Solve each inequality. (Lesson 0-6) -14 n ≥ 42

The conic section which is represented by the provide equation is the equation of ellipse and represent ellipse conic section.

To of identify the type of conic section from an equation whether it is circle, or ellipse a let suppose the equation as,

\(Ax^2+By^2+Cx+Dy+E=0\)

In this equation, if,

\(A\neq B\)

Then it is the equation of circle.

If In this equation,

\(A\neq B\)

But both A and B has same sign (either positive or negative) then it is the equation of ellipse.

The given equation in the problem is,

\(3x^2 - 7x+ 8y^2 - 2y+ 1 = 0\)

Here, in the equation,

\(A=3\\B=8\)

The A is not equal to B but the sign of both are positive. Hence this equation is the equation of ellipse.

Hence, the conic section which is represented by the provide equation is the equation of ellipse and represent ellipse conic section.

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Answer:

below <3

Step-by-step explanation:

The function f(x) = x^3 - 3x^2 - 6x + 5 has an inflection point at (1, -3). The function is concave up for x > 1 and concave down for x < 1.


To find the intervals on which the function f(x) = x^3 - 3x^2 - 6x + 5 is concave up or down, we need to analyze the second derivative of the function. Let's begin by finding the second derivative:

f'(x) = 3x^2 - 6x - 6 (first derivative)

f''(x) = 6x - 6 (second derivative)

To determine the intervals of concavity, we need to find where the second derivative changes sign.

Setting f''(x) = 0 and solving for x:

6x - 6 = 0

x = 1

The inflection point occurs at x = 1. Now, we can analyze the concavity on either side of the inflection point.

For x < 1:

Choosing a test point, let's evaluate f''(0):

f''(0) = 6(0) - 6 = -6

Since f''(0) is negative, the function is concave down for x < 1.

For x > 1:

Choosing another test point, let's evaluate f''(2):

f''(2) = 6(2) - 6 = 6

Since f''(2) is positive, the function is concave up for x > 1.

Therefore, we have the following intervals:

Concave up: (1, ∞)

Concave down: (-∞, 1)

The inflection point of f is (1, f(1)) = (1, 1 - 3 - 6 + 5) = (1, -3).

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The region is shown below; The limits of integration for x are 0 and 1, and y varies from y = 0 to y = 1.

The area of the shaded region is equal to.

For the region to the left of the y-axis, the equation of the curve becomes y = -sqrt(x). The limits of integration for y are 0 and 1.

The area can also be computed as a difference of two integrals:$$A = \int_0^1 1 dx - \int_0^1 \sqrt{x}dx$$$$A = x\Bigg|_0^1 - \frac{2}{3}x^{\frac{3}{2}}\Bigg|_0^1$$

Hence, The area of the shaded region is given by the integral $$\int_0^1 (1-\sqrt{x})dx = \frac{1}{3}.$$

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There are 64 boards in the stack.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

A stack of boards is 24 inches high.

Each board is 3/8 of an inch thick.

As, When dividing fraction, multiply the first fraction by the reciprocal of the second fraction. (A reciprocal is an upside down fraction)

Then, number of boards

= 24 x 8/3

= 8 x 8

= 64

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Answer:

Your answer (x + 4)2 =-11 x + 4)2 13 x + 4)221 Correct answer.

Answer:

152.4 centimeters.

Step-by-step explanation:

1 inch = 2.54 centimeters

60 inches = x centimeters

Where x is the number of centimeters equivalent to 60 inches.

To solve for x, we can set up a proportion:

1 inch / 2.54 centimeters = 60 inches / x centimeters

Cross-multiplying, we get:

1 inch * x centimeters = 2.54 centimeters * 60 inches

Simplifying, we get:

x = (2.54 cm/in) * (60 in)

x = 152.4 cm

Therefore, 60 inches is equivalent to 152.4 centimeters.

Answer:

9) 30 years

10) line passing through points AB and BC are perpendicular

Step-by-step explanation:

9) p = 5t + 150    

Current pop. (in thousands) is 150

Double pop. (in thousands) is 300

300 = 5t + 150

150 = 5t

t = 30

10) line passing through points AB and BC are perpendicular because their slopes are opposite and reciprocal

slope of AB = 3

slope of BC = -1/3

The area is 10 units^2

Right side triangle: A = 1/2bh

A = 1/2(8 units^2)

A = 4 units^2

Left side triangle: A = 1/2bh

A = 1/2(4 units^2)

A = 2 units^2

Square: A = lw

A = 2x2 units^2

A = 4 units^2

Total area: right triangle + left triangle + square

Total area = 10 units^2

\(\text{Hello! :)}\)

\(\large\boxed{10 \text{ units} ^{2} }\)

\(\text{To find the volume, we can divide the shape into 3 different shapes}\\\\\text{A triangle with b = 2 h = 2, a square with s = 2, and a triangle of b = 4 and h = 2}\\\\\text{Therefore:}\\\\\)\(\text{Area of a triangle: A = 1/2(bh), Area of a square: } A = s^{2} \\ \\A = 1/2(2 * 2)\\A = 1/2(4)\\A = 2 \\\\A = 2^{2} \\A = 4\\\\A = 1/2(4 * 2)\\A = 1/2(8)\\A = 4\\\\\text{Add up the areas:}\\\\2 + 4 + 4 = 10 \text{ units} ^{2}\)

Answer:

420 cm

Step-by-step explanation:

I think you multiple 42 by 10

Step-by-step explanation:

The given equations are :

-x+6y = 16 ...(1)

8x-6y = -2 ...(2)

The y-variable will be eliminated when adding the system of  equations.

Adding equations (1) and (2).

-x+6y+8x-6y = 16+(-2)

7x = 14

x = 2

Put the value of x in equation (1).

-2+6y = 16

6y = 16+2

y = 3

There is only one solution to the system of equations i.e. (2,3).

The bank should sample 429 customers.

To determine the number of customers that should be sampled, we need to use the formula for sample size calculation in estimating a population mean. The formula is given by:

n = (Z * σ / E)^2

Where:

n = sample size

Z =  corresponding to the desired level of confidence (98% confidence corresponds to a z-score of approximately 2.33)

σ = population standard deviation

E = desired margin of error

Plugging in the given values, we have:

n = (2.33 * 300 / 89)^2

n ≈ 429

Therefore, the bank should sample approximately 429 customers.

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Answer:

the answer is c. ........

Answer:

C.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x - 8 = 38 - x \\ x + x = 38 + 8 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23\)

The number is 23 if the difference between a number and eight is the same as 38 less the number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The difference between a number and eight is the same as 38 less the number.

Let x be the number

x - 8 = 38 - x

2x = 38 + 8

2x = 46

x = 46/2 = 23

Thus, the number is 23 if the difference between a number and eight is the same as 38 less the number.

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Jennifer Davis will earn $910.00 in simple interest on her investment.

The principal amount is $2,600.

The interest rate is 7% per year.

The time period is 5 years.

To calculate the simple interest, we can use the following formula:

simple interest = principal * interest rate * time

Plugging in the values for the principal, interest rate, and time period, we get:

simple interest = 2600 * 0.07 * 5 = 910

Therefore, Jennifer Davis will earn $910.00 in simple interest on her investment in 5 years.

In words, the simple interest is calculated by multiplying the principal amount by the interest rate and the time period. In this case, the principal amount is $2,600, the interest rate is 7%, and the time period is 5 years. Therefore, the simple interest is $910.00.

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Answer:

K would equal to:

K= 50

Hope that helps! :)

Step-by-step explanation:

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

\(\cfrac{y}{5}=\cfrac{11}{y}\implies y^2=55\implies y=\sqrt{55}\implies y\approx 7.4 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{5}=\cfrac{16}{x}\implies x^2=80\implies x=\sqrt{80}\implies x\approx 8.9\)

The sum of three consecutive number is 63, hence the number is 20.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Let x represent the number. The sum of three consecutive number is 63, hence:

x + (x + 1) + (x + 2) = 63

x = 20

The sum of three consecutive number is 63, hence the number is 20.

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The standard deviation of the profit levels is approximately $83.70. The standard deviation provides a measure of the variability or risk associated with the different profit outcomes in the given scenario.

To calculate the standard deviation of the profit levels given the probabilities associated with each state of nature, we can follow these steps:

1. Multiply each profit level by its corresponding probability. This will give us the weighted profit for each state of nature.

Optimistic: $683.00 * 0.1 = $68.30

Most likely: $103.00 * 0.6 = $61.80

Pessimistic: -$519.00 * 0.3 = -$155.70

2. Calculate the expected value by summing up the weighted profits for each state of nature.

Expected Value = $68.30 + $61.80 + (-$155.70) = -$25.60

3. Calculate the squared difference between each profit level and the expected value.

Optimistic: ($68.30 - (-$25.60))^2 = $5,760.49

Most likely: ($61.80 - (-$25.60))^2 = $4,962.44

Pessimistic: (-$155.70 - (-$25.60))^2 = $11,522.49

4. Multiply each squared difference by its corresponding probability.

Optimistic: $5,760.49 * 0.1 = $576.05

Most likely: $4,962.44 * 0.6 = $2,977.46

Pessimistic: $11,522.49 * 0.3 = $3,456.75

5. Calculate the variance by summing up the weighted squared differences.

Variance = $576.05 + $2,977.46 + $3,456.75 = $7,010.26

6. Take the square root of the variance to get the standard deviation.

Standard Deviation ≈ √$7,010.26 ≈ $83.70

Therefore, the standard deviation of the profit levels is approximately $83.70. The standard deviation provides a measure of the variability or risk associated with the different profit outcomes in the given scenario.

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Answer:

Step-by-step explanation:

-3x + 1 + 10x = x + 4

      -1                  -1

        7x  = x  + 3  

       -x          -x

        6x = 3

      ÷6      ÷6

         x = 1/2

Answer:

in fraction form a = -1/2

in decimal for a = -0.5

hope this helps

Step-by-step explanation:

As per the concept of unitary method, Linda read 5/6 of the book.

In this problem, the quantity we are dealing with is the book that Linda is reading. Let's call the total number of units in the book "x". Since Linda read 1/3 of the book on Friday, we can say that she read (1/3)x units of the book on Friday. Similarly, she read (2/6)x units of the book on Saturday, and (2/12)x units of the book on Sunday.

Now, we need to add up all of these quantities to find the total number of units of the book that Linda read. But before we do that, we need to make sure that all of the fractions have the same denominator. The smallest common multiple of 3, 6, and 12 is 12. So, we will convert all of the fractions to twelfths.

(1/3)x = (4/12)x

(2/6)x = (4/12)x

(2/12)x = (2/12)x

Now, we can add up all of these quantities:

(4/12)x + (4/12)x + (2/12)x = (10/12)x

So, Linda read (10/12)x units of the book in total. But we can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

(10/12)x = (5/6)x

Therefore, the resulting value of x is 5/6

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The mode is usually better for understanding categorical data.

The mode is a statistical measure used to identify the most frequently occurring value or category in a dataset. It is particularly useful when dealing with categorical or qualitative data, where values are divided into distinct categories or groups. Categorical data does not have a numerical value but represents different groups or labels. Examples of categorical data include gender (male or female), color (red, blue, green), or educational level (high school, college, graduate).

The mode is particularly suited for understanding categorical data because it provides information about the most common category or group within the dataset. By identifying the mode, we can determine the category that occurs with the highest frequency, allowing us to gain insights into the distribution and prevalence of different groups. This can be helpful in various fields and applications, such as market research, social sciences, or customer segmentation. The mode helps researchers or analysts understand the most prevalent category, making it a valuable tool for understanding categorical data.

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Answer: 3.  (3,-3) and 4. (-3,4)

Step-by-step explanation: Number 4 is self explanatory of what they are and number 3, you need to figure out what minus 6 equals -3 and that happens to be 3.

He made $112 each week

The total amount earned in three weeks before his weekly earning was doubled = $168

The amount earned each week before his weekly earning was doubles = $168/3

The amount earned each week before his weekly earning was doubled = $56

If his weekly earning was doubled:

The amount earned each week = 2 x $56

The amount earned each week = $112

The line /TV/ that we have been asked to find from the information is the question is obtained as 7.

The sine rule, also known as the law of sines, is a trigonometric formula used to find an unknown side or angle in a triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle.

We know that the missing angle U is obtained from;

180 - (58.3 + 80)

= 41.7°

Then;

8.9/Sin 58.3 = /TV//Sin 41.7

/TV/ = 8.9 Sin 41.7/Sin 58.3

/TV/ = 5.9/0.85

= 7

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