The data set below shows the number of homework assignments required in math classes for a month. Write both at TRUE and a FALSE statement about this dataset. 22 23 23 21 18 4 17 15 23 20 24 15 25 16

a = 281.25 Gm / (1 - (-0.57)²) = 667.3 Gm

b = √(667.3 Gm² * (-0.57)²) = 420.3 Gm

c = √(667.3 Gm² - 420.3 Gm²) = 558.0 Gm

What is the hyperbola?

Hyperbola is the locus of all those points in a plane such that the difference in their distances from two fixed points in the plane is a constant.

To calculate the parameters a, b, c, and e for a hyperbolic orbit, we need to know the perihelion distance (p), semi-latus rectum (l), and eccentricity (e) of the orbit.

l = p / (1 + e)

where e is the eccentricity of the orbit. We can solve for e using the given distances:

e = (p - l) / l = (120 Gm - 281.25 Gm) / 281.25 Gm = -0.57

a = l / (1 - e²)

b = √(a^2 * e²)

c = √(a^2 - b²)

a = 281.25 Gm / (1 - (-0.57)²) = 667.3 Gm

b = √(667.3 Gm² * (-0.57)²) = 420.3 Gm

c = √(667.3 Gm² - 420.3 Gm²) = 558.0 Gm

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The area of the sector is evaluated to be equal to 220 square centimeters.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius and π = 22/7.

We have the angle of the sector = 175° and radius = 12 cm, hence the area of the sector is calculated as follows:

(175°/360°) × 22/7 × 12 × 12

we simplify by division and multiplication

(35/72) × 22/7 × 12cm × 12cm

{35/7 = 5 and 72/12 = 6}

(5/6) × 22 × 12cm²

{12/6 = 2}

5 × 22 × 2cm²

220 cm².

Therefore, the area of the sector is evaluated to be equal to 220 square centimeters.

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A polynomial f (x) of degree 4 that has the following zeros, 0, 6 (multiplicity 2), -2 is: x (x+2) (x-6)²

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminate's and coefficients. Nearly all areas of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

given that,

a polynomial f(x) of degree 4 and has the zeros are 0, 6 (multiplicity 2), -2

We know that If a polynomial P(x) is, of degree 4 and has Zeros are a, b, c (multiplicity 2) then polynomial P(x) will be:

P(x) = (x - a)' (x - b)' (x - c)²

P(x) = (x - a)' (x - b)' (x - c)²

So, here polynomial of degree 4 will be:

F(x) = (x- (-2)) [x-6]² (x-0)

F(x) = x (x+2) (x-6)²

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The list in highest tο lowest οrder is as follows :

0.2

27%

25​

Percentage is a way οf expressing a number as a fractiοn of 100. It is often used to cοmpare or describe relative values, such as prοportions, growth rates, or percentages of a whole.

Percentage is calculated by dividing a part of sοmething by the whole and then multiplying by 100. Fοr example, if a class has 25 students and 5 οf them are absent, we can find the percentage οf absent students by dividing the number οf absent students (5) by the tοtal number of students (25) and then multiplying by 100

Accοrding to given information:

The list in οrder from highest to lowest is:

0.2

27%

25​

Petruta Ciοran 13

8%

0.19 << < < <<

4

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Answer:

Step-by-step explanation:

multiple by the domanatior to get the answer

"What is the area of the floor in this classroom?" is not a statistical question.

Statistical Reasoning is the first course in statistics for students whose college and career paths require knowledge of the fundamentals of the collection, analysis, and interpretation of data.

All statistical questions contain gathering numerical statistics (normally from a set of human beings) after which studying it to attract conclusions approximately the reviews of human beings of a positive phenomenon because the statistics vary relying on the reaction of every person.

This method isn't required to decide the location of the ground due to the fact this has a completely unique solution and might certainly be located via way of means of measuring the peak and width of the school room after which multiplying each number.

therefore, this doesn't mean accumulating loads of statistics and the statistics does now no longer vary.

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Answer:

351.68

Step-by-step explanation:

Given:

The radius of the cylinder = r = 4 cm

Height of the cylinder = h = 7 cm

The volume of the cylinder is given by the formula:

V = πr²h

Using π = 3.14

so, the volume of the cylinder will be:

[tex]3.14 X4^{2} X7 = 3.14 X 16 X 7 = 351.68[/tex]

Volume of the cylinder = 351.68

Answer:

y=2/5x+1

Step-by-step explanation:

Answer:

y = 2/5 x + 1

Step-by-step explanation:

The slope is the change in y over the change in x

[tex]\frac{3-1}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]

slope: [tex]\frac{2}{5}[/tex]

The y-intercept is 1.  When x = 0, the y is the intercept. (0,1)

Answer:

about 1.67

Step-by-step explanation:

24x=40

Answer:

Below

Step-by-step explanation:

Gravel is  4 / (4+3+2) = 4/9 ths of the total

    4/9 x 27 m^3 = 12 m^3 gravel

Similarly  sand is 3/9th    3/9 * 27 = 9 m^3

  and the rest is cement   6 m^3

63, 69, 75 and 81 is the first four terms of the seqence

Given the recursive formula of the given sequence

an = 63 + (n - 1)*6

We need to determine the first four terms of the sequence

When n = 1;

a1 = 63 + (1 - 1)*6

a1 = 63

When n = 2;

a2 = 63 + (2 - 1)*6

a2 = 69

When n = 3;

a3 = 63 + (3 - 1)*6

a3 = 75

When n = 4;

a4 = 63 + (4 - 1)*6

a4 = 81

Hence the first four terms of the sequence are 63, 69, 75 and 81.

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Answer:

y=1/5x +4

Step-by-step explanation:

Write an equation for the line that is parallel to the given line and passes through the given point. y = 5x + 10; (2, 14) y=1/5x +4

The outputs for the given inputs are:

Input:   -2  -1   0  1

Output: 2   2  0  4

What is a linear function?

A linear function is a mathematical function that has a constant rate of change, or slope, between its input and output variables. In other words, the output of a linear function changes at a constant rate as the input changes.

The given function y = x(x + 3) is not a linear function because it contains a squared term (x^2) and thus has a non-constant rate of change.

To complete the table for the given function, we substitute each input value into the equation and simplify:

Input: -2

Output: (-2)(-2 + 3) = 2

Input: -1

Output: (-1)(-1 + 3) = 2

Input: 0

Output: (0)(0 + 3) = 0

Input: 1

Output: (1)(1 + 3) = 4

Therefore, the outputs for the given inputs are:

Input:   -2  -1   0  1

Output: 2   2  0  4

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The probability that the word formed STATISTICS will be; 1/10! = 1/3628800

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.

The total number of tiles in a bag is; 10

WE are given that once a tile is drawn, we will not place the tile back in the bag.

We should find the probability that randomly selected tiles spell the word, STATISTICS, that is a 10 letter word.

Now when we draw the first tile,

1 st tile = 1/10

Now there are only 9 tiles left.

2nd tile probability = 1/9

Now only 8 tiles left then

3rd tile probability = 1/8

Therefore the probability that the word formed is STATISTICS would be

= 1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2

= 1/10! = 1/3628800

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For the inequality k≥0, all the integers which satisfies the given inequality are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The inequality,

k ≥ 0

The inequality k ≥ 0 means that k is greater than or equal to 0. This can be represented on a number line as follows:

-------------k-------------

where the line represents all real numbers and the arrow points to the right to indicate that k can be any real number greater than or equal to 0.

All one-digit integers that satisfy the inequality k ≥ 0 are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

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The value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.

Central Limit Theorem states that as the sample size increases the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, for a sample of 8 two-lined salamanders, the standard deviation of the sample means is:

σ = σ/√n = 2.2/√8 = 0.89

We are looking for the value of x such that the probability of the sample mean being between 13.6-x and 13.6+x is 0.6827. This corresponds to the area under the normal curve within x standard deviations of the mean.

We can use a standard normal table or calculator to find the value of x corresponding to 0.6827. The result is approximately x = 0.89.

So, the value of x such that the probability of the sample mean being between 13.6-0.89 and 13.6+0.89 is 0.6827 is approximately x = 0.89.

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The cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.

The average rate at which the prices of goods and services change within a year is called the average inflation rate.

Given that, a meal in a restaurant cost $40 in 2000, we need to find its price in 1992 dollars,

The dollar had an average inflation rate of 2.45% per year between 1992 and today,

The year change = 2000 - 1992 = 8

Therefore, the $40 in 1992 =

= 40 - (40 × 8 × 2.45 / 100)

= 40 - (7.84)

= 32.16

Hence, the cost of the meal that cost $40 in 2000 would have cost $32.16 in 1992.

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The intersection of sets P and Q is given as follows:

P and Q = {2}.

The sets P and Q for this problem are defined as follows:

The intersection between two sets is composed by the elements that belong to both of the sets.

Hence the intersection of sets P and Q is given as follows:

P and Q = {2}.

As the element 2 belongs to both sets P and Q.

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The independent variable affects the dependent variable. The correct option is B.

A variable is something whose value can change and is not fixed. Typically, the letters x, y, z, etc. are used to indicate variables. (b) Constants: An object whose value is fixed for the current circumstance is referred to as a constant. The constant's value may not be known, but we do know that it is fixed.

A variable is an object that you are trying to measure. It has two types; independent and dependent variables. An independent variable is a variable that is not affected b other variables.

A dependent variable on the other hand is a variable that depends on other variables. Suppose you want to know the quality of sleep of the students in their academic performance. The quality of sleep is the independent variable and academic performance is the dependent variable.

The complete question is given below.

What is the relationship between the independent variable and the dependent variable?

a. The dependent variable affects the independent variable.

b. The independent variable affects the dependent variable.

c. Both the independent variable and the dependent variable affect each other.

d. Neither the dependent variable nor the independent variable affects each other.

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The traveler's luggage should weigh around 806.722 ounces.

To convert kilograms to ounces, you can use the conversion factor of 35.274 ounces per kilogram.

Here's the formula to convert kilograms to ounces:

Ounces = Kilograms * 35.274

When it comes to measuring weight, the metric system and the imperial system use different units of measurement. The metric system uses kilograms as its unit of measurement for weight, while the imperial system uses ounces.

To convert between the two systems, it is necessary to know the conversion factor between kilograms and ounces. One kilogram is approximately equal to 35.274 ounces. This means that to convert from kilograms to ounces, you can multiply the number of kilograms by 35.274.

In the case of the traveler in Spain, they wanted to ensure that their luggage did not exceed 23 kilograms in weight. To determine this weight in ounces, they multiplied 23 kilograms by the conversion factor of 35.274 ounces/kilogram, which gives a result of 806.722 ounces.

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The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.

There is a connection between one set of values about one variable and an other number of values. direct variation With the equations y = mx + b, you have the direct variant function y = mx (often written y = kx). Equations that describe the relation between independent variables in a language also explain how those variables vary between one another. There are various types of variations, including linear, inverse, joint, among combination variations. If y and x are said to be directly connected, then y must equal kx, where k is a number that is every now and again referred to as the perpetual of variation. If y and x have such an inverse connection, then y equals k/x, where k is just the variance constant.

given

1a. Every patient day, the predetermined overhead rate is $970.

compute the combined expected overhead expenses for the ICU and other:

ICU: $3,200,000 plus $236 each patient-day multiplied by 2,000 patient-days equals $3,672,000.

$14,000,000 plus ($96 for each patient day)

(15,728,000 patient-days) divided by 18

Add the anticipated overhead expenses for ICU and Other:

$3,672,000 + $15,728,000 = $19,400,000

19,400,000 divided by 20,000 patient days equals 970 each patient day.

1b. The overall expense allocated to Patients A and B.

The estimated overhead costs for ICU and other are $970 per patient day, or $19,400,000 divided by 20,000 patient days.

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The answers for each polynomial are:

a) 4x³ - 8: degree is 3, and the number of terms is 2.

b) 2x⁴ - 7x² - 5x + 1: degree is 4, and there are 4 terms.

c) x³ +5x² + 28 - x:   standard form is: x³ +5x²  - x + 28 And the leading coefficient is 1.

d) 24 - x³ + x:   standard form is:  -x³ + x + 24 and the leading coefficient is -1.

The degree of a polynomial is equal to the maximum exponent in the variable, and the number of terms is just the number of "elements" separated by the symbols + or -.

For the first one:

4x³ - 8

The degree is 3, and the number of terms is 2.

For the second one:

2x⁴ - 7x² - 5x + 1

The degree is 4, and there are 4 terms.

In the next part you need to write them in standard form and write the leading coefficient. The leading coefficient is the coefficient on the term with the largest exponent.

For the first one:

x³ +5x² + 28 - x

The standard form is:

x³ +5x²  - x + 28

And the leading coefficient is 1.

And the last one is:

24 - x³ + x

The standard form is:

-x³ + x + 24

The leading coefficient is -1.

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a). The formula that expresses v in terms of t is v = 22 - 2t, b).  As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.

What is the volume?

'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3, etc. Sometimes, volume is also termed capacity.

a). The volume of water in the tank, v, decreases by 2 gallons per hour, so the formula for v in terms of t is v = 22 - 2t.

b). As t increases from 3 to 5, v varies from 16 to 12. That is, as t goes from 3 to 5, v decreases from 22 - 2(3) = 16 to 22 - 2(5) = 12.

c). As t varies from 3 to 5, t changes by 5 - 3 = 2, and v changes by 16 - 12 = 4.

Hence,  a). The formula that expresses v in terms of t is v = 22 - 2t, b).  As t increases from 3 to 5, v varies from 16 to 12, c). As t varies from 3 to 5, v changes by 16 - 12 = 4.

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Answer:

D.

Step-by-step explanation:

The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs of the trapezoid.

Therefore, the answer is D.

Hope it helped!

Answer:

Step-by-step explanation: To calculate the total amount of money Paul will have saved after three years, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = the total amount after t years

P = the initial principal, which is $150

r = the annual interest rate, which is 2.5% or 0.025

n = the number of times the interest is compounded per year, which is 12 since it is compounded monthly

t = the number of years, which is 3

Substituting the values into the formula, we get:

A = 150 * (1 + 0.025/12)^(12*3)

= 150 * 1.081567

= $162.23

Therefore, Paul will have saved up $162.23 after three years have passed.

Yes, Liam is correct as the graph depicts a positive correlation as the temperature increases the ice cream sales also increases.

A correlation between two variables shows a statistical connection between them. Causation is the process whereby a change in one variable causes a change in another.

While conducting research, you may have come across the proverb "correlation doesn't imply causality." Although correlation and causality are related ideas, understanding how they differ helps improve your capacity to assess and critically analyze scientific data.

Armonte said the graph depicts causation and yes Armonte is correct as causation means that changes in one variable bring about changes in the other; there is a cause-and-effect relationship between variables. The two variables are correlated with each other and there is also a causal link between them.

So here the change in the temperature brought about the change in the ice cream sales. As the temperature rose the ice cream sales too started increasing.

Now two reasons as to why this represents causation instead of correlation:

Therefore, the graph shows a positive correlation, but it represents causation.

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Answer: B. 200

Step-by-step explanation:

Since "rafts" and "tubes" takes up exactly 50% of the circle graph, the answer is 50% of 400, or 200. The correct answer is option B. 200

Reduced the equation to one of the standard forms

(a) z²/36 = 4x²/36 + 9y²/36 + 1

(b) x = 2y² + 3z

(c) (x + y + 2z)²

(d) (x - y + z)²

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

z²/36 = 4x²/36 + 9y²/36 + 1

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.

(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

x² + y² + 4z² - 4y - 24z + 36 = 0

= (x + y + 2z)²

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:

x² - y² + z² - 4x - 2y - 2z + 1 = 1

= (x - y + z)²

This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.

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After reducing the equation to one of the standard forms, the equations will be (a) z²/36 = 4x²/36 + 9y²/36 + 1, (b) x = 2y² + 3z, (c) (x + y + 2z)², and (d) (x - y + z)²

It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

(a) The equation z² = 4x² + 9y² + 36 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

z²/36 = 4x²/36 + 9y²/36 + 1

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3/2, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(b) The equation x = 2y² + 3z² is a standard parabolic cylinder equation. The surface is a cylinder and is classified as a parabolic cylinder.

(c) The equation 4x² + y² + 4z² - 4y - 24z + 36 = 0 can be reduced to the standard form of an ellipsoid by dividing both sides by 36:

x² + y² + 4z² - 4y - 24z + 36 = 0

= (x + y + 2z)²

This is the equation of an ellipsoid with center at the origin and semi-axes of length 3, 3, and 6, respectively. The surface is a solid and is classified as an oblate ellipsoid.

(d) The equation x² - y² + z² - 4x - 2y - 2z = 0 can be reduced to the standard form of a hyperboloid of two sheets by subtracting 1 from both sides:

x² - y² + z² - 4x - 2y - 2z + 1 = 1

= (x - y + z)²

This is the equation of a hyperboloid of two sheets with center at the point (-2, -1, -1) and semi-axes of length √2, √2, and √6, respectively. The surface is a solid and is classified as a hyperboloid of two sheets.

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Answer:the answer is 90

Step-by-step explanation:

Answer:9

Step-by-step explanation: