If you use a graph and a table to solve an equation that shows two expressions equal to one another, how can you use algebra to check your answer?

Answer:

Step-by-step explanation:

Formula of sum:

Substitute values:

Answer:

The answer is no.

Step-by-step explanation:

For something to be a function it cannot repeat an x. In this example, on the left side, the -1 goes to two numbers, so written out that means (-1,2) and (-1,-1). This means that the number set has two -1's which means it cannot be a function.

Answer:

V = 113.1 in³

Step-by-step explanation:

→ V = (4/3)πr³

→ V = (4/3) × (3.14) × 3³

→ V = (4/3) × (3.14) × 27

→ V = 113.09734

→ [ V = 113.1 in³ ]

Hence, the volume is 113.1 in³.

The weather map of Florida with an L in northern Florida and an H in southern Florida indicates that there is a low-pressure system in the north and a high-pressure system in the south.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

In a few sentences, describe what this weather map tells you about the weather.

The map is given in the attached image.

The weather map of Florida with an L in northern Florida and an H in southern Florida indicates that there is a low-pressure system in the north and a high-pressure system in the south.

This pattern could result in potentially cooler temperatures, increased chances of precipitation, and cloudy skies in the north, while the south may experience warmer temperatures, clear skies, and drier weather conditions.

Therefore, the required meaning of L and H is given above.

To learn more about the expression;

brainly.com/question/24242989

#SPJ1

Answer:

\(\frac{dy}{dx} =\frac{1}{x} +1\)

Step-by-step explanation:

\(y=ln(xe^x)\)

  \(=ln(x)+ln(e^x)\)

  \(=ln(x)+x\)

Therefore,

\(\frac{dy}{dx} =\frac{1}{x} +1\)

Therefore , the solution of the given problem of probability comes out to be a)1/78 ,b)65/624 ,c)1/4 ,d)0 and e)12/13.

The basic goal of any considerations technique is to assess the probability that a statement is accurate or that a specific incident will occur. Chance can be represented by any number range between 0 and 1, where 0 normally indicates a percentage but 1 typically indicates the level of certainty. An illustration of probability displays how probable it is that a specific event will take place.

Here,

a.

P(Bert gets a Jack and Ernie rolls a five) = P(Bert gets a Jack) * P(Ernie rolls a five)

= (4/52) * (1/12)

= 1/78

b.

P(Bert gets a heart and Ernie rolls a number less than six) = P(Bert gets a heart) * P(Ernie rolls a number less than six)

= (13/52) * (5/12)

= 65/624

c.

P(Bert gets a face card and Ernie rolls an even number) = P(Bert gets a face card) * P(Ernie rolls an even number)

= (12/52) * (6/12)

= 1/4

d.

P(Bert gets a red card and Ernie rolls a fifteen) = 0

e.

Ernie rolls a number that is not twelve, and Bert draws a card that is not a Jack:

A regular 52-card deck contains 48 cards that are not Jacks,

so the likelihood that Bert will draw one of those cards is 48/52, or 12/13.

On a 12-sided dice with 11 possible outcomes,

Ernie rolls a non-12th-number (1, 2, 3, etc.).

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The polygon with 128.57° as every interior angle is a septagon.

If the interior angle = 128. 57°

Using ( n-2) × 180 = sum of interior angles

Let's say n= 7

We have that,

(7-2) × 180 = 900

Let's find out the polygon

= 7 × 128.57

= 900

A polygon with seven sides is a septagon

Thus, the polygon with 128.57° as every interior angle is a septagon.

Learn more about polygons here:

https://brainly.com/question/1592456

#SPJ1

Answer:

B) 6

Step-by-step explanation:

Let the number be x

Product of 6 and square of number plue 15 : (6x²) + 15

Coefficient of x² = 6

The only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Inconsistent System

For a  system of equations to have no real solution, the lines of the equations must be parallel to each other.

Consistent System

1. Dependent Consistent System

For a system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.

2. Independent Consistent System

For a system of equations to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.

As discussed above the Dependent consistent system has infinitely many solutions as their line are coinciding, therefore, the only solution that is true about the dependent system of equations is "There are infinitely many solutions".

Learn more about the System of equations:

https://brainly.com/question/12895249

#SPJ1

Answer:

2.5

Step-by-step explanation:

Given expression:

\(6 \times \left(\dfrac{2}{3} \div 2\right)+0.5\)

Following the order of operations (PEDMAS), carry out the calculation inside the parentheses first.

When dividing a fraction by a whole number, first covert the whole number into a fraction:

\(\implies 6 \times \left(\dfrac{2}{3} \div \dfrac{2}{1}\right)+0.5\)

When dividing fractions, flip the second fraction (swap the numerator and denominator), then multiply:

\(\implies 6 \times \left(\dfrac{2}{3} \times \dfrac{1}{2}\right)+0.5\)

\(\implies 6 \times \left(\dfrac{2 \times 1}{3\times2}\right)+0.5\)

\(\implies 6 \times \left(\dfrac{2}{6}\right)+0.5\)

\(\implies 6 \times \dfrac{2}{6}+0.5\)

Now carry out the multiplication:

\(\implies \dfrac{6 \times2}{6}+0.5\)

\(\implies \dfrac{\diagup\!\!\!\!6 \times2}{\diagup\!\!\!\!6}+0.5\)

\(\implies 2+0.5\)

Finally carry out the addition:

\(\implies 2.5\)

2.5

6*(2/3)/2 + 0.5

6*1/3 + 0.5

2 + 0.5

=2.5

Step-by-step explanation:

Just multiply the two dimensions to get m^2  area

7.2 m * 11 m = 79.2 m^2

Answer:

It seems like there is a mistake in the variable provided. The variable mentioned is "Gender" but the data provided is about "Age" and "f" (frequency). Assuming that "f" is the frequency of participants at each age, here are the answers to your questions:

For the variable "f", the most appropriate measure of central tendency would be the mode, which represents the most frequently occurring value. For the variable "Age", the most appropriate measure of central tendency would be the median, as it is less affected by outliers than the mean.

Mode = 8; Median = 11; Mean = 10.11 (rounded to two decimal places)

Range = 15 - 7 = 8; Variance = 8.99 (rounded to two decimal places); Standard deviation = 2.99 (rounded to two decimal places)

To calculate the age range that reflects 68% of the sample, we need to find the mean age and the standard deviation. The mean age is 10.11, and the standard deviation is 2.99. 68% of the data falls within one standard deviation of the mean. Using the empirical rule, we can say that the ages of participants that reflect 68% of the sample are between (10.11 - 2.99) and (10.11 + 2.99), which is between 7.12 and 13.10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the variable Gender is not given in the data, we cannot compute any measure of central tendency for it. For the variable Age, the most appropriate measure of central tendency would be the mode, since all the observations have the same value for this variable.

To calculate the mode, median and mean for Age, we can first arrange the data in ascending order of age:

7, 2

8, 2

9, 0

10, 1

11, 1

12, 1

13, 1

14, 1

15, 1

The mode is the most frequently occurring value, which is 1 for all ages. The median is the middle value when the data is arranged in ascending order. Since there are 9 observations, the median is the average of the 5th and 6th values, which are 12 and 13. So, the median is (12+13)/2 = 12.5. The mean is the sum of all the values divided by the number of observations, which is:

(72 + 82 + 90 + 101 + 111 + 121 + 131 + 141 + 15*1) / 9 = 11.44 (rounded to two decimal places)

Therefore, the mode is 1, the median is 12.5 and the mean is 11.44.

To calculate the range, variance and standard deviation for Age, we can use the following formulas (assuming the data is a population):

Range = maximum value - minimum value = 15 - 7 = 8

Mean = 11.44 (computed in step 2)

Variance = Σ(x - μ)^2 / N, where μ is the mean, x is each value, and N is the number of observations. Plugging in the values, we get:

Variance = [(7-11.44)^2 + (8-11.44)^2 + (9-11.44)^2 + (10-11.44)^2 + (11-11.44)^2 + (12-11.44)^2 + (13-11.44)^2 + (14-11.44)^2 + (15-11.44)^2] / 9 = 5.72 (rounded to two decimal places)

Standard deviation = square root of variance = √5.72 = 2.39 (rounded to two decimal places)

Therefore, the range is 8, the variance is 5.72, and the standard deviation is 2.39.

Since the data is approximately normally distributed, we can use the empirical rule to estimate the ages that reflect 68% of the sample. According to the empirical rule, 68% of the data falls within one standard deviation of the mean. So, we can compute the lower and upper limits of this range by subtracting and adding one standard deviation from the mean, respectively:

Lower limit = mean - standard deviation = 11.44 - 2.39 = 9.05 (rounded to two decimal places)

Upper limit = mean + standard deviation = 11.44 + 2.39 = 13.83 (rounded to two decimal places)

Therefore, the ages of participants that reflect 68% of the sample are between 9.05 and 13.83 years old.

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

To learn more about radius of curvature click on,

https://brainly.com/question/31403088

#SPJ1

Answer:

\((-27)^\dfrac{2}{3}\) = 9

Step-by-step explanation:

Given that,

Asn expression : \((-27)^\dfrac{2}{3}\)

We need to evaluate the above expression.

We know that, \((-3)^3=-27\)

So,

\((-27)^\dfrac{2}{3}=(-3)^{3\times \dfrac{2}{3}}\)

or

\(=(-3)^2\\\\=-3\times -3\\\\=9\)

So, the value of \((-27)^\dfrac{2}{3}\) is 9. Hence, the correct option is (b).

The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.

Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.

To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.

Direct method:

Calculate the mean wage (F) for the distribution:

Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10

Mean = 34

Calculate the differences between each wage and the mean wage:

20 - 34 = -14

22 - 34 = -12

27 - 34 = -7

30 - 34 = -4

31 - 34 = -3

32 - 34 = -2

35 - 34 = 1

45 - 34 = 11

40 - 34 = 6

48 - 34 = 14

Square each of the differences:

(-14)² = 196

(-12)² = 144

(-7)² = 49

(-4)² = 16

(-3)² = 9

(-2)² = 4

1² = 1

11² = 121

6² = 36

14² = 196

Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756

Divide the sum of the squared differences by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

√75.6 = 8.739

Shortcut method:

The mean wage (F) for the distribution:

(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34

The sum of the squares of the differences between each wage and the mean wage:

(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756

Divide the sum by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

Standard deviation = √75.6 = 8.739

Therefore,

Read more about standard deviation at: https://brainly.com/question/475676

#SPJ1

Complete question is:

Calculate standard deviation for the following

distribution by direct and shortcut method.

Assume mean as 32.

Serial No. of Workers

1

2

3

4

5

6

7

8

9

10

Wage (F)

20

22

27

30

31

32

35

45

40

48

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

Read more about tangent lines at

https://brainly.com/question/21595470

#SPJ1

The experimental probability that the next spin falls in a black region is given as follows:

0.205 = 20.5%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

205 out of the previous 1000 trials fell in the black region, hence the experimental probability is given as follows:

p = 205/1000

p = 0.205.

p = 20.5%.

The problem asks for the experimental probability that the next spin falls in a black region.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

20 m i think

The average rate of change for the function f(x)= 3^x + 25 using the intervals of x=2 to x=6 is 6.75

The function is given as:

f(x) = 3^x + 25

The interval is given as:

x = 2 to 6

Start by calculating f(2) and f(6)

f(2) = 3^2 + 25 = 34

f(6) = 6^2 + 25 = 61

The average rate of change is then calculated as:

\(m = \frac{f(6) - f(2)}{6 -2}\)

This gives

\(m = \frac{61 - 34}{6 -2}\)

\(m = \frac{27}{4}\)

m = 6.75

Hence, the average rate of change is 6.75

Read more about average rate of change at:

https://brainly.com/question/8728504

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

For more such questions on compounded visit:

https://brainly.com/question/24274034

#SPJ8

A symbols to describe the event that an industry increased in value but was not in the manufacturing sector: X ∩ M'

The correct answer is an option (b)

Let us assume that event A : an industry increased in value

event B: an industry increased in the manufacturing sector

We need to describe the event that an industry increased in value but was not in the manufacturing sector.

We know that the event A but not B represents the sample values/ outcomes which are in set A but not in set B.

It is represented as A ∩ B' which is equal to  A – A ∩ B.

Thus in above case the event that an industry increased in value but was not in the manufacturing sector means  A ∩ B'

Here event A = X and B = M

Therefore, the symbolic form of required event = X ∩ M'

The correct answer is an option (b)

Learn more about the event here:

https://brainly.com/question/17089724

#SPJ4

Find the complete question below.

Answer:

x ≈ 2.5

Step-by-step explanation:

Use tan∅ to solve this problem:

tan23° = x/6

x(tan23°) = x

x = 2.54685

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

x = 21

Step-by-step explanation:

Step 1: Write out equation

-5x - 72 = -12x + 75

Step 2: Add 5x to both sides

-72 = -7x + 75

Step 3: Subtract 75 on both sides

-147 = -7x

Step 4: Divide both sides by -7

21 = x

Step 5: Rewrite

x = 21

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The m’s would all be the same number.Another way of adding the same number to each other would be to multiply that number by the number of times you want to add it to each other.

With m + m + m you are adding it 3 times.

So instead multiply m by 3:

The answer is 3m

Answer:

In the Question the concept used is the algebra

We know that

\( \sf \: x \times x = {x}^{2} \)

and

\( \sf \: x + x = 2x\)

Similarly

\( \sf \: m + m + m = 3m\)

The method is also known as property of addition in algebra

Answer:

C) It will not change

Hope this helps! :)