1: A study group is interested in estimating the average monthly income of 1,500 employees. It decides to select a random sample of 60 female and 80 male employees using proportional allocation. Identify: a) the population and sample b) the scope of data collection (censes or sample survey) (c) The variable of interest d) The possible sources of data collection colfaction e) The type of statistics used ​

we know that

discriminant of quadratic is [tex]b^{2}[/tex]-4ac

putting values we get

81-32

= 49

hence the discriminant is 49

The fraction expression 2 1/2 - 4 1/4 when evaluated is -1 3/4

To solve 2 1/2 - 4 1/4, we need to convert the mixed numbers into improper fractions, then find a common denominator and subtract the two fractions.

First, we convert 2 1/2 and 4 1/4 into improper fractions:

2 1/2 = 5/2

4 1/4 = 17/4

Next, we find a common denominator. In this case, the smallest common denominator is 4:

5/2 = 10/4

17/4 = 17/4

Now we can subtract the fractions:

10/4 - 17/4 = -7/4

Finally, we can convert the resulting improper fraction back into a mixed number:

-7/4 = -1 3/4

Therefore, 2 1/2 - 4 1/4 = -1 3/4.

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According to the information, if the radio selects listerners randomly, the sample is random. But if they select listerners are selected without random method the sample may be biased.

If the radio station randomly selected a subset of their listeners and asked them to call in, then the sample would be random. This would help ensure that the sample is representative of the overall population of the radio station's listeners, and would allow for valid conclusions to be drawn about the preferences of the wider population based on the results of the survey.

However, if the radio station did not use a random sampling method, then the sample may be biased and not representative of the overall population of the radio station's listeners. For example, if the radio station only advertised the survey during certain times of day or on certain shows, then the sample may be biased towards listeners who are more likely to be listening during those times or shows. Similarly, if the radio station only advertised the survey on certain social media platforms or websites, then the sample may be biased towards listeners who use those platforms or websites.

Note: This question is incomplete. Here is the complete information:

State whether or not the sample is random. If it is not random, explain why

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The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.

We have:

cos²θ + sin²θ = 1

Since sine is negative and cosine is positive, we know that:

sinθ = -sqrt(1 - cos²θ)

Substituting cosθ = 3√(2)/2, we get:

sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2

Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.

Since cosine is positive in the fourth quadrant, we have:

cos⁻¹(3√(2)/2) = π/4

Substituting this value, we get:

sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4

Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.

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Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)

Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.

x - 2 | x^2 - 4x + 7

            x^2 - 2x

           ---------

                 -2x + 7

                 -2x + 4

                 -------

                        3

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Answer:

x = [tex]\frac{5u+4y}{2-6z}[/tex]

Step-by-step explanation:

2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side

2x - 4y = 6xz + 5u ( add 4y to both sides )

2x = 6xz + 5u + 4y ( subtract 6xz from both sides )

2x - 6xz = 5u + 4y ← factor out x from each term on the left side

x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)

x = [tex]\frac{5u+4y}{2-6z}[/tex]

Answer: each package weighs 3.25lb 

Step-by-step explanation:

looking at the weight of each package (3lb 4oz), we can convert the 4oz to pounds by dividing by 16oz/lb; 4/16 = 0.25lb 

Answer:

No Solution

Step-by-step explanation:

Because this solution deals with absolute value equations.

A. The slopes are the same but the y - intercepts are different.

In a graph, the slope is the steepness of a line, which is a measure of how quickly the y-coordinate changes with respect to the x-coordinate. It is represented by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

The slope is often denoted by the letter m, and is calculated as:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

In a graph, the y-intercept is the point where a line or curve intersects the y-axis. It is the value of the dependent variable (usually denoted by y) when the independent variable (usually denoted by x) is equal to zero.

The y-intercept is often denoted by the letter b, and is expressed as a coordinate point (0, b), where 0 represents the x-coordinate and b represents the y-coordinate. For example, in the equation of a line y = mx + b, the y-intercept is the value of b.

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The solution to the prompt of multiple square roots is 5.

To obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.

So this gives

√30 =5.47

5.47 + 5.47 + 5.47 + 5.47

= 21.88

=4.67 approximately 5

So. option 5 is the solution.

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An equivalent fraction to 1 whole and 7/8 is 15/8.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. It is, in other words, a "top-heavy" fraction since the fraction represents a value greater than one full unit.

1 whole and 7/8 can be written as a mixed number, which is a combination of a whole number and a fraction:

1 whole and 7/8 = 1 + 7/8

To find an equivalent fraction, we can convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction, and then adding the numerator. The result is the numerator of the improper fraction, and the denominator stays the same:

1 + 7/8 = (1 × 8 + 7)/8 = 15/8

Therefore, an equivalent fraction to 1 whole and 7/8 is 15/8.

For instance, the improper fraction 7/4 results from the numerator's (7), which is greater than the denominator (4).

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Answer:

$52.50

Step-by-step explanation:

1500 * 3.5% = 52.50

Answer:

$52.5 for the first year

Step-by-step explanation:

You can derive a decimal from a percentage by dividing by 100.

For example, 1% is 0.01

3.5% is 0.035

You can also move the decimal point back 2 places, but that's cringy.

So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.

Therfore, we must multiply:

1500 by 3.5%

We stated that 3.5% is 0.035, so we can replace that

1500 * 0.035

Plug that into a caluclator and we get.....

$52.5 for the first year

ANSWER CHOICE 1

Phew! That was a long problem! May I please have Brainliest?

Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.

Here,

Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).

The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.

To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:

P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)

= (1/2) x (1/3)

= 1/6

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Let the number of twin births in 2000 be x.

According to the problem, the number of twin births in 2015 increased by 14%, which means the number of twin births in 2015 is:

x + 0.14x = 1.14x

We also know that the number of twin births in 2015 is approximately 133,950, so we can set up the following equation:

1.14x = 133,950

Solving for x, we get:

x = 117,500

Therefore, there were approximately 117,500 twin births in 2000.

Answer:

Casey's monthly payment is $150.
Anita's monthly payment is $230.

Step-by-step explanation:

Part A:

The system of equations that describes this situation is:

a + c = Total monthly bill

a = c + 80

where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.

Part B:

To solve the system, we can substitute the second equation into the first equation and get:

(c + 80) + c = Total monthly bill

Simplifying this equation, we get:

2c + 80 = Total monthly bill

We also know that over the course of 4 months, their combined bills are $1,520. So we can write:

4(Total monthly bill) = 1520

Substituting the equation for Total monthly bill from the previous step, we get:

4(2c + 80) = 1520

Simplifying this equation, we get:

8c + 320 = 1520

Subtracting 320 from both sides, we get:

8c = 1200

Dividing both sides by 8, we get:

c = 150

So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:

a = c + 80

a = 150 + 80

a = 230

Therefore, Anita's monthly payment is $230.

Answer:

x ≥ -5

Step-by-step explanation:

Since we see the dot is filled in, we know the sign is either ≤ or ≥. Then, we can see that x is greater than -5 as the arrow is pointing in the positive direction (to the right). Therefore, it would be x ≥ -5

Answer: Directly proportional.

Step-by-step explanation:

      y = -x is directly proportional for a few reasons.

➜ The graph of this equation is a straight line, so all the ratios of points are equal.

➜ The constant of proportionality (k) is equal to -1.

➜ This line intersects the graph at the origin (0, 0).

➜ See the graph below.

An expression to show how many books would be on each table is a/10

To find out how many books would be on each table, we need to divide the total number of books by the number of tables.

First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.

Next, we need to divide a by 10, the number of tables. This gives us the expression:

a/10

So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.

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Complete question is:

Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.

Answer:

translation

hope this helps:) !!

The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = 2x = 0

∂f/∂y = 2y = 0

From these equations, we can see that the critical point occurs at (x,y) = (0,0).

To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 0

At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.

Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.

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Answer:

Step-by-step explanation:

There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.

To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:

(1/36) x 180 = 5

So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.

Answer:

--------------------------

As per given, the distance from the center to both of the chords is same, therefore both chords have same length:

The length of each chord is:

Use Pythagorean theorem to find the radius, the distance from the center to one end of the chord:

Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!

Answer:

1/6

Step-by-step explanation:

Chances of getting 2 = 1/6

Answer:

m<H = 62.7°

Step-by-step explanation:

If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.

Answer:

H = 62.7 degrees

Step-by-step explanation:

Because this is a right triangle, we can use one of the trigonometric functions to find angle H:

Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):

sin(H) = 8/9

We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:

arcsin(8/9) = H = 62.7 degrees

Answer:

9.38

Step-by-step explanation:

I did the math

The length of circumference of this circle is 21.9911 inches.

The area of this circle is, approximately, 38.4845 (in²).

The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:

[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.

The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.

Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.

So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:

[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]

We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:

[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].

Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.

The length of circumference of this circle is 21.9911 inches.

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These are the most commonly used formulas for the area of circles:

[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.

[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.

Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.

Let's use the area formula that directly involves diameter to avoid any conversions.

Substitute letter "d" by the length of the diameter (7 inches).

[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]

Therefore, the area of this circle is, approximately, 38.4845 (in²).

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The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).

Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)

Where:

(h, k) = vertex

4p = distance between the vertex and focus

Comparing this with (x + 3)² = -20(y + 1) will gives us

(x + 3)² = -20(y + 1)

= (x - (-3))² = -20(y - (-1))

The vertex of the parabola is = (-3, -1)

4p = -20

p = -20/4

p = -5

The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.

The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.

The endpoints of the latus rectum are:

(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).

Therefore, the correct option is f.

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We can set up the equation :

0.9x = 110 ,

where x is the unknown number. To solve for x, we can divide both sides by 0.9 :

x = 110 ÷ 0.9

x = 122.22 (rounded to two decimal places)

So the unknown number is approximately 122.22.

To find 9% of that number, we can multiply 122.22 by 0.09 :

0.09 × 122.22 = 11.00 (rounded to two decimal places)

Therefore, 9% of the number is approximately 11.

Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.

Using a calculator, you can directly evaluate the expression to get:

2430 + 15√2 ≈ 2462.11

Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:

2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21

Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.

Step-by-step explanation: