What does x equal? log6 x = 4



A. 36
B. 216
C. 222
D. 1296

Answer:

mean=3

range=6

median=4

mode=5

extreme value=2

central tendency=1

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The required closest integer to [tex]\sqrt{63}[/tex] is 8 and 9.

Given that,

To find the integers that are closest to the number in the middle.

[tex][ ] < \sqrt{63} < [ ][/tex]

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,

Let the two numbers be x and y which are close to [tex]\sqrt{63}[/tex],

[tex]\text{x} < \sqrt{63} < \text{y}[/tex] - - - - (1)

The closest root to [tex]\sqrt{63}[/tex] can be given as [tex]\sqrt{59}[/tex] and [tex]\sqrt{72}[/tex]

Now, [tex]\text{x} = \sqrt{59}[/tex] and [tex]\text{y} = \sqrt{72}[/tex]

Put these values in inequality 1

[tex]\sqrt{59} < \sqrt{63} < \sqrt{72}[/tex]

[tex]8 < \sqrt{63} < 9[/tex]

Thus, the required closest integer to [tex]\sqrt{63}[/tex] is 8 and 9.

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Answer:

D. 37

Step-by-step explanation:

Step 1:

order the values from lowest to highest

15, 22, 37, 49, 72

Step 2:

the median is the value in the middle of the set of numbers, which in this case is 37

So the answer is D. 37

A point-slope equation for the line that has slope 3 and passes through the point (5, 21) is y - 21 = 3(x - 5).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (5, 21) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 21 = 3(x - 5)  

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Since the p-value (.040) is greater than the significance level (.01), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to support the claim that there are more than 70,000 defined words in the dictionary. The mean number of words per page is not significantly greater than 48.1 words.

To test the claim that the mean number of words per page is greater than 48.1 words, we will use a one-sample t-test. We will follow these steps:

Step 1: Identify the null and alternative hypotheses
H0: µ ≤ 48.1 (null hypothesis: the mean number of words per page is less than or equal to 48.1)
H1: µ > 48.1 (alternative hypothesis: the mean number of words per page is greater than 48.1)

Step 2: Calculate the test statistic (t-score)
t = (x - µ) / (s / √n)
t = (53.5 - 48.1) / (16.5 / √20)
t ≈ 1.84

Step 3: Calculate the P-value
Using a t-distribution table or calculator, find the P-value associated with the t-score 1.84 and degrees of freedom (n-1) = 19. Since this is a one-tailed test, we don't need to divide the P-value by 2. The P-value is approximately 0.041.
Test Statistic: To calculate the test statistic, we will use the formula:

t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the given values, we get: t = (53.5 - 48.1) / (16.5 / √20) = 1.86.
P-value: Using a t-distribution table with 19 degrees of freedom (n-1), we find the p-value to be .040 (one-tailed).

Step 4: Compare the P-value with the significance level (α)
Since the P-value (0.041) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Step 5: State the final conclusion
We do not have sufficient evidence to support the claim that the mean number of words per page is greater than 48.1 words at a 0.01 significance level. Consequently, we cannot support the claim that there are more than 70,000 defined words in the dictionary.

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We can conclude that the correlation coefficient of -0.587 is statistically significant at the 0.05 level of significance with a sample size of 19.

To determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size, follow these steps:

Step 1: Identify the correlation coefficient (r), level of significance (alpha), and sample size (n).
- r = -0.587
- alpha = 0.05
- n = 19

Step 2: Calculate the degrees of freedom (df).
- df = n - 2
- df = 19 - 2
- df = 17

Step 3: Look up the critical value for the correlation coefficient in a table of critical values or use a statistical software.
- For an alpha level of 0.05 and df = 17, the critical value for a two-tailed test is approximately 0.444 (you can find this value in a table or using software).

Step 4: Compare the absolute value of the correlation coefficient (r) with the critical value.
- |r| = |-0.587| = 0.587

Step 5: Make a decision based on the comparison.
- Since 0.587 > 0.444, we can conclude that the correlation coefficient of -0.587 is statistically significant at the 0.05 level of significance with a sample size of 19.

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The distance between the two points is 19.2 units.

Let the point (7, 8) be A and point (-5, -7) be B.

By joining these two points and drawing a right-angled triangle ABC with AB as the hypotenuse, we get point C at (7, -7)

The altitude of triangle ABC, AC = A - C

AC = 15 units

The base of the triangle ABC, BC = C - B

BC = 12 units

According to Pythagoras Theorem,

√(AC² + BC²) = AB

AB = √(12² + 15²)

AB = 19.2 units

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The transfer function for a filter is a mathematical expression that describes how the filter affects the input signal.
Once we have determined the type of filter, we can derive the transfer function (part b) using standard methods for that type of filter. The transfer function will be a mathematical expression that relates the input signal to the output signal for the filter.
Finally, using the transfer function (part c), we can determine the parameters requested in the textbook. These parameters might include things like the cutoff frequency, the resonance frequency, or the Q factor of the filter.

Since I don't have access to your specific textbook, I'll provide a general outline on how to approach this type of problem using the terms you've provided: functions, function, and parameters.

1. Determine the type of filter by observation:
Analyze the given circuit diagram or description and identify the type of filter based on its components and configuration. Common filter types include low-pass, high-pass, band-pass, and band-stop filters. In this problem, we are dealing with functions and their parameters. A function is a mathematical equation or relationship that relates one variable (or set of variables) to another. In this case, we are dealing with transfer functions, which relate the input and output signals of a filter.

2. Derive the transfer function and determine the type of filter:
The transfer function, which is a function that relates the output to the input of a system, can be derived by analyzing the circuit using techniques such as Laplace transforms or phasor analysis. The transfer function typically takes the form H(s) = Y(s) / X(s), where Y(s) is the output and X(s) is the input. To derive the transfer function, we need to determine the relationship between the input and output signals for the filter.


Once you have derived the transfer function, the type of filter can be determined based on the mathematical form of the function. For example, a low-pass filter may have a transfer function that decreases as the frequency increases, while a high-pass filter may have a transfer function that increases as the frequency increases.

3. Determine the parameters requested in the textbook:
Using the derived transfer function, identify the parameters that the textbook asks for. These parameters may include cutoff frequency, gain, or other circuit component values. To calculate these parameters, you may need to rearrange the transfer function equation or use mathematical techniques such as solving for the roots or poles.

Remember, the specific steps to solve the problem will depend on the given problem in your textbook. The outlined steps above provide a general approach to help you understand and tackle this type of problem using the terms functions, function, and parameters.

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The word you could used to describe the probability is (c) unlikely

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

Ms. Evan's Reward Wheel

Also from the wheel, we have

This means that probability of the 5-point bonus section from the wheel is

P = Sections that are 5-point /Number of sections

This gives

P = 2/16

Evaluate

P = 0.125

As a general rule

probability values between 0 and 0.5 are unlikely or less likely

Using the above as a guide, we can conclude that the word to use is (c) unlikely

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When the uniform wire of resistance r is cut into three equal lengths, each length will have a resistance of r/3. One of these lengths is formed into a circle, which means its resistance remains r/3. This circle is then connected between the other two equal lengths, resulting in a circuit as shown in figure 1.

Since the two equal lengths are connected in parallel, their combined resistance will be half of their individual resistance, which is r/6. This resistance is in series with the resistance of the circle, which is r/3. Therefore, the total resistance of the circuit can be calculated as:

Total resistance = r/6 + r/3
Total resistance = 3r/6
Total resistance = r/2

So, the resistance of the circuit with the wire cut into three equal lengths is equal to half of the resistance of the original wire.

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Yup! I would just get rid of the plus sign after the 1.5x^2 because you don't really need it

yh but it must be y=1.5x^-7.5x+3

The area of the Caldwell that is covered by the concrete patio would be = 280.86ft²

A semi circle is derived from an intact circle that is equally divided into two.

To calculate the area of the semi circle, the formula that should be used is given as follows;

Area of a circle = πr²/2

where r = diameter/2= 26.75/2 = 13.375

area = 3.14 ×13.375²

= 561.72ft²

But the shape of the Caldwell which was given is a semi-circle not a full circle. Therefore it's final area will be = 561.72ft²/2 = 280.86ft².

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A, C, and E are linear transformations.  To justify:  A: T(A) = ASA-I is linear because it satisfies the two properties of linearity:

1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

C: T(A) = A from R to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R. This can be shown by plugging in kA for A in T(A) and simplifying.

E: T(A) = A from R2x2 to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.

B, D, and J are not linear transformations.

To justify:

B: T(A) = A from R2xs to R2x5 is not linear because it does not satisfy the additivity property of linearity. Specifically, T(A+B) ≠ T(A) + T(B) for some matrices A and B in R2xs.

D: T(A) = 2A from R6x4 to R6x4 is not linear because it does not satisfy the homogeneity property of linearity. Specifically, T(kA) ≠ kT(A) for some scalar k and matrix A in R6x4.

J: T(A) = A+Is from RSx5 to RSx5 is not linear because it does not satisfy either the additivity or homogeneity properties of linearity. Specifically, T(A+B) ≠ T(A) + T(B) and T(kA) ≠ kT(A) for some matrices A and B in RSx5 and scalar k.

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The sampling technique used for the following study is E) Cluster Sampling, where the scientist selects randomly chosen voting districts in a county and then interviews each member from each selected district.

Cluster sampling involves dividing a population into groups or clusters based on some criteria and then selecting a random sample of clusters to include in the study. In this case, the voting districts are the clusters, and the scientist interviews each member of the selected clusters, which is called complete enumeration.

Cluster sampling is a useful technique when it is impractical or too expensive to sample individuals from the entire population. It can also be helpful when studying populations that are geographically dispersed. However, it is important to keep in mind that cluster sampling may introduce some degree of bias if the clusters are not representative of the population as a whole. To minimize this risk, it is important to ensure that the clusters are selected randomly and that the members within each cluster are sampled using an appropriate technique, such as simple random sampling.

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Answer:

f = 11 2/7 (B)

Step-by-step explanation:

3 + f = 14 2/7

3+f-3 = 14 2/7 -3

f = 11 2/7

Thus, it's B.

Answer:

b) f = 11 2/7

Step-by-step explanation:

Now we have to,

→ Find the required value of f.

The equation is,

→ 3 + f = 14 2/7

Then the value of f will be,

→ 3 + f = 14 2/7

Converting mixed fraction to proper:

→ 3 + f = ((14 × 7) + 2)/7

→ 3 + f = (98 + 2)/7

→ 3 + f = 100/7

Subtract the Right hand side with 3:

→ f = (100/7) - 3

→ f = (100/7) - (21/7)

→ f = (100 - 21)/7

→ f = 79/7

Converting proper fraction to mixed:

→ f = (77 + 2)/7

→ f = (77/7) + (2/7)

→ [ f = 11 2/7 ]

Hence, the value of f is 11 2/7.

The angles are vertical opposite angles and the value of x is 25.

Each of the pairs of the opposite angles made by two intersecting lines are called vertical opposite angles.

When Two angles whose sum is 180° are called supplementary angles.That means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

We are given the angles as;

125 and 5x degrees.

Thus, both the angles makes vertical opposite angles means;

125 = 5x

x = 125/5

x = 25

Hence, the value of x is 25.

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The area of the rod is 1.46 * 10^4 mm^2

The diameter of the rod is  136 mm

We have to note that the elasticity or the Young modulus of the material can be given by the formula which is;

E = F/A/e/l

E = elasticity

F = force

A = area

e = elasticity

l = length

Thus we have that;

20500 = 20 * 10^3/A * 3000/0.2

20500 = 6 * 10^7/0.2A

20500  * 0.2 A =  6 * 10^7

A = 6 * 10^7/20500  * 0.2

A = 1.46 * 10^4 mm^2

Then

A = πr^2

r=√A/ π

d = 2√A/ π

d = 2*√1.46 * 10^4 /3.14

d = 136 mm

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Answer:

C

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{4}[/tex] y = 32

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

2x + y = 128

The probability that there will be exactly 7 calls within the next hour is approximately 0.104. The probability that there will be exactly 7 calls within the next three hours is approximately 0.010.

For the first question, we can use the Poisson distribution formula:
P(X = x) = (e^-λ * λ^x) / x!
Where λ is the mean (in this case, λ = 5) and x is the number of calls we are interested in (in this case, x = 7).
Plugging in the values, we get:
P(X = 7) = (e^-5 * 5^7) / 7!
P(X = 7) ≈ 0.104
For the second question, we need to adjust the mean to account for the longer time period. Since we are interested in the number of calls within the next three hours, the new mean is:
λ = 5 * 3 = 15
Using the same formula as before, we get:
P(X = 7) = (e^-15 * 15^7) / 7!
P(X = 7) ≈ 0.010

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Answer:

1 B

2 A

3 A

4 five times

Step-by-step explanation:

6.3×10-11/7×10-5

0.9×10-6

9×10-5

Answer:

no she is not.

Step-by-step explanation:

2 divided 7 is the same as 2/5 so

2/5 = 0.4

dividing 5 by 7 would be 0.714 so its not equal

hope this helps you <3

The metric unit from pounds to tons is 250 pounds = 0.125 tons

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

250 pounds = how many tons

As a general rule, we have

1 pound = 0.0005 tons

Multiply both sides of the equation by 250

So, we have

250 * 1 pound = 0.0005 tons * 250

Evaluate the products

250 pounds = 0.125 tons

Hence, the conversion is 250 pounds = 0.125 tons

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The linear equation that can be used to find the hourly parking rate is III. 7+4.50x = 16.00

Given that

Next, we calculate the unit rate for hours after 2 hours from the above values using the following formula

Rate = Change in price/Change in time

So, we have the following equation

Rate = (20.50 - 16.00)/(5 - 4)

Rate = 4.5

So, the function would be

f(x) = 4.5x + 7

From the list of options, the correct equation is (III) 7 + 4.50x = 16.00

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Finding the area under a curve using technology requires knowledge of calculus or a graphing calculator with a built-in integral function.

We can use either method to find the area between the edge of the garden bed and the side of the house.

To find the area between the edge of the garden bed and the side of the house, we need to integrate the function that represents the distance between the two. In this case, the distance between the edge of the garden bed and the side of the house is given by the equation y = x + 1.

To integrate this function, we can use calculus or a graphing calculator with a built-in integral function. Calculus involves finding the antiderivative of the function, while a graphing calculator can use numerical methods to approximate the integral.

If using a graphing calculator, we can graph the function y = x + 1 and then use the integral function to find the area between the curve and the x-axis. The result will be the area between the edge of the garden bed and the side of the house, which can be used to calculate the amount of mulch needed for the job.

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The probability that a person will wait for more than 9 minutes is approximately 0.0228, or 2.28% when rounded to four decimal places

To find the probability that a person will wait for more than 9 minutes, we'll use the z-score formula and a standard normal distribution table (Z-table).

First, calculate the z-score using the formula:
z = (X - μ) / σ

Where X is the value we're interested in (9 minutes), μ is the mean (5 minutes), and σ is the standard deviation (2 minutes).

z = (9 - 5) / 2
z = 4 / 2
z = 2

Now, look up the probability for a z-score of 2 in a Z-table. You'll find a value of 0.9772, which represents the probability of waiting less than or equal to 9 minutes. To find the probability of waiting more than 9 minutes, subtract this value from 1:

Probability of waiting more than 9 minutes = 1 - 0.9772 = 0.0228

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.

The equations can be solved as shown below.

a) We have that;

( x+2 ) ( 10-x ) = 0

10x - x^2 + 20 - 2x = 0

x^2 + 2x - 10x - 20 = 0

x^2 -8x - 20 = 0

x = 10 or - 2

b) 7x + 15 = 6x + 3

7x - 6x = 3 - 15

x = - 12

c) 5x ( 3x + 5 ) = 0

15x^2 + 25x = 0

x = 0 or -5/3

d) (2x-1) ² = 0

(2x - 1) (2x - 1)

4x^2 - 2x - 2x + 1 =0

4x^2 - 4x + 1 = 0

x = 1/2(twice)

e) 4x² +13 = 14

4x² + 13 -14 = 0

4x² - 1 = 0

x = ±1/2

f) ( x-9 )² =16

(x - 9) (x - 9) = 16

x^2 - 9x - 9x + 81 = 16

x^2 - 18x +81 - 16 = 0

x^2 - 18x + 65 = 0

x = 13 or x = 5

These are the solutions of the equations.

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True. The method of least squares is a commonly used technique in regression analysis, which involves finding the line (or curve) that best fits the data points.

In multiple regression models, this method is used to estimate the regression coefficients, which are the values that determine the relationship between the independent variables and the dependent variable. The aim of this method is to minimize the sum of the squares of the differences between the observed values and the predicted values, also known as the error.

True, the method of least squares is used to estimate the regression coefficients in multiple regression models. It aims at minimizing the summation of the squared errors between the observed values and the predicted values based on the model.

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There is no sufficient evidence at the 0.01 level of significance to conclude that the proportion of women physicians at the university health system exceeds 27.9%.

To answer your question, we'll perform a hypothesis test using the given information. We'll test if the proportion of women physicians at the university health system exceeds 27.9%. Here's the setup:

Null hypothesis (H0): p = 0.279 (The proportion of women physicians is 27.9%)
Alternative hypothesis (H1): p > 0.279 (The proportion of women physicians exceeds 27.9%)

In this case,
- Sample size (n) = 119
- Number of women physicians in the sample (x) = 34
- Significance level (α) = 0.01

Now, we'll calculate the sample proportion (p') and the test statistic (z):

p' = x / n = 34 / 119 ≈ 0.2857

z = (p' - p) / √(p * (1-p) / n) ≈ (0.2857 - 0.279) / √(0.279 * (1-0.279) / 119) ≈ 0.467

Next, we'll find the critical z-value for the given significance level (α):

For a one-tailed test with α = 0.01, the critical z-value (z_critical) is approximately 2.33.

Now, compare the test statistic (z) with the critical z-value (z_critical):

Since z ≈ 0.467 is less than z_critical ≈ 2.33, we fail to reject the null hypothesis.

In conclusion, we do not have sufficient evidence to conclude that the proportion of women physicians at the university health system exceeds 27.9% at the 0.01 level of significance.

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When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.

When the switch is closed, a current flows through the primary coil of the transformer, which creates a changing magnetic field. This changing magnetic field induces a voltage in the secondary coil of the transformer, which is connected to resistor R. The ratio of the number of turns in the secondary coil to the number of turns in the primary coil is given by the turns ratio, which is represented by n2/n1.
Since the potential difference across a resistor is given by Ohm's law (V = IR), the potential difference across resistor R is proportional to the current flowing through it. Therefore, when the potential difference across resistor R connected to the secondary coil of the transformer is n2 > n1, it means that the current flowing through the secondary coil is greater than the current flowing through the primary coil. This is because the voltage induced in the secondary coil is greater than the voltage applied to the primary coil due to the turns ratio of the transformer.
When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.

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Answer:

29.46 cubic inches is the answer

Step-by-step explanation: