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65. Solve for in the logarithmic equation 3 log x = 2.
O * = 1,000,000
O * = 150
O * = 56.423
O * = 4.642

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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The equation is 0 + 59 = 17 which can help Aly calculate the number of more toy cars than trucks. which is the correct answer would be an option (C).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Aly has 59 toy cars and 17 toy trucks.

To determine the equation can help Aly calculate number of more toy cars than trucks she has

We have to subtract 17 from both sides and add 0

0 + 59 = 17

0 + 59 - 17 = 42

Therefore, the equation is 0 + 59 = 17 which can help Aly calculate the number of more toy cars than trucks.

Hence, the correct answer would be option (C).

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To find the height of the person, we can set up a proportion using the given information.

Let's denote the height of the person as 'x'.

The proportion can be set up as follows:

(Height of building) / (Shadow of building) = (Height of person) / (Shadow of person)

Plugging in the given values:

100 ft / 25 ft = x / 1.5 ft

To solve for 'x', we can cross multiply:

(100 ft) * (1.5 ft) = (25 ft) * x

150 ft = 25 ft * x

Dividing both sides of the equation by 25 ft:

x = 150 ft / 25 ft

x = 6 ft

Therefore, the person is 6 feet tall.

In conclusion, the height of the person is 6 feet, based on the given proportions and calculations.

The height of the building is 100ft and the building cast a shadow of 25ft.

A person cast a shadow of 25ft so by using the proportion comparison the height of a person is 6ft.

Given that the height of a building is 100ft and the length of its shadow is 25ft. Let's assume that the height of a person is x whose length of the shadow is 1.5ft.

The ratio of the building's height to its shadow length is the same as the person's height to their shadow length.

Therefore, by using the proportion comparison we get,

(Height of building) / (Shadow of the building) = (Height of person) / (Shadow of person)

100/25= x/1.5

4= x/1.5

Multiplying both sides by 1.5 we obtain,

1.5×4= 1.5× (x/1.5)

x =1.5×4

x=6.0

Hence, the height of a person is 6ft if they cast a shadow of 1.5ft.

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Using the formula of circumference of circle, the number of rotations is 1000

To determine the number of rotations the bicycle will make, we need to use the formula of circumference of a circle and then divide the distance covered per rotation by the total length of the road.

circumference of the wheel = 2πr

circumference = 2 * 3.14 * 0.4

circumference = 2.512m

The number of rotations required will be;

Number of rotations = 2512 / 2.512

Number of rotations = 1000

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Answer:

\(3b \geq -22\)

Step-by-step explanation:

Product of of 3 and b is 3b

At least means greater than or equal too.

\(3b \geq -22\)

Answer:

answer: 20

Step-by-step explanation:

To find the area of a parellologram you just have to do base × height are base here is 10 and our height is 2 so 10 × 2 = 20 So 20 is the area! Hope that helps/explains well!

Answer:

A goes to K. C goes to M. B goes to L.

Step-by-step explanation:

:)

To the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

The probability that an earthquake will occur while you are at work can be calculated by dividing the number of hours you are at work by the total number of hours in a year.
Step 1: Calculate the total number of hours in a year:
There are 24 hours in a day, so multiplying 24 by 365 (the number of days in a year) gives us 8,760 hours in a year.
Step 2: Calculate the number of hours you are at work in a year:
Since you work 8 hours per day, multiply 8 by 250 (the number of days you work in a year) to get 2,000 hours.
Step 3: Calculate the probability:
Divide the number of hours you are at work (2,000) by the total number of hours in a year (8,760) and multiply by 100 to convert to a percentage.
Probability = (2,000 / 8,760) * 100 = 22.83%
Therefore, to the nearest percent, the probability that an earthquake will occur while you are at work is approximately 23%.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.201 or 20.1%.

a. Estimation of the probability of being a member of an environmental group:The probability of being a member of an environmental group can be estimated by calculating the fraction of the total number of people surveyed that are members of an environmental group.P(GRNGROUP) = Total number of people in environmental group/ Total number of people surveyed= 119/1113=0.1069The probability of being a member of an environmental group is approximately 0.107 or 10.7%.b. Estimation of the probability of being willing to pay higher prices to protect the environment:The probability of being willing to pay higher prices to protect the environment can be estimated by calculating the fraction of the total number of people surveyed that are very willing to pay higher prices to protect the environment.P(GRNPRICE) = Total number of people who are very willing to pay higher prices/ Total number of people surveyed= 31+88/1113= 0.106The probability of being very willing to pay higher prices to protect the environment is approximately 0.106 or 10.6%.c. Calculation of the probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment, given the variables are independent:In this case, if the variables are independent, then the joint probability can be calculated by multiplying the two probabilities together.P(GRNGROUP and GRNPRICE) = P(GRNGROUP) x P(GRNPRICE)=0.1069 x 0.106=0.011The probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment is approximately 0.011 or 1.1%.d. Estimation of the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment directly using the counts in the table:The probability of a person being a member of an environmental group or very willing to pay higher prices to protect the environment can be estimated by calculating the fraction of the total number of people surveyed that fall into either of these two categories.P(GRNGROUP or GRNPRICE) = (Total number of people in environmental group + Total number of people who are very willing to pay higher prices - Number of people in both categories) / Total number of people surveyed= (119 + 31 + 88)/1113= 0.134The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.134 or 13.4%.e. Estimation of the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment by applying the appropriate probability rule to the estimated probabilities found in (a) and (b):P(GRNGROUP or GRNPRICE) = P(GRNGROUP) + P(GRNPRICE) - P(GRNGROUP and GRNPRICE)= 0.1069 + 0.106 - 0.011= 0.201The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.201 or 20.1%.

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Answer: A: y= 3x + 3

Step-by-step explanation:

The y intercept has to be 3 which is found when x = 0 that eliminates B and C. Then just plug in -1 or 1 into A or D and you will find that plugging in either with get you the y value provided on A.

Answer:

A. If two figures have the same shape, then they are congruent.

The metric designators and trade sizes are for identification purposes only and are not actual dimensions, as pointed out in the note in table 300.1(C).

[Refer The table 300.1(C) below.]

Therefore, the metric designators and trade sizes are for identification purposes only and are not actual dimensions, as pointed out in the note in table 300.1(C).

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The correct question is given below:

The metric designators and trade sizes are for identification purposes only and are not actual dimensions as pointed out in the note to Table?

If each unit costs 105 dollars and Marcle wants to spend a maximum of 1,365 dollars on classes, then she can take up to 13 classes.

To calculate the maximum number of classes Marcle can take, we need to divide the maximum cost she is willing to spend by the cost of each unit. So, we have:

Maximum cost Marcle is willing to spend = $1,365

Cost of each unit = $105

Number of classes Marcle can take = Maximum cost Marcle is willing to spend / Cost of each unit

Number of classes Marcle can take = $1,365 / $105

Number of classes Marcle can take ≈ 12.98

Since Marcle cannot take a fraction of a class, we round down to the nearest whole number to get the maximum number of classes she can take without exceeding her budget. Therefore, Marcle can take up to 13 classes.

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The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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the integral is:∬s(x y z)ds = (4/3 - 24/5 + 2/7 - 2/9) = -6/45

∬s(x y z)ds = ∬r(u,v)(2u v)(u − 2v)(u 3v)dudv

= ∫0^1∫0^2 (4uv^2 - 8uv^3 + u^2v^4 -2u^2v^5)dudv

= (4/3 - 24/5 + 2/7 - 2/9) = -6/45

We can evaluate the integral by first rewriting it in terms of parametric equations.

The surface s is defined parametrically by r(u,v) = (2u v)i (u − 2v)j (u 3v)k for 0 ≤ u ≤ 1, and 0 ≤ v ≤ 2.

Therefore, the integral can be written as ∬s(x y z)ds = ∬r(u,v)(2u v)(u − 2v)(u 3v)dudv.

Next, we can evaluate the integral by using double integrals.

We can evaluate the integral by first evaluating the inner integral with respect to v, and then evaluating the outer integral with respect to u.

The inner integral with respect to v is:

∫0^2 (4uv^2 - 8uv^3 + u^2v^4 -2u^2v^5)dv

= (4/3 - 24/5 + 2/7 - 2/9)

The outer integral with respect to u is:

∫0^1 (4/3 - 24/5 + 2/7 - 2/9)du = (4/3 - 24/5 + 2/7 - 2/9)

Therefore, the integral is:

∬s(x y z)ds = (4/3 - 24/5 + 2/7 - 2/9) = -6/45

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Answer: 46.619 units.

Step-by-step explanation:

To find the length of the spiraling polar curve, we need to use the formula:

L = int_a^b sqrt[r^2 + (dr/d\theta)^2] d\theta

where r is the polar curve, dr/d\theta is its derivative with respect to theta, and a and b are the limits of integration.

In this case, we have:

r = 7 e^{4 \theta}

dr/d\theta = 28 e^{4 \theta}

And the limits of integration are a = 0 and b = 2\pi.

Substituting these into the formula, we get:

L = int_0^(2\pi) sqrt[(7e^{4\theta})^2 + (28e^{4\theta})^2] d\theta

Simplifying this expression using algebra, we get:

L = int_0^(2\pi) 7e^{4\theta} sqrt[1 + 16e^{8\theta}] d\theta

This integral cannot be solved analytically, so we need to use numerical methods to approximate its value. One way to do this is to use a numerical integration technique such as the trapezoidal rule or Simpson's rule.

Using Simpson's rule with a step size of h = \pi/1000, we get:

L \approx 46.619

Therefore, the length of the spiraling polar curve r = 7 e^{4 \theta} from 0 to 2 \pi is approximately 46.619 units.

The wavelength λ1 for gamma rays of frequency f1 = 5.50×1021 Hz is 5.45 × 10-14 m.

To calculate the wavelength λ1 for gamma rays of frequency f1 = 5.50×1021 Hz, we can use the formula:
λ1 = c/f1

where c is the speed of light in a vacuum, which is approximately 3.00 × 108 m/s.
Substituting the values given, we get:

λ1 = 3.00 × 108 m/s / 5.50 × 1021 Hz
λ1 = 5.45 × 10-14 m

Therefore, the wavelength λ1 for gamma rays of frequency f1 = 5.50×1021 Hz is 5.45 × 10-14 m.

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The city circle has a total of 12 points when plotted on a scratch paper.

The city circle with a center at (0, 0) and a radius of 5.5 blocks can be plotted on a scratch paper. To determine the number of points on the city circle, we need to understand that each point on the circle corresponds to a unique pair of coordinates (x, y) that satisfy the equation of a circle.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the city circle is (0, 0), and the radius is 5.5 blocks. Thus, the equation of the city circle is:

x^2 + y^2 = (5.5)^2

To plot the city circle, we can start by drawing a coordinate grid on the scratch paper. Then, using the equation of the circle, we can plot various points on the circle by substituting different values of x and solving for y.

By selecting different values of x such as -5.5, -4, -3, -2, -1, 0, 1, 2, 3, 4, and 5.5, we can calculate the corresponding values of y using the equation of the circle. These points will lie on the circumference of the city circle.

Since the circle is symmetric with respect to both the x-axis and the y-axis, we can reflect the plotted points across these axes to obtain the complete circle. By doing so, we will have a total of 12 unique points on the city circle.

Therefore, the city circle has a total of 12 points when plotted on a scratch paper.

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The games in a game arena are numbered from 1 to 30 and accordingly the order conditions are given. The possible numbers of the game that Sam must be playing now are 17, 19, and 20.

Since Sam earned 4 bands, he must have won 4 sets of 4 games in a row. Each set of 4 games consists of consecutive game numbers.

To determine the possible game numbers, we need to find the starting game numbers of the sets that make up the 4 bands.

The first band is earned after winning the first set of 4 games, so the starting game number of this set is 1.

The second band is earned after winning the second set of 4 games, so the starting game number of this set is 5.

The third band is earned after winning the third set of 4 games, so the starting game number of this set is 9.

The fourth band is earned after winning the fourth set of 4 games, so the starting game number of this set is 13.

Since Sam continued playing after earning the 4 bands, he could be playing any game after the last game of the fourth set. Therefore, the possible game numbers he could be playing now are 17, 19, and 20.

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Answer:

Associative property of addition

Answer:

5750

Step-by-step explanation:

add the 3 populations together, divide by the number of populations (3)

Answer:

I would say A. Yes, there are three numbers and three sections.

Step-by-step explanation:

The spinner that Pamilla drew is a good model because most of the spinners have 3 equal sections, not all.

Answer:

No, the three events are not equally likely to occur.

Step-by-step explanation:

I just had this question in a quiz so I know it's right. But fyi you should've added the table with the results so ppl know it's not equal.

Answer:

the given are not correct the real answer is 15/29 or 0.517...

Step-by-step explanation:

7-58z = -23

-58z = -23 -7

-58z =-30 the negatives will cancel each other out

-58. -58

z = 30/58 divide both by 2

z= 15/29 which can also be equal to 0.517...

Answer:

Step-by-step explanation:

Population density is:

Correct option is A

\(\tt Step-by-step~exlpanation:\)

To find out the answer, we would have to try and divide all the numbers.

\(\tt \frac{34,776}{2}= 17,388\\ YES\)

\(\tt \frac{34,776}{3}= 11,592\\YES\)

\(\tt \frac{34,776}{9}=3,864\\ YES\)

\(\tt \frac{34,776}{6}= 5,796\\YES\)

\(\large\boxed{\tt Our~final~answer:~ALL ~(2,3,9,6)}\)

How to do?

First graph cosine function

Now increase it's frequency by π

Half the amplitude

Answer:

D

Step-by-step explanation: