15-7 x 2 x 2 to the 3rd power

, the rule is verified.

We are given a table and we need to fit an equation that follows the pattern. We also need to describe the relationship between the two columns in words.Given table,|a|b| |5|65|6|78|8|1010|11|13|13|We see that the value of b is 13 less than the value of a. We can describe this relationship as: "The value of b is 13 less than the value of a."Hence, we can write the rule as:b = a - 13We can check this rule by substituting values from the table in the above equation as follows:When a = 5, b = 5 - 13 = -8When a = 6, b = 6 - 13 = -7When a = 8, b = 8 - 13 = -5When a = 10, b = 10 - 13 = -3When a = 13, b = 13 - 13 = 0The values of b obtained are the same as in the given table.

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Answer:

Step-by-step explanation:

\(\frac{(12a - 6bc - 3)}{20ab-5c)} \\\\\frac{3 . (4a - 2bc - 1)}{5 . (4ab - c)}\\\\\)

Answer:

slope: 150

y-intercept: 250

y= 150x+250

Step-by-step explanation:

The number of goals scored by individual players on a hockey team represents an example of a discrete variable.

In the context of hockey, a discrete variable refers to a characteristic that can only take specific, separate values. The number of goals scored by players on a hockey team is an example of a discrete variable. Each player can score a certain number of goals, and these values are distinct and separate from one another. It is not possible to have fractional or continuous values for the number of goals scored.

Each goal scored is counted as a whole number, making it a discrete variable. Discrete variables, such as the number of goals scored by players in a hockey team, are distinct and separate values that do not fall on a continuum. They are typically counted or enumerated and can only take specific values without any intermediate values between them.

This is in contrast to continuous variables, which can take any value within a given range. Understanding the difference between discrete and continuous variables is essential in various fields, including statistics, mathematics, and data analysis.

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Answer:

9

Step-by-step explanation:

IL and KL have the same length so we can set them equal.

3x = x+6

Subtract x from each side.

3x-x = x+6-x

2x = 6

Divide by 2.

2x/2 = 6/2

x=3

KL = x+6

     =3+6

    = 9

Answer:

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

40% of the total number is 6.

Find the total number x:

Answer:

Or the rate of change. The percentage change.

Slope.

Answer:

(6, 4)

Step-by-step explanation:

R(2,4)=(2+4, 4)=(6, 4)

answer

explanation

(6,4)

The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;

\( \frac{1}{x} + \frac{1}{y}= \frac{1}{z}\)

From the given information, we have;

According to the ratio of corresponding sides of similar triangles, we have;

\( \frac{x}{z} = \mathbf{\frac{BD}{QD} }\)

\( \frac{y}{z} = \frac{BD}{ BQ} \)

Which gives;

\( \mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D} \)

\( \frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}\)

QD × x = BD × z

BD × z = (1 - QD/BD) × y = y - (QD × y/BD)

Therefore;

BD × z = y - (QD × y/BD)

BQ × y = y - (QD × y/BD)

BQ × y = y - (z × y/x) = y × (1 - z/x)

(1 - z/x) = BQ

BD × z = y × (1 - z/x)

BD = (y × (1 - z/x))/z

Therefore;

QD × x = y × (1 - z/x)

(BD-BQ) × x = y × (1 - z/x)

(BD-(1 - z/x)) × x = y × (1 - z/x)

BD = (y × (1 - z/x))/x + (1 - z/x)

BQ + QD = (1 - z/x) + (y × (1 - z/x))/x

BD = BQ + QD

(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z

(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z

Dividing both sides by (1 - z/x) gives;

y/x + 1 = y/z

Dividing all through by y gives;

(y/x + 1)/y = (y/z)/y

Therefore;

\( \frac{1}{x} + \frac{1}{y}= \frac{1}{z}\)

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B. The group frequency distribution involves organizing the data into groups or classes and counting the frequency of observations within each class.

To create a group frequency distribution, we need to determine the intervals or classes and count how many data points fall into each interval.

C. a. The number of classes can be determined based on the desired level of detail and the range of the data. To find the number of classes, we can use the square root rule or Sturges' formula.

The square root rule suggests taking the square root of the total number of data points. Sturges' formula recommends using the formula k = 1 + log2(n), where k is the number of classes and n is the total number of data points.

b. The width of each interval can be calculated by dividing the range of the data by the number of classes. The range is the difference between the highest and lowest values in the data set.

Once we have the number of classes and the range, we can divide the range by the number of classes to determine the width of each interval.

It's important to note that without the specific data provided, we cannot provide the exact solution for the number of classes or the width of the interval. These calculations require the actual data points to determine the range and other relevant values.

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Step-by-step explanation:

= (c - 4) ( c - 5)

= c ( c- 5 ) -4 (c - 5)

= c² - 5c - 4c + 20

Grouping of like terms since it have already been arranged.

=c² - 9c + 20

since we're finding for the coefficient of c

than we will square both sides or value

given as

\( \sqrt{c {}^{2} } - \sqrt{9c} + \sqrt{20} = 0 \\ c - \sqrt[3]{3c} + \sqrt[2]{10} = 0 \\ c - c + 5 = 0 \\ 0 = 0 - 5 \\ 0 = - 5\)

sorry but I tried.

Answer:

244=t+295

Step-by-step explanation:

Answer:

D) - 3v³ + 3v²

Step-by-step explanation:

( v³ + v²) + ( 2v² - 4v³)

= v³ + v² + 2v² - 4v³

= - 3v³ + 3v²

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

B. The denominator is twice the numerator.

Step-by-step explanation:

Answer:

a. no

b. no

c. no

d. yes

Step-by-step explanation:

Case I

x = -1

y = -4

7( -1) + 4 ( -4) = -23

-7 - 4 = -23

- 11 \(\neq\) -23

Case II

x = 2

y= 6

7 (2) + 4 ( 6) = -23

14 + 24 = -23

38 \(\neq\) -23

Case III

x = 6

y = -7

7 ( 6) + 4 (3) =- 23

42+ 12 = -23

54 \(\neq\) -23

Case IV

x = -5

y = 3

7 (-5) + 4 ( 3) =- 23

-35 + 12 = -23

-23 = -23

The value of the angle Q is 25 degrees

It is important to note the following;

From the information given, we have that;

m<P = 90 degrees

m<R = 2x - 5

m<Q = x - 10

Now, equate the angles

m<P +m<R + m< Q = 80 substitute the values

90 + 2x - 5 + x - 10 = 180

collect the like terms

3x = 180 - 75

subtract the values

3x = 105

Divide by the coefficient of x

x = 35

Then, m<Q = 35 - 10 = 25 degrees

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The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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Answer:

76.0 degrees

Step-by-step explanation:

Just got it right on the Khan Academy quiz.

Answer:\(c=60+0.05d\)

Step-by-step explanation:

Given

Company charges \(\$60\)  for  \(1\ GB\) data

and charges \(\$0.05/MB\)

If c is the total cost and d represent no of additional megabyte then

Cost is given by the sum of fixed price + additional data charge

\(c=60+0.05\times d\)

Therefore final charge is given by

\(c=60+0.05d\)

The equations of the vertical asymptotes can be given as x = -4, -2, and 1. The function f(x) does not have any horizontal asymptotes.

The function, f(x) is given as f(x)=5 - f ′(x)>0 on (−2,1)∪(1,[infinity]) f ′(x)<0 on (−[infinity],−2)f ′′(x)>0 on (−[infinity],−4)∪(1,4)f ′′(x)<0 on (−4,−2)∪(−2,1)∪(4,[infinity])

To sketch the graph of the original function, we have to determine the critical points, intervals of increase and decrease, the local maximum and minimum, and asymptotes of the given function.

Using the given information, we can form the following table of f ′(x) and f ′′(x) for the intervals of the domain.

The derivative is zero at x = -2, 1.

To get the intervals of increase and decrease of the function f(x), we need to test the sign of f ′(x) at the intervals

(−[infinity],−2), (-2,1), and (1,[infinity]).

Here are the results:

f′(x) > 0 on (−2,1)∪(1,[infinity])f ′(x) < 0 on (−[infinity],−2)

As f ′(x) is positive on the intervals (−2,1)∪(1,[infinity]) which means that the function is increasing in these intervals.

While f ′(x) is negative on the interval (−[infinity],−2), which means that the function is decreasing in this interval.

To find the local maximum and minimum, we need to determine the sign of f ′′(x).

f ′′(x)>0 on (−[infinity],−4)∪(1,4)

f ′′(x)<0 on (−4,−2)∪(−2,1)∪(4,[infinity])

We find the inflection points of the function f(x) by equating the second derivative to zero.

f ′′(x) = 0 for x = -4, -2, and 1.

The critical points of the function f(x) are -2 and 1.

The inflection points of the function f(x) are -4, -2, and 1.

Hence, the equations of the vertical asymptotes can be given as x = -4, -2, and 1.The function f(x) does not have any horizontal asymptotes.

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Answer:

Variables with no number have a coefficient of 1.

Step-by-step explanation: x is really 1x.

The equation given models the distance from the ground of a person riding on a ferris wheel. it takes 80 seconds for the Ferris wheel to make one revolution.

To determine how long it will take for the ferris wheel to make one revolution, we need to find the period of the function. The period is the amount of time it takes for the function to complete one full cycle.
In this case, the function is d = 30sin(pi/40t) + 20, where t is measured in seconds. The period of the function can be found using the formula T = (2pi)/b, where b is the coefficient of t in the argument of the sine function. In this case, b = pi/40, so T = (2pi)/(pi/40) = 80 seconds.
Therefore, it will take 80 seconds for the ferris wheel to make one full revolution. The answer is option C, 80 seconds.
The time it takes for a Ferris wheel to make one revolution can be determined using the given equation: d = 30 * sin((π/40) * t) + 20. In this equation, d represents the distance (in feet) of the person above the ground, and t represents the time in seconds.
A full revolution occurs when the angle inside the sine function completes a cycle of 2π radians. To find the time it takes for this to happen, we need to equate the angle (π/40) * t to 2π:
(π/40) * t = 2π
To solve for t, we can divide both sides of the equation by (π/40):
t = 2π * (40/π)
The π in both the numerator and denominator cancels out:
t = 2 * 40
t = 80 seconds
Therefore, it takes 80 seconds for the Ferris wheel to make one revolution.

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Answer:

The area of the triangle is 6 units squared.

Step-by-step explanation:

The formula for the area of a triangle is A=1/2B*H. The base in this situation is 4, and the height is 3. 4x3 is 12. We are half 12 because we only need 1/2 of the area, as a triangle is half a square. Thus, our answer is 6 units squared.

Answer:

Step-by-step explanation:

A= 1/2 bh             >formula

A= 1/2 (3)(4)         >turn triangle so 3 is your base, substitute

A=6

To construct a confidence interval for the population proportion, we can use the formula:

CI = p ± z * sqrt((p(1 - p))/n)

where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

Given:

Sample size (n) = 50

Number of phones with over 100 apps (x) = 13

Desired confidence level = 99%

z-score for a 99% confidence level (z0.005) = 2.576

First, calculate the sample proportion p:

p = x / n

p = 13 / 50

p = 0.26

Next, calculate the margin of error:

ME = z * sqrt((p(1 - p))/n)

ME = 2.576 * sqrt((0.26 * (1 - 0.26))/50)

ME ≈ 0.15

Finally, construct the confidence interval:

CI = p ± ME

CI = 0.26 ± 0.15

Therefore, the 99% confidence interval for the population proportion of phones with over 100 apps is:

Option B: 0.26 ± 0.15

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Answer:

4 weeks

Step-by-step explanation:

The number of weeks for a total of 16 quizzes will be 4 weeks.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

It is given that Jacob took a total of 12 quizzes over the course of 3 weeks. The number of weeks for 16 quizzes will be calculated as below:-

12 quizzes = 3 weeks.

1 quizzes = 3 / 12 weeks

16 quizzes = ( 3 / 12 ) x 16 = 4 weeks

Therefore, the number of weeks for a total of 16 quizzes will be 4 weeks.

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