage, a relative value indicating hundredth parts of any quantity.

Given that top rate paid one year for a 30 - second TV ad during the Super Bowl was 6% greater than the previous year's top rate.

If the new top rate paid was $2.4 million then we need to find the top rate paid the previous year.

Convert 6% to the decimal by dividing with 100 is 0.06

0.06×2400000

144000

Now subtract 144000 from 2.4 million.

2400000-144000

2256000

Hence, the top rate paid the previous year is $2256000.

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The required value of 'a' in the equation of proportionality is 32.

What is direct proportion?

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

It is symbolised by the proportional sign ∝.

For instance, if x and y are two quantities or variables that are intimately linked to one another, we can say x & y. The ratio of x and y becomes equal to a constant when the proportionality sign is removed, for example, x/y = C, where C is a constant.

Given, a = 8b

When b = 4 then

So, a = 8*4 = 32

Hence, the required value of 'a' in the equation of proportionality is 32.

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The value of x will make on similar to SRQ by the SSS similarity theorem is 25.

From the figure :

NM = 10

SR = 20

NO = 8

QR = x

SAS Similarity Theorem:

states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

NO/NM = SR/QR

substitute the values

8/10 = 20/x

cross multiplication

8x = 200

dividing both sides by 8

x = 25

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Full question :

What value of x will make △ONM similar to △SRQ by the SAS similarity theorem?What value of will make the triangles similar by the similarity theorem?; How do you find similar triangles in SSS?; How do you find the value of X that makes triangles similar?

Answer:

I believe the answer is 5

Step-by-step explanation: