The (fictional) numbers of people/week consulting campus health services for a type of flu, N(t), where t = 0 corresponds to the first week of winter quarter, are given in the table: t 0 1 2 3 4 5 6 7 8 9 10 N(t) 20 27 68 158 269 189 174 96 129 70 54 Estimate the number of people who consulted campus health services in the 11 weeks of winter quarter using TRAP(10) rounded to the nearest whole number.

Answer:

-19.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

-9 x 2.2 = -19.8

1

2.2

X -9

-----------

- 19. 8

Answer:

8²+x²=11²

64+x²=121

x²=121-64

x²=57

x=square root 57

(somewhere to 7.5)

Answer:

40,600

hope helpful :)

The series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

To determine whether the series ∑ₙ=₁ to ∞ (n/n² + 6) is convergent or divergent, we can use the Integral Test.

The Integral Test states that if f(x) is a continuous, positive, and decreasing function on the interval [1, ∞) and f(n) = aₙ for all positive integers n, then the series ∑ₙ=₁ to ∞ aₙ and the integral ∫₁ to ∞ f(x) dx either both converge or both diverge.

In this case, let's consider the function f(x) = x/(x² + 6). We can check if it meets the conditions of the Integral Test.

Positivity: The function f(x) = x/(x² + 6) is positive for all x ≥ 1.

Continuity: The function f(x) = x/(x² + 6) is a rational function and is continuous for all x ≥ 1.

Decreasing: To check if the function is decreasing, we can take the derivative and analyze its sign:

f'(x) = (x² + 6 - x(2x))/(x² + 6)² = (6 - x²)/(x² + 6)²

The derivative is negative for all x ≥ 1, which means that f(x) is a decreasing function on the interval [1, ∞).

Since the function f(x) = x/(x² + 6) satisfies the conditions of the Integral Test, we can evaluate the integral to determine if it converges or diverges:

∫₁ to ∞ x/(x² + 6) dx

To evaluate this integral, we can perform a substitution:

Let u = x² + 6, then du = 2x dx

Substituting these values, we have:

(1/2) ∫₁ to ∞ du/u

Taking the integral:

(1/2) ln|u| evaluated from 1 to ∞

= (1/2) ln|∞| - (1/2) ln|1|

= (1/2) (∞) - (1/2) (0)

= ∞

The integral ∫₁ to ∞ x/(x² + 6) dx diverges since it evaluates to ∞.

According to the Integral Test, since the integral diverges, the series ∑ₙ=₁ to ∞ (n/n² + 6) also diverges.

Therefore, the series ∑ₙ=₁ to ∞ (n/n² + 6) is divergent.

To know more about divergent check the below link:

https://brainly.com/question/927980

#SPJ4

Incomplete question:

Use the Integral Test to determine whether the series is convergent or divergent.

∑ₙ=₁ to ∞ = n/n² + 6

Evaluate the following integral ∫₁ to ∞ x/x²+6 . dx

The only option that represents an independent event is: Option C: "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

Independent events are defined as those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other.

Looking at the given options, the only one that represents an independent event is "Spinning a Spinner with eight evenly spaced sections, then spinning it again.".

This is because each event does not depend on another one of the events being described.

Read more about Independent Events at: https://brainly.com/question/22881926

#SPJ1

A self-selecting sample is not likely to be representative. The reason why a self-selecting sample is not likely representative would be discussed below.

A self-selection sample is determined by the individual that are used as data for the research. They are the ones that will determine the inclusion or exclusion of the sample units by either affirming or declining to participate.

The reason self-selecting sample is not likely to be representative is that it is too bias as the individuals that volunteered may not be able to satisfy the goals of the research.

Therefore, a self-selecting sample is not likely to be representative.

Learn more about research here:

https://brainly.com/question/26436072

If you don't know, you can just search it up.

1 liter equals 2.11338 pints, meaning a liter is more.

Debra drinks more milk.

But holy duck?!?!?! That's a WHOLE LOTTA MILK MAN.

9514 1404 393

Answer:

  Debra

Step-by-step explanation:

A pint is about 0.473 liters, so Debra drinks more.

If 300 people were sampled instead of 200, and the confidence level remained the same, it would produce a more accurate result.

Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students. In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

This is because a larger sample size allows for a better representation of the population, providing a more accurate result. Additionally, with a larger sample size, the confidence interval of the sample would be narrower, indicating a higher level of confidence in the accuracy of the result.

To learn more about sampling refer :

https://brainly.com/question/6979326

#SPJ11

Answer:

the answer is B) 1/2, 3.

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to graph both lines and find the point where they intersect. This point will be the solution to the system.

The equation y = -1/2x+2 has a y-intercept of 2 and a slope of -1/2. We can plot this on a graph by starting at the y-intercept (0, 2) and then going down 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The equation y=1/2x-1 has a y-intercept of -1 and a slope of 1/2. We can plot this on the same graph by starting at the y-intercept (0, -1) and then going up 1 unit and to the right 2 units to get another point on the line. We can then draw a straight line through these two points.

The point where these two lines intersect is the solution to the system of equations. From the graph, we can see that this point is approximately (1/2, 3).

the answer is B) 1/2, 3.

To solve the system of linear equations by graphing, we need to plot the lines represented by the equations on the same coordinate plane and find the point of intersection.

|

3 | .

| \

2 | \

| \

1 | . \

| \

0 |_____________

0 1 2 3 4

The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.

Proof by mathematical induction:

Base case: n = 1
1^(3) = ((1(1+1))/(2))^(2)
1 = ((2)/(2))^(2)
1 = 1^(2)
1 = 1
The base case is true.

Inductive step:
Assume that the statement is true for n = k, that is:
1^(3)+2^(3)+3^(3)+...+k^(3) = ((k(k+1))/(2))^(2)

Now we need to prove that the statement is also true for n = k+1:
1^(3)+2^(3)+3^(3)+...+k^(3)+(k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)

Substituting the assumption into the left-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)((k+1)+1))/(2))^(2)

Expanding the right-hand side of the equation:
((k(k+1))/(2))^(2) + (k+1)^(3) = (((k+1)(k+2))/(2))^(2)

Simplifying the equation:
(k^(2)(k+1)^(2))/(2^(2)) + (k+1)^(3) = ((k+1)^(2)(k+2)^(2))/(2^(2))

Multiplying both sides of the equation by 2^(2):
(k^(2)(k+1)^(2)) + 2^(2)(k+1)^(3) = (k+1)^(2)(k+2)^(2)

Expanding the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = (k+1)^(2)(k^(2)+4k+4)

Simplifying the equation:
k^(2)(k+1)^(2) + 2^(2)(k+1)^(3) = k^(2)(k+1)^(2) + 4k(k+1)^(2) + 4(k+1)^(2)

Subtracting k^(2)(k+1)^(2) from both sides of the equation:
2^(2)(k+1)^(3) = 4k(k+1)^(2) + 4(k+1)^(2)

Factoring out (k+1)^(2) from the right-hand side of the equation:
2^(2)(k+1)^(3) = (k+1)^(2)(4k+4)

Simplifying the equation:
2^(2)(k+1)^(3) = 4(k+1)^(2)(k+1)

Dividing both sides of the equation by (k+1)^(2):
2^(2)(k+1) = 4(k+1)

Simplifying the equation:
2^(2)(k+1) = 2^(2)(k+1)

The equation is true for n = k+1, so the statement is true for all n>=1 by mathematical induction.

Learn more about mathematical induction

brainly.com/question/29503103

#SPJ11

The main difference between everyday logic and mathematical logic is that everyday logic is based on general observations and opinions, while mathematical logic is based on precise statements and facts.

Differences:
- Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.
- Everyday logic is often used to make decisions or solve problems in daily life, while mathematical logic is used to solve complex mathematical problems.
- Everyday logic can be subjective and influenced by personal beliefs or experiences, while mathematical logic is objective and follows a set of universally accepted principles.

Similarities:
- Both everyday logic and mathematical logic use reasoning to draw conclusions.
- Both everyday logic and mathematical logic rely on evidence and facts to support their conclusions.
- Both everyday logic and mathematical logic can be used to solve problems and make decisions.

In conclusion, while everyday logic and mathematical logic have some similarities in terms of their use of reasoning and evidence, they differ in their approach and application. Everyday logic is based on common sense and intuition, while mathematical logic is based on strict rules and formulas.

Know more about mathematical logic here:

https://brainly.com/question/28052598

#SPJ11

The function for the surface area of the closed box with a square base is \(S(x) = 4x^2 + 8xh\), where x represents the length of the side of the square base and h represents the height of the box. This function takes into account the areas of the square base and the four rectangular sides.

To determine the surface area function, we need to consider the different components of the box's surface. The box has a square base, so the area of each side of the base is \(x^2\). Since there are four sides to the base, the total area of the base is \(4x^2\). Additionally, there are four identical rectangular sides with dimensions x by h, resulting in a total area of 4xh.

Combining the areas of the base and the four sides, we have the surface area function \(S(x) = 4x^2 + 8xh\), which represents the total surface area of the closed box.

To learn more about the Surface area, visit:

https://brainly.com/question/20771646

#SPJ11

Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

To know more about Inventory visit:

https://brainly.com/question/31146932

#SPJ11

Every eigenvalue of K has absolute value 1, as required. To prove that ||Kv||2 = ||v||2 for all v ∈ R n , we start by writing out the norms in terms of the dot product:

||Kv||2 = (Kv)⋅(Kv) = v⋅(K⊤Kv) (since K is orthogonal, K⊤K = I)

= v⋅v = ||v||2

So, ||Kv||2 = ||v||2 for all v ∈ R n , as required.

Now, let λ be an eigenvalue of K, with eigenvector v. Then we have:

Kv = λv

Taking norms of both sides, we have:

||Kv|| = |λ| ||v||

But, from the previous result, we know that ||Kv|| = ||v||. Therefore:

||v|| = |λ| ||v||

Since ||v|| is nonzero (by definition of an eigenvector), we can cancel it from both sides to get:

1 = |λ|

So, every eigenvalue of K has absolute value 1, as required.

Learn more about eigenvalue

https://brainly.com/question/29749542

#SPJ4

Answer:

a = 60

Step-by-step explanation:

4 + 6 = 10

6 = a/10

10*6 = 60

6 = 60/4+6

Hope this helps!

Answer:

a=60

Step-by-step explanation:

\(6 = \frac{a}{4 + 6} \)

\(6 \times 10= \frac{a}{10} \times 10\)

\(60 = a \: or \: a = 60\)

Hope this helped you out! no problem.

The function that represents the given equation is:

f(x) = 3x + 8

The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.

Adding 12x to both sides, we get 4y = 12x + 32.

To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.

Hence, the function that expresses y as a function of x is:

f(x) = 3x + 8.

Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.

In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.

Therefore, the function that represents the given equation is:

f(x) = 3x + 8

Learn more about function :

https://brainly.com/question/29633660

#SPJ11

Answer: About 43 sq: ft. About 86 sq.

Step-by-step explanation:

The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.

The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.

Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.

Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.

Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.

To know more about the exponential function:

https://brainly.com/question/2456547

#SPJ11

Answer:

\(\textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)\)

Step-by-step explanation:

Given:

Therefore, point P on the segment AB should be 3/7 of the way from point A.

\(x_P=\dfrac{3}{7}(x_B-x_A)+x_A=\dfrac{3}{7}(0-(-11))-11=\dfrac{-44}{7}\)

\(y_P=\dfrac{3}{7}(y_B-y_A)+y_A=\dfrac{3}{7}(-3-1)+1=-\dfrac{5}{7}\)

\(\implies \textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)\)

or P = (-6.3, -0.7) to 1 decimal place

(Please see attached image, where the segment AB has been divided into 7 equal parts.)

The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

To determine whether the medication affects performance, we can perform a one-sample t-test with the following hypotheses:

Null hypothesis: The mean score for the population (μ) is 64.

Alternative hypothesis: The mean score for the population (μ) is less than 64.

We will use a significance level of α = 0.1.

First, we need to compute the t-statistic:

t = (M - μ) / (s / sqrt(n))

t = (58 - 64) / (7 / sqrt(16))

t = -2.29

Next, we need to find the corresponding p-value for this t-value with 15 degrees of freedom (n-1=16-1=15). We can use a t-distribution table or calculator to find that the p-value is 0.017.

Since the p-value (0.017) is less than the significance level (0.1), we reject the null hypothesis and conclude that the medication affects performance.

To measure the size of the treatment effect, we can calculate Cohen's d, which is a standardized measure of effect size. Cohen's d is computed as the difference between the sample mean and population mean, divided by the sample standard deviation:

d = (M - μ) / s

d = (58 - 64) / 7

d = -0.86

The negative sign indicates that the medication decreases performance compared to the population mean. According to Cohen's guidelines, a d-value of -0.86 represents a moderate effect size.

Learn more about population mean here

https://brainly.com/question/19538277

#SPJ4

There are total of 152 students in 5th grade, then the number of pencils altogether will be equal to 2,736 pencils.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total number of students in 5th grade = 152

Amount of pencil each student have = 18

Then, the total number of pencils altogether,

= 152 × 18

= 2,736 pencils.

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ1

Answer:

The answer is 19.

f'(x): Negative Zero Negative Zero Zero Zero Positive Positive

f''(x): Positive Negative Negative Zero Zero Positive Zero

The continuous function f is defined on the closed interval [−5,5] and we know that the graph of f consists of a parabola and two line segments.

Let g be a function such that g′(x)=f(x).The given figure is as follows: the function f is continuous on the closed interval [-5,5].

Where : f'(x)Negative Zero Negative Zero Zero Zero Positive Positive

: f''(x)Positive Negative Negative Zero Zero Positive Zero__

f'(x)  is the slope of f(x) function.

When x < -3, f(x) is decreasing since f'(x) is negative.

When -3 < x < -1, f(x) is constant since f'(x) is zero.

When -1 < x < 2, f(x) is decreasing since f'(x) is negative.

When x > 2, f(x) is increasing since f'(x) is positive. f''(x) tells us how much f'(x) is changing as x increases.

When x < -3, f'(x) is increasing since f''(x) is positive.

When -3 < x < -1, f'(x) is decreasing since f''(x) is negative

Learn more about slope at:

https://brainly.com/question/3493733

#SPJ1

#complete question:

The continuous function f is defined on the closed interval [−5,5]. The graph of f consists of a parabola and two line segments, as shown in the figure above. Let g be a function such that g′(x)=f(x) (a) Fill in the missing entries in the table below to describe the behavior of f′ and f′′. Indicate Positive, Negative, or 0 . Give reasons for your answers.

Answer:

1.) A.) -5/2

2.) B. {(–5, 8), (–5, 2), (–3, 3), (–3, 1), (0, 4), (0, 5), (–5, 7), (–3, 6)}

Step-by-step explanation:

Imma genius

Answer:

\(9/20,\) \(45.4/100,\) \(5/11,\) \(\sqrt{2}\)

Step-by-step explanation:

Convert the values into decimals.

\(5/11=0.45454545454\)

\(\sqrt{2}=1.41421356237\)

\(45.4/100=0.454\)

\(9/20=0.45\)

With decimals, it is especially important to understand place value.

\(0.45454545454, 1.41421356237, 0.454, 0.45\)

Order from smallest to largest.

\(0.45, 0.454, 0.45454545454, 1.41421356237\)

\(9/20,\) \(45.4/100,\) \(5/11,\) \(\sqrt{2}\)

Answer:

k < -1 or k > 11

Step-by-step explanation:

Given quadratic equation:

\(3x^2-x+ k = kx-1\)

First, rearrange the given quadratic equation in standard form ax² + bx + c = 0:

\(\begin{aligned}3x^2-x+ k &= kx-1\\3x^2-x+ k-kx+1&=0-kx+1\\3x^2-x-kx+ k+1&=0\\3x^2-(1+k)x+ (k+1)&=0\end{aligned}\)

\(3x^2-(1+k)x+ (k+1)=0\)

Comparing this with the standard form, the coefficients a, b and c are:

\(\boxed{\begin{minipage}{7 cm}\underline{Discriminant}\\\\$\boxed{b^2-4ac}$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}\)

If the quadratic equation has two distinct roots, its discriminant is positive.

\(b^2-4ac > 0\)

Substitute the values of a, b and c into the discriminant:

\((-1 - k)^2-4(3)(k+1) > 0\)

Simplify:

\((-1 - k)(-1-k)-12(k+1) > 0\)

\(1+2k+k^2-12k-12 > 0\)

\(k^2+2k-12k+1-12 > 0\)

\(k^2-10k-11 > 0\)

Factor the left side of the inequality:

\(k^2+k-11k-11 > 0\)

\(k(k+1)-11(k+1) > 0\)

\((k-11)(k-1) > 0\)

If we graph the quadratic k² - 10k - 11, it is a parabola that opens upwards (since its leading coefficient is positive), and crosses the x-axis at k = -1 and k = 11. Therefore, the curve will be positive (above the x-axis) either side of the x-intercepts, so when k < -1 or k > 11.

Therefore, the range of values of k for which the given quadratic equation has two distinct roots is:

\(\boxed{k < -1 \; \textsf{or} \;k > 11}\)

Answer:

its b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

 Slope = 1.500/2.000 = 0.750

 a-intercept = 0/3 = 0.00000

 b-intercept = 0/-4 = -0.00000

Step-by-step explanation:

Notice that when a = 0 the value of b is 0/-4 so this line "cuts" the b axis at b=-0.00000

 b-intercept = 0/-4  = -0.00000

When b = 0 the value of a is 0/3 Our line therefore "cuts" the a axis at a= 0.00000

 a-intercept = 0/3  =  0.00000

Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is 0.000 and for a=2.000, the value of b is 1.500. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of 1.500 - 0.000 = 1.500 in b. (The change in b is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.500/2.000 =  0.750