Two people at a university start a rumor, and now it is spreading throughout the university. The following function represents the number of people who have heard the rumor after h hours.
R(h)=2 × 10^(0.5h)
How many hours will it take for the rumor to be heard by 2,000 people?
A. 1.5
B. 6
C. 24
D. 12​

Answer: Check below

Step-by-step explanation:

Okay so the Pythagorean Theorem was made by some old guy and the formula is a^2+b^2=c^2. You ALWAYS have to subtract the leg of the triangle when your finding a leg. You squareroot the square of the two legs if your finding the hypotnuse. The Theorem can be used to find any side of the triangle ONLY IF its a right triangle. An adult might use it in real life like when your an architect trying to find how much material you should use to make something thats in the shape of a right triangle.

Ps. Sorry if there's a bunch of grammar mistakes since this is kinda rushed

Answer:

7.a) 5

7.b) 1/2

8. 1

Step-by-step explanation:

7.

a)

Read the points on the graph (0, 0) and (1, 5).

slope = (5 - 0)/(1 - 0) = 5/1 = 5

b)

read the points on the graph (0, 0) and (4, 2).

slope = (2 - 0)/(4 - 0) = 2/4 = 1/2

8.

Points (1, 4) and (5, 8)

slope = (8 - 4)/(5 - 1) = 4/4 = 1

In addition to state, federal, and private financing, Mercyhurst awards scholarships to incoming students based on academic distinction, financial need, and athletic and artistic achievement.

The majority of new freshmen and transfer students are eligible for the following funding opportunities:

A funding opportunity refers to a provision that is made available by either:

Sufficient funding of education by various educational stakeholders is a crucial step in decreasing the burden of education costs on parents and students.

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Answer:

fg(2) = 9 means that f(g(2)) = 9

We know that g(2) = 6

So f(6) = 9 which means that

6a - b = 9 (note 1)

And we know that g(f(1/2)) = 2

And we know that f(1/2) = 1/2(a) - b

So g(1/2(a) - b) = 2

Meaning that 1/2(a) - b + 4 = 2

So 1/2(a) - b = - 2 (note 2)

Using note 1 and 2 we can solve the equation

11/2(a) = 11 so a = 2 and b = 3

Kari's total financial aid each year will be the sum of her scholarships grants and her earnings from work-study is $6,000.

Kari plans to attend a 2-year community college, she will receive $4,500 in scholarships grants each year and she will earn $1,500 each year through a work-study program.

What is Kari's total financial aid each year?

Scholarships and grants are free money that does not have to be repaid, unlike loans. Kari will receive a total of $4,500 in scholarships and grants each year.

Work-study programs provide part-time jobs for students to help cover their college expenses. Kari will earn $1,500 each year through a work-study program.

Thus, Kari's total financial aid each year will be the sum of her scholarships grants and her earnings from work-study:

              $4,500 + $1,500 = $6,000

Therefore, Kari's total financial aid each year is $6,000.

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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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16/25 is 64%

64% of owners prefer walks

Answer:

\(^{}\) in a file

ly/3fcEdSx

bit.\(^{}\)

Step-by-step explanation:

Answer:

x = 12.633, -0.633

Step-by-step explanation:

x^2 -12x + 36 = 44

the underlined part is (x - 6) ^2

(x - 6)^2 = 44

(x - 6) = ± \(\sqrt{44}\)  (both positive and negative)

(x - 6 ) = + 6.6332495807108

x = 12.6332495807108 = 12.633

(x - 6 ) = - 6.6332495807108

x = - 6.6332495807108 + 6

= -0.6332495807108 = -0.633

-1 + 2 - 3 + 4 - 5 + 6 - … - 999 + 1000

= -(1 + 3 + 5 + … + 999) + (2 + 4 + 6 + … + 1000)

= -((2 - 1) + (4 - 1) + (6 - 1) + … + (1000 - 1)) + 2 (1 + 2 + 3 + … + 500)

= -((2 + 4 + 6 + … + 1000) - 500) + 2 (1 + 2 + 3 + … + 500)

= -(2 (1 + 2 + 3 + … + 500) - 500) + 2 (1 + 2 + 3 + … + 500)

Let S = 1 + 2 + 3 + … + 500. Then this sum is equal to

= -(2S - 500) + 2S

= -2S + 500 + 2S

= 500

and multiplying by 4 gives 2000.

Answer:

\(4\times \left(\left(-1+2-3+4-5+6-7+1000\right)\right)\)

\(calculate\: within \: the \:parentheses\)

\(-1+2=1\)

\(=1-3+4-5+6-7+1000\)

\(1-3=-2\)

\(=-2+4-5+6-7+1000\)

\(-2+4=2\)

\(=-3+6-7+1000\)

\(3-7+1000\)

\(=-4+1000\)

\(=996\)

\(Multiply:-\)

\(4\times996\)

\(=3984\)

--------------------------

Hope it helps..

Have a great day!!

Answer: $60

Step-by-step explanation:

From the question, we are told that Venus and Molly are selling candies to raise money for charity and that they buy 80 bags of candy for $0.50 each. This means that the total cost will be:

= 80 × $0.50

= $40

They sell all of them for $1.25 each. This means that the total selling price will be:

= 80 × $1.25

= $100

Profit = Selling price - Cost price

= $100 - $40

= $60

According to the question of theorem, the value of ((131)³⁹ +11.(-11))mod13 is 10.

A theorem is a statement in mathematics that has been proven to be true, usually through a logical argument. Theorems are often used as the basis for further logical reasoning and arguments in mathematics. Theorems can be used to prove other theorems, or to provide a starting point for other mathematical proofs. Examples of famous theorems include the Pythagorean theorem, the fundamental theorem of calculus, and the prime number theorem. Theorems are typically expressed in formal language, and a proof of the theorem usually follows.

This can be solved by using the Chinese Remainder Theorem. We first need to find the remainder when dividing both terms in the equation by 13.

((131)³⁹ +11.(-11))mod13

= (1 + 0) mod 13

= 1 mod 13

= 10

Therefore, the value of ((131)³⁹ +11.(-11))mod13 is 10.

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Answer:

If you take 324 apples from 25, you will have -299 apples.

If you take 25 apples from 324, you will have 299 apples.

Good luck, hope this helped!

The samples of size n = 2 that can be drawn from this population is 28

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

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

substitute the known values in the above equation, so, we have the following representation

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Answer:

A

Step-by-step explanation:

Reflected across the x-axis => but then moved up 4 units

this makes it in a way "flipped"

We see a's coordinates = (-3, 3)

b's coordinates = (-1, 1)

c's coordinates = (-2, 3)

Hope this helps!

Answer:

Choice A

Step-by-step explanation:

Step 1 - reflection across x-axis, affects y-coordinate only

Step 2- 4 units up, affects y-coordinate only

So for the given points we have:

Choice A is correct

The triangles are not similar. Option E

Similar triangles are those triangles that may not be of the same size but a related in the sense of the proportionality in the following ways;

Looking at the two triangles as shown, we can see that they are not related in any of the ways by which we define proportionality of two triangles as such, the triangles are not similar. Option E

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Answer:

\(\begin{array}{| c | c | c |c| c| c | c| c |}

\cline{1-8} x & - 3 & - 2 & - 1 & 0& 1 & 2 & 3\\

\cline{1-8} y & 6 &\textbf{0} &\textbf{ - 4} & - 6 & \textbf{ - 6}& \textbf{ - 4}& \textbf{0} \\

\cline{1-8}

\end{array}\)

Step-by-step explanation:

The 2nd column of the table means that when x= -3, y= 6.

Since this table of values is for the equation of y= x² -x -6,

substitute the given values of x into the equation to find the respective values of y.

3rd column:

y= x² -x -6

When x= -2,

y= (-2)² -(-2) -6

y= 4 +2 -6

y= 0

4th column:

y= x² -x -6

When x= -1,

y= (-1)² -(-1) -6

y= 1 +1 -6

y= -4

6th column:

y= x² -x -6

When x= 1,

y= 1² -1 -6

y= 1 -1 -6

y= -6

7th column:

y= x² -x -6

y= 2² -2 -6

y= 4 -2 -6

y= -4

8th column:

y= x² -x -6

y= 3² -3 -6

y= 9 -3 -6

y= 0

Answer:

y=-2x+2

slope-intercept form --> y=mx+b

m= slope. the slope in the graph is down 2 over 1, -2/1 which is the same as -2.

b = y-intercept. the y-intercept is 2.

Answer:

5/8

To find:

x

Step-by-step explanation:

1/4x = 2/5

by cross multiplying,

4x × 2=5 × 1

8x=5

x=5/8

hope it helps you

Answer:

\(\sf y= \dfrac{1}{2}x-5\)

Explanation:

slope:

\(\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}\)

\(\rightarrow \sf \dfrac{-2--5}{6-0}\)

\(\rightarrow \sf \dfrac{1}{2}\)

equation in slope intercept form:

\(\sf y= \dfrac{1}{2}x-5\)

Answer:

\(y=\frac{1}{2}x-5\)

Step-by-step explanation:

Slope-intercept form: y = mx + b

m = slope

\(m=\frac{y_2-y_1}{x_2-x_1}\)

To find slope, we use points on the line.

Here, I will be suing (-6, -8) and (8, -1)

\(m=\frac{1-(-8)}{8-(-6)} \\\\m=\frac{-1+8}{8+6} \\\\m=\frac{7}{14}\\\\m=\frac{1}{2}\)

\(y=mx+b\)

\(y=\frac{1}{2} x+b\\\)

Now, we use either of our points (-6, -8) OR (8, 1) to find b.

I will be using (8, -1):

\(y=\frac{1}{2}x+b\\\\-1=\frac{1}{2}(8)+b\\\\-1=4+b\\\\-4-4\\\\-5=b\)

\(y=\frac{1}{2}x+b== > y=\frac{1}{2}x-5\)

Check your answer manually: (-6, -8)

\(y=\frac{9}{14}x-\frac{29}{7}\\\\-8=\frac{9}{14}(-6)-\frac{29}{7}\\\\-8=\frac{9}{7}(-3)-\frac{29}{7}\\\\-8=-\frac{27}{7}-\frac{29}{7}\\\\-8=-\frac{56}{7}\\\\-8=-8\)

This statement is correct.

*You can also view the attached graph to verify the answer, meaning that those two points should lie on the same line.*

Hope this helps!

Answer:

Hello! Your answer would be B)B

Step-by-step explanation:

Hope I helped! Brainiest plz!♥ Have a nice morning! Hope you make a 100%! -Amelia

Answer:

Step-by-step explanation:

B) cos a

The equation of this circle in standard form include the following: B. (x - 3)² + (y + 15)² = 3.

In Mathematics and Geometry, the standard form of the equation of a circle can be modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided above, we have the following parameters for the equation of this circle:

By substituting the given parameters, we have:

(x - h)² + (y - k)² = r²

(x - 3)² + (y - (-15))² = √3²

(x - 3)² + (y + 15)² = 3

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Answer:

x = 0

Step-by-step explanation:

y = x + 4 and y = 2x + 4

Let's solve

x + 4 = 2x + 4

-x  + 4 = 4

-x = 0

x = 0

So, there is only one solution is x = 0

A basis for W⊥ is {(2, 6, 1, 0), (0, -2, 0, 1)}. To find a basis for the orthogonal complement W⊥ of the subspace W spanned by w1 and w2, we need to find all vectors that are orthogonal to both w1 and w2.

Let v = (x, y, z, w) be a vector in W⊥. Then we have the following two equations:

w1 · v = 0

w2 · v = 0

where "·" denotes the dot product. Substituting the given vectors and the components of v, we get the following system of linear equations:

x - y + 4z - 2w = 0

y - 3z + w = 0

We can solve this system of equations to find an equation for the plane that contains all vectors orthogonal to W. Adding the two equations, we get:

x - 2z = 0

Solving for x, we get x = 2z. Then substituting into the first equation, we get:

y = 6z - 2w

So a vector v in W⊥ can be written as v = (2z, 6z - 2w, z, w) = z(2, 6, 1, 0) + w(0, -2, 0, 1).

Therefore, a basis for W⊥ is {(2, 6, 1, 0), (0, -2, 0, 1)}.

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(a) The bird watcher's displacement is approximately 3.34 km.

(b) The bird watcher's average velocity is approximately 2.61 km/h in a direction 46.9 degrees north of east.

To determine the bird watcher's displacement, we need to find the straight-line distance from the starting point to the ending point. This can be calculated by treating the east and south components as negative and the north of west component as positive. Using vector addition, we can find the resultant vector which represents the displacement. The magnitude of the resultant vector gives us the displacement, which is approximately 3.34 km.

To find the average velocity, we divide the displacement by the time taken. The direction of the average velocity can be found by calculating the angle with respect to the positive x-axis. By using trigonometry, we can determine the angle to be approximately 46.9 degrees north of east. The magnitude of the average velocity is the displacement divided by the time, giving us approximately 2.61 km/h.

Therefore, the bird watcher's displacement is approximately 3.34 km, and their average velocity is approximately 2.61 km/h in a direction 46.9 degrees north of east.

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Answer:

d(1) = 2

d(n) = d(n-1) + 2

I'm not exactly sure I'm really sorry if it's wrong

Answer:

Inequality Form: x > −8

Interval Notation: (−8, ∞)

Step-by-step explanation:

−2 < x/4

Rewrite so x is on the left side of the i nequality.

x/4 > −2

Multiply both sides of the equation by 4.

x > −2 ⋅ 4

Multiply −2 by 4.

x > −8

The result can be shown in multiple forms.

Inequality Form:

x > −8

Interval Notation:

(−8, ∞)

Answer:

c

Step-by-step explanation:

To find the volume of the solid of revolution formed by rotating the region bounded by the curves f(x) = 5 sin(x), x = π, x = 2π, and y = 0 about the y-axis, we can use the disk method.

The volume can be calculated by integrating the cross-sectional areas of the infinitesimally thin disks formed by revolving the region.

The cross-sectional area of each disk can be represented as A(x) = πr², where r is the distance from the y-axis to the curve f(x).

Since the region is rotated about the y-axis, the radius r is equal to x.

To determine the limits of integration, we need to find the x-values corresponding to the intersection points of the curve and the given boundaries.

The curve f(x) = 5 sin(x) intersects the x-axis at x = 0, π, and 2π. Therefore, the limits of integration are π and 2π.

The volume V of the solid of revolution can be calculated as follows:

V = ∫[π, 2π] A(x) dx

= ∫[π, 2π] πx² dx

Integrating the expression, we get:

V = π[(1/3)x³]∣[π, 2π]

= π[(1/3)(2π)³ - (1/3)(π)³]

= π[(8π³ - π³)/3]

= π(7π³)/3

= (7π⁴)/3

Therefore, the exact value of the volume of the solid of revolution is (7π⁴)/3.

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