Which is the exponential form of log8 x = 12?

The rate of change of the side of the square is 1.5 centimeters per second when the area is 3 square centimeters.

Let's denote the side length of the square as s, and the area of the square as A. Then we know that \(A = s^2\). We are given that \(dA/dt = 30 cm^2/s\), which means that the area of the square is increasing at a rate of \(30 cm^2/s\). We want to find ds/dt, the rate of change of the side of the square.

Using the chain rule, we have:

\(dA/dt = d/dt (s^2) = 2s ds/dt\)

Solving for ds/dt, we get:

\(ds/dt = (1/2s) dA/dt\)

When the area is \(3 cm^2\), the side length is \(s = \sqrt{3} cm\). Plugging in dA/dt = 30 cm^2/s and s = sqrt(3) cm, we get:

\(ds/dt = (1/2(\sqrt{3})) (30) = 1.5 cm/s\)

Therefore, the rate of change of the side of the square is 1.5 cm/s when the area is 3 cm^2.

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The point that is 2/5 of the way from A(3,-2) to B(3,13) has the coordinates (3, 2).

To find the point that is 2/5 of the way from A to B, we need to determine how much the x-coordinate and y-coordinate of the point need to change from A to B. Since the x-coordinate of both A and B is 3, the change in x-coordinate is 0. To find the change in y-coordinate, we subtract the y-coordinate of A from the y-coordinate of B:

13 - (-2) = 15

So the change in y-coordinate is 15. To find the point that is 2/5 of the way from A to B, we multiply the change in y-coordinate by 2/5:

15 * 2/5 = 6

This tells us that the point we are looking for needs to be 6 units above A. Since the y-coordinate of A is -2, we add 6 to it to get the y-coordinate of the point:

-2 + 6 = 4

Therefore, the point that is 2/5 of the way from A(3,-2) to B(3,13) has the coordinates (3, 4).

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Wyatt's mix will be more watery compared to Emma's mix.

What does it mean for a mixture to be "more watery"?

The percentage of water in a mix is an essential factor that determines its taste, texture, and consistency. A higher percentage of water in a lemonade mix will make it more watery and less concentrated. In contrast, a lower percentage of water will make the mix less watery and more concentrated. The right balance of water and lemon mix is crucial to make a perfect lemonade.

Calculation for percent of water in the lemon drink mix:

To find the percent of water in the lemonade mixes, we need to divide the amount of water by the total volume of the mix and then multiply by 100.

For Wyatt's mix:

Percent of water = (2 cups water / (2 cups water + 1 cup lemon mix)) x 100

Percent of water = 66.67%

For Emma's mix:

Percent of water = (12 cups water / (12 cups water + 7 cups lemon mix)) x 100

Percent of water = 63.16%

From the calculations, we can see that Wyatt's mix has a higher percentage of water than Emma's mix. Therefore, Emma's mix will be less watery compared to Wyatt's mix.

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Answer:

the answer is 48

Step-by-step explanation:

Answer: k=1

Step-by-step explanation: PQ already equals ST

Answer:

4+8=12

Step-by-step explanation:

BC=4

CE=8

Answer:

x=1

Step-by-step explanation:

x + 7 = 4x + 4

7 = 3x +4

3 = 3x

1 =x

Answer: The blimp is 82% full

Step-by-step explanation:

To find the percentage of the blimp that is filled with gas, we need to divide the volume of the gas that is in the blimp by the total volume of the blimp and then multiply the result by 100%.

The blimp is filled with 28,700 cubic feet of gas, and it has a total volume of 35,000 cubic feet when fully expanded, so the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we need to multiply the result by 100%, so the blimp is 82% full.

Here's the complete solution:

The blimp is filled with 28,700 cubic feet of gas.

The blimp has a total volume of 35,000 cubic feet when fully expanded.

Therefore, the percentage of the blimp that is filled with gas is 28,700 / 35,000 = 0.82.

To express this as a percentage, we multiply the result by 100%, so the blimp is 82% full.

Answer: C has the three equivalent numbers.

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

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Answer:

let the decided no. be x

Now

\( \frac{5}{6} \times \frac{1}{x} = \frac{3}{5} \)

\(5 \times 5 = 3 \times 6x\)

\(x = \frac{25}{18} or1 \frac{7}{18} \)

is a required answer.

when

no. divided by 5/6 equals 5/3

now

\( \frac{5}{6} \times \frac{1}{x} = \frac{5}{3} \)

\(5 \times 3 = 5 \times 6x\)

\(x = \frac{15}{30} \)

\(x = \frac{1}{2} \)is a required answer.

Answer:

90000

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(\sqrt{49}\) = 7

Answer: 7

We should divide 49 by 7, it's only factor that is not 1.

49 ÷ 7 = 7.

So, the answer is 7.

If angle a is 50 degrees and angle c is 28 degrees, the measure of angle b is 102 degrees. Correct option is C.

To find the measure of angle b, we need to use the fact that the sum of the angles in a triangle is always 180 degrees. Therefore, we can set up an equation:

angle a + angle b + angle c = 180 degrees

Substituting the given values:

50 degrees + angle b + 28 degrees = 180 degrees

Simplifying:

angle b = 180 degrees - 50 degrees - 28 degrees

angle b = 102 degrees

Therefore, Option C is correct answer.

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If you wanted to measure satisfaction with this course on a scale from 1, not very satisfied, to 7, very satisfied, you would use an ordinal scale.

An ordinal scale is a type of scale used to measure variables that have an inherent order or ranking, such as the level of satisfaction in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

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If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

Given,

The percentage of people own dogs= 51%

We know,

Probability = Number of favorable outcomes / Total outcomes.

If you choose random guy and probability that guy own a dog = 0.51

Here the probability of having a dog is independent events

Then,

Probability that they both own a dog = Probability of first person own a dog × Probability of second person own a dog

= 0.51×0.51

=0.2601

Hence, If 51% of people owns dogs and you randomly pick two people,  then probability that they both own a dog is 0.2601

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a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer:

The area of the room is 432 square feet

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The scale drawing of the room is 1 inch: 3 feet

→ That means each 1 inch in the drawing represents 3 feet in real

∵ The drawing is 8 inches long by 6 inches wide

∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→  inches  :  feet

→  1            :  3

→  8           :  L

→  6           :  W

→ By using the cross multiplication

∵ 1 × L = 8 × 3

∴ L = 24

∴ The actual length of the room is 24 feet

∵ 1 × W = 6 × 3

∴ W = 18

∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

∵ Area of rectangle = length × width

∴ Area of the room = 24 × 18

∴ Area of the room = 432 feet²

∴ The area of the room is 432 square feet

The SSS Similarity Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are similar. This theorem is also known as the Side-Side-Side Similarity Theorem or the SSS Similarity Postulate.

What is the similarity theorem of triangles?

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle similarity is indicated here by the symbol (~).

SSS or Side-Side-Side Similarity.
If all three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.
From this result, we can conclude that-
∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
Hence, we have described the SSS similarity theorem.

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The Laplace transform of the functions is 6√π/s^4

Given functions:\(f(t) = 2√t-4tf(t)\)

= 4t3/2e-4t

We have to find their Laplace transforms:

Laplace transform of \(f(t) = 2√t-4t\)

Let's apply the formula of Laplace transform to f(t) to obtain

F(s):∫[0, ∞] e^(-st) f(t) dt∫[0, ∞] e^(-st) (2√t-4t) dt

F(s) = 2 ∫[0, ∞] e^(-st) √t dt - 4 ∫[0, ∞] e^(-st) t dt

The Laplace transform of √t is given by:

\(L{√t} = 1/2s^1.5\)

Therefore, we get: F(s) = 2[∫[0, ∞] e^(-st) √t dt] - 4[∫[0, ∞] e^(-st) t dt]

= 2[∫[0, ∞] e^(-st) √t dt] - 4[∫[0, ∞] e^(-st) t d(t)]/s

= 2[1/2s^1.5]/s^(1.5) - 4[3/s^2]/s

= 1/s^1.5 - 12/s^3

Laplace transform of \(f(t) = 4t3/2e-4t\)

Let's apply the formula of Laplace transform to f(t) to obtain F(s):∫[0, ∞] e^(-st) f(t) dt∫[0, ∞] e^(-st) 4t3/2e-4t dt

F(s) = ∫[0, ∞] 4t3/2 e^(-(4+s)t) dt

We know that the Laplace transform of t^n is:\(L{t^n} = n!/s^(n+1)\)

Therefore, we get: F(s) = 4∫[0, ∞] t3/2 e^(-(4+s)t) dt

= 4/s^2 [∫[0, ∞] t3/2 d(e^(-(4+s)t))]

(By integration by parts)= 4/s^2 [-e^(-(4+s)t) * t^3/2 |[0, ∞]] + 6/s^2 ∫[0, ∞] t^1/2 e^(-(4+s)t) dt

= 4/s^2 * 0 + 6/s^2 ∫[0, ∞] t^1/2 e^(-(4+s)t) dt

= 6/s^2 ∫[0, ∞] t^1/2 e^(-(4+s)t) dt

Laplace transform of f(t) = 4t3/2e-4t is 6/s^2 * L{t^1/2}

Where L{t^1/2} is given by: L{t^1/2} = Γ(3/2)/s^(3/2)

= √π/s^(3/2)

Therefore, we get:

F(s) = 6/s^2 * L{t^1/2}= 6/s^2 * √π/s^(3/2)

= 6√π/s^4

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Answer:

A harvest = 11 pound (Approx)

B harvest = 7 pound (Approx)

C harvest = 15 pound (Approx)

D harvest = 15 pound (Approx)

Step-by-step explanation:

Given:

A - 6

B - 4

C - 8

D - 8

Total harvest = 48 pound

Computation:

Total hour = 6+4+8+8

Total hour = 26 hour

A harvest = 48(6/26)

A harvest = 11 pound (Approx)

B harvest = 48(4/26)

B harvest = 7 pound (Approx)

C harvest = 48(6/26)

C harvest = 15 pound (Approx)

D harvest = 48(6/26)

D harvest = 15 pound (Approx)

Answer:

Step-by-step explanation:

We can say with 90% confidence that the proportion of people who leave one space after a period when typing is between 0.800 and 0.866.

To create a confidence interval for the proportion of people who leave one space after a period, we can use the following formula:

\(CI = \hat{p} \pm z*\sqrt{( \hat{p}(1- \hat{p})/n) }\)

where:

\(\hat{p}\)  is the sample proportion (i.e., the proportion of people in the sample who leave one space after a period)

n is the sample size (i.e., the number of people surveyed)

z is the z-score corresponding to the desired confidence level (i.e., 90% confidence level)

First, we need to calculate \(\hat{p}\)  :

\(\hat{p}\)   = 429/515

\(\hat{p}\)   = 0.833

Next, we need to calculate the z-score corresponding to the 90% confidence level. We can use a table or a calculator to find this value.

For a 90% confidence level, the z-score is approximately 1.645.

Now, we can plug in the values we have into the formula and solve for the confidence interval:

CI = 0.833 ± 1.645*√(0.833(1-0.833)/515)

CI = 0.833 ± 0.033

CI = (0.800, 0.866),

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The radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 0.08π square inches

The base and lid are made of plastic and have a radius of R.

The base and lid have a combined surface area of:

πr² + πr² = 2πr² square inches

The total surface area of the oatmeal container is 40 square inches.

The surface area of the cardboard is 16πr square inches and the surface area of the plastic is 2πr² square inches.

Thus, we have the equation:

40 = 16πr + 2πr²

We can solve for R as follows:

16πr + 2πr² = 40

2πr^2 + 16πr - 40 = 0

2πr^2 + 20πr - 4πr - 40 = 0

20r(πr + 2) - 4(πr + 2) = 0

(20r - 4)(πr + 2) = 0

20r - 4 = 0 or πr + 2 = 0

20r = 4 or πr = -2

r = 0.2

Thus, the radius of the oatmeal container is 0.2 inches.

The surface area of the plastic is 2πr² = 2π(0.2)² = 0.08π square inches

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Answer: a

Step-by-step explanation:

Answer:

B) y=2x

Step-by-step explanation:

For the x value, there's 1.5 cups of sugar

For the y value, there's 3 cups of flour

So 1.5x2=3

Hope this helps!

Answer:

m < 3

Step-by-step explanation:

Cookies to decorate = 60

Time < 180 minutes

The inequality

60m < 180

Where,

m = number of minutes

60m < 180

m < 180/60

m < 3

Less than 3 minutes decorating each cookie