an industrial comp machine has the ability to reduce image dimensions by a certain percentage each time it copies. A design began with a length of 16 inches, represented by the point (0,16). after going through the comp machine once, the length is 12, represented by the point (1,12). Enter the correct answer in the box by replacing the values of a and b. f(x)=a(b)^x

Answer:

1/2

Step-by-step explanation:

Let's check if this is a positive of negative slope. Remember that when checking slope, you need to read the graph from left to right.

So let's see: When we look at the graph from left to right, is it moving up or down?

It is moving up, correct!

Therfore, this must be a positive slope.

Ok, now we need to pick 2 points.

I will choose: ( 6 , 0 ) & ( 2 , -2 )

To move between those pouints, we need to move up 2 and 4 units to the right.

Slope is defined as:

Change is y over change in x

Change in y is positive 2

Change in x is positive 2

Therfore, slope is [tex]\frac{2}{4}[/tex]

or, 1/2

Answer:

-1.5

Step-by-step explanation:

Remember that the slope is the rise over the run, or: Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

[tex]\frac{6 - -3}{-1 - 5} = \frac{9}{-6} = -1.5[/tex]

So, your slope is -1.5.

Answer: The greatest distance a person could be from the sprinkler and get sprayed by it is 14 feet.

Step-by-step explanation:

The equation given describes a circle with the general equation (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

In the provided equation, (z + 6)^2 + (y - 9)^2 = 196, we can identify the values for h, k, and r^2:

1. h = -6 (from z + 6)

2. k = 9 (from y - 9)

3. r^2 = 196

Now, we need to find the radius r, which is the greatest distance a person could be from the sprinkler and still get sprayed by it. To do this, we take the square root of r^2:

r = √196

r = 14

Answer:

To prove that there exist infinitely many integers n such that n^2 + 1 is squarefree, we can use a proof by contradiction.

Assume the contrary, that there are only finitely many integers n such that n^2 + 1 is squarefree. Let's denote these integers as n_1, n_2, ..., n_k, where k is a finite positive integer.

Consider the number N = (n_1^2 + 1) * (n_2^2 + 1) * ... * (n_k^2 + 1) + 1.

Note that N is an integer and is greater than each of the numbers n_i^2 + 1 for i = 1 to k. Since n_i^2 + 1 is squarefree for each i, N is also squarefree, as it is not divisible by any square number other than 1.

However, N cannot be equal to any of the n_i^2 + 1, as N is strictly greater than each of them. This contradicts our assumption that n_1, n_2, ..., n_k are all the integers such that n^2 + 1 is squarefree.

Therefore, our assumption must be false, and there exist infinitely many integers n such that n^2 + 1 is squarefree. This completes the proof by contradiction.

Step-by-step explanation:

Answer:

This is the equation we have to use in order to find the eigenvalues and eigenvectors of matrix A:

det(A - λI) = 0

where λ is the eigenvalue and I is the identity matrix.

So we have:

A - λI = [ -5-λ 1 2 ]

[ 0 -2-λ 0 ]

[ 4 2 -3-λ ]

And the determinant is:

det(A - λI) = (-5-λ)(-2-λ)(-3-λ) - 8(2+λ) = -λ^3 + 4λ^2 + 23λ - 40

We can factor this to get:

det(A - λI) = -(λ - 5)(λ - 2)(λ + 4)

So the eigenvalues are λ1 = 5, λ2 = 2, and λ3 = -4.

To find the eigenvectors for each eigenvalue, we need to solve the system of linear equations:

(A - λI)x = 0

For λ1 = 5, we have:

[ -5-5 1 2 ] [ x1 ] [ 0 ]

[ 0 -2-5 0 ] [ x2 ] = [ 0 ]

[ 4 2 -3-5] [ x3 ] [ 0 ]

which simplifies to:

[ -10 1 2 ] [ x1 ] [ 0 ]

[ 0 -7 0 ] [ x2 ] = [ 0 ]

[ 4 2 -8 ] [ x3 ] [ 0 ]

We can solve this system to get:

x1 = -1/2 x2

x3 = -1/2 x2

So the eigenvector for λ1 = 5 is:

v1 = [ x1, x2, x3 ] = [ -1/2, 1, -1/2 ]

For λ2 = 2, we have:

[ -5-2 1 2 ] [ x1 ] [ 0 ]

[ 0 -2-2 0 ] [ x2 ] = [ 0 ]

[ 4 2 -3-2] [ x3 ] [ 0 ]

which simplifies to:

[ -7 1 2 ] [ x1 ] [ 0 ]

[ 0 -4 0 ] [ x2 ] = [ 0 ]

[ 4 2 -5 ] [ x3 ] [ 0 ]

We can solve this system to get:

x1 = -2/3 x2

x3 = -4/3 x2

So the eigenvector for λ2 = 2 is:

v2 = [ x1, x2, x3 ] = [ -2/3, 1, -4/3 ]

For λ3 = -4, we have:

[ -5+4 1 2 ] [ x1 ] [ 0 ]

[ 0 -2+4 0 ] [ x2 ] = [ 0 ]

[ 4 2 -3+4] [ x3 ] [ 0 ]

which simplifies to:

[ -1 1 2 ] [ x1 ] [ 0 ]

[ 0 2 0 ] [ x2 ] = [ 0 ]

[ 4 2 1 ] [ x3 ] [ 0 ]

We can solve this system to get:

x1 = -2/5 x2

x3 = 1/2 x2

So the eigenvector for λ3 = -4 is:

v3 = [ x1, x2, x3 ] = [ -2/5, 0, 1/2 ]

To determine matrix A's sign definiteness, we must compute the determinant of all of A's primary submatrices. A square submatrix generated by eliminating the equal amount of rows and columns from the top left corner of A is known as a primary submatrix.

The principal submatrices of A are:

A1 = [-5]

A2 = [ -5 1 ]

[ 0 -2 ]

A3 = [ -5 1 2 ]

[ 0 -2 0 ]

[ 4 2 -3 ]

The determinants of these matrices are:

det(A1) = -5

det(A2) = (-5)(-2) - (0)(1) = 10

det(A3) = (-5)(-2)(-3) + 2(0)(4) + (1)(0)(2) - (-3)(1)(4) - 2(0)(-5) - (-2)(2)(-5) = -92

Because A1's determinant is negative, A is not positive definite. A is not negative definite since the determinants of A1 and A2 have different signs. As a result, A is infinite.

The probability, expressed as a percent rounded to the nearest tenth, that the sample mean will be within $1 of the population mean is 91.5%.

To find the probability that a random sample of size two will have a sample mean within $1 of the population mean, we need to first calculate the population mean and standard deviation.

The population mean is the average of the given values:

(2 + 4 + 4 + 5 + 5 + 7) / 6 = 4.5

The population standard deviation can be calculated using the formula:

σ = [tex]\sqrt{S(x-u)^{2}/N }[/tex]

where S represents the sum of, x is each value, u is the population mean, and N is the population size.

Using this formula, we get:

σ = [tex]\sqrt{(2-4.5)^{2}+ (4-4.5)^{2}+(4-4.5) +(5-4.5)^{2} +(5-4.5)^{2}+ (7-4.5)^{2} /6}[/tex] = 1.5

Now we can find the probability of getting a sample mean within $1 of the population mean using the t-distribution since the population standard deviation is unknown and the sample size is less than 30. Since we are looking for the probability of the sample mean being within $1 of the population mean, we need to find the probability of getting a sample mean between 3.5 and 5.5 dollars.

We can use a t-distribution table or a calculator to find the probability. For a sample size of 2, the degrees of freedom is 1, and using a t-distribution table with a significance level of 0.05, we get a t-value of 12.71.

Therefore, the probability of getting a sample mean between 3.5 and 5.5 dollars is approximately 91.5% (calculated using a t-distribution calculator or the t-distribution table), rounded to the nearest tenth.

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27 can be written as a product of 3 and 9, where 9 is a perfect square.

In mathematics, a perfect square is an integer that is equal to the square of another integer. In other words, a perfect square is a non-negative integer that can be expressed as the product of an integer with itself.

To write 27 as a product of two integers such that one of the factors is a perfect square, we need to find a perfect square that divides 27.

The perfect square that divides 27 is 9, which is equal to [tex]3^2[/tex].

So, we can express 27 as the product of two factors, 3 and 9. One of the factors, 9, is a perfect square because it is equal to [tex]3^2[/tex]. Therefore, we have written 27 as a product of two integers where one of the factors is a perfect square.

We can also express 27 as 1 x 27 or 27 x 1, but neither of these representations includes a perfect square as a factor.

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Answer:

y=3x

Step-by-step explanation:

y=kx

21/7=3

15/5=3

6/2=3

Each relationship in the table has a constant of proportionality of 3.

The solution of the expression is; |y-x| = y - x without using absolute value.

Numerical articulation is characterized as the assortment of the numbers factors and works by utilizing tasks like expansion, deduction, increase, and division.

Given that;

from the question the expression is;

⇒ |y−x| , if y > x

⇒ If y > x,

⇒ y - x > 0

then |y-x| is equal to (y-x),

since (y-x) is always positive in this case.

Therefore, The solution of the expression is; |y-x| = y - x

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The value of tetha is 330°

If a ray rotates in an anticlockwise direction, then the angle formed as a product of the rotation is called a positive angle.

In other words if it rotates in clockwise direction, it is a negative angles.

If sin(tetha) = -0.5

to find the value of tetha we multiply both sides with the inverse of sin

therefore;

tetha = sin^-1(-0.5)

tetha = -30

therefore -30 is a negative angle, to find the positive angle of tetha, we add 360

therefore tetha = -30+360

= 330°

therefore the value if tetha that will be greater than 279 but less than 360 is 330°

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Answer:

Step-by-step explanation:

Q:

In a particular class of 29 students, 11 are men. What fraction of the students in the class are women?

A:

29-11=18

18/29 are women

Answer:

yes she is correct

Step-by-step explanation:

The proposition can be proven by showing that the left and right cosets of H in G form a partition of G.

As H is a G subgroup, it comprises the identity element e within G. For any g element in G, the left coset gH comprises ge = g and the right coset Hg contains eg = g. Thus, there are non-empty left as well as right cosets.

G's each element belongs to both the left and the right cosets of H. Hence, all left (or right) cosets' union in G covers every G element. The left and right cosets of H in G build non-empty subsets that do not intersect with one another. Their union equals G; thus, they certainly construct a partition for G.

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Answer:

12 minutes

Step-by-step explanation:

11/x = 55/60

11 x 5 = 55

60/5=12

12.01 minutes

time = distance / speed

where distance is the distance traveled, speed is the average speed of the travel, and time is the time taken to cover the distance.

We are given that the distance traveled is 11 miles and the average speed is 55 miles per hour. To convert the speed to miles per minute, we can divide it by 60 since 1 hour is equal to 60 minutes:

55 miles per hour = 55/60 miles per minute

= 0.9167 miles per minute (rounded to four decimal places)

Now we can substitute the values into the formula:

time = distance / speed

= 11 miles / 0.9167 miles per minute

≈ 12.01 minutes (rounded to two decimal places)

Therefore, it would take approximately 12.01 minutes to travel 11 miles at an average speed of 55 miles per hour.

*IG:whis.sama_ent

Answer:

1984

________________________________________________________

Given:

To find the inverse of f(x), we first switch x and y and then solve for y. So, x = y-3/y+4, which we can rewrite as x(y+4) = y-3. Simplifying, we get xy + 4x = y-3, and then we can isolate y on one side: y-xy = 4x-3. Factoring out y on the left side, we get y(1-x) = 4x-3, and then we can divide both sides by (1-x) to get y = (4x-3)/(1-x). This is our inverse function.

Find:

To find the inverse of g(x), we follow the same process of switching x and y and solving for y. So, x = 4y+3/1-y, which we can rewrite as x(1-y) = 4y+3. Simplifying, we get -xy + y = 4x+3, and then we can isolate y on one side: y(-x+1) = 4x+3. Dividing both sides by (-x+1), we get y = (4x+3)/(-x+1). This is our inverse function.

Solve:

As for the given set of values, we have 187, 191, 202, 209, 218, and 1984. The outlier is obviously 1984, and its presence will not affect the range because the range is simply the difference between the largest and smallest values, which will be the same regardless of the presence of an outlier. However, the outlier will greatly affect the interquartile range, which is the difference between the upper and lower quartiles. This is because the upper and lower quartiles are the median of the upper half and lower half of the data, respectively, and including an outlier in one of these halves can greatly skew the median and thus the interquartile range.

Answer:

No solution

Step-by-step explanation:

-2(11-12x) = -4(1-6x)

Distribute the -2 and -4:

-22 + 24x = -4 + 24x

Subtract 24x from both sides:

-22 = -4

Since this is a contradiction, there is no solution. The equation is inconsistent.

Answer:

No Solution.

Explanation:

When solving for x, the two values do not equate to each other.

(i)  distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex]  . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex]  (iv)  to distribute the balls   [tex](1+2+1)[/tex].

(i) Both balls and boxes are labeled:

Since one box already contains a ball, there are four options for where to place the first ball, and only three options remain for the second ball. The two balls can be distributed in  [tex]4 \times 3 = 12[/tex] different ways.

(ii) Balls are labeled, but boxes are unlabeled:

There is just one method to arrange the balls if there is only one ball in each box. There are two ways to determine which box receives both balls if only one box possesses them. The statistical distribution of the balls is done in one of three ways.

(1 + 2 = 3).

(iii) Balls are unlabeled, but boxes are labeled:

There are four alternatives available to the box if they are both in the same box. If they are in different boxes, the first ball's box has two options, leaving the second ball with just one. Accordingly, there are 6 ways to divide the balls.

(4 + 2 * 1).

(iv) Both balls and boxes are unlabeled:

There is only one method to arrange the balls if there is one ball in each box. There are two methods to decide which box gets both balls if only one box has both balls.

There is just one method to arrange the balls if neither box incorporates a ball. There are therefore a total of 4 options to distribute the balls (1+2+1).

Therefore,(i)  distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex]  . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex]  (iv)  to distribute the balls   [tex](1+2+1)[/tex].

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This requires the circle theorem and the angle at the center postulate.

It simply states that the angle subtended by an arc at the centre is twice the angle subtended at the circumference.

Thus

8) m∡CA = 72 x 2 = 144°

9) m∡AD = 144/2 = 72°  - Angle Bisected by radius.

10) m∠C = ∠∡CA/2 = 72/2 = 36°

11) where the angles in the polygon are given as:

4y + 14)°
105°

7y+1)°
7x +1)°


Then, x and y are given as follows.

Note that 105° and (7y+1)° are opposite angles in a polygon = 180°
Also

(4y + 14)° + (4y + 14)° = 180

Thus

105° + (7y+1)° = 180 ......1

(7x +1)° + (4y + 14)° = 180 .....2



Simplifying the first equation:

105° + (7y+1)° = 180

7y + 106 = 180

7y = 74

y =  10.57


(7x +1)° + (4y + 14)°  = 180

(7x + 1)° + (4  (10.57) +  14)° = 180

(7x + 1)° + 54.28° = 180

7x + 55.28   = 180

7x =  124.72

x = 17.82

So we can conclude that , x is approximately 17.82 and y is approximately 10.57.

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Check the picture below.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=15 \end{cases}\implies \cfrac{f(15)-f(0)}{15 - 0}\implies \cfrac{11-5}{15}\implies \cfrac{6}{15}\implies \cfrac{2}{5}[/tex]

Answer: 3 meters

Step-by-step explanation:

The area of the rectangular region is given by:

(18 + 2x) * (30 + 2x) = 18*30 + 36x + 60x + 4x^2

Simplifying this expression, we get:

4x^2 + 96x - 1300 = 0

Dividing both sides by 4, we get:

x^2 + 24x - 325 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 24, and c = -325.

Plugging in these values, we get:

x = (-24 ± sqrt(24^2 - 4(1)(-325))) / 2(1)

x = (-24 ± sqrt(936)) / 2

x = (-24 ± 30) / 2

x = 3 or -27

Since the width of the path cannot be negative, the only possible solution is x = 3 meters. Therefore, the width of the path surrounding the pool is 3 meters.

[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex] which is the desired equation.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Let P(ej) denote the probability of outcome ej for j=1,2,...,N. Then we know that:

P(ej+1) = 2P(ej) for j=1,2,...,N-1

Also, we know that the sum of probabilities of all outcomes is 1:

P(e1) + P(e2) + ... + P(eN) = 1

We can use the geometric sequence formula to find P(ek) in terms of P(e1) as follows:

[tex]P(ek) = P(e1) * (2^{(k-1)})[/tex]

Substituting for P(ej+1) in terms of P(ej) gives:

[tex]P(ej+1) = 2P(ej) = 2^1 * P(ej)[/tex]

[tex]P(ej+2) = 2P(ej+1) = 2^2 * P(ej)[/tex]

...

[tex]P(ek) = 2^{(k-1)} * P(e1)[/tex]

We can sum the probabilities of all outcomes to get:

[tex]1 = P(e1) + 2P(e1) + 2^2 P(e1) + ... + 2^{(N-1)}P(e1)[/tex]

Using the formula for the sum of a geometric series, we get:

[tex]1 = P(e1) * [(2^N - 1)/(2 - 1)][/tex]

Simplifying, we get:

[tex]P(e1) = 1/(2^N - 1)[/tex]

Substituting this value for P(e1) in the expression for P(ek) gives:

[tex]P(ek) = (1/(2^N - 1)) * (2^{(k-1)})[/tex]

Simplifying, we get:

[tex]P(ek) = 2^{(k-N)} / (2 - 1/2^{(N-k+1)})[/tex]

Multiplying by 2/2, we get:

[tex]P(ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

Substituting k=N, we get:

P(Ek) = 1/2

Substituting k=1, we get:

[tex]P(E1) = 2^{(N-1)} / (2^N - 1)[/tex]

Therefore, we have shown that:

[tex]P(Ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

for k=1,2,...,N.

To show that PEk=2k-1/2N-1, we can substitute k=N-j+1 for j=1,2,...,N:

[tex]PEk = P(EN-j+1) = 2^{(N-j)} / (2^j - 1)[/tex]

Letting t = j-1, we can rewrite this as:

[tex]PEk = 2^{(N-t-1)} / (2^{(t+1)} - 1[/tex]

Multiplying the numerator and denominator by 2, we get:

[tex]PEk = 2^{(N-t)} / (2^{(t+2)} - 2)[/tex]

Substituting t = N-k, we get:

[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

which is the desired result.

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Answer:

$97.50

Step-by-step explanation:

Purchase Price:

$150

Discount:

(150 x 35)/100 = $52.50

Final Price:

150 - 52.50 = $97.50

The calculated median and the mean gasoline prices per gallon in California are 3.25 and 4.49, respectively

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

Prices = 3.14, 3.21, 3.28, 3.53

Start by sorting the number of prices in ascending order

So, we have

3.14, 3.21, 3.28, 3.53

As a general rule.

The median is the middle number

Using the above as a guide, we have the following:

Median = middle number = 1/2 *(3.21 + 3.28)

Evaluate

Median = middle number = 3.25

For the mean, we have

Mean = (3.14 + 3.21 + 3.28 + 3.53)/3

Evaluate

Mean = 4.49

Hence, the value of the median is 3.25

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Based on calculation, the highest hourly wage is $2,840 per month which gives us $17.75 per hour.

For purpose of making a comparison, we can calculate the hourly wage for each option.

Hourly wage for $34,000 per year:

= $34,000 / (40 hours per week * 52 weeks per year)

= 16.3461538

= $16.35 per hour.

Hourly wage for $2,840 per month:

= $2,840 / (4 weeks per month * 40 hours per week)

= $17.75 per hour

Hourly wage for $650 per week:

= $650 / 40 hours per week

= $16.25 per hour

Hourly wage for $18 per hour.

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To find the volume of a ball, we use the formula V = (4/3)πr³, where r is the radius of the ball. We are given the diameter of the ball, which is 9 inches.

The radius of the ball is half of the diameter, so

r = 9/2 = 4.5 inches.

Substituting this value of r in the formula, we get:

V = (4/3)π(4.5)³V = (4/3)π(91.125)V = 4.1888 × 91.125V ≈ 381.71

Therefore, the volume of the ball is approximately 381.71 cubic inches.

When rounded to the nearest hundredth, the answer is 381.71.

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Answer:

complementary since the angles sum up to 90

The correct answer is d. observations, which is only the pretest summary.

A pretest summary is a summary of the data collected during a preliminary test or trial run.

The correct answer is d. observations.

The pretest summary is a summary of the data collected during a preliminary test or trial run, and it typically includes summary statistics such as the mean, variance, and degrees of freedom (df). However, the number of observations or sample size is typically not included in the pretest summary, as it is generally assumed to be the same as the number of observations in the full dataset. The number of observations is usually included in the full dataset summary, along with other descriptive statistics.

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