22. The Department of Mathematics offers two different 3-level elective courses,namely,E1 and E2. There are 120 registered for E2. and 6 students registered for both courses, while 48 students didnt register for any of these students currently enrolled in the deparment and are eligible to register for the elective courses,such that 30 students courses.Estimato the probability of registering for only E1 course. A0.20 B0.25 C0.35 00.40

Answer:

-2 and 1/4

Step-by-step explanation:

1/4 is equal to 0.25

2/5 is equal to 0.40

Because it is negative, 1/4 is considered greater.

a. To calculate a 95% confidence interval for b0, you need the necessary statistical information and data from Exercise 11.7.

b. The interpretation of H0: b0 = 0 for the problem in Exercise 11.7 needs to be explained.

c. You need to test the hypotheses H0: b0 = 0 versus Ha: b0 ≠ 0.

d. The p-value of the test of H0: b0 = 0 needs to be determined.

a. To calculate a 95% confidence interval for b0, you would need to refer to the Minitab output for the data provided in Exercise 11.7. The confidence interval would give you a range of values within which the true value of b0 is likely to fall with 95% confidence.

b. The interpretation of the null hypothesis H0: b0 = 0 in the context of Exercise 11.7 would suggest that there is no significant relationship between the presence of pectin and the firmness of canned sweet potatoes. It implies that the coefficient b0, representing the effect of the pectin concentration, is not significantly different from zero.

c. To test the hypotheses H0: b0 = 0 versus Ha: b0 ≠ 0, you would typically perform a hypothesis test using the estimated coefficient b0, the standard error, and the appropriate test statistic (e.g., t-test or z-test). The test would assess whether the coefficient b0 is significantly different from zero, indicating a significant effect of pectin concentration on firmness.

d. The p-value of the test of H0: b0 = 0 would quantify the strength of evidence against the null hypothesis. A small p-value (typically less than the significance level, such as 0.05) would indicate strong evidence to reject the null hypothesis and conclude that there is a significant relationship between pectin concentration and firmness.

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Answer:

Step-by-step explanation:

If 148/4 is 37, he will drive 37 miles in 1 hour.

Answer:

$79.6

Step-by-step explanation:

74.95 + 24.55 = 99.5

99.5(4/5) = 79.6

Jessie and Marvin have different book download services with linear cost functions. Jessie's cost is described by y = 0.45x + 8, while Marvin's costs vary based on the number of books downloaded.

In Jessie's case, the coefficient of x is 0.45, which means that for each additional book downloaded, the cost increases by $0.45.

In Marvin's case, we can observe the differences in cost for each increment of 5 books downloaded: $4.45, $8.90, $13.35, $17.80, and $22.25. The rate of change for Marvin's service is not constant but rather depends on the number of books downloaded. However, we can calculate the average rate of change for the given data points. The  average rate of change is the difference in cost divided by the difference in the number of books, which gives us (22.25 - 4.45) / (25 - 5) = $17.80 / 20 = $0.89.

Comparing the rates of change, we can see that Jessie's service has a greater rate of change ($0.45 per book) compared to Marvin's average rate of change ($0.89 per book). This means that for each additional book downloaded, Jessie's service will cost less compared to Marvin's service.

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Answer:

\(m = (5n/4) -7\)

Step-by-step explanation:

\(n = 4/5(m + 7);m\\(5)n = 4(m + 7)\\5n/4 = m + 7\\m = (5n/4)/7\)

A tangent of two circles is a common internal tangent if the intersection of the tangent and the line segment joining the centers is not empty.

In this case, the lines represent interior tangents

Answer:

12

Step-by-step explanation:

Answer:

C & D because vertical angles have the same measures and thoses angles intersects each other

Step-by-step explanation:

A rescue worker that weighs 60 is hanging from the end of a 125 meter cable whose other end is attached to a helicopter. The total work required is approximately 91,875 Joules.

To calculate the work done, we need to determine the gravitational potential energy of the system. The gravitational potential energy is given by the formula \(PE = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

First, we need to find the mass of the cable. The mass can be calculated by multiplying the cable's mass per unit length (0.5 kg/m) by its length (125 m), giving us a cable mass of 62.5 kg.

Next, we calculate the height by considering the total length of the cable, which is 125 meters. Since the rescue worker weighs 60 kg and is hanging from the end of the cable, the height is equal to the total length of the cable minus the worker's height, which is \(125 - 60 = 65\) meters.

Now we can calculate the gravitational potential energy: \(PE = (m_{\text{worker}} + m_{\text{cable}}) \cdot g \cdot h\). Plugging in the values, we have \(PE = (60 + 62.5) \cdot 9.8 \cdot 65 = 91,875\) Joules.

Therefore, the work done to haul the rescue worker up to the helicopter is approximately 91,875 Joules.

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Answer:

120miles

Step-by-step explanation:

I am not sure exactly I just guessed that since it's 40 miles an hour, it would be 40 x 3 ~ but am not sure... hope it works out!

btw am rlly bad at this :'')

- sry if am wrong

 f(t) = L^(-1){1 / (s^2 + s)} Inverse Laplace transform tables or techniques, determine the time-domain function f(t) that satisfies the given integral equation.

The Laplace transform is a powerful mathematical tool that can be used to solve complex integral equations, like the one you've provided: f(t) + t * ∫(t - τ)f(τ)dτ = t.

To solve this equation using the Laplace transform, follow these steps:

1. Apply the Laplace transform to both sides of the equation. The Laplace transform of f(t) is F(s), and the Laplace transform of t is 1/s^2. The integral equation becomes:

  L{f(t)} + L{t * ∫(t - τ)f(τ)dτ} = L{t}

  F(s) + L{t * ∫(t - τ)f(τ)dτ} = 1/s^2

2. Next, apply the convolution theorem to the integral term. The convolution theorem states that L{f(t) * g(t)} = F(s) * G(s). In this case, f(t) = t and g(t) = (t - τ)f(τ):

  F(s) + L{t} * L{(t - τ)f(τ)} = 1/s^2

3. Now, substitute the known Laplace transforms for t and f(t):

  F(s) + (1/s^2) * F(s) = 1/s^2

4. Combine the terms containing F(s):

  F(s) * (1 + 1/s^2) = 1/s^2

5. Isolate F(s) by dividing both sides of the equation by (1 + 1/s^2):

  F(s) = (1/s^2) / (1 + 1/s^2)

6. Simplify the expression for F(s):

  F(s) = 1 / (s^2 + s)

7. Finally, apply the inverse Laplace transform to F(s) to obtain the solution for f(t):

  f(t) = L^(-1){1 / (s^2 + s)}

Using inverse Laplace transform tables or techniques, you can determine the time-domain function f(t) that satisfies the given integral equation.

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Answer:

x = 75°

y = 105°

Step-by-step explanation:

Angle subtended on the circumference of the circle is half of the angle subtended on the center of the circle.

\( \therefore m\angle SRQ = \frac{1}{2} \times m\angle SOQ\\\\

\therefore x = \frac{1}{2} \times 150\degree \\\\

\red{\bold{\therefore x =75\degree}} \\\)

Quadrilateral PQRS is a cyclic quadrilateral.

\( \therefore m\angle R + m\angle P= 180\degree \\\\

\therefore x + y = 180\degree \\\\

\therefore 75\degree + y = 180\degree \\\\

\therefore y = 180\degree - 75\degree \\\\

\purple {\bold {\therefore y = 105\degree}} \\\)

The given paragraph states that a stationery shop has been running for 10 years near campus in Jakarta.

Students like the asker often visit this store to purchase stationery, markers, rulers, and photocopiers.

The word "been" is a past participle of the verb "be." It is used to show the completion of an action in the past.

In this case, it implies that the stationery shop has been operating for the past 10 years near the campus.

The sentence can be rewritten as follows to make use of the word "been":

"The stationery shop has been providing stationery, markers, rulers, and photocopiers to students near the campus for 10 years."

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Answer: 4 19/36 inches

Step-by-step explanation:
To add the two measurements together, you need to find a common denominator. In this instance, it will be 36.

2 * 4 = 8, 9 * 4 = 36, which means our first measurement turns into 10 8/36

1 * 9 = 9, 4 * 9 = 36, which means our second measurement turns into 5 9/36

Adding these together we get 15 17/36.

Subtract this from 20.

The amount of string that is left is 4 19/36 inches.

Hope this helped!

Answer:

2

steps

7.50+2.50=10.00

10.00+2.50=12.50

so you have 2 cups of food u can buy

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The power series representation for the function f(x) = x sin(4x) can be found as follows:

Firstly, we can find the power series representation of sin(4x) using the formula for the sine function:$

$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

Substitute 4x for x to obtain:$$\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}(4x)^{2n+1}

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+1}$$

Multiplying this power series by x gives:

$$x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function

f(x) = x sin(4x) is:$$f(x)

= x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function f(x) = x sin(4x) is:$$f(x) = x\sin 4x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

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Mallory should adjust her consumption of candy and cookies until the marginal utility per dollar for each good is equal, and she has spent all of her income.

Marginal utility refers to the additional satisfaction or benefit that a person receives from consuming one additional unit of a good or service. It is a concept in economics that is based on the idea that the value of each additional unit of a good or service diminishes as a person consumes more of it.

For example, if you are hungry and you eat a slice of pizza, the first slice of pizza may provide a high level of satisfaction or utility. However, as you continue to eat more slices of pizza, the marginal utility of each additional slice decreases. At some point, you may become full and may even start to feel sick if you continue to eat more pizza.

To determine whether Mallory should consume more cookies, more candy, or leave her consumption unchanged, we need to calculate the marginal utility per dollar for each good. This will tell us which good is providing the most additional utility for each dollar spent.

The marginal utility per dollar for candy is calculated as follows:

MUc/Pc = 12 utils / $1 = 12 utils per dollar

The marginal utility per dollar for cookies is calculated as follows:

MUk/Pk = 6 utils / $0.50 = 12 utils per dollar

Since the marginal utility per dollar for cookies and candy is the same (12 utils per dollar), Mallory should consume either more cookies or more candy, or a combination of both, until the marginal utility per dollar for both goods is equal. This means that the last dollar spent on both goods should provide the same additional utility.

Therefore, to maximize her total utility, Mallory should adjust her consumption of candy and cookies until the marginal utility per dollar for each good is equal, and she has spent all of her income.

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Answer:

2.58

Step-by-step explanation:

3 1/3% = 0.03333

2.5 x 1 + 0.33333 gets us 2.5833

Simplify to 2.58

We add the 1 to 0.33333  to get us the original number.

Hope this Helps!

Answer:

The price of a child ticket in dollars $8.00

Step-by-step explanation:

Rhetorical algebra has never really gone away, as evidenced by a 19th century school notebook that includes a rule for computing the area of a triangle using algebraic operations.


The quote highlights the fact that algebraic methods for solving problems have been around for centuries and continue to be used in modern mathematics. The rule provided demonstrates the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for the area of a triangle. This underscores the enduring importance of algebra in mathematical problem-solving and the relevance of historical approaches to modern mathematical education.

The inclusion of a rule for computing the area of a triangle in a 19th century school notebook is evidence that rhetorical algebra has never really gone away. Rhetorical algebra refers to the use of words and symbols to express mathematical ideas and solve problems, and has been an important tool in mathematics for centuries.

The rule provided for computing the area of a triangle involves several algebraic operations, including addition, subtraction, multiplication, and the square root function. The process involves taking half the sum of the three sides of the triangle, subtracting each side severally, multiplying the half sum and the three remainders continually together, and taking the square root of the last product to arrive at the area of the triangle. This rule demonstrates the use of rhetorical algebra to solve a geometric problem, and underscores the enduring importance of algebra in mathematical problem-solving.

Furthermore, the inclusion of this rule in a 19th century school notebook highlights the relevance of historical approaches to modern mathematical education. While the specific methods used in rhetorical algebra may have evolved over time, the underlying principles and problem-solving strategies remain relevant to this day. As such, the study of rhetorical algebra can provide valuable insights into the development of mathematical thought and the historical context in which mathematical ideas have been developed and applied.

In conclusion, the inclusion of a rule for computing the area of a triangle in a 19th century school notebook serves as a reminder of the enduring importance of rhetorical algebra in mathematical problem-solving. This example highlights the use of algebraic operations such as addition, subtraction, multiplication, and the square root function to arrive at a solution for a geometric problem, and underscores the relevance of historical approaches to modern mathematical education.

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The general form of the quadraic function is f(x) = x² + 12x + 35

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

Vertex, (h, k) = (-6, -1)

(x, y) = (-9, 8)

The equation in vertex form is represented as

y = a(x - h)² + k

So, we have

y = a(x + 6)² - 1

Using the points, we have

a(-9 + 6)² - 1 = 8

9a = 9

a = 1

So, we have

y = (x + 6)² - 1

When expanded, we have

y = x² + 12x + 36 - 1

y = x² + 12x + 35

So, the function is f(x) = x² + 12x + 35

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Answer:

1.6x1

Step-by-step explanation:

Answer:

The equation of the line is;

Explanation:

Given that the line has a slope of;

And passes through the point;

Applying the point-slope equation of straight line;

substituting the given values and solving;

Therefore, the equation of the line is;

Answer:

Step-by-step explanation:

Answer:

20 miles a gallon

Step-by-step explanation:

120 miles/6 gallons = 20 miles/gallons

Solution

Firstly, we will find the third angles of both triangles,

The sum of angles in a triangle is 180 degrees.

If we know that two angles of one triangle are 112° and 39°

Let the third angle be x

The third angle is 29 degrees

And two angles of another triangle are 39° and 29°

Let the third angle be y

The third angle is 112 degrees

Two triangles are similar if their corresponding angles are equal.

Since, their corresponding angles are equal

Hence, then the two triangles must be similar (option d)

Answer:

C

Step-by-step explanation:

A variable is the letter (AKA: Unknown value)

Answer: C. F

Step-by-step explanation: