Given f(x) =-3x^2 - 2r

Find f(8)

The volume of the cube is 1.82 in³

We know that the formula for the area of the cube, as a function of the volume, is:

A = 326*V^(2/3)

Solving that equation for V, we will get.

V = (A/326)^(3/2)

Then the volume of a cube whose surface area is A = 486 square inches is:

V = (486 in²/326)^(3/2)

V = 1.82 in³

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The equation in standard form is (x- (-12))² + (y - 0)²  = (√164)²

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Using the completing square method on the given equation:

24x + y² = -x² + 20

x²+ 24x + y² = 20

[x² + 24x + (12)²] + [y² + 0x + (0)²] = 20 + (12)²

(x + 12)² + (y + 0)² = 164

(x - (-12))² + (y - 0)² = 164

(x- (-12))² + (y-0)²  = (√164)²

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The width of the river is approximately 45m.

Let's say the illustration may be explained as follows:

The big right triangle is located inside the river, with its base extending down one of its sides and its height spanning its breadth.

The base of the little right triangle lies on the opposite bank of the river, outside of it.

Triangles don't cross over one another. Their bases' endpoints contact, as does the end of their hypotenuses.

Let's assume the two right triangles are similar (which means they have proportional sides).

H1/B1 = H2/ B2

which is H1/55 = 21.4/26

=21.4/26 x 55

= 45.27

It is the larger triangle is the width of the river

If the smaller triangle represents the land on one side of the river and the larger triangle includes both the land and the river, we need to find the width of the river by subtracting the base of the smaller triangle from the base of the larger triangle:

Width of the river = 55 - 26 = 29 meters

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Answer:

36

Step-by-step explanation:

Given:

1/6 of the marbles are red

1/3 of the marbles are blue

There are 18 green marbles in the jar

We can set up the following equations based on the given information:

Number of red marbles = 1/6 * x

Number of blue marbles = 1/3 * x

Number of green marbles = 18

Since the total number of marbles in the jar is "x", we can write the equation for the sum of all the marbles as:

(Number of red marbles) + (Number of blue marbles) + (Number of green marbles) = x

Substituting the values from the given information:

1/6 * x + 1/3 * x + 18 = x

Multiplying through by 6 to eliminate the fraction:

x/6 + 2x/6 + 18 = 6x/6

x + 2x + 108 = 6x

Combining like terms:

3x + 108 = 6x

Subtracting 3x from both sides of the equation:

3x + 108 - 3x = 6x - 3x

108 = 3x

Dividing both sides by 3 to solve for x:

108/3 = 3x/3

36 = x

Answer:

First, we can multiply both sides of the equation by the absolute value of x plus 8, to get rid of the fraction:

52 = 4(|x| + 8)

Now we can solve for the absolute value of x:

| x | + 8 = 13

| x | = 5

This means that x could be either positive 5 or negative 5. Therefore, the possible values of x are {-5, 5}.

So the answer is option D: {-5, 5}.

If a taxi company charges ​f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.

To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.

f(2.7) = 2.20 + 0.6[4(2.7)]

f(2.7) = 2.20 + 0.6[10.8]

f(2.7) = 2.20 + 6.48

f(2.7) = 8.68

The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.

The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.

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The value of x for the angles of the quadrilateral is: x = -4

We know that the sum of angles in a quadrilateral is 360 degrees.

The angles are given as:

(11x + 140)°

(13x + 143)°

(4x + 98)°

(11x + 135)°

Thus:

(11x + 140)° + (13x + 143)° + (4x + 98)° + (11x + 135)° = 360°

Thus:

39x + 516 = 360

39x = 360 - 516

39x = -156

x = -156/39

x = -4

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The volume of the cylinder below is 5595.48 in².

Volume is the space accuppied by a solid shape.

To calculate the volume of the cylinder, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Use a calculator to solve this problem!

Answer:

Step-by-step explanation:

775625 is the correct answer

y=-1/2x-1 is equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.

The slope of given line is 2

The slope of perpendicular line is -1/2

Now let us find the y intercept

1=-1/2(-4)+b

1=2+b

b=-1

Now the equation is y=-1/2x-1

Hence,  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3 is y=-1/2x-1.

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Answer:

2/3 pizza is left!

Step-by-step explanation:

You take 1/3 from a whole pizza (3/3), leaving 2/3 for ur 2 buddies :D

Answer: 59 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees so we subtract that by the values we already know the get the last angle.
180-31-90= 59 degrees

The equation for the axis of symmetry for the given parabolic graph is found as: x = 3.

A parabola is the graph of a quadratic function and features a vertical line passing through its vertex as its axis of symmetry.

The graph is also symmetric, with the axis of symmetry being a vertical line that passes through the vertex.

Thus, the equation for the axis of symmetry for the given parabolic graph is found as: x = 3.

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This is the formula for calculating the present value of a future payment, where P1 is the present value, P2 is the future payment, and R is the interest rate.

To use the formula, you need to know the value of P2, the future payment, and the interest rate, R. Then, you can solve for P1, the present value of that payment. The formula works by discounting the future payment to account for the time value of money, which means that money today is worth more than the same amount of money in the future.

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Answer:

12 square units

Step-by-step explanation:

interior angles of rectangles are right angles

Area of the triangle: 6 x 4 / 2

The intercepts of the graph of y = x²- 25 are (-5, 0), (5, 0), and (0, -25).

Data can also be presented as a table. However, when the information is presented graphically, it is much easier to understand. There are many types of charts and each of them serves specific purposes in different fields.  

To find the x-intercepts of the graph, we need to set y = 0 and solve for x:

0 = x²- 25

Adding 25 to both sides gives:

25 = x²

Taking the square root of both sides gives us:

x = ±5

So the x-intercepts are (-5, 0) and (5, 0).  To find the y-intercept, we need to set x = 0 and solve for y:

y = 0²-25

y = -25

So the y-intercept is (0, -25).  

Therefore, the intercepts of the graph of y = x² - 25 are (-5, 0), (5, 0), and (0, -25).

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The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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The volume of the cone is 1960.64 cubic yards.

We have,

The formula for the volume of a cone is:

V = (1/3)πr²h

where π is approximately 3.14, r is the radius, and h is the height.

Substituting the given values, we get:

V = (1/3) x 3.14 x 12² x 13

V = (1/3) x 3.14 x 144 x 13

V = 1/3 x 3.14 x 1872

V = 1960.64

Rounding to the nearest hundredth, we get:

V = 1960.64

Therefore,

The volume of the cone is 1960.64 cubic yards.

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The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.

To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.

The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:

H0: μ = $9820

The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:

Ha: μ > $9820

The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.

To calculate the test statistic, we can 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.

Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:

s = θ / √n = $1580 / √50 = $223.61

Now we can calculate the test statistic:

t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45

Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.

Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.

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--The given question is incomplete, the complete question is given

"  a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.

A. state the null and alternate hypothesis.

B. Compute the   or t va;ue of the sample test statistic.

C. Find the critical value(s).

D. based on the answers to a-c, what is your conclusion?"--

False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.

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A circle with center Q and equilateral triangle NOP, where points N and O lie on the circle

What is a circle?

A circle is a two-dimensional shape with a perfectly round boundary that has no corners or edges. It is defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the boundary of the circle is called the radius.

The circumference of a circle is the distance around the boundary of the circle, and it is calculated as 2π times the radius. Circles are found in many natural and man-made objects, such as wheels, planets, and coins, and they have a wide range of applications in mathematics, science, and engineering.

To construct a circle with center Q and equilateral triangle NOP where points N and O lie on the circle, follow these steps:

Draw line segment PQ as the base of the equilateral triangle NOP.

Draw a perpendicular bisector of PQ, which intersects PQ at its midpoint, say M. This bisector will be the axis of symmetry of the equilateral triangle NOP.

With M as the center and MP (or MQ) as the radius, draw a circle that intersects PQ at two points, say X and Y.

Using Q as the center and QX (or QY) as the radius, draw two arcs that intersect the circle drawn in step 3 at two points, say N and O.

Draw the lines NQ and OQ to complete the equilateral triangle NOP.

Now, you have a circle with center Q and equilateral triangle NOP, where points N and O lie on the circle.

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Answer:

Step-by-step explanation:

1.To arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 ways to arrange all 6 tables in a line.

2.To choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

C(6,4) = 6! / (4! x 2!) = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1) = 15

Therefore, there are 15 ways to choose 4 out of the 6 tables.

There are 720 ways to arrange all 6 tables in a line.

And, there are 15 ways to choose 4 out of the 6 tables.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom.

Now, After arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Hence, there are 720 ways to arrange all 6 tables in a line.

And, For choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

Thus, there are 15 ways to choose 4 out of the 6 tables.

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By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.

The CDF function of a Normal distribution is calculated by translating the random variable to the Normal Standard, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the normal standard. The Normal Standard, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).

Let x1, x2, .... be the scores on the test.

X ~ N (82, 64)

P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)

Step-by-step explanation:

cores Distribution and Percentile

The scores on a test are normally distributed, with a mean of 82 and a standard deviation of 8. What percent of scores are less than 90? Explain

To find the percentage of scores that are less than 90 in a normally distributed test with a mean of 82 and a standard deviation of 8, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF of a normal distribution gives the probability that a random variable falls below a particular value. In this case, we want to find the probability that a score is less than 90.

The formula for the CDF of a normal distribution is:

CDF(x) = (1/2) * (1 + erf((x - μ) / (σ * sqrt(2))))

where erf is the error function, μ is the mean, σ is the standard deviation, and x is the value we want to find the cumulative probability for.

Plugging in the given values:

μ = 82

σ = 8

x = 90

We can calculate the cumulative probability using the formula:

CDF(90) = (1/2) * (1 + erf((90 - 82) / (8 * sqrt(2))))

Using a calculator or statistical software that provides the error function, we can find that erf(1.0) is approximately 0.6827.

Plugging this value back into the formula, we get:

CDF(90) = (1/2) * (1 + 0.6827) = 0.8414

So, the cumulative probability that a score is less than 90 is approximately 0.8414, or 84.14%.

Therefore, about 84.14% of the scores are less than 90 in this normally distributed test.

The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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yes very cool math problem

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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