determine whether the given function is continuous on its domain. if it is not continuous, determine all points of discontinuity (a) f (x)

\(6 + \sqrt{15} \)

Step-by-step explanation:

First simplify any radical. This is only allowed with √12 since it's the only one that can be simplified. √12 is equivalent to 6. Now you have the expression √3(6+√5). You can't simply the remaining 2 radicals. You also can't multiple a radical and a constant. BUT you can combine √3 and √5. You multiple 5 and 3 as that's that it's telling you to do. Thus, leaving you with 6 + √15. Having a radical and a constant, this is the simplest you can go as you can't combine these 2 together.

Answer:

To find the interest earned on a savings account by depositing $9800 for 15 months at 5% simple interest, we can use the formula:

Interest = (Principal x Rate x Time) / 100

Where:

Principal = $9800

Rate = 5%

Time = 15 months

First, we need to convert the time from months to years by dividing 15 by 12:

Time = 15/12 = 1.25 years

Now, we can substitute the values into the formula:

Interest = (9800 x 5 x 1.25) / 100

Interest = $612.50

Therefore, the interest earned on the savings account is $612.50.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

Answer:

7A, 8D

Step-by-step explanation:

The compound interest formula is as followed

\(A = P(1+\frac{r}{n} )^{nt}\\\)

A = accumulated amount

P = principle

r = interest rate

n = compounding

t = time

The accumulated amount is represented by f(x).

The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000

The interest rate is 5%. This needs to be converted into a decimal.

5% = 0.05 = r

The money is compounded annually, thus n = 1.

The time is represented by x. x = t.

thus

\(f(x) = 2000(1+0.05)^{x}\)

After six years, you simply find f(6), or substitute 6 into x.

f(6) = 2000(1.05)^6 = $2,680.19

Answer:

\(tan\)(θ) \(=\frac{\sqrt{3} }{3}\)

Explanation:

Tangent trigonometric ratio is defined as the quotient of the opposite leg divided by the adjacent leg of an angle in a right triangle.

In a unit circle, the length of the opposite leg is the y-coordinate and the length of the adjacent leg is the x-coordinate.

As per the description the radius goes to point:

\((\frac{\sqrt{3} }{2} ,\frac{1}{2})\)

Thus, the tangent is:

\(tan\)(θ) \(=y/x=(\frac{1}{2} )/(\frac{\sqrt{3} }{2}) =\frac{\sqrt{3} }{3}\)

Answer:

so then A edge 23'

Step-by-step explanation:

Answer:

what is harry unpaid balance

0$74.89

Answer:

x = 960

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large triangle )² = ( part of hypotenuse below it) × ( whole hypotenuse), so

x² = 576 × (576 + 1024) = 576 × 1600 = 921600 ( take square root of both sides )

x = \(\sqrt{921600}\) = 960

Answer:

453.592 grams or 454 grams if you round up

Answer:

1 pound = 454 grams

Step-by-step explanation:

Multiply 454 into the value.

The average number of credit hours per semester for all students at the local college is 9.2.

It is given that,

at the local college a study sound that students earned an average of 9.2 credit hours per semester.

⇒ x = 9.2 credit hours per semester

Therefore by the central limit theorem,

x = μ  = 9.2 credit hours per semester

The central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Therefore the average number is 9.2 credit hours per semester for all students at the local college.

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The consecutive odd numbers are 7, 9, and 11. The three consecutive odd numbers that satisfy the given condition are -5, -3, and -1.

Let's assume the first odd number is x. Since the numbers are consecutive odd numbers, the second odd number would be (x + 2) and the third odd number would be (x + 4).

According to the given information, eight times the third number plus twice the first number is equal to six times the second number. Mathematically, we can represent this as:

8(x + 4) + 2x = 6(x + 2)

Simplifying the equation:

8x + 32 + 2x = 6x + 12

Combining like terms:

10x + 32 = 6x + 12

Subtracting 6x from both sides:

4x + 32 = 12

Subtracting 32 from both sides:

4x = -20

Dividing both sides by 4:

x = -5

Now that we have the value of the first odd number, we can find the consecutive odd numbers:

The first odd number is -5.

The second odd number is -5 + 2 = -3.

The third odd number is -5 + 4 = -1.

Therefore, the three consecutive odd numbers that satisfy the given condition are -5, -3, and -1.

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Answer:

3

Step-by-step explanation:

15.839 rounded to the nearest hundredths place would be 15.83.

Answer:

4

Step-by-step explanation:

If rounded to the nearest hundredth of a second, you would get 15.84, as you round up if the last number is 5 or above.

The values asked in the question are clearly mentioned in the table uploaded in the answer. Percentage Workers that spend more than 10 minutes a day is 25%.

a. A value's frequency is how frequently it appears in the data collection.

b. The frequency is divided by the total frequency to determine the relative frequency.

c. The frequency multiplied by the frequency of the preceding classes is the cumulative frequency.

d. The cumulative relative frequency is calculated by dividing the total frequency by the cumulative frequency.

e. Using the cumulative frequencies, create the histogram.

Each bar's upper border and the upper bounds of the next bars are connected by an ogive.

Then take the histogram's bars off.

f. The cumulative relative frequency of the range 1–5 is the proportion of office tasks that take 5 minutes or less:

0.6 = 60%

The cumulative relative frequency of the interval 6–10 decreases the proportion of office tasks that take longer than 10 minutes by 1:

1−0.75=0.25=25%

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Complete question: Office workers' productivity is impacted by sorting through spam and unwanted e-mail. An InsightExpress poll tracked office workers to discover how much time is wasted each day on spam and unwanted e-mail (USA Today, November 13, 2003). The minutes spent on this work are shown in the data below as an example.

2 4 8 4

8 1 2 32

12 1 5 7

5 5 3 4

24 19 4 14

Create the following summary of the data: Classes 1–5, 6–10, 11–15, 16–20, and so on) a. A frequency distribution b. A relative frequency distribution c. A frequency distribution that is cumulative. A total relative frequency distribution An ogive. f. What proportion of office workers spend five minutes or less reading spam and unwanted e-mail? How many office workers do this for more than ten minutes each day?

Answer:

1 1/2

Step-by-step explanation:

i did it on a calculator

hope this helps

Answer:

9/22

Step-by-step explanation:

-2 1/4 ÷ (-11/2)

= -9/4 ÷ (-11/2)

= -9/4 × (-2/11)

= 9/22

I hope this helped!

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

Answer:

list 3

Step-by-step explanation:

if you look at list 3 "4.5 feet, 4.25 feet, 4 feet, 3.99 feet, 3.5 feet" you can easily see that it is going from greatest to smallest because 4.5 is larger than 4.25 and 4.25 is larger than 4 and 4 is larger that 3.99 by 0.01 as you see its only 0.01 diffrence but it is still larger

Answer:

List 3

Step-by-step explanation:

I got it right (;

The maximum value of xTAx where the maximum is taken over all x that are the unit eigenvectors of A is option (c) 3.

To find the eigenvectors corresponding to each eigenvalue, we solve the system of linear equations (A - λI)x = 0. For λ₁ = 3, we have:

[0 11 2; 0 0 0; 0 0 0][x₁; x₂; x₃] = [0; 0; 0]

This system has infinitely many solutions, but we can choose a unit vector by setting x₁ = 0, x₂ = 1/√(122), and x₃ = -11/√(122). Similarly, for λ₂ and λ₃, we get:

x₂ = [1/√(34); -3/√(34); 0] and x₃ = [1/√(34); 3/√(34); 0]

To maximize this expression subject to the condition |c₁|² + |c₂|² + |c₃|² = 1, we can use the method of Lagrange multipliers. Let f(c₁, c₂, c₃) = c₁²λ₁ + c₂²λ₂ + c₃²λ₃ and g(c₁, c₂, c₃) = |c₁|² + |c₂|² + |c₃|² - 1. Then the critical points of f subject to the constraint g = 0 satisfy the equations:

∂f/∂c₁ = 2c₁λ₁ = λ₁c₁

∂f/∂c₂ = 2c₂λ₂ = λ₂c₂

∂f/∂c₃ = 2c₃λ₃ = λ₃c₃

and

∂g/∂c₁ = 2|c₁|sign(c₁) = 2c₁/|c₁| = 2c₁

∂g/∂c₂ = 2|c₂|sign(c₂) = 2c₂/|c₂| = 2c₂

∂g/∂c₃ = 2|c₃|sign(c₃) = 2c₃/|c₃| = 2c₃

where sign(c) is the sign function of c, which is 1 if c > 0, -1 if c < 0, and 0 if c = 0.

Solving these equations, we get:

λ₁c₁ = 2c₁, λ₂c₂ = 2c₂, λ₃c₃ = 2c₄, |c₁|² + |c₂|² + |c₃|² = 1

Since λ₁ = 3, λ₂ > 3, and λ₃ < 3, the maximum value of xTAx is attained when c₁ = 1 and c₂ = c₃ = 0, which corresponds to the unit eigenvector x1 = [0; 1/√(122); -11/√(122)]. Therefore, the maximum value of xTAx is:

x₁TAx₁ = 3(1)² + λ₂(0)² + λ₃(0)² = 3

Therefore, the correct answer to the problem is (c) 3.

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The axis of symmetry is the one in option D, x = 2-

For a quadratic equation whose vertex is (h, k), the axis of symmetry is:

x = h

Here we have the quadratic equation:

y = −3(x − 2)² +1

We can see that the vertex is (2, 1) because the equation is in vertex form, and thus, we can conclude that the axis of symmetry of the equation is:

x = 2

So the correct option is D.

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The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.

A fraction is a mathematical expression that represents a part or a proportion of a whole.

Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.

Now, let's consider the area of the circle. The formula for the area of a circle is

=>  A=πr².

Therefore, the area of the circle is πr².

The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is

=> (2r)²=4r²,

and the area of the inner square is

=> (r√2)²=2r².

Hence, the area between the two squares is

=> 4r²−2r²=2r².

The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is

=> πr²−2r²=(π−2)r².

Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,

ratio = (π - 2)r² / 2r

We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,

ratio = (π - 2) / 2

This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.

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Solution

The population of a city is modeled by the function

where y is the population of the city after t years starting in the year 2000

In what year will the population be 5000

Therefore in 32 years time the population will be 5000

Answer:

error= 0.1/2, 0.05

4.8 + 0.05 = 4.85

6.3 + 0.05 = 6.35

4.85 x 6.35 = 30.7975 cm (when rounded, gives 30.80 cm).

Step-by-step explanation:

\(\Large\underline{\rm Solution :- }\)

According to the Question ,

\(\implies Volume = \pi r^2 h \)

And ,

Therefore ,

\(\implies Volume = \pi r^2h \\\\\implies Volume = \pi \times (2x + 4)^2 \times (-3x ) \\\\\implies Volume = \pi ( 4x^2 + 16x + 16 ) (-3x) \\\\\implies \underline{\boxed{Volume = \pi ( -12x^3 - 48x - 48 ) }}\)

The discounted price of a pizza will be $1.8.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The pizza shop offers a 15 percent discount for veterans and senior citizens.

And, The price of a pizza = $12

Now,

Since, The price of a pizza = $12

And, The pizza shop offers a 15 percent discount for veterans and senior citizens.

Hence, The discounted price of pizza = 15% of $12

                                                          = 15 x 12 / 100

                                                          = $1.8

Thus, The discounted price of a pizza will be $1.8.

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Answer:

You can subtract the discount percent from 100% and then multiply that by the original price.

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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C, x is greater than or equal to 2

Step-by-step explanation:

Both equations have X equaling to 2

Answer:

\((x+y+z+1 {)}^{2} \)

Step-by-step explanation:

\((x+y+z {)}^{2} +2(x+y+z)+1\)

\((x+y+z+1 {)}^{2} \)

Here is your answer hope this helps you.

Answer:

918

Step-by-step explanation:

Answer:

Here a pic on how

Hope that help now <3

Answer:

8,000 words

Step-by-step explanation:

If a typewriter types 750 words per hour and she types 8 hours a day she would write 8,000 words a day because 750 x 8 = 8,000.

Answer:

a = 0

b = 5

y = 0

Step-by-step explanation:

Answer: x=0

Step-by-step explanation:

x in (-oo:+oo)

((15*x)/5)*x = 0

3*x^2 = 0 // : 3

x^2 = 0

x = 0

x = 0

The sum of the first 30 consecutive whole numbers is 465.

To find the sum of the first 30 consecutive whole numbers, we can use the formula for the sum of an arithmetic series. In this case, the first term is 1 and the last term is 30. Plugging these values into the formula, we get:

Sum = (30/2)(1 + 30) = 15(31) = 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

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The sum of the first 30 consecutive whole numbers is 465.

The consecutive whole numbers are 1, 2, 3, 4, 5, 6, 7,.....,30.

The sum of first n consecutive numbers is Sₙ=n/2(2a+(n-1)d)

Here, from the given sequence n=30, a=1 and d=1

Now, S₃₀= 30/2 (2×1+(30-1)1)

= 15 (2+29)

= 15×31

= 465

Therefore, the sum of the first 30 consecutive whole numbers is 465.

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