At which points is the function​ continuous?

Answer:

a)

[tex] \frac{1}{( - 7)^{4} } [/tex]

Answer:

[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]

Step-by-step explanation:

The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.

According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.

Thus, the negative exponent rule is given as:

[tex]b^-^n=\frac{1}{b^n}[/tex]

Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]

Answer:

5) tan A = 0.42

6) Acute angle is less than 90°

7) Right angle is exactly 90°

8) Obtuse angle is greater than 90° but less than 180°

9) Straight angle is exactly 180°

10) Complementary angles add up to 90°

11) Supplementary angles add up to 180°

Step-by-step explanation:

tan A = opposite / adjacent

= 5/12

= 0.42

The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is

The best measure of center of the data is (a) mean; because the data are close together

From the question, we have the dataset of 10 values

In the given dataset, we can see that there are no outliers present in the dataset

By definition, outliers are extreme values.

Since there are no outliers, it means that the mean is the best measure of center

This is because the mean is affected by the presence of outliers and since no outlier is present, we use the mean

From the list of options, we have the mean value to be 42.536

Hence, the true statement is (a)

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Answer:

30

Step-by-step explanation:

22/33=20/x

cross multiply

22x=33x20

22x=660

x=660/22

x=30

Answer:

Step-by-step explanation:

To calculate the future value of Francine's 401k account in 10 years, considering an annual contribution of $8,000 and an average annual return of 4%, we can use the formula for the future value of a series of regular payments, also known as an annuity.

The formula for the future value of an annuity is:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value

P is the payment amount

r is the interest rate per period

n is the number of periods

In this case:

P = $8,000 (annual contribution)

r = 4% or 0.04 (annual interest rate)

n = 10 (number of years)

Calculating the future value:

FV = $8,000 * [(1 + 0.04)^10 - 1] / 0.04

FV = $8,000 * (1.04^10 - 1) / 0.04

FV ≈ $8,000 * (1.480244 - 1) / 0.04

FV ≈ $8,000 * 0.480244 / 0.04

FV ≈ $8,000 * 12.0061

FV ≈ $96,048.80

Therefore, Francine will have approximately $96,048.80 in her 401k account in 10 years if the account averages a 4% annual return and she contributes $8,000 each year.

Answer:

The consecutive interior angles are supplementary, so we have:

3x + 20 + 2x = 180

5x + 20 = 180

5x = 160, so x = 32

The cost of a single unit is given as follows:

$1.05.

El costo de un plátano es el seguiente:

$1.05.

The cost of a single unit is obtained applying the proportions in the context of the problem.

The cost of 22 units is of $23.10, hence the cost of a single unit is obtained dividing the total cost by the number of units, as follows:

23.1/22 = $1.05.

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Answer:

Step-by-step explanation:

His total expenditure is $100. After that, he sold the CD player for $125. As a result, he earned $25.

Al initially bought a CD player for $100 and then sold it for $125. After that, he bought it back for $150 and later sold it for $175. The question is whether Al made money, lost money, or broke even.

Let's examine the transactions in more detail to determine the answer.

Initially, Al bought the CD player for $100.

Now his total income is $25 and his expenditure remains at $100. Next, he purchased the same CD player again for $150. This adds to his expenditure, which is now $250.

Later, he sold the CD player for $175, which means he earned another $25, bringing his total income to $50 (i.e., $25 from the first sale and $25 from the second sale).

Since Al's total expenditure was $250 and his total income was $50, he lost money. He spent more than he earned.

He sold the CD player twice and earned a total of $50, which is less than what he spent on the CD player, which was $250. Al had a net loss of $200 ($250 - $50). Therefore, he lost money.

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It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:

                          1             2           3            4          5          6

                   1    ( 1 , 1 )   ( 1 , 2 )   ( 1 , 3 )   ( 1 , 4 )   ( 1 , 5 )   ( 1 , 6 )

                   2   ( 2 , 1 )  ( 2, 2 )   ( 2 , 3 )  ( 2 , 4 )  ( 2 , 5 )  ( 2 , 6 )

                   3   ( 3 , 1 )  ( 3 , 2 )  ( 3 , 3 )   ( 3 , 4 )  ( 3 , 5 )  ( 3 , 6 )

                   4   ( 4 , 1 )  ( 4 , 2 )  ( 4 , 3 )   ( 4 , 4 )  ( 4 , 5 )  ( 4 , 6 )

                   5   ( 5 , 1 )  ( 5 , 2 )  ( 5 , 3 )  ( 5 , 4 )  ( 5 , 5 )  ( 5 , 6 )

                   6   ( 6 , 1 )  ( 6 , 2 )  ( 6 , 3 )  ( 6 , 4 )  ( 6 , 5 )  ( 6 , 6 )

- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.

- Now locate and highlight all the even pairs shown in bold.

- The total number of even pairs outcomes are = 9.

- The total possibilities are = 36.

- The probability of getting even pairs as favorable outcome can be expressed as:

                 P ( Even pairs ) = Favorable outcomes / Total outcomes

                 P ( Even pairs ) = 9 / 36

                 P ( Even pairs ) = 1 / 4.

- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4

Answer:

W = V/(LH)

Step-by-step explanation:

All we are doing is isolating W. Since V=LWH, then dividing both sides by LH will put W by itself on the right-hand side, you have V/(LH) = W as your equation

Answer:

i believe by creating radii of equal lengths.

Step-by-step explanation:

it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.

Wish you good luck.

Answer:

Step-by-step explanation:

Step 1.   Determine the dollar amount of the markup

          175 - 79 = 96

Step 2:   Divide the markup Amount by the Cost

          96/79 = 1.215

Step 3:   Multiply by 100 and add the % sign

           1.215 x 100 = 121.5%

Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

a + c= 131

9.60a + 5.20c= 1020

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable c from the first equation:

c= 131 -a

Substituting the expression in the second equation:

9.60a + 5.20×(131 -a)= 1020

Solving:

9.60a + 5.20×131 -5.20a= 1020

9.60a + 681.2 -5.20a= 1020

9.60a -5.20a= 1020 - 681.2

4.4a= 338.8

a= 338.8÷ 4.4

a= 77

In summary, 77 adult tickets were sold that day.

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Answer:

Step-by-step explanation:

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

We have,

The monthly basic salary of the married Chief Secretary of Nepal Government is given as Rs 74,000.

This is the fixed amount he receives as his base salary every month, before any additional allowances or deductions are considered.

Now,

In this case, the dearness allowance of Rs 2,000 is added to the basic salary.

This allowance is provided to compensate for the rising cost of living and is a fixed amount added to the basic salary.

Additionally, he receives 1 month's basic salary as a festival allowance. Since his monthly basic salary is Rs 74,000, his festival allowance would also be Rs 74,000.

Therefore, his total monthly salary can be calculated as follows:

Basic salary + Dearness allowance + Festival allowance

= Rs 74,000 + Rs 2,000 + Rs 74,000

= Rs 1,50,000

Thus,

The Chief Secretary's total monthly salary, including basic salary, dearness allowance, and festival allowance, is Rs 1,50,000.

Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

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Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

Answer:

Step-by-step explanation:

The limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.

To find the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches a certain value, we can simplify the expression and evaluate the limit.

First, let's simplify the expression:

lim (x² - √x⁴ + 3x²)

= lim (4x² - x² - √x⁴)

= lim (3x² - √x⁴)

Now, let's consider the behavior of the expression as x approaches a value.

As x approaches any finite value, the term 3x² will approach a finite value.

For the term √x⁴, as x approaches a finite value, the square root of x⁴ will approach the absolute value of x².

Therefore, the limit becomes:

lim (3x² - √x⁴) = lim (3x² - |x²|)

Next, let's consider the different cases as x approaches positive infinity, negative infinity, and zero.

1. As x approaches positive infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:

lim (3x² - |x²|) = lim (∞ - ∞)

In this case, the limit is indeterminate (∞ - ∞).

2. As x approaches negative infinity, the term 3x² will tend to positive infinity, and |x²| will also tend to positive infinity. Thus, the expression becomes:

lim (3x² - |x²|) = lim (∞ - ∞)

Again, in this case, the limit is indeterminate (∞ - ∞).

3. As x approaches zero, the term 3x² will tend to zero, and |x²| will also tend to zero. Thus, the expression becomes:

lim (3x² - |x²|) = lim (0 - 0) = 0

Therefore, the limit of the expression lim (x² - √x⁴ + 3x²) as x approaches any value is indeterminate (∞ - ∞), except when x approaches zero, where the limit is 0.

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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.

The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).

In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:

g(x) = f(x) + c

In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).

It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).

Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

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Answer: 3

Step-by-step explanation: just 3

Edge 2020

Answer:

it's easy

Step-by-step explanation:

first take a deep breath and then search it

Answer:

2, 4, 10, 20, 50, and 100.

Step-by-step explanation:

Answer: -27

Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.

3, 9, -3, 3, -9, -3, -15, -9, -21, ?

We can start by looking at the differences between consecutive terms in the list:

9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12

Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:

-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21

Therefore, we predict that the most probable next number in the list is -27.

Common ratio of the geometric sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

As we know that,

Common ratio of any G.P. is a constant number that is multiplied by the previous term to obtain the next term.

So, r= (n+1)th term / nth term

where r ⇒ common ratio

          (n+1)th term⇒ succeeding term

          nth term⇒ preceding term

According to the given question, r = (9/8) / (3/4)

                                                       r = (2/3)

We also know,

Any term of a G.P. [nth term] can be obtained by the formula:

Tₙ= a[tex]r^{n-1}[/tex]

where, Tₙ= nth term

            a= first term of G.P.

            r=common ratio

Since last term of the G.P. is given to be 8/81; putting this in the above formula will yield us the total number of terms.

   Tₙ= a[tex]r^{n-1}[/tex]

⇒ (8/81) = (9/8) x ([tex]2/3^{n-1}[/tex])

⇒ (64/729)= ([tex]2/3^{n-1}[/tex])

⇒[tex](2/3)^{6}[/tex] = ([tex]2/3^{n-1}[/tex])

⇒ n-1 = 6

⇒ n = 7

∴ The total number of terms in G.P. is 7.

Therefore, Common ratio of the sequence 9/8, 3/4, 1/2,...,8/81 is 2/3 and the number of all terms in this sequence is 7.

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The Common Ratio for this geometric sequence is 2/3 and the total number of terms in the sequence is 6.

The given mathematical sequence appears to be a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the Common Ratio. In a geometric sequence, you can find the Common Ratio by dividing any term by the preceding term.  

So in this case, the second term (3/4) divided by the first term (9/8) equals 2/3. Therefore, the Common Ratio for this geometric sequence is 2/3.

To find the total number of terms in this sequence we use the formula for the nth term of a geometric sequence: a*n = a*r^(n-1), where a is the first term, r is the common ratio, and n is the number of terms. This gives us: 8/81 = (9/8)*(2/3)^(n-1). Solving this for n gives us n = 6. Therefore, the total number of terms in this sequence is 6.

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