What is the value of log 256/ log 1024

Answer:

21

Step-by-step explanation:

since 3 and 7 are prime numbers, its LCM is simply 3*7 = 21

The least common factor of the numbers 3 and 7 will be 21.

The corresponding value integer that can be divided by both is known as the lowest relevant multiple, commonly referred to as the lowest common multiple of pair (or more) numerals a and b.

The numbers are given below.

3 and 7

The factor of the number 3 is given as,

3 = 1 x 3

The factor of the number 7 is given as,

7 = 1 x 7

Then the LCM of the number 3 and 7 will be given as,

LCM = 1 x 3 x 7

LCM = 21

The LCM of the numbers 3 and 7 will be 21.

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Answer:

Step-by-step explanation:

y varies directly as x.

y = 18 , x = 5

y =36 then x also double,

x = 10

Rounding to three decimal places, the equation becomes:

y = (0.071)x + (2.475).

To find the equation of the line tangent to a curve at a given point, we need to determine the slope of the curve at that point and then use the point-slope form of a line.

For the curve y = e^(2x), we can find the derivative of y with respect to x to determine the slope of the tangent line at any point on the curve. Taking the derivative, we have:

dy/dx = d/dx(e^(2x)) = 2e^(2x).

Now, we can evaluate the slope of the tangent line at the point (x, y) on the curve by substituting x into the derivative:

m = 2e^(2x).

Since we want to find the equation of the tangent line at a specific point, we substitute the coordinates of the point (x, y) = (1, e^(2)) into the slope equation:

m = 2e^(2(1)) = 2e^2.

The equation of the tangent line is given by y = mx + b, where m is the slope and (x, y) is a point on the line. We have the point (1, e^(2)), so the equation becomes:

y = 2e^2x + b.

To find the value of b, we substitute the coordinates of the point (x, y) = (1, e^(2)) into the equation:

e^(2) = 2e^2(1) + b,

b = e^(2) - 2e^2.

Therefore, the equation of the tangent line to y = e^(2x) at the point (1, e^(2)) is:

y = 2e^2x + (e^(2) - 2e^2).

Simplifying further, we get:

y = 2e^2x + e^(2) - 2e^2,

y = 2e^2x + e^(2) - e^2,

y = 2e^2x + e^(2).

For the curve y = ln(5x + 9), we can follow a similar process to find the equation of the tangent line.

Taking the derivative of y with respect to x:

dy/dx = d/dx(ln(5x + 9)) = 1/(5x + 9).

To find the slope of the tangent line at the point (1, ln(14)), we substitute x = 1 into the derivative:

m = 1/(5(1) + 9) = 1/14.

The equation of the tangent line is given by y = mx + b, where m is the slope and (x, y) is a point on the line. Substituting the coordinates of the point (1, ln(14)):

ln(14) = (1/14)(1) + b,

ln(14) = 1/14 + b,

b = ln(14) - 1/14.

Therefore, the equation of the tangent line to y = ln(5x + 9) at the point (1, ln(14)) is: y = (1/14)x + (ln(14) - 1/14).

Rounding to three decimal places, the equation becomes:

y = (0.071)x + (2.475).

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If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Answer:

Infinitely many solutions

Step-by-step explanation:

multiply -x+5y=-6 with 2

-2x+10y=-12

2x-10y=12

add:

0=0

A statement that compares two expressions that are not equal is called an inequality. An inequality is a mathematical expression that shows that two quantities are not the same, unlike an equation which shows that two quantities are equal. Inequalities use symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to) to compare two expressions.

For example, 4 < 7 is an inequality because 4 is less than 7. Inequalities are commonly used in algebra and real-world scenarios to represent situations where there are limits, ranges or restrictions. Solving inequalities involve finding the values of the unknown variable that make the inequality true. There are several methods to solve inequalities, including adding or subtracting the same value to both sides of the inequality, multiplying or dividing by a positive or negative number, and graphing the inequality on a number line.

Understanding inequalities is crucial for various fields such as economics, engineering, physics, and computer science.

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Answer:

•The Prime Factors of 35 are 1, 5, 7, 35 and its Factors in Pairs are (1, 35) and (5, 7).

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The probability that two or more of the events will occur is 0.683594.

The probability that two or more of the events will occur is equal to 1 minus the probability that none of the events will occur. Since the probability of each event occurring is 0.25, the probability that none of the events will occur is (1 - 0.25) * (1 - 0.25) * (1 - 0.25) * (1 - 0.25) = 0.316406. Therefore, the probability that two or more of the events will occur is 1 - 0.316406 = 0.683594.

Alternatively, you can find the probability that two or more of the events will occur by adding up the probabilities of each of the ways that two or more of the events can occur.

There are four ways that two events can occur (for example, event A and event B), six ways that three events can occur (for example, event A, event B, and event C), and four ways that all four events can occur.

Thus, the probability that two or more of the events will occur is (4 * 0.25 * 0.25) + (6 * 0.25 * 0.25 * 0.25) + (4 * 0.25 * 0.25 * 0.25 * 0.25) = 0.683594, which is the same result as before.

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Answer: |81-x|<5

Step-by-step explanation:

Given: Temperature of an enclosure for a pet corn snake should be an average of 81° F.

Temperature in the enclosure should not vary by more than 5° F.

Let x= Temperature in the enclosure

Then, difference between average and current temperature should less the 5.

i.e. |81-x|<5     (required absolute value equation  )

hence, the absolute value equation could be used to determine the minimum and maximum temperatures recommended for the corn snake enclosure:

|81-x|<5

Using absolute value, it is found that the equation that could be used to determine the minimum and maximum temperatures recommended for the corn snake enclosure is:

\(|T - 81| = 5\)

\(|x| = x, x \geq 0\)

\(|x| = -x, x < 0\)

In this problem, the temperature T should be within 5º F of 81ºF, hence, the absolute value of the difference between T and 81 should be of 5, that is:

\(|T - 81| = 5\)

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Answer:

6.4

Step-by-step explanation:

70.4/11

= 6.4

The lines p and q are perpendicular lines.

According to the question,

We have the following information:

Line p passes through points (18, 11) and (-17, 22). Line q passes through points (2, 37) and (-9, 72).

We will find the slope of both the lines to check whether they are perpendicular or parallel. If their slope is equal then they are parallel and if their slope is not equal or inverse of the other one then they are perpendicular.

(Slope is denoted by m.)

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

For line p:

x1 = 18, y1 = 11, x2 = -17 and y2 = 22

m = (22-11)/(-17-18)

m = -11/35

For line q:

x1 = 2, y1 = 37, x2 = -9 and y2 = 72

m = (72-37)/(-9-2)

m = -35/11

Now, the slope is inverse.

Hence, the lines p and q are perpendicular lines.

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An equation to model the relationship between the number of weeks, x, and the number of site visits, f(x) is 4800 = a(1.5)^x.

He found that before launching the new marketing plan, there were 4,800 visits.

Over the course of the next 5 weeks, the number of site visits increased by a factor of 1.5 each week.

Over the course of the next 5 weeks, initial visitor at x = 0, 4800

Increasing factor = 1.5

Equation of the model is given as:

f(x) = a(b)^x

From the question b = 1.5

Now the equation of model is:

f(x) = a(1.5)^x

At x = 0, f(x) = 4800

Now the equation of the model is:

4800 = a(1.5)^x

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Answer:

x = 2  (One of many options)

Step-by-step explanation:

See attached worksheet.

Given :

Insurance cost , $693.00 .

Gas cost , $452.00 .

Average charge per fare , $7.00 .

Tuition fee , $3280.00 .

To Find :

The fare he have to get to pay his fee .

Solution :

Let , number of fair required is n .

Therefore , total profit is :

\(Profit = earning - expenditure \\Profit = 7n - 693-452\\Profit = 7n-1145\)

Now , to pay his fee this profit must be equal to his fee because he don't have other expenditure .

So ,

\(7n-1145=3280\\\\7n=4425\\\\n=\dfrac{4425}{7}\\\\n=632.1\)

But number of rides cannot be in decimal so minimum rides he must get is

632+1 = 633 .

Hence, this is the required solution .

The estimated value of the explanatory variable is not statistically significant at the 5%-level if a. the t-statistic is greater than 2.5.

The t-test is a hypothesis testing technique used to decide whether the estimated coefficient of a linear regression model is statistically significant or not. The t-value is used to measure the size of the difference between the estimated coefficient and the hypothesized value. When the t-value exceeds a critical value, such as 2.5, the estimated value of the explanatory variable is not significant at the 5%-level. It implies that the null hypothesis, which assumes that the explanatory variable's coefficient is zero, cannot be rejected.

The p-value is a measure of the probability of obtaining a more extreme value of the test statistic than the observed value if the null hypothesis is true. A small p-value implies that the null hypothesis should be rejected. When the p-value is less than 0.05, it means that the estimated value of the explanatory variable is significant at the 5%-level.

The confidence interval is a range of values that is expected to include the true value of the population parameter with a specified level of confidence. A 95% confidence interval means that the true value of the population parameter lies within the range 95% of the time. The 95% confidence interval does not contain zero implies that the estimated value of the explanatory variable is statistically significant at the 5%-level since it suggests that the population parameter is different from zero at the 5%-level. Conversely, if the 95% confidence interval contains zero, the estimated value of the explanatory variable is not statistically significant at the 5%-level since it means that the population parameter is not different from zero at the 5%-level. Therefore, it is essential to examine the t-statistic, p-value, and confidence interval while conducting hypothesis testing to make an informed decision.

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Answer:

d. 40 feet

Step-by-step explanation:

Perimeter = 140 ft

Width = L + 10

P = 2w + 2L

140 = 2(L + 10) + 2L

140 = 2L + 20 + 2L

120 = 4L

L = 30

w = L + 10

w = 30 + 10

w = 40

Answer:

A,,45.25

B,657.2

Step-by-step explanation:

its the answer

Answer:

non

Step-by-step explanation:

A linear equation = straight line in a graph,

whereas non-linear equations = represent curves.

linear is in the form of y=mx+b

where m is the slope of the equation and b is the y-intercept.

Note x can only = power of one

.

examples y=8x+24

“non-linear” = not graphed using straight lines. examples y=6x²+43

The y-intercept of the given equation is (B) -2.

So, the y-intercept will be:

Plot the equation on the graph as follows:

Therefore, the y-intercept of the given equation is (B) -2.

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Answer:

1 or 2

Step-by-step explanation:

one of the parentaziz has to equal 0 because anything multiplies by 0 is 0

Answer:

(−1)(−2)(0−3)=0

(−1)(−2)(−3)=0

−3(−1)(−2)=0

−32+6+3(−2)=0

−32+6+3−6=0

−32+9−6=0

= −9+3/−6 = 1

= −9−3/−6 = 2

Step-by-step explanation:

Answer:

2.6

Step-by-step explanation:

The angular velocity of the stone is 12.56 rad/s and the linear velocity of the stone is 31.4 m/s.

Given,The length of the sling = 5m.

Number of revolutions per second = 2 rev/s

The angular velocity formula is given as:

Angular velocity,

w = 2πf

where

f = frequency of rotation,

π = 3.14

The frequency of rotation is given as 2 rev/s.

So, the angular velocity is calculated as:

w = 2πf= 2 × 3.14 × 2= 12.56 rad/s.

The formula for linear velocity is given as:

Linear velocity,

v = rw,

Where

r = radius and w = angular velocity.

The radius of the sling,

r = 5/2= 2.5 m.

Substitute the values in the formula,We get,

v = rw= 2.5 × 12.56= 31.4 m/s.

Therefore, the angular velocity of the stone is 12.56 rad/s and the linear velocity of the stone is 31.4 m/s.

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Answer:

C

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Line segment SU is a bisector of angle <TSV which means it divided the angle into two equal parts:

The measure of <TSV = 62 in this case the measure of <VSU = 62/2 = 31

we can write the following equation to find the value of x

5x + 1 = 31 subtract 1 from both sides

5x = 30 divide both sides by 5

x = 6

The probability that x is between 40 and 50 will be 0.5.

From the information, the continuous random variable x is uniformly distributed on the interval [35, 45].

The probability that x is between 40 and 50 will be:

(45 - 40)/(45 - 35)

= 5/10

= 0.5

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Given:

The coordinates of line are, (-3,2) and (1,10).

The objective is to choose the correct equation of line.

Explanation:

Consider the given coordinates as,

The general formula to find the equation of line using two points is,

On plugging the coordinates in the above equation.

Thus, the equation of the line obtained is y - 10 = 2(x - 1).

Hence, option (A) is the correct answer.

A) Yes, the graph represents a proportional relationship because the rate at which the plane's altitude increases is directly proportional to the amount of time that has elapsed since takeoff.

B) The unit rate of change is the number of feet per minute that increases over time, which can be calculated by finding the slope of the line. To do this, we choose two arbitrary points on the line and calculate the change in altitude divided by the change in time for each point. Therefore, if we choose the points (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 12000), then the unit rate of change is (12000 - 0) / (2 - 0).

The unit rate of change is 6000 feet per minute, calculated by (12000 - 0) / (2 - 0).

If you have any additional questions or need further assistance, please let me know.

Answer:

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

Proportional relationship is:

At x = 0, the function gets the value of zero regardless the value of k. Hence the line passes through the origin.

A) The given graph passes through the origin and therefore it is a proportional relationship.

B) The value of y = k when x = 1 is the rate of change.

As per graph it is: