The mean of 6 pieces of data is 7. Five of the data values are 9, 4, 8, 8, and 7. What is the sixth data value?​

9514 1404 393

Answer:

  32.8 m/s

Step-by-step explanation:

The function is actually ...

  \(v(d) = \sqrt{2gd}\)

Filling in the given values, the velocity is about ...

  \(v(55) = \sqrt{2\cdot9.8\cdot55}=\sqrt{1078}\approx32.8\text{ m/s}\)

The velocity at the end of the free-fall is about 32.8 meters per second.

Answer:

C :) Hope this helps!

Step-by-step explanation:

The solution set is empty: {}. To solve the equation |x² + x - 2| = x + 3, we can consider two cases: when the expression inside the absolute value is positive, and when it is negative. Let's solve each case separately:

Case 1: x² + x - 2 is positive (x² + x - 2 > 0):

To find the values of x that satisfy this inequality, we can factorize the quadratic expression:

x² + x - 2 = (x + 2)(x - 1)

For the expression to be positive, both factors must have the same sign. Considering the signs of each factor:

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

(x - 1) > 0 => x > 1

Since both factors must be positive, we can take the intersection of the two intervals: x > 1.

Case 2: x² + x - 2 is negative (x² + x - 2 < 0):

Again, factorizing the quadratic expression:

x² + x - 2 = (x + 2)(x - 1)

For the expression to be negative, the factors must have opposite signs. Considering the signs of each factor:

(x + 2) < 0 => x < -2

(x - 1) > 0 => x > 1

Since the factors have opposite signs, we can take the union of the two intervals: x < -2 or x > 1.

Combining the solutions from both cases, we have:

x > 1 or x < -2

Now let's verify the solutions by substituting them back into the original equation:

For x > 1:

|x² + x - 2| = x + 3

Substituting x = 2:

|2² + 2 - 2| = 2 + 3

|4 + 2 - 2| = 5

|4| = 5

4 = 5 (Not true)

For x < -2:

|x² + x - 2| = x + 3

Substituting x = -3:

|-3² - 3 - 2| = -3 + 3

|-9 - 3 - 2| = 0

|-14| = 0

14 = 0 (Not true)

Since neither solution satisfies the equation, there are no valid solutions to the equation |x² + x - 2| = x + 3.

Therefore, the solution set is empty: {}

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Answer:

25 feet in one second

Step-by-step explanation:

125 divided by 5 is 25

Answer:

25 feet per second

Step-by-step explanation:

Answer: A≈1385.44m²

Step-by-step explanation:

A=πr2=π·212≈1385.44236m²

Answer:

When the bases are the same, we can combine the exponents. Therefore, we can rewrite the equation as:

4^-2x * 4^x = 4^(-2x+x) = 4^(-x) = 64

To solve for x, we need to isolate x on one side of the equation. We can rewrite 64 as a power of 4:

4^3 = 4^(-x)

Now we can equate the exponents:

3 = -x

Therefore, x = -3.

To check the solution, we can substitute x = -3 back into the original equation:

4^-2(-3) * 4^(-3) = 4^6 * 4^(-3) = 4^3 = 64

So x = -3 is indeed a solution to the equation.

Answer:

below

Step-by-step explanation:

Domain is the set of all x values a function can have

 this one goes from    - inf to the asymtope at x = 2

(-∞, 2)     domain

range is the y values the function can have

   looks like 0   to - inf

(- ∞, 0]       ( but it COULD be  ( -∞, 0)    <===cannot tell from graph)

Applying the Gaussian Elimination variant to the augmented matrix of the given system of linear equations results in the solution x = 1, y = -2, and z = 2.

Explanation: To solve the system of linear equations using Gaussian Elimination, we first represent the system in augmented matrix form, where the coefficients of the variables and the constants are organized in a matrix. The augmented matrix for the given system is:

[1   0   5   |   11]

[-2  2   4   |   -4]

[3   7   0   |   -1]

We start by performing row operations to eliminate the coefficients below the main diagonal. First, we multiply the first row by 2 and add it to the second row, resulting in the modified matrix:

[1   0   5   |   11]

[0   2   14  |   18]

[3   7   0   |   -1]

Next, we multiply the first row by -3 and add it to the third row, giving us:

[1   0   5   |   11]

[0   2   14  |   18]

[0   7   -15 |   -34]

We can now eliminate the coefficient 7 in the third row by multiplying the second row by -7 and adding it to the third row:

[1   0   5   |   11]

[0   2   14  |   18]

[0   0   -113|   -250]

At this point, we have an upper triangular matrix. We can back-substitute to find the values of the variables. From the last row, we find that -113z = -250, which implies z = 250/113. Substituting this value into the second row, we get 2y + 14z = 18, which gives us y = -2. Finally, substituting the obtained values of y and z into the first row, we find x + 5z = 11, which gives us x = 1. Therefore, the solution to the system of linear equations is x = 1, y = -2, and z = 2.

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Answer:

3. 45, 4. 24

Step-by-step explanation:

use formula: hypotenuse²= side² + other side ²

3.

x²= 27²+36² calculate the squares then add

x²=2025 square root both sides

x= √2025= 45

4.

25²= x²+7² isolate the vaiable by subtracting 7² from both sides

25²-7² = x² square then subtract

576 =x² square root both sides

24=x

Answer:

To visit his grandmother, Luis takes a train 6.37 kilometers and a car 5.45 kilometers. How many kilometers is Luis's journey in total? Answer: Luis traveled 11.82 km to visit her grandmother.

Step-by-step explanation:

Answer:

11.82

Step-by-step explanation:

Answer:

Area of the base is 10.5 cm².

Step-by-step explanation:

Formula for the volume of the given oblique prism = Area of the triangular base × Vertical height between two triangular bases

Vertical height = 6 cm

Volume = 63 cm³

From the formula,

63 = Area of the triangular base × 6

Area of the base = \(\frac{63}{6}\)

                            = 10.5 cm²

Therefore, area of the base is 10.5 cm².

Answer:

24

Step-by-step explanation:

An angle bisector splits an angle into two congruent parts, so -6+2x=10x-78, and thus x=9.

This means angles STV and UTV both measure 12°.

Therefore, angle STU measures 24°.

Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

The simplified expression is sin²x + √(4sin²x - cos⁴x).

To simplify the expression √(sin⁴x - 4cos²x) + √(4sin²x - cos⁴x), let's break it down step by step:

Factor out common terms

We can observe that both terms inside the square roots have a common factor of sin²x. Let's factor it out:

√(sin²x(sin²x - 4cos²x)) + √(4sin²x - cos⁴x)

Simplify the square roots

We can further simplify the square roots by noticing that sin²x - 4cos²x can be written as -(4cos²x - sin²x) using the property of negative square roots. Similarly, cos⁴x can be written as (cos²x)². Applying these transformations, we get:

√(sin²x(1 - 4cos²x)) + √(4sin²x - (cos²x)²)

Simplify the expressions inside the square roots

Let's simplify the expressions inside the square roots:

√(sin²x - 4sin²x cos²x) + √(4sin²x - cos⁴x)

Factor out sin²x from the first square root

We can factor out sin²x from the first square root:

√(sin²x(1 - 4cos²x)) + √(4sin²x - cos⁴x)

Apply trigonometric identity

Using the trigonometric identity sin²x + cos²x = 1, we can rewrite 1 - 4cos²x as sin²x:

√(sin²x(sin²x)) + √(4sin²x - cos⁴x)

Simplify further

√(sin⁴x) + √(4sin²x - cos⁴x)

Simplify the square roots

Since sin⁴x and cos⁴x are both squared terms, their square roots simplify to their absolute values:

|sin²x| + √(4sin²x - cos⁴x)

Simplify the expression

The absolute value of sin²x is simply sin²x. Therefore, the simplified expression is:

sin²x + √(4sin²x - cos⁴x)

This is the simplified form of the given expression.

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Answer:

  300

Step-by-step explanation:

Fill in the given value and solve for x.

  C(x) = 500x +100000

  250000 = 500x +100000

  500 = x + 200 . . . . . . divide by 500

  300 = x

300 items were produced if the month's expenses were $250,000.

The required result of the sliding filament model given below.

The mechanism by which muscles contract is described by the sliding filament model. Actin and myosin myofilaments move over one another as a result of a cycle of repeated occurrences, constricting the sarcomere and creating tension in the muscle.

The A band is the middle, darkly pigmented area of the sarcomere that runs the entire length of the thick filaments. The portion of the thin filaments that cross over the thick filaments is also included. The I band is formed by the remaining thin filaments within the sarcomere but not by any thick filaments. Each A band has a narrow region in the middle called the H zone, which is made up entirely of dense filaments.

Myosin heads pull the thin filaments in the direction of the M line during muscle contraction. Because of this, the thin filaments glide inward, allowing their ends to overlap and connect at the sarcomere's core. The I band and H zone become smaller as a result.

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Answer:

Median = 1

Step-by-step explanation:

0, 0, 1, 1, 1, 1, 2, 2, 3, 4

Middle - 1 + 1

2 ÷ 2 = 1

Hope this helps! :)

Answer:

yes

Step-by-step explanation:

In situation a, the predictor variable is age, as it is being tested to see if it affects the outcome variable, which is the number of risky behaviors. So, age is the independent variable and the number of risky behaviors is the dependent variable.

In situation b, the predictor variable is the number of family members, as it is being tested to see if it affects the outcome variable, which is the level of education of children. So, the number of family members is the independent variable and the level of education of children is the dependent variable.

It is important to identify the predictor variable and the outcome variable in any study as this helps in understanding the relationship between the two variables and in interpreting the results accurately.

For situation A, the predictor variable is "age," and the outcome variable is "number of risky behaviors." As age increases, the study aims to see if the number of risky behaviors changes.

For situation B, the predictor variable is "number of family members," and the outcome variable is "level of education of children." The study examines whether the children's level of education changes based on the number of family members.

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Answer: 12 claps per second

Step-by-step explanation: divide both by 60 and yield 12 times -1 second

Answer:

7 Celsius to Fahrenheit is 44.6.

There is a five hour gap.

The tempature drops two degrees per hour. So, multiply.

2 x 5 = 10.

Subtract 10 from 44.6.

You get 34.6.

34.6 is the answer.

The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Given that N is the incenter of △ABC, NS = 4.

Given the image where:

NQ = 2x

NR = 3x − 2

NQ = NR = NS (equidistant from the incenter)

Thus:

2x = 3x - 2

2x - 3x = -2

-x = -2

x = 2

NQ = NS = 2x

NS = 2(2)

NS = 4

Therefore, given that N is the incenter of △ABC, NS = 4.

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Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

6:12=1:2

Step-by-step explanation:

as we will cut 6:12 by 6 . please mark me as brainliest and follow me

Answer:

1:2

Step-by-step explanation:

6 and 12 are divisible by 6

6 ÷ 6 = 1

12 ÷ 6 = 2

The time it takes the ball to hit the ground is 0.375 seconds.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the amount of time it takes the ball to hit the ground, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

Hence, the time is 0.375 seconds.

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The correct answer is "98i; n = 77".

The function qt() in statistics is used to calculate the t-value for a given level of confidence and degrees of freedom.

In this case, qt(.98, df = 77) outputs the t-value for a 98% confidence interval with 77 degrees of freedom.

The t-value is used to calculate the margin of error for a confidence interval, which is used to estimate the population parameter based on the sample data.

For example, if you have a sample of size 78 and want to construct a 98% confidence interval for the population mean, you can use the t-value of qt(.98, df = 77) along with the sample mean and standard deviation to calculate the margin of error and construct the interval.

Therefore, the correct answer is "98i; n = 77".

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Answer: She is incorrect because 0 + 0 = 0

Answer:

112°

Step-by-step explanation: