find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, are not divisible by either 5 or 7.

The  dimensions of the rectangle is 1mm x 0.5mm.

The area of a sector of a circle can be calculated using the formula A = (1/2)*r2*θ,  

 where r is the radius of the circle and

θ is the angle of the sector.

Therefore, the area of the sector given in the question is A = (1/2)*r²*1, where r = 1.

Since the rectangle has the same area as the sector,

the area of the rectangle can be calculated as A = l*w,

 where l is the length and

w is the width.

This equation can be rearranged to give l = A/w,

 where A = (1/2) and w is the width.

Substituting the values for A and w into the equation gives l = (1/2) / w.

Since the width of the rectangle is the same as the radius of the circle,

w = 1.

Therefore, the length of the rectangle is l = (1/2), which gives the dimensions of the rectangle as 1mm x 0.5mm, rounded to the nearest millimeter.

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The compounding formula is used to create the quarterly compounding formula. To the nearest cent, the compounded balance is $ [tex]12,832.27.[/tex]

To reflect the quarterly interest computation as the only change, the interest rate is increased by 4*2.

[tex]A = P(1 + r/n)(nt)[/tex]

Assume that we have a $  [tex]10,000[/tex] Initial investment, a 6% yearly interest rate, and a 5-year investment period. We have n = 4 and t = 5 since the interest is compounded every three months.

Plugging in these values, we get:

[tex]A = 10,000(1 + 0.06/4)(4*5)[/tex]

[tex]= 10,000(1.015)^20[/tex]

[tex]= 12,835.72[/tex]

Hence, the final balance is $ [tex]12,835.72[/tex] to the nearest penny.

If the money is compounded continually, we may use the following formula to determine the balance:

[tex]A = Pe(rt)[/tex]

With the identical values as before, we obtain:

[tex]A = 10,000e(0.06 \times5)[/tex]

[tex]= 10,000e(0.3)[/tex]

[tex]= 12,832.27[/tex]

Therefore, So the balance, to the nearest cent, is $ [tex]12,832.27.[/tex]

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Answer:153

Step-by-step explanation:

P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).

0.5333

A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly

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The probability of getting a green golf ball from the machine is 19/83 or 0.2289. The result is obtained by the number of green golf balls divided by the total number of golf balls.

Probability of an event can be calculated by

P(A) = n(A) / n(S)

Where

You have 19 green golf balls, 24 red golf balls, 20 blue golf balls, and 20 yellow golf balls.

Find the probability of getting a green golf ball from the machine!

The total number of golf balls in the machine is

n(S) = 19 + 24 + 20 + 20 = 83 balls

You will end up with a green golf ball with the probability of

P(A) = n(A) / n(S)

P(A) = 19/83

P(A) = 0.2289

Hence, the probability that you will end up with a green golf ball is 19/83 or 0.2289.

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The expression shows the height, in meters, of the sail is 2(sin 40°) (option A)

One way to approach this problem is to use the sine function.

We know that sin(40 degrees) is equal to the length of the side opposite angle 40 degrees divided by the length of the hypotenuse. In other words, sin(40 degrees) = b/c.

We want to find the length of the segment that drops from the top of the sail to side a, which we will call h.

This segment is the side adjacent to angle 40 degrees, so we can use the cosine function to relate it to the length of side b. Specifically, cos(40 degrees) = h/b. Solving for h, we get

h = 2 x sin(40 degrees) = 2(sin 40°)

Hence the option (A) is correct.

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The correct answer is option (C).

Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six functions (cot).

The equation t = Q - P, where Q and P are the specified locations, can be used to determine the components of the vector t. Therefore:

t = (–18, 2) – (–13, 11) = (–18 + 13, 2 – 11) = (–5, –9) (–5, –9)

The vector's magnitude is given by:

|t| = √(–5)^2 + (–9)^2 = √106 ≈ 10.296

The formula = tan1 (y/x), where x and y are the vector's components, can be used to determine the direction of the vector t. The direction must be expressed in terms of sine and cosine functions because we are required to represent the vector in trigonometric form.

θ = tan⁻¹ (–9/–5) ≈ 60.945°

In trigonometric form, the vector t is thus represented as follows:

t = [t|cos|i] + [t|sin|j]

We get the following by altering the values of |t| and:

t = 10.296 cos I + 10.296 sin j of angle 60.945

As a result, the following is the proper trigonometric representation of the vector t:

t = 10.296 cos I + 10.296 sin j of angle 60.945

Thus, alternative is the right response (C).

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The integers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 have been written on a chalkboard by Dayna. She then erased the integers from 1 through 6, as well as their multiplicative inverse $\mod{13}$.

We can find the multiplicative inverse of an integer { a modulo 13 } by using the extended Euclidean algorithm.The integers from 1 to 6 are 1, 2, 3, 4, 5, and 6.The multiplicative inverse of : 1 modulo 13 is 1, 2 modulo 13 is 7,  3 modulo 13 is 9, 4 modulo 13 is 10, 5 modulo 13 is 8, and 6 modulo 13 is 11.The only integer that Dayna does not erase is 12.

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The Simple random sampling method is equivalent to a lottery system in which all the available names are placed in a container, the container is shaken, and the names of the "winners" or participants are then drawn out in an unbiased manner.

What is Simple random sampling?

The Simple random sampling is a sampling technique in which every member of the population has an equal chance of being chosen as a sample. The samples are chosen randomly, without any specific criterion. In this method, the selection of individuals for the sample is done without any specific pattern. This means that each member of the population is equally likely to be selected as a sample.In Simple random sampling, each member of the population is assigned a number, and the samples are selected using a random number generator or drawing names out of a hat. The selected samples are then analyzed to make predictions about the entire population.For example, if a researcher wanted to know the average age of students in a school, they might use Simple random sampling to choose a sample of 50 students. The researcher would assign each student a number and then use a random number generator to select the samples.There are some advantages and disadvantages of Simple random sampling, which are listed below:Advantages of Simple random sampling It is easy to understand and conduct the process.Each member of the population has an equal chance of being selected as a sample.It ensures that the sample is representative of the entire population.Disadvantages of Simple random sampling It can be time-consuming to select the samples.There may be a chance of human error when selecting samples.The sample size may not be large enough to draw meaningful conclusions.

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To summarize, the 95% confidence interval for the proportion of vaccinated preschool children in Camperdown is [tex]0.5040 ≤ μ ≤ 0.6960[/tex], indicating that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

A 95% confidence interval for the proportion of preschool children in Camperdown who have been vaccinated is [tex].5040 ≤ μ ≤ .6960.[/tex] This indicates that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

To calculate this interval, we first need to calculate the sample proportion of vaccinated preschool children. To do this, we divide the number of vaccinated children (60) by the total number of children in the sample (100). This yields a sample proportion of 0.6.

Next, we need to calculate the standard error of the proportion, which is calculated by taking the square root of (sample proportion * (1 - sample proportion) / sample size). Plugging in our values yields a standard error of 0.0435.

We then use the standard error to calculate the 95% confidence interval, which is equal to (sample proportion +/- (1.96 * standard error)). Plugging in our values yields an interval of 0.5040 ≤ μ ≤ 0.6960. This indicates that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

To summarize, the 95% confidence interval for the proportion of vaccinated preschool children in Camperdown is 0.5040 ≤ μ ≤ 0.6960, indicating that we can be 95% confident that the true proportion of vaccinated preschool children in Camperdown lies between 50.4% and 69.6%.

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The test statistic based on the number of students who preferred to get out early equals 3.65.

A test statistic is a numerical summary of the sample data that is employed to determine the strength of the evidence for a hypothesis. It is a quantitative measure that compares the observed data to the hypothesis. The t-value, Z-score, F-value, and chi-squared value are examples of common test statistics. In statistical hypothesis testing, a test statistic is used to make decisions about whether or not to reject the null hypothesis.

Based on the given problem, the number of students who preferred to get out of class early is 80, while the number of students who preferred a 10-minute break is 40. Hence, the number of students who had no preference is 30.

Now, we will find the test statistic based on the number of students who preferred to get out of class early as follows:

Test Statistic = (Observed Value - Expected Value) / Standard Deviation

To find the observed value, we need to calculate the proportion of students who preferred to get out of class early in the sample as follows:

Proportion of students who preferred to get out of class early = 80 / (150-30)= 80 / 120= 0.67

Therefore, the observed value is 0.67.

To find the expected value, we need to assume that there is no difference in students' preferences, and the proportion of students who preferred to get out of class early is the same as the proportion of students who preferred a 10-minute break.

Expected value = Proportion of students who preferred to get out of class early * Total number of students= 0.5 * 150= 75

Therefore, the expected value is 75.

To find the standard deviation, we need to use the formula for the standard deviation of a proportion as follows:

Standard Deviation = √[(p*q) / n]

where p is the proportion of students who preferred to get out of class early, q is the proportion of students who preferred a 10-minute break, and n is the total number of students.

Standard Deviation = √[(80/120)*(40/120) / 150]= √(0.1778 / 150)= 0.048

Therefore, the standard deviation is 0.048.

Now, we will substitute the values in the formula for the test statistic as follows:

Test Statistic = (0.67 - 0.5) / 0.048= 3.65

Therefore, the test statistic based on the number of students who preferred to get out early equals 3.65.

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Model: S(t) = 5000 + 3000t. With a starting value of 5000 subscribers in 1970 and a steady rise of 3000 subscribers each year, this model predicts a linear increase in the number of subscribers through time.

With a starting value of 5000 subscribers in 1970 and a steady rise of 3000 subscribers each year, this model predicts a linear increase in the number of subscribers through time. Simply enter the value of t into the equation to get the number of subscribers after t years. For example, if you want to know the number of subscribers in 1990, which is 20 years after 1970, you would enter in t=20 into the equation and obtain S(20) = 5000 + 3000(20) = 65000. As a result, our model predicts that there would be 65,000 members in 1990. It's crucial to note that this is a simplified model and may not adequately reflect the genuine behaviour of subscriber growth over time.

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The area of a triangle is calculated by multiplying the base of the triangle by the height and dividing by 2. Therefore, the number of sides of the triangle is relevant to calculating its area.

Triangle is a three-sided polygon that is considered one of the most basic shapes in geometry. It is composed of three line segments that intersect at three points called vertices. The angles formed by the three line segments are the angles of the triangle. A triangle has three sides, three angles, and three vertices. Depending on the length of the sides and the angles, triangles can be classified as acute, right, or obtuse. Acute triangles have all three angles measuring less than 90 degrees, right triangles have one angle measuring 90 degrees, and obtuse triangles have one angle measuring more than 90 degrees. Triangles are also classified by their sides, such as equilateral, isosceles, and scalene. An equilateral triangle has three equal sides and three equal angles, an isosceles triangle has two equal sides and two equal angles, and a scalene triangle has three sides and three angles that are all different. Triangles are used in many areas of mathematics and are seen in many engineering structures and designs.

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The area of a triangle is calculated by multiplying the base of the triangle by the height and dividing by 2. Therefore, the number of sides of the triangle is relevant to calculating its area.

Triangle is a three-sided polygon that is considered one of the most basic shapes in geometry. It is composed of three line segments that intersect at three points called vertices. The angles formed by the three line segments are the angles of the triangle. A triangle has three sides, three angles, and three vertices. Depending on the length of the sides and the angles, triangles can be classified as acute, right, or obtuse. Acute triangles have all three angles measuring less than 90 degrees, right triangles have one angle measuring 90 degrees, and obtuse triangles have one angle measuring more than 90 degrees.

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Complete Question:
Place a checkmark by the situations that indicate area1 is a triangle.

The weighted mean takes into account the weight of each investment and can provide a more accurate measure of the overall rate of return on the portfolio than the mean or median.

The weighted mean, mean, and median overall rate of return on this investment portfolio can be calculated using the following formulas:

Weighted Mean: Weighted mean = (R1 x W1) + (R2 x W2) + (R3 x W3) + ...

Mean: Mean = (R1 + R2 + R3 + ...) / N

Median: Median = (N + 1) / 2

where R1, R2, etc. are the returns on individual investments, W1, W2, etc. are the weights assigned to each investment, and N is the total number of investments in the portfolio.

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Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

An illustration of data or mathematical functions is a graph. It is a method for presenting numerical data in a way that is simple to comprehend and interpret. A set of axes, one for each variable being represented, and one or more plots or lines that reflect the data or function being graphed are the main components of a graph. There are many distinct graph kinds, each of which is appropriate for displaying various sorts of data, including line graphs, bar graphs, scatter plots, and pie charts.

given

The axes cannot be identified because they are not specified in the query.

The blue ABC bar graph is as follows:

Using the equation (x, y) (y, -x), rotate AABC 90 degrees clockwise by applying the following transformation to each point:

A(-3, 0) → A' (0, 3) (0, 3)

B(-2, 4) → B' (-4, -2) (-4, -2)

C(1, -1) → C' (1, -1) (1, -1)

The red A'B'C' coordinates are as follows: A' (0, 3), B' (-4, -2), and C' (1, -1).

We take the y-coordinate of each point and subtract 3 to translate AA'B'C' three units down:

A' (0, 3) → A" (0, 0) (0, 0)

B' (-4, -2) → B" (-4, -5) (-4, -5)

C' (1, -1) → C" (1, -4) (1, -4)

Hence, AA"B"Ccoordinates "'s in green are: A" (0, 0), B" (-4, -5), and C" (1, -4).

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The complete question is:-  

1. Label the axes.

2. Graph: A(-3, 0) B(-2, 4) C(1,-1) Draw ABC in blue.

3. Rotate AABC 90° clockwise to

create ▲A'B'C' in red. List the coordinates below:

Formula: (x, y) → (y, -x)

A(-3, 0) A' ()

B(-2, 4)→ B' ()

C(1, -1) C' ()

4. Translate AA'B'C' three units down to create ▲A"B"C" in green. What are the coordinates of AA"B"C"?

Answer:

if it is perpendicular to eacha other I e 0

Answer:

We can represent the constraints of this situation with the following system of linear inequalities:

x ≥ 20 (the company needs at least 20 managers)

y ≤ 500 (the company needs no more than 500 employees)

x + y ≥ 400 (the company must hire a total of at least 400 people)

So the system of linear inequalities is:

x ≥ 20

y ≤ 500

x + y ≥ 400

Answer:

Step-by-step explanation:

.

The area of the isosceles trapezoid is 37.25 unit².

An isοsceles trapezοid is a trapezοid with cοngruent base angles and cοngruent nοn-parallel sides. A trapezοid is a quadrilateral with οnly οne side parallel.

An isοsceles trapezοid can be defined as a trapezοid whοse nοn-parallel sides and base angles have the same measure. That is, if the twο οppοsite sides (bases) οf a trapezοid are parallel and the twο nοn-parallel sides are οf equal length, it is an isοsceles trapezοid. See the diagram belοw.

Area of trapezium = 1/2(h)(a + b)

where h =  height

a =  smaller base = 10

b = larger base = 15

Now to find height, we see a triangle at the end of trapezium, draw the imaginary altitude

Now, the base = 5/2     ⇒(15 - 10= 5)/2

= 2.5

Using trigonometry ratio

tan(θ) = Height/ Base

tan(40°) = Height/ 2.5

0.8391 = Height/ 2.5

Height = 2.5/ 0.8391

Height ≈ 2.98

Now, The area = 1/2(2.98)(10 + 15)

= 1/2(2.98)(10 + 15)

= 37.25 unit²

Thus, The area of the isosceles trapezoid is 37.25 unit².

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Answer:

0, 4, 16, 36, 64

Step-by-step explanation:

Divide the area by 10 , then the format for graphing would be (0,0) , (40, 4) , (160, 16) and so on.

All answers are listed below:

The area of the parallelogram (A), in square feet, is equal to the product of the base (b) and the height (h), both in feet. By applying the rigid transformation of dilation on each side, we have the following formula:

[tex]A = k^2 \times b \times h[/tex]   (1)

Where k is the scale factor.

And we can derive a scale factor by comparing two areas:

[tex]k=\sqrt{\frac{A}{A_o} }[/tex]   (2)

Where  is the original area, in square feet.

If we know that [tex]A_o=10 \ ft^2[/tex], then the scales factors are shown below:

For A = 0 ft², the scale factor is 0.

For A = 40 ft², the scale factor is 2.

For A = 160 ft², the scale factor is 4.

For A = 360 ft², the scale factor is 6.

For A = 640 ft², the scale factor is 8.

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Answer:

its 3

Step-by-step explanation:

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a) The domain of the function is {0,1,2,3,4,...}. The range is also a non-negative integer.

b) The largest decimal digit is 9, thus the domain of the function is all positive integers and the range is {9}.

c) The domain of the function is all bit strings of length n and the range is all integers between -n and n.

d) The domain of the function is all positive integers and the range is also all positive integers.

e) The domain of the function is all bit strings and the range is a non-negative integer.

Domain and range of the function that assigns to each pair of non-negative integers the first integer of the pair.In the given problem, (a) the function that assigns to each pair of non-negative integers the first integer of the pair. The first integer of the pair is always non-negative. Therefore, the domain of the function is {0,1,2,3,4,...}. The range is also a non-negative integer.

Domain and range of the function that assigns to each positive integer its largest decimal digit. In this problem, (b) the function that assigns to each positive integer its largest decimal digit. For all positive integers, the largest decimal digit is 9, thus the domain of the function is all positive integers and the range is {9}.

Domain and range of the function that assigns to a bit string the number of ones minus the number of zeroes in the string.In the problem,  the function that assigns to a bit string the number of ones minus the number of zeroes in the string. The possible bit strings have a length of n. Therefore, the domain of the function is all bit strings of length n and the range is all integers between -n and n.

Domain and range of the function that assigns to each positive integer the largest integer not exceeding the square root of the integer.In the given problem, the function that assigns to each positive integer the largest integer not exceeding the square root of the integer. Let’s say f(n) is the largest integer not exceeding the square root of n, then the domain of the function is all positive integers and the range is also all positive integers.

Domain and range of the function that assigns to a bit string the longest string of ones in the string.In the given problem, the function that assigns to a bit string the longest string of ones in the string. In this case, the domain of the function is all bit strings and the range is a non-negative integer.

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The integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.

Step 1: Find the Taylor series of the given function f(x).

f(x) = e^(x^2)cos(x)

Therefore, we can say that the Taylor series of the given function is: f(x) = 1 + x^2 + (1/2)x^4 + (1/6)x^6 + (1/24)x^8 + ...

Step 2: Substitute the required value of x into the Taylor series. Let us substitute x = 1 into the Taylor series we got above.

f(1) = 1 + 1^2 + (1/2)1^4 + (1/6)1^6 + (1/24)1^8 + ...

f(1) = 1 + 1 + (1/2) + (1/6) + (1/24) + ...

Step 3: Simplify the expression to get the answer. We can simplify the above expression by using the formula for the sum of an infinite geometric series. The formula is given as follows:

Sum of infinite geometric series = a / (1 - r), where a is the first term and r is the common ratio. Here, a = 1 and r = 1/4. Sum of the series = a / (1 - r) = 1 / (1 - 1/4) = 4/3.

Therefore, we can say that the integration of the given function using substitution and matching it with the Taylor series is equal to 4/3.

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We can calculate that sin 30 degrees is equal to the opposite side divided by the hypotenuse, which is x√3/(2x) = √3/2. Therefore, sin 30 degrees is equal to √3/2 in this case.

A 30-60-90 triangle is a type of right triangle where the angles measure 30, 60, and 90 degrees. Its side lengths are in a fixed ratio of 1 : √3 : 2, with the shortest side opposite the 30-degree angle having length x, the side opposite the 60-degree angle having length √3x, and the hypotenuse having length 2x. To find sin 30 degrees, we use the sine function, which is the ratio of the opposite side to the hypotenuse. Thus, sin 30 degrees is equal to x divided by 2x, or 1/2. Therefore, in this specific case where the side lengths are in the ratio 1 : 3 : 2, sin 30 degrees is equal to 1/2.

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Answer:

Let A represent the cost of purchasing a pool membership from the Aquatics Club and let S represent the cost of purchasing a pool membership from the Swimming Hole. Then, we can write the following system of inequalities:

A ≤ y

A = 75 + 20x

S ≤ y

S = 15 + 65x

The first two inequalities represent the cost of purchasing a membership from the Aquatics Club, while the last two represent the cost of purchasing a membership from the Swimming Hole. The inequalities ensure that the cost of purchasing a membership from either company does not exceed Alfonso's budget of y dollars.

The distance from the point (15,-21) to the line is 5.39 units.

The equation of a line in point-slope form is:

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is a point on the line and m is the slope of the line. When we are unsure of the y-intercept but are aware of the line's slope and a point on the line, we can utilise this form of the equation.

To calculate the equation of a line using the point-slope method, we must first determine the slope of the line using the following formula:

m = (y2 - y1)/(x2 - x1) (x2 - x1)

where the two points on the line are (x1, y1) and (x2, y2). We may enter the slope, along with one of the line's points, into the point-slope form to obtain the equation of the line.

Given that, the line has the following values f(4)=-8 and f(8)=-18.

The coordinates of the line are (4, -8) and (8, -18)

Thus, the slope of the line is:

m = y2 - y1/ x2 - x1

m = -18 + 8 / 8 - 4

m = -10/4 = -5/2

Now the slope intercept form is given as:

y - y1 = m (x - x1)

Substitute the values:

y + 8 = -5/2(x - 4)

2y + 16 = -5x + 20

2y = -5x + 20 - 16

2y = -5x + 4

The distance from the line to point is given as:

Distance = |ax + by + c| / √(a² + b²)

Substituting the values:

Distance = |-5(15) + -2(-21) + 4| √(-5² + -2²)

Distance = |-29|/ 5.38

Distance = 5.39

Hence, the distance from the point (15,-21) to the line is 5.39 units.

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We have established that the answer to the equation,  [tex]x = 24/7[/tex] , is that the left side equals the right side.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation [tex]3x + 5 = 14[/tex]  consists of the two equations  [tex]3x + 5[/tex] and 14, which are separated by the 'equal' sign.

The equation is as follows:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

This equation can be made simpler by first merging like terms:

[tex]\frac{1}{2}\times (x-2)+ 1+2/3x-3[/tex]

[tex]= 1/2x + 2/3x - 4[/tex]

[tex]= 7/6*x - 4[/tex]

As a result, the equation becomes [tex]7/6*x - 4 = 0.[/tex]

We can now get the value of x by multiplying both sides by 6/7 after adding 4 on both sides: [tex]7/6*x = 4 x = 24/7.[/tex]

We rewrite the original equation with x = 24/7 to confirm the solution:

[tex]1/2*(24/7-2)+1+2/3(24/7)-3[/tex]

[tex]= 1/2*(10/7)+1+16/21-3[/tex]

[tex]= 5/7+1-2/3[/tex]

[tex]= 6/7[/tex]

Therefore, 6/7 demonstrates the equality.

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After calculating, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is: 3 log²2 (5 - 3 log 3)

We can start by simplifying the logarithmic expressions inside the parentheses:

log²(2^18) + log²(4) = (18 log 2)^2 + (2 log 2)^2 = 324 log²2 + 4 log²2 = 328 log²2

log²(32) + log²(216) = (5 log 2)^2 + (3 log 6)^2 = 25 log²2 + 27 log²3

Now, we can express the original expression as:

HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) = HCF(328 log²2, 25 log²2 + 27 log²3)

To find the highest common factor of these two terms, we can factor out the common factor of log²2:

HCF(328 log²2, 25 log²2 + 27 log²3) = log²2 HCF(328, 25 + 27 log²3)

Now, we need to find the highest common factor of the two integers 328 and 25 + 27 log²3.

We can factor out 3 from 25 and 27, and then use the difference of squares formula to write:

25 + 27 log²3 = (5 + 3 log 3)(5 - 3 log 3)

So, the highest common factor of 328 and 25 + 27 log²3 is the product of the common factors, which is:

HCF(328, 25 + 27 log²3) = 3(5 - 3 log 3)

Therefore, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is:

log²2 HCF(328, 25 + 27 log²3) = log²2 * 3(5 - 3 log 3) = 3 log²2 (5 - 3 log 3)

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Answer:

The answer is 4

Step-by-step explanation:

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Answer:

4

Step-by-step explanation:

25% of 16

Change the percent to decimal form.

.25 * 16

4