prove the statement if it is true; find a counterexample for statement if it is false, but do not use theorem 4.6.1 in your proofs:

Answer:

3x - x + 4 = 0

2x = -4

x = -4 ÷ 2

x = -2

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Answer:

Answer:

\(-8.57\)

Step-by-step explanation:

\(-4.5+(-4.07)\\-4.5-4.07\\-8.57\)

Answer:

-8.57

Step-by-step explanation:

Simplify the expression

For tax year 2018, Ben's standard deduction is $12,000. As a single filer, the standard deduction amount he can claim is $12,000.The standard deduction is a fixed amount of money that reduces the amount of income subject to taxation.

A taxpayer can choose to claim the standard deduction or itemize their personal deductions. If the sum of all itemized deductions exceeds the standard deduction, the taxpayer should opt to itemize. If the sum of itemized deductions is less than the standard deduction, the taxpayer should opt to take the standard deduction.A legally blind taxpayer may qualify for a higher standard deduction.

For tax year 2018, the additional standard deduction amount for a taxpayer who is blind is $1,600.

Since Ben is legally blind, his standard deduction amount could have been $12,000 + $1,600 = $13,600 if he had chosen to take the higher standard deduction.

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Answer:

Slope= -5/3 when using y^2-y^1 divided by x^2-x^1

The value of c for which the limit of the function does not exist is given as follows:

c = -2.

The limit of a function will not exist if a function has different lateral limits, that is, if the to the right of x = c the graph has a different numeric value than to the left of x = c.

For this problem, we look at the graph at x = -2, hence:

This means that the function has different lateral limits, hence the limit of the function does not exist for c = -2.

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Answer:

y=41^2

Step-by-step explanation:

Answer: y=1

Step-by-step explanation: You’ll need to isolate the variable by dividing each side by factors that don't contain the variable.

The equation of line is y = -10x + 1500 , where the slope is m = -10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = -10x + 1500   be equation (1)

where x is the number of minutes

and y is the altitude in feet

when x = 0

Substituting the value of x = 0 in the equation , we get

y = 1500 feet

when x = 5

Substituting the value of x = 5 in the equation , we get

y = -10 ( 5 ) + 1500

y = -50 + 1500

y = 1450 feet

when x = 8

Substituting the value of x = 8 in the equation , we get

y = -10 ( 8 ) + 1500

y = -80 + 1500

y = 1420 feet

when x = 10

Substituting the value of x = 10 in the equation , we get

y = -10 ( 10 ) + 1500

y = -100 + 1500

y = 1400 feet

when x = 30

Substituting the value of x = 30 in the equation , we get

y = -10 ( 30 ) + 1500

y = 300 + 1500

y = 1200 feet

So , the plane's altitude after 5 minutes would be 1450 feet and after 30 minutes, the plane's altitude would be 1200 feet

Now , the plane will reach the ground when y = 0

0 = -10x + 1500

10x = 1500

x = 150 minutes

Hence , the equation of line is y = -10x + 1500

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54 outcomes are  in A

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

Here (x) = 3x-1 and h (x) =x²-3x+8

Now lim x→3 x   g (x) = lim x→3 3x -1

=3x³-1

=9-1

=8

and lim x→3 h (x) = lim x→3 x²-3x+8

=9-9+8

= 8

value of f (x) when x approaches 3

since lim x →3  g (x) =8 and lim x→3 h (x) = 8

Then lim x→3 f (x) =8

hence lim x→3 f (x) = 8 

hence 54 outcomes  are in A

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Answer:

draw a line that goes up to 8 from the origin.

Step-by-step explanation:

The sum of the vector 2u and vector 4v is 2i+12j and it can be drawn with the coordinates point (2, 12) on the coordinate plane.

It is defined as a physical quantity that has magnitude as well as direction. Vector always follows a triangle rule for the sum of the two vectors.

We have given two vectors shown in the coordinate plane that is:

u(-1, 2) and v(1, 2)

We can write these two vectors in the form of i and j

\(\rm \vec{u}= -\hat{i}+2\hat{j}\\\rm \vec{v}= \hat{i}+2\hat{j}\)

Finding vector 2u:

\(\rm \vec{2u}= -2\hat{i}+4\hat{j}\\\)   (multiply by scalar value 2 in the vector u)

Finding vector 4v:

\(\rm \vec{4v}= 4\hat{i}+8\hat{j}\)      (multiply by scalar value 4 in the vector v)

Now find the sum of the vector 2u and vector 4v:

\(\rm \vec{2u}+ \vec{4v}= -2\hat{i}+4\hat{j}+4\hat{i}+8\hat{j}\)

\(\rm \vec{2u}+ \vec{4v}= 2\hat{i}+12\hat{i}\)

Now representing the vector (2u+4v) on the coordinate plane with coordinates (2, 12) as shown in the picture.

Thus, the sum of the vector 2u and vector 4v is 2i+12j and it can be drawn with the coordinates point (2, 12) on the coordinate plane.

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Answer:

95

Step-by-step explanation:

180-144=36

180-121=59

59+36=85

180-85=95

For a person to become obese, the "Set point" must change and this would be due to a permanent change in the sensor.

The term obesity refers to a situation in which a person gathers excess fat in the body to a point that it becomes unhealthy and a potential health risk to the individual. A person is said to be obese if he/she has a body mass index above 25.

For a person to become obese, the "Set point" must change and this would be due to a permanent change in the sensor.

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Answer:

Option (4)

Step-by-step explanation:

Table for the points from the graph attached,

      x           y        \(x^{2}\)            \(y^{2}\)            xy

    2.2       1.8       4.84        3.24       3.96

    3.2       1.8       10.24       3.24       5.76

    3.6        3        12.96         9           10.8

    4.8       3.5      23.04      12.25      16.8

    5.2       6.2      27.04      38.44      32.24

    6.4       4.5      40.96      20.25     28.8

    7.5       7.8       56.25     60.84      58.5

    8.5       6.2      72.25      38.44      52.7

\(\sum x=41.4\)

\(\sum y=34.8\)

\(\sum x^2=247.58\)

\(\sum y^2=185.7\)

\(\sum xy=209.56\)

n = 8

Formula for the correlation coefficient  \(r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{[{n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}}\)

\(r=\frac{8(209.56)-(41.4)(34.8)}{\sqrt{[{8(247.58)-(41.4)^2][8(185.7)-(34.8)^2]}}}\)

r = \(\frac{1676.48-1440.72}{\sqrt{266.52\times 274.56} }\)

r = \(\frac{235.76}{\sqrt{73175.73}}\)

r = \(\frac{235.76}{270.51}\)

r = 0.87

r ≈ 0.9

Therefore, Option (4) is the answer.

The required sign between -12.7a and -12.7b should be greater than sign (>).

If a is less than b, then -12.7a will be greater than -12.7b, because multiplying a smaller number by a negative constant (-12.7 in this case) will result in a larger negative value than multiplying a larger number by the same constant.

To see this, suppose we have two positive numbers x and y such that x < y. Then, multiplying both by a negative constant c will result in two negative numbers with magnitudes that are greater for x:

cx < cy, because c is negative and (x < y)

Therefore, if a is less than b, then:

-12.7a > -12.7b

So the sign between -12.7a and -12.7b should be greater than sign (>).

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Answer:

35.7% chance

Step-by-step explanation:

First pull is 5/8 chance, but then becasue you don't replace it next pull is 4/7, so you multiply them together

The standard deviation measures the dispersion or spread of the data. In this case, it indicates that the number of employees in the branches tends to vary around the mean of 12.73 by approximately 2.727 units

Frequency distribution with 4 class intervals, we need to determine the range of the data and calculate the width of each interval. Here are the steps to construct the frequency distribution:

The range is the difference between the maximum and minimum values in the data set. In this case, the maximum value is 19 and the minimum value is 9. So the range is 19 - 9 = 10.

Divide the range by the desired number of class intervals. Since we want 4 class intervals, divide the range (10) by 4: 10 / 4 = 2.5. Round up to the nearest whole number to determine the interval width. In this case, the interval width will be 3.

Start with the minimum value and add the interval width successively to determine the upper boundary for each class. The lower boundary for each class will be one less than the upper boundary. Using the given data, the class boundaries are

Class Interval  Frequency

8.5 - 11.5            17

11.5 - 14.5    18

14.5 - 17.5    11

17.5 - 20.5    4

A) The proportion of branches with more than 14 employees, we sum up the frequencies of the last two class intervals (14.5 - 17.5 and 17.5 - 20.5). The sum is 11 + 4 = 15. There are 50 branches in total. So the proportion is 15/50 = 0.3, or 30%.

B) The mean, median, and mode, we need to use the midpoint of each class interval as the representative value. We can calculate these measures using the frequency distribution table.

Mean: Sum up the products of each midpoint and its corresponding frequency, and divide by the total number of observations.

Mean = (8.5 × 17 + 11.5 × 18 + 14.5 × 11 + 17.5 × 4) / 50 = 12.73

Median: The median is the middle value when the data is arranged in ascending order. Since the data is grouped, we can estimate the median by finding the cumulative frequency that is closest to half of the total number of observations, which is 50/2 = 25. The median falls within the second class interval (11.5 - 14.5). To estimate the median more accurately, we can use the following formula:

Median = L + ((n/2 - F) / f) × i

Where:

L = Lower boundary of the median class interval

n = Total number of observations

F = Cumulative frequency of the class interval before the median class

f = Frequency of the median class interval

i = Interval width

Using the given data, the median can be calculated as:

Median = 11.5 + ((25 - 17) / 18) × 3

= 11.5 + (8 / 18) × 3

= 11.5 + (4/3)

= 12.83

Mode: The mode is the class interval with the highest frequency. In this case, it is the first class interval (8.5 - 11.5) with a frequency of 17.

C) The 50th percentile represents the value below which 50% of the observations fall. We can estimate the 50th percentile using the cumulative frequency. The cumulative frequency closest to 50% of the total number of observations (50/100 × 50) is 25. The 50th percentile falls within the second class interval (11.5 - 14.5). Using the same formula as the median calculation, we can estimate the 50th percentile as:

50th Percentile = 11.5 + ((50 - 17) / 18) × 3

= 11.5 + (33 / 18) × 3

= 11.5 + (11/2)

= 17

This means that 50% of the branches have 17 or fewer employees.

D) The standard deviation, we need to calculate the variance first. Since we have grouped data, we can use the following formula:

Variance = (Sum of (midpoint² × frequency)) / Total number of observations - Mean²

Variance = (8.5² × 17 + 11.5² × 18 + 14.5² × 11 + 17.5² × 4) / 50 - 12.73² = 7.437

Standard Deviation = √Variance = √7.437 = 2.727

The standard deviation measures the dispersion or spread of the data. In this case, it indicates that the number of employees in the branches tends to vary around the mean of 12.73 by approximately 2.727 units.

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Answer:

the range is the set of possible output of values

Step-by-step explanation:

The range is the set of y-values (OUTPUT) that map to the set of x-values (INPUT).

Answer:

B

Step-by-step explanation:

\(\dfrac{5}{2x} + \dfrac{4}{3y}=\dfrac{15y+8x}{6xy}\)

The answer of the given question is  the radius of the cylinders is approximately 1 unit, based on the chosen point on the graph.

Radius is a fundamental geometric property of a circle, which is defined as the distance from the center of the circle to any point on the circle's circumference. It is a one-dimensional measurement and is usually denoted by the symbol "r". The radius is defined similarly as the distance from the center of the shape to its outer boundary.

The radius is an important parameter in many mathematical equations and formulas that involve circles or three-dimensional shapes, like calculating the area or volume of a circle, cylinder, or sphere.

To find the radius of the cylinders given the equation V = πR²h, we can rearrange the equation to solve for R. We know that the radius is constant for all cylinders in the graph, so we can use any point on the graph to find its value.

Let's choose a point on the graph where the height is h=1 and the volume is V=3.14 (using 3.14 as an approximation for π):

V = πR²h

3.14 = πR²(1)

3.14/π = R²

R = √(3.14/π)

R ≈ 1.0

So the radius of the cylinders is approximately 1 unit, based on the chosen point on the graph.

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Here is a graph of the relationship between the height and volume of some cylinders that all have the same radius, R. An equation that represents this relationship is V =πR²h (use 3.14.as an approximation for π). What is the radius of these cylinders?​

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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Answer:

576 (square yards)

Step-by-step explanation:

length of slanted height of triangle = √(6² + 8²)

= √100

= 10.

surface area = area of 2 triangle faces + area of 3 lengths

= 2 (1/2 X 12 X 8) + 3 (10 X 16)

= 576 (square yards)

Answer:

6 is 1 bigger than 5

Step-by-step explanation:

Answer:

oasdkopdpoasdkpoadkaopsdkposposdadas

Step-by-step explanation:

Answer:

1620°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 11 , then

sum = 180° × 9 = 1620°

1) Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. 2) The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. 3) trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

1. Trigonometric ratios for similar triangles state that the ratios of corresponding sides of similar triangles are equal. Therefore, the ratios of the sine, cosine, and tangent of the corresponding angles in similar triangles will also be equal.

2. The sine and cosine of complementary angles have the property of being not only equal but also complementary to one another. This means that the sine of an angle is equal to its complement's cosine, and vice versa.

3. Using the appropriate formula based on the given information, trigonometric ratios can be used to solve for a missing side or angle of a right triangle.

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Step-by-step explanation:

312 × 25 ÷ 100

7800/100 = 78

Now,

312 - 78 = 234

Thus, 234 students eat in the cafeteria

The coordinates of the point which is of the way from A to B are (-1, 1).

We have to find the coordinates of the point which is of the way from A(-6, -7) to B(4, 9).

To do this, we can use the midpoint formula. Midpoint formula is used to find the midpoint of a line segment and is given by the following formula:(x₁+x₂)/2, (y₁+y₂)/2

where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints of the line segment. Let's apply this formula to find the midpoint of the line segment AB:((x₁+x₂)/2, (y₁+y₂)/2) = ((-6+4)/2, (-7+9)/2) = (-1, 1)

Therefore, the midpoint of the line segment AB is (-1, 1). This point is halfway from A to B. To find the point which is of the way from A to B, we can use the section formula.

Section formula is used to find the coordinates of the point which divides a line segment into two parts in a given ratio. Let's apply this formula to find the point which is of the way from A to B:x = [(m × x₂) + (n × x₁)] / (m + n)y = [(m × y₂) + (n × y₁)] / (m + n)

where m:n is the ratio in which the line segment is divided. Let's assume that the point which is of the way from A to B divides the line segment AB in the ratio of m:n.

Since the midpoint of the line segment AB is (-1, 1), it divides the line segment AB in the ratio of 1:1.

Therefore, we can substitute m = 1 and n = 1 in the section formula and get the coordinates of the point which is of the way from A to B:x = [(1 × 4) + (1 × -6)] / (1 + 1) = -1y = [(1 × 9) + (1 × -7)] / (1 + 1) = 1

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The sum of two numbers is 13 more than twice the first number:

x + y = 2x +13

x - y = y - 14

solve the system of equations:

x - (x + 13) = (x +13) - 14

x = -12

y = 1

Answer:

$82,500

Step-by-step explanation:

Since each share is 8250 and we want to find to find 10 shares, we can do 8250 (price of each share) x 10 (amount of shares) and we get $82500