Graph the line that passes through the points (2, 1) and (4, 4) and determine the equation of the line.

Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

Rika

Step-by-step explanation:

The side opposite the 30° angle is longer than the side opposite the 60° angle.

Answer:

Step-by-step explanation:

Given expression:

Solving for p:

Answer:

Step-by-step explanation:

here you go mate

step 1

- 10p + 3(8 + 8p) = -6(p - 4)  equation

step 2

- 10p + 3(8 + 8p) = -6(p - 4)  simplify by distributing

14p+24=-6p+24

step 3

14p+24=-6p+24  subtract 24 from each sides

20p=0

step 4

20p/20=0/20  divide both sides by 20

answer

p=0

The true statements about the function are; vertex of the function is at (1,-25)

Given Part of the graph of the function f(x) = (x + 4)(x-6)

We will convert to vertex form

the vertex of the function is: (1,-25)

We choose a. The vertex of the function is at (1,-25)

Since graph is increasing only on the interval -4< x < 6.

Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.

therefore the graph is increasing in the domain (1, +∞)

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Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

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There is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

To determine if there is sufficient evidence to substantiate the publisher's claim, we need to conduct a hypothesis test.

Let's assume the null hypothesis is that the proportion of readers who own a personal computer is equal to 0.32.

The alternative hypothesis is that the proportion is greater than 0.32.

We can use a one-tailed z-test for proportions to test the hypothesis.

At the 0.05 level of significance, the critical z-value for a one-tailed test is 1.645.

If our calculated z-value is greater than 1.645, we reject the null hypothesis and conclude that there is sufficient evidence to support the publisher's claim.

Assuming we take a random sample of readers and find that 350 out of 1000 readers own a personal computer, the calculated z-value can be computed as:

\(z = (p - P) / \sqrt( P(1-P) / n )\)

where

p = sample proportion = 350/1000 = 0.35

P = hypothesized proportion = 0.32

n = sample size = 1000

z = (0.35 - 0.32) / sqrt( 0.32 * 0.68 / 1000 )

z = 1.42

Since the calculated z-value (1.42) is less than the critical z-value (1.645), we fail to reject the null hypothesis.

Therefore, there is insufficient evidence to substantiate the publisher's claim at the 0.05 level of significance.

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Answer:

I hope this helps!

Step-by-step explanation:

Hope it will help you...

Answer:

Step-by-step explanation:

y-2=6x+6

y=6x+8

Answer:

She can travel 7 miles in the taxi.

Step-by-step explanation:

2.75×7=19.25

Answer:

Answer:

Step-by-step explanation:

1.)5000mg

2.)0.875g

3.)15000g

4.)25g

5.)850mg

I hope it's helpful!

Answer:

D. 3/9

Step-by-step explanation:

Attached below is a picture with each fraction illustrated.

The total volume of three cubes is: 64 cubic inches (volume of one cube) x 3 (number of cubes) = 192 cubic inches. So, the total volume of the cubes is 192 cubic inches.

The problem involves calculating the total volume of three cubes that are lined up side by side. Each cube has a side measurement of 4 inches, which means that the volume of each cube can be calculated by multiplying the length, width, and height. To calculate the total volume of all three cubes, we need to add the individual volumes of each cube together. This can be done by multiplying the volume of one cube by three. Therefore, the total volume of the three cubes can be found by multiplying the length, width, and height of one cube (4 x 4 x 4 = 64) by 3, which gives us a total volume of 192 cubic inches.

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The probability that P(X1 < X2 < X3) is 1/8.

We can solve this problem using the fact that if X1, X2, X3 are independent exponential random variables with the same rate parameter λ, then the joint density function of the three variables is given by:

f(x1, x2, x3) = λ^3 e^(-λ(x1+x2+x3))

We want to find the probability that X1 < X2 < X3. We can express this event as the intersection of the following three events:

A: X1 < X2

B: X2 < X3

C: X1 < X3

Using the joint density function above, we can compute the probability of each of these events using integration. For example, the probability of A is:

P(X1 < X2) = ∫∫ f(x1, x2, x3) dx1 dx2 dx3

= ∫∫ λ^3 e^(-λ(x1+x2+x3)) dx1 dx2 dx3 (integration over the region where x1 < x2)

= ∫ 0^∞ ∫ x1^∞ λ^3 e^(-λ(x1+x2+x3)) dx2 dx3 dx1

= ∫ 0^∞ λ^2 e^(-2λx1) dx1 (integration by substitution)

= 1/2

Similarly, we can compute the probability of B and C as:

P(X2 < X3) = 1/2

P(X1 < X3) = 1/2

Note that these probabilities are equal because the three exponential random variables are identically distributed.

Now, to compute the probability of the intersection of these events, we can use the multiplication rule:

P(X1 < X2 < X3) = P(A ∩ B ∩ C) = P(A)P(B|A)P(C|A∩B)

Since A, B, and C are independent, we have:

P(B|A) = P(B) = 1/2

P(C|A∩B) = P(C) = 1/2

Therefore:

P(X1 < X2 < X3) = (1/2)(1/2)(1/2) = 1/8

Thus, the probability that X1 < X2 < X3 is 1/8.

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The b-coordinate vector for 2 − 5t 4t^2 is:

[−11 34 −12]

To find the change-of-coordinates matrix from basis b to the standard basis c, we need to express each vector in b in terms of the vectors in c, and then use those coefficients to form the matrix.

Let's first express b in terms of c. We want to find constants a, b, and c such that:

1 − 3t t^2 = a(1) + b(t) + c(t^2)

2 − 5t 3t^2 = a(0) + b(1) + c(t^2)

2 − 3t 6t^2 = a(0) + b(0) + c(1)

From the third equation, we can see that c = 6t^2. Substituting into the first equation and solving for a and b, we get:

1 − 3t t^2 = a(1) + b(t) + 6t^2(t^2)

1 − 3t t^2 = a + (b + 6)t^2

a = 1

b = −3

Substituting c = 6t^2, a = 1, and b = −3 into the second equation, we get:

2 − 5t 3t^2 = −3t + 6t^2(t^2)

2 − 5t 3t^2 = 6t^4 − 3t

change-of-coordinates matrix from b to c is:

[1 −3 0]

[0 6 −3]

[0 0 6]

To find the b-coordinate vector for 2 − 5t 4t^2, we need to express this vector in terms of the basis vectors in b:

2 − 5t 4t^2 = a(1 − 3t t^2) + b(2 − 5t 3t^2) + c(2 − 3t 6t^2)

Substituting the values we found for a, b, and c, we get:

2 − 5t 4t^2 = 1(1 − 3t t^2) − 2(2 − 5t 3t^2) + 4(2 − 3t 6t^2)

Simplifying, we get:

2 − 5t 4t^2 = −12t^2 + 34t − 11

So the b-coordinate vector for 2 − 5t 4t^2 is:

[−11 34 −12]

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Answer: -4

Step-by-step explanation:reverse the steps

3(x-7)= -9

3(x-7)/3= -9/3

x-7= -3

x= -3+7

x= -4

Answer:

so The answer would be the last one, I did the math, difficult stuff here gem lol, i almost got stumped O.O

Step-by-step explanation:

the answer that you have chosen was wrong  but the answer that the upper number that has to be divided by x+6 leaving only 1 answer left that involves addition in the denomonatior

The statements that must be true are (i) f is 1-to-1 (injective) and (iii) if y is a value between f(a) and f(b) for some a, b in I, then y = f(c) for some c in I. However, statement (ii) f'(2) > 0 for all x is not necessarily true.

The first statement (i) states that f is one-to-one. Since f is strictly increasing, it means that if x and y are distinct points in I, then f(x) and f(y) will also be distinct. This follows from the definition of strictly increasing functions, where if x < y, then f(x) < f(y). Therefore, f is injective or one-to-one.

The third statement (iii) asserts that if y is a value between f(a) and f(b) for some a, b in I, then there exists a point c in I such that y = f(c). This is also true because of the intermediate value theorem for continuous functions. Since f is differentiable, it is also continuous. The intermediate value theorem guarantees that for any value between f(a) and f(b), there exists a point c in the interval [a, b] (which is a subset of I) such that f(c) = y.

However, the second statement (ii) f'(2) > 0 for all x is not necessarily true. The fact that f is strictly increasing does not guarantee that the derivative f'(x) is positive for all x. The derivative measures the rate of change of the function, and while f is increasing, it could have points where the derivative is zero or negative. Therefore, statement (ii) is not necessarily true.

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Answer:

T = 3

Step-by-step explanation:

To find the period, find the distance it takes to complete one cycle.

To calculate the weekday without code, use the formula: w = (day + int(2.6 * \(month_num\) - 0.2 * century - 2 * (cm - 1) + year + year // 4 + cm // 4)) % 7. Convert the numeric weekday value (0-6) to the weekday name (Sunday-Saturday). For example, July 1, 2023, is a Saturday.

Without writing any code, you can perform the following steps to determine the weekday:

1. Determine the modified century (cm):

  - Divide the year by 100 to get the century.

  - If the month is either January or February and the century is divisible by 4, subtract 1 from the century. Otherwise, use the original century.

2. Convert the month name to the corresponding month number:

  - Assign a number to each month: January = 1, February = 2, March = 3, and so on.

3. Calculate the weekday using the formula:

  - Use the formula: w = (day + int(2.6 * \(month_num\) - 0.2 * century - 2 * (cm - 1) + year + year // 4 + cm // 4)) % 7.

  - Here, w is the numeric value for the weekday, ranging from 0 (Sunday) to 6 (Saturday).

4. Convert the weekday number to the weekday name:

  - Assign a name to each weekday: 0 = Sunday, 1 = Monday, 2 = Tuesday, and so on.

For example, let's find the weekday of July 1, 2023:

1. Determine the modified century:

  - Year = 2023, Century = 20, cm = 20 - 1 = 19.

2. Convert the month name to the month number:

  - July corresponds to month number 7.

3. Calculate the weekday using the formula:

  - w = (1 + int(2.6 * 7 - 0.2 * 20 - 2 * (19 - 1) + 2023 + 2023 // 4 + 19 // 4)) % 7

  - w = (1 + int(18.2 - 4 - 36 + 2023 + 505 + 4)) % 7

  - w = (1 + int(2512.2)) % 7

  - w = 1 + 2512 % 7

  - w = 1 + 5

  - w = 6

4. Convert the weekday number to the weekday name:

  - The weekday is Saturday.

Therefore, July 1, 2023, falls on a Saturday.

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1. When t = 0, the position (displacement) of the object can be found by substituting t = 0 into the given equation of motion:d = 3sin(8π(0)) - 2 = 0 - 2 = -2 meters.2. The maximum displacement of the object from its t=0 position can be found by taking the amplitude of the displacement function. Since the function is of the form d = Asin(ωt) - B, where A is the amplitude, ω is the angular frequency and B is the vertical shift, it can be seen that the amplitude in this case is A = 3 meters. So, the maximum displacement is 3 meters.3. The time taken for one oscillation can be found by dividing the period, T, of the oscillation by the number of oscillations in that period. The period of the oscillation is the time taken for one complete cycle of the sine wave, which is 1/8 seconds. Thus, the time taken for one oscillation is:1 oscillation = T/1/8 s = 8T s4. The frequency of the oscillation is the reciprocal of the period, which is f = 1/T. Thus, the frequency is:f = 1/T = 1/(1/8) Hz = 8 Hz.

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

Note that the angles of the triangle whose vertexes are the centers of the circles are  50.48°, 58.99°, 70.53°.

Three circles with radii 4, 5, and 6 from a triangle whose sides are the sum of their radii in pairs.

Thus, the sides of the triangle are

4 + 5, 4 + 6, and 5+6.

⇒ 9,, 10, 11.

To find the interior angles

CosC = a² + b² + c²/ 2ab

Cost C = (9² + 10² -11²) / (2 x9x10)

= 81 + 100 -121/180

= 60/180

= 1/3

C = 70.53°

Similar

Cos A =  (10² + 11² - 9²) / (2 x10x11)

= 100 + 12181 + /180

= 140/220

= 7/11

A = 50.48°

Cos B = 9² + 11² - 10²/ 2x 9 x 11

= 102/198

B = 58.99°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

The answer is "$11".

Step-by-step explanation:

Chloe bought a pull, which costs \(\$24\), and a shirt which costs \(\frac{5}{8}\) times as much as the pullout.

Sweater cost = \(\$24\)

Shirt cost \(= \frac{5}{8} \times 24=15\)    

Therefore, total shirt and sweater costs\(= 24+15=39\).

Then she gave \(\$ 50\) to her officer.

Thus, she got changes \(= 50-39=11\)

therefore, Chloe received a change of 11 dollars if she gave her employer \(\$50\).

The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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Answer:

-55

Step-by-step explanation:

Assuming the opposite of 625 means -625, the equation to solve is \(10x-75=-625\) where x represents the number.

Adding 75 to both sides of the equation:

\(10x=-550\)

Dividing both sides by 10:

\(x=-55\)

Answer: C

Step-by-step explanation:

Median is the middle number out of the distribution. Cancel out the numbers at each end of the distribution until you get the median number. You will get 42 cm for Cityview and 40 cm for Countryside, thus making C correct.

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Answer:

1. C) 3

2. D) -1

3. D) 7^2 - 8*2 - 16

4. B) 75

5. B) 6^2 + (2 - 8)*sqrt(81)

Step-by-step explanation:

1. (10 - (6-4)^2)/2

= (10 - 2^2)/2

= (10 - 4)/2

= 6/2

= 3

2. PEMDAS states that Multiplication is before Subtraction

8 - (5^2-7)/2

= 8 - (25-7)/2

= 8 - 18/2

= 8 - 9

= -1

3. D) 7^2 - (8*2) - 16

= 49 - 16 - 16

= 49 - 32

= 17

4. 3(2 + 3)^2

= 3(5)^2

= 3(25)

= 75

5. 6^2 + (2 - 8)*sqrt(81)

= 36 + (-6*9)

= 36 - 54

= -18

Answer:

corresponding, supplementary, alternate interior, same side interior, vertical, alternate exterior, corresponding, alternate exterior, vertical, and alternate interior

In the figure 10, the pair of angles are alternate interior angles.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

From the given figure,

1) corresponding angles

2) Adjacent angles (Supplementary)

3) Alternate interior angles

4) Allied angles (Same side interior)

5) Vertically opposite angles

6) Alternate exterior angles

7) corresponding angles

8) Alternate exterior angles

9) Vertically opposite angles

10) Alternate interior angles

Therefore, in the figure 10, the pair of angles are alternate interior angles.

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