Given that m-log a, n log b, and k - log(ab), (a) express a, b, and ab as powers of 10; (b) use your knowledge of exponents to discover a relationship among m,n, and k
(c) conclude that log(ab) log a+ log b.

Answer:

x = 30

Step-by-step explanation:

if A||B, then 4x + 2x must equals to 180 (interior angles of 2 parallel lines)

6x = 180

x = 30

The dimensions of the rectangular garden are 8.5 meters and 7.5 meters.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

The diagram is given below.

Given,

Perimeter of a rectangle = 2 (l + w), where l is the length and width.

Length of the rectangle = 4 + 3x

Width of rectangle = x + 6

Perimeter = 32 meters

Substituting,

2 (l + w) = 32

2(4 + 3x + x + 6) = 32

2(4x + 10) = 32

4x + 10 = 16

4x = 6

x = 6 / 4 = 3/2 = 1.5

Length = 4 + 3x = 8.5 meters

Width = x + 6 = 7.5 meters

Hence the length and width of the rectangle are 8.5 meters and 7.5 meters respectively.

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The domain has infinite solutions, and real number can be the answer. And the range is 2.

Answer:

Step-by-step explanation:

\(\sqrt{(6-1)^{2}+(3-5)^{2} }\)=\(\sqrt{29}\)

                               =5.39(correct to nearest hundredth)

Answer: if u looking for x it - 1

Answer:

x=-1

Step-by-step explanation:

30=25-5x

5=-5x

-1=x

This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.

One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.

This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).

Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).

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The complete question is:

A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?

a. Standard Deviation Study

b. Type 1 Study

c. Case-Control Study

d. Non-Blinded Randomized Controlled Trial

e. Single-Blinded Randomized Controlled trial

Given equation is:

let us simplify,

use the formula

The answer is

Answer:

6.35 x 10-5

Step-by-step explanation:

5.15 x 10-4 = 47.5

6.35 x 10.5 = 58.5

therefore 6.35 x 10-5 is greater

There is sufficient evidence for significance level 10%  to conclude students with study skills course have higher exam scores using hypothesis test.

To conduct a hypothesis test,

set up the null and alternative hypotheses and perform the necessary calculations.

Null Hypothesis (H₀),

The study skills course did not have a significant effect on the mean final exam scores. µ = 77.6.

Alternative Hypothesis (Hₐ),

The study skills course had a significant effect on the mean final exam scores. µ > 77.6.

To test this hypothesis, use a one-sample t-test since we have a sample mean and population standard deviation.

Sample mean (X) = 79.5

Population mean (µ) = 77.6

Population standard deviation (σ) = 7.2

Sample size (n) = 36

Significance level (α) = 0.10 (10%)

First, let's calculate the test statistic (t-value),

t

= (X - µ) / (σ / √n)

= (79.5 - 77.6) / (7.2 / √36)

= 1.9 / (7.2 / 6)

= 1.9 / 1

= 1.9

Next, determine the critical t-value from the t-distribution calculator.

Since the alternative hypothesis is one-sided (µ > 77.6), interested in the upper tail of the distribution.

At a significance level of 0.10 with 35 degrees of freedom (n - 1 = 36 - 1 = 35), the critical t-value is approximately 1.310.

Since the calculated t-value (1.9) is greater than the critical t-value (1.310), we have evidence to reject the null hypothesis.

Therefore, using hypothesis test there is sufficient evidence at 10% significance level to conclude that students who took study skills course had higher exam scores.

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The estimated probability is 0.0294

To estimate the probability of getting between 45 and 50 correct answers on the multiple-choice test, we can use the binomial probability formula and a calculator.

The binomial probability formula is given by P(X = k) = (nCk) * p^k * q^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial.

q is the probability of failure (1 - p), and nCk represents the number of combinations.

In this case, n = 160 (number of questions), p = 0.25 (probability of guessing a correct answer), and we want to find P(45 ≤ X ≤ 50), which means the probability of getting between 45 and 50 correct answers.

Using a calculator such as TI-83, TI-83 Plus, or TI-84, we can calculate the individual probabilities for each value of X (45, 46, 47, 48, 49, 50) using the binomial probability formula.

Then, we sum up these probabilities to find the total probability of getting between 45 and 50 correct answers.

By performing the calculations, we find that the estimated probability is 0.0294, rounded to four decimal places.

This means that with random guessing, there is approximately a 2.94% chance of getting between 45 and 50 correct answers on the multiple-choice test.

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The value of 5.37/3 is 1.79.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given term is 5.37 divided by 3,

The mathematical expression for 5.37 divided by 3,

= 5.37/3

= 1.79

The value of 5.37 divided by 3 is 1.79.

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Answer:

Heart sounds

Step-by-step explanation:

a) Using fast modular exponentiation, 4^1045 mod 9 is approximately equal to 7.

b) The statement "If a ≡ b (mod m) then a^2 ≡ b^2 (mod m)." is true.

c) The proof for any non-negative integer n, if the sum of the digits of n is divisible by 9, then n is divisible by 9 is explained in detailed steps below.

a) To compute 4^1045 mod 9 using fast modular exponentiation, we can use the following steps:

Convert the exponent to binary: 1045 = 2^10 + 2^9 + 2^6 + 2^3 + 2^2 + 1 = 10000010001.

Start with the base: 4 mod 9 = 4.

Square the base and take the result modulo 9 repeatedly, skipping the first bit of the binary exponent (since it corresponds to the most significant bit, which is always 1).

Multiply the intermediate results together, taking the product modulo 9.

Here are the steps in detail:

4^1 mod 9 = 4

4^2 mod 9 = 7

4^4 mod 9 = 4

4^8 mod 9 = 1

4^16 mod 9 = 1

4^32 mod 9 = 1

4^64 mod 9 = 1

4^128 mod 9 = 1

4^256 mod 9 = 1

4^512 mod 9 = 1

4^1024 mod 9 = 1

So, 4^1045 mod 9 = (4^1024 * 4^16 * 4^4 * 4^1) mod 9 = (1 * 1 * 4 * 4) mod 9 = 7.

b) The statement is true. If a ≡ b (mod m), then a = b + km for some integer k. Then, a^2 = (b + km)^2 = b^2 + 2bkm + k^2m^2. Since k and m are integers, 2bkm and k^2m^2 are both multiples of m. Therefore, a^2 ≡ b^2 (mod m).

c) To prove that for any non-negative integer n, if the sum of the digits of n is divisible by 9, then n is divisible by 9, we can follow the same idea as in the example:

Let n = d_k 10^k + d_{k-1} 10^{k-1} + ... + d_1 10 + d_0 be the decimal representation of n. Then, the sum of the digits of n is S = d_k + d_{k-1} + ... + d_1 + d_0.

We can express n as follows:

n = (d_k 10^{k-1} + d_{k-1} 10^{k-2} + ... + d_1) 10 + d_0

= (d_k 10^{k-1} + d_{k-1} 10^{k-2} + ... + d_1) 9 + (d_k + d_{k-1} + ... + d_1 + d_0)

The first term on the right-hand side is clearly divisible by 9. Since S is also divisible by 9, the second term is also divisible by 9. Therefore, n is divisible by 9. This holds for any non-negative integer n, so the statement is true.

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\(\cfrac{6}{7}\div \left(-\cfrac{11}{2} \right)\implies \cfrac{6}{7}\cdot \left(-\cfrac{2}{11} \right)\implies -\cfrac{12}{77}\)

Answer:

He scored 14 points per game.

84/6

Step-by-step explanation:

Good luck!

Answer:

14

Step-by-step explanation:

To find the unit rate for the question you have to divide 84 by 6

Answer:

\(\frac{108}{125}\)

Step-by-step explanation:

\(\frac{3}{5}\)*\(\frac{25}{24}\)= \(\frac{72}{125}\)

\(\frac{72}{125}\)÷\(\frac{2}{3}\)=\(\frac{108}{125}\)

Hope this helps you!

Answer:

Hey There!

Let's solve...

We have

\( \angle \: odb = \angle \: cao \\ \\ \angle \: dbo = \angle \: aco \\ \\ \)

Using AA Criterion of Similarity we have

\( \triangle \: obd \: - \triangle \: oac \\ \\ \)

This implies that

\( \frac{od}{ob} = \frac{oa}{oc} \to \frac{6}{3 + 2 } \: or \: \frac{6}{5} = \frac{oa}{oc} \\ \\ \to \: oa = \frac{6}{5} oc \)

Now,

\(ab = ao - bo \\ \\ = \frac{6}{5}oc - bo = \frac{6}{5}(od - oc) \\ - bo \\ \\ = \frac{6}{5}(6 + 4cm) - 5cm \\ \\ = 7cm \)

Note:Every letters should be in capital, i don't have any option here so i can't do.

The sampling method used is systematic sampling.

This is because each 49th student is chosen from the population of 496 students.

In systematic sampling, a starting point is selected randomly, and then each nth item in the populace is selected.

In this case, the start line might also have been randomly chosen, however we do not have information approximately that.

However, when you consider that every 49th pupil is selected, this is a clear indication that methodical sampling has been employed.

This sampling technique is often used in conditions in which the population is huge and it isn't viable to select each single item from the population.

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The perimeter of the triangle is 11x² + 2x - 3.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The perimeter of a triangle is the sum of the whole sides of the triangle.

Therefore, the triangle has the side length 2x² + 3x -5, 5x² - 2x + 3, and 4x²+ x - 1.

Hence,

perimeter of the triangle = 2x² + 3x -5 + 5x² - 2x + 3 + 4x²+ x - 1

combine like terms

perimeter of the triangle = 2x² + 5x² + 4x² + 3x - 2x + x - 5 + 3 - 1

perimeter of the triangle = 11x² + 2x - 3

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The correlation coefficients are expressed on a standard scale that always ranges from -1.00 up to +1.00.

Correlation does not mean equal causation. Just because two variables have a relationship does not necessarily mean that changes in one variable cause changes in the other. Correlations indicate that there is a relationship between variables, but this does not necessarily determine that one variable causes the other to change.

Correlations range from -1.00 to +1.00. The correlation coefficient (expressed as r ) shows the strength and direction of a relationship between two variables. The closer the r value is to +1 or -1, depending on how stronger the linear relationship between the two variables is.

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Answer:

Step-by-step explanation:

2 cups of sparkling water with every 3 cups of apple juice = sparkling juice

Sparkling water : apple juice

2 : 3

How much sparkling water does Jada need if she uses 8 cups of apple juice.

Sparkling water : apple juice

x : 8

Equate both ratios

2 : 3 = x : 8

2/3 = x / 8

2*8 = 3*x

16 = 3x

x = 16 / 3

= 5.33 cups

Sparkling water = 5.33 cups

How much apple juice does Jada need if she uses 8 cups of sparkling water

Sparkling water : apple juice

8 : y

Equate both ratios

2 : 3 = 8 : y

2/3 = 8 / y

Cross product

2 * y = 3 * 8

2y = 24

y = 24 / 2

= 12

y = 12

Apple juice = 12 cups

NOTE: There is an error in your question, you wrote "How much sparkling water does Jada need if she uses 8 coups of sparkling water." but I solved for both sparkling water and apple juice using 8 cups since your question was not clear enough.

Based on the Central Limit Theorem, we know that with sufficient sample size, the sampling distribution of proportions is approximately normal.

The Central Limit Theorem (CLT) states that when independent random variables are summed or averaged, their distribution becomes approximately normal, regardless of the original distribution shape. This applies to proportions as well. For a sampling distribution of proportions, when multiple random samples of sufficient size are taken from a binary population, the distribution of sample proportions will be approximately normal, centered around the true population proportion. The CLT allows us to make statistical inferences about the population proportion using normal-based techniques, such as constructing confidence intervals and conducting hypothesis tests.

In summary, the CLT assures us that with an adequate sample size, the sampling distribution of proportions approximates a normal distribution, enabling us to apply standard statistical methods for making inferences about proportions.

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Answer:

12

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define 1st equation

16x - 2 = 30

Step 2: Solve for x

Step 3: Solve equation

And we have our final answer!

The square root of 6 is equal to 2.449489742783178, which can also be written as 2.44 or rounded to 2.4. The square root of 6 is the number which when multiplied by itself, gives us 6 as the result. This is because when we square a number, we are multiplying it by itself.

In mathematics, the square root of 6 can be written as √6. It is an irrational number, which means that it cannot be expressed as a fraction or a ratio of two integers. The value of √6 is approximately equal to 2.449489742783178, and it is an irrational number because it is not a perfect square.The square root of 6 can be calculated by using the long division method or by using the Babylonian method. It can also be calculated by using a calculator, which is the easiest way to find the value of √6.The square root of 6 is an important number in mathematics, as it can be used to solve equations and to calculate areas of certain geometric shapes. It is also useful for calculating the volume of a cylinder or a cone.The square root of 6 is a real number, which means that it can be used in scientific calculations, such as determining the speed of a particle or the acceleration of a moving object. It is also useful in physics and engineering, such as in calculating the energy of a particle or the torque of a rotating object.The square root of 6 has a wide range of applications in mathematics, physics, engineering, and other sciences. It is an important number to remember and is useful in a variety of calculations

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The square root of 6 is equal to 2.449489742783178, which can also be written as 2.44 or rounded to 2.4. The square root of 6 is the number which when multiplied by itself, gives us 6 as the result. This is because when we square a number, we are multiplying it by itself.

In mathematics, the square root of 6 can be written as √6. It is an irrational number, which means that it cannot be expressed as a fraction or a ratio of two integers. The value of √6 is approximately equal to 2.449489742783178, and it is an irrational number because it is not a perfect square.The square root of 6 can be calculated by using the long division method or by using the Babylonian method. It can also be calculated by using a calculator, which is the easiest way to find the value of √6.The square root of 6 is an important number in mathematics, as it can be used to solve equations and to calculate areas of certain geometric shapes. It is also useful for calculating the volume of a cylinder or a cone.The square root of 6 is a real number, which means that it can be used in scientific calculations, such as determining the speed of a particle or the acceleration of a moving object. It is also useful in physics and engineering, such as in calculating the energy of a particle or the torque of a rotating object.The square root of 6 has a wide range of applications in mathematics, physics, engineering, and other sciences. It is an important number to remember and is useful in a variety of calculations

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Answer:

Remove parentheses.     xy³ z^4

4Step-by-step explanation:

Answer:

x^4y^12z^16 is the answer let me know if i'm right and pls brainllest me if i'm right

A good way to get a small standard error is to use a Large sample. the correct answer is option 1.

The standard error is a measure of the variability of the sampling distribution of a statistic. A smaller standard error indicates that the statistic is more precise and is likely closer to the true population value.

One way to obtain a smaller standard error is to use a larger sample size. This is because a larger sample size tends to produce a more accurate estimate of the population parameter, with less variability. Therefore, option 1, "Large sample," is the correct answer.

The other options, such as a large population, repeated sampling, small sample, or small population, are not necessarily related to obtaining a small standard error.

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Answer:

The largest digit to be placed on the blank in the 5_,310 to make it divisible by 6 is 9 to give 59,310

Step-by-step explanation:

The given question requires the digit to be placed in the space left blank in 5_,310 to make it divisible by 6

To answer the question, we note that given that 51,000, 54,000, 57,000, and 60,000 are divisible by 6, and that 310 is not divisible by 6, we have

1,310 is not divisible by 6, but 2,310 is divisible by 6

Therefore, the complete number will be 57,000 + 2,310 = 59,310 which gives;

59310/6 = 9,885

Therefore, the complete number is 59,310, and the required digit is 9.

Answer:

14.4

Step-by-step explanation:

20.4-6 = 14.4

So his balls should grow 14.4 inches/feet/centimeters (whatever measuring tool you're asked to use)

Are you sure it's balls though

Answer:

20.4-6=14.4

since he wants his balls to grow you need to subtract how much he wants them tp grow by how tall the already are

Step-by-step explanation:

Using the speed formula we know that the speed of the runner is 7.55 m/s.

Speed is calculated as follows: speed = distance/time.

Knowing the units for distance and time is necessary to calculate the units for speed.

The units will be in meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

For instance, if a car drives 120 miles in 2 hours, we may calculate the speed as 120 x 2 = 60 miles per hour.

So, we know that the speed formula is:

Speed = distance/time

Distance = 275-50 = 225 meters

Time = 29.8 sec

Now, place the values in the formula as follows:

Speed = distance/time

Speed = 225/29.8

Speed = 7.55 m/s

Therefore, using the speed formula we know that the speed of the runner is 7.55 m/s.

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Concept and uses of image translation are explain below.

In math, a change is an activity that moves, flips, or changes a shape (called the preimage) to make another shape (called the picture). An interpretation is a sort of change that moves each point in a figure a similar distance in a similar course.

An interpretation is a kind of change that takes each point in a figure and slides it a similar distance in a similar course. This interpretation maps △ X Y Z \triangle{XYZ} △XYZtriangle, X, Y, Z onto the blue triangle. The outcome is another figure, called the picture. The picture is consistent to the first figure.

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