What is the Range of the data set

Answer:

domain: [tex](-\infty, \infty)[/tex]

range: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]

The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.

The given quadratic equation is : 8x² + 16x + 3 = 0

Comparing this equation with  ax² + bx + c = 0 we get :

a = 8 , b = 16 and c = 3

Now we will use the quadratic formula:

[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]

Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.

[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]

The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.

A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.

Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].

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The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:[tex]\frac{14}{42}*100[/tex]%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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The proportion of cats in the sample suffers from separation anxiety is 33%

Given 432 cats, a sample of 42 cats is taken.

Out of these 42, cats 14 are suffering from separation anxiety.

The proportion of cats suffering from separation anxiety is: 14/42

The percentage of Cats suffering from separation anxiety is:(14/42)*100%

This is equal to 33%, rounding off to the nearest percentage value.

Therefore, The proportion of cats in the sample who suffers from separation anxiety is 33%.

The sample proportion (p^hat) describes the proportion of people in a sample who have a particular attribute or trait. Divide the number of persons (or items) who have the characteristic of interest by the total number of people (or items) in the sample to get the sample proportion.

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The value of the summation will be equal to 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that X=3/5, Y=1/3, and z=2⁴/₅.

The value of the Z+ ( X x Y ) will be calculated as,

E = Z + ( X x Y )

E = 2⁴/₅ + ( 3 / 5 ) x ( 1 / 3 )

E = 14 / 5 + 1 / 5

E = 15 / 5

E = 3

Therefore, the value of the summation will be equal to 3.

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The number of wrapped present with 20 centimeters of tape is given as 5 presents.

In this question, we have the following values

12 centimeters of tape was used to wrap 3 presents

hence we would have

12 = 3 presents - - - - 1

Then we are to know the presents that would be wrapped with the use of 20 centimeters of tape.

we would have

20 = ? presents - - - 2

We have to bring the equations together

12 = 3 presents

20 = ? presents

? is the presents that is to be wrapped with 20 centimeters of tape. It is our unknown.

We would have to cross multiply

12 x ? = 3 x 20

12? = 60

We would have to divide through by 12 in order to get the unknown

? = 60 / 12

? = 5

Hence the number of presents that she wrapped is given as 5

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Answer:

-1/4 * x + 2

Step-by-step explanation:

first figure out the slope. You can easily read the point where the graph is crossing the y axis. From there, more right and read how much the graph goes up wor down. You see the graph goes down, so you know the slope must be a negative value. To get the full value of the slope, you need to work out how much the graph goes down if you go 1 right. So when you move 1 right from the point 2 on the y axis, you can't easily read how much it went down. But you can see that the graph passes the pont of x = 4 and y = 1. So it went 4 right and 1 down. To only got 1 down you divide y/x -> 1/4
So the slope is -1/4
and because the graph hits the y axis at 2 and not at 0, you need to add +2 to the equation.

Answer: The volunteers are unaware of which surgery they receive.

Step-by-step explanation:

Step-by-step explanation:

[tex](3x + 2) + x = 180 \\ 3x + x = 180 - 2 \\ 4x = 178 \\ x = 44.5[/tex]

Answer:

x° = 44.5°

Step-by-step explanation:

x° and (3x + 2)° are supplementary angles, which means they add up to 180°.

Equation: x + 3x + 2 = 180

Step 1: Combine like terms.

[tex]\implies 4x + 2 = 180[/tex]

Step 2: Subtract 2 from both sides.

[tex]\implies 4x + 2 - 2 = 180 - 2[/tex]

[tex]\implies 4x = 178[/tex]

Step 3: Divide both sides by 4.

[tex]\implies \dfrac{4x}{4}=\dfrac{178}{4}[/tex]

[tex]\implies x = 44.5[/tex]

Step 4: Substitute 44.5 as the value of x in (3x + 2) to find its measure.

[tex]\implies 3(44.5)+2[/tex]

[tex]\implies 135.5[/tex]

Therefore, the measure of x° is 44.5°, and the measure of (3x + 2)° is 135.5°. Together, they add up to 180°.

The area of the parallelogram shown in this problem is of:

A = 432 units squared.

The area of a parallelogram of base b and height h is given by the multiplication of these two dimensions, as presented as follows:

A = b x h.

In this problem, these dimensions are given as follows:

(the height is perpendicular to the sides of the parallelogram, forming an angle of 90º, as is the case in this problem).

Hence the area of the parallelogram, applying the multiplication of the obtained base and height, is calculated by the multiplication of the base and of the height given as follows:

A = 27 x 16 = 432 units squared.

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Answer:

432

Step-by-step explanation:

The area of a parallelogram is the product of a side length (the base) and the perpendicular distance between that side and the opposite side (the height). In this case, we can use (line)DC as a base and (line)EG as the matching height, so the area is equal to

(DC) ∙ (EG) = 27 ∙ 16 = 432.

An equation relating x and y is given by y = 3x/4 - 11/2.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For the slope of this line using point AB, we have:

Slope of AB = (2 - (-1))/10 - 6)

Slope of AB = (2 + 1)/4

Slope of AB = 3/4

Since point AB and points (2, -4), (x, y) all lie on the same straight line, they would all of the same slope. Therefore, an equation relating x and y can be calculated as follows:

3/4 = (y + 4)/(x - 2)

3(x - 2) = 4(y + 4)

3x - 6 = 4y + 16

4y = 3x - 6 - 16

4y = 3x - 22

y = 3x/4 - 22/4

y = 3x/4 - 11/2

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There are no pair of numbers that multiply to 36 and add up to -7

The factors of number refers to any of various numbers multiplied together to form some whole. For instance, 3 is a factor of 12, as are 2, 4 and 6.

The pairs of factors of 36 that multiply to 36 are:

From the pair of numbers above, none add up to -7

Therefore, there is no pair of numbers whose product is 36 and sum is -7

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ANSWER: 137

Step-by-step explanation:

This can be rewritten as:

18 × 7 - (-1)² -(-9)

Using BODMAS

firstly open the brackets using the negative sign, we have;

18 × 7 +1² + 9

Now you can apply your BODMAS.

126 + 1 + 9

ANS = 137

There are 6188 ways are there to choose two dozen croissants with at least two of each kind.

A combination is the combination of two or more distinct things. Although it is not necessary to combine things in pairs, the term "combining" comes from the Latin word for "joining together two by two."Combination repetition is permitted.

There are six different varieties of croissants (n = 6), and we must select two dozen croissants (r = 12) with at least two of each type.

In combination, The order does not matter and repetition is allowed.

thus, according to combination,

[tex]C( n+ r - 1,r) = \frac{(n + r - 1 )!}{r! (n-1)!} \\\\C( 6+ 12 - 1,12) = \frac{(6 + 12 - 1 )!}{12! (6-1)!} \\\\ = \frac{17!}{12!5!} \\= 6188[/tex]

thus, there are 6188 ways possible to choose two dozen croissants with at least two of each kind.

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Answer:

Step-by-step explanation:

weknr f not sure

Answer:

12

Step-by-step explanation:

1/2x+1/3x=10

We simplify by making common denominator and adding them (if you don’t know how to do that please tell me)

3/6x+2/6x=10

5/6x=10

Now divide 5/6 on both sides

5/6x=10

/5/6. /5/6

x=10*6/5

x=60/5

x=12

Hopes this helps please mark brainliest

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Equation of a line:

y = 2x  - 3

y = 2 x 0 - 3 = -3

y = 2 - 3 = -1

y = 2 x 2 - 3 = 4 - 3 = 1

Table

x   0     1     2

y  -3    -1     1

The graph of the straight line is given below.

Thus,

The table is

x   0     1     2

y  -3    -1     1

The graph of the line is given below.

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The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units

A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.

Angle ∠A = 45°

The length of the segment the altitude CD divides AB into = 20 and 21 units

Please find attached a drawing created using MS Word based on the question parameters.

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

AD = 20

Therefore;

[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]

CD = 20 × tan(45) = 20

Pythagorean theorem applied to right triangle ΔCBD, indicates that;

[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]

DB = 21 units, which gives;

[tex]\overline{BC}^2[/tex] = 20² + 21² = 841

BC = √(841) = 29

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The image of (5, 8) after a reflection over the line y = - x is (-5, -8 ).

To see the graph.

Given,

In the question:

What is the image of (5,8) after the reflection over the line y= -x?

Now, According to the question:

The image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

But, It is given that  the reflection over the line y= -x

Hence, The image of (5, 8) after a reflection over the line y = - x is

(-5, -8 ).

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Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

Answer:

m = -2

Step-by-step explanation:

slope of AB

(4-3)/(-1-2)= 1/-3 = -1/3

parallel lines have the same slope

slope of CD = -1/3

we can now find the line that passes through the point C

y-5= -1/3(x-4)

y = -1/3 x +4/3 +5

y = -1/3 x + (4+15)/3

y = -1/3 x + 19/3

this line must passes also through the point D

we know its y, so:

7 = -1/3 x + 19/3

(7 * 3) = (-1/3 x + 19/3) * 3

21 = - x + 19

x = 19 - 21

x = -2

The correct way to write 0.0000250 m in scientific notation is 2.5 · 10⁻⁵ m.

Scientific notation is a convenient way to write numbers that are very large or very small. A number written in scientific notation consists of a number greater than or equal to 1 but less than 10 multiplied by a power of 10. Here are some examples of numbers written in scientific notation:

Since you're given a number less than 1, move the decimal point to the right until you have a number between 1 and 10. Then, count the number of times you moved the decimal and write that as negative exponent over a base of 10. Finally, write out number multiplied by the power. You'll get 2.5 · 10⁻⁵ if you do those things correctly.

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Answer:

A. 2.50 Times. 10–5 m

Step-by-step explanation:

other one is wrong

The the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is the function -

x = y

We have the function -

y = x

Now, we can define locus as -

A curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.

This equation -

y = x

is a straight line.

Refer to the graph attached.

The slope of the line is [m] = 1

The [y] intercept is at [c] = 0

Therefore, the the locus of the equation y = x is a straight line. The slope of the linear function → y = x is [m] = 1 and the [y] intercept is at [c] = 0.

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Answer: the slope is unidentified

Step-by-step explanation:

The probability that Roger Federer wins at least 2 Grand Slam titles is 60.82%

Given data:

To calculate the probability that Roger wins at least 2 Grand Slam titles out of the 20 competitions during the 5-year period, we can use the binomial distribution.

The binomial distribution calculates the probability of obtaining a certain number of successes (in this case, Roger winning a Grand Slam) in a fixed number of independent trials (the 20 competitions), given the probability of success in a single trial (0.1).

We need to calculate the probability of Roger winning 2, 3, 4, ..., up to 20 Grand Slam titles and then sum those probabilities to find the overall probability of winning at least 2 titles.

Using a binomial probability formula, the probability of getting exactly k successes in n trials is given by:

[tex]P(X = k) = C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]

Where:

C(n, k) is the binomial coefficient (n choose k)

p is the probability of success in a single trial (0.1)

n is the number of trials (20)

To find the probability of winning at least 2 Grand Slam titles, we calculate the probabilities for k = 2, 3, 4, ..., 20, and sum them up:

P(X ≥  2) = P(X = 2) + P(X = 3) + ... + P(X = 20)

P(X ≥  2) = Σ(P(X = k)) from k = 2 to 20

Calculating each individual probability P(X = k) and summing them up can be tedious. However, use complementary probability to simplify the calculation:

P(X ≥  2) = 1 - P(X = 0) - P(X = 1)

[tex]P(X = 0) = C(20, 0) * 0.1^0 * (1 - 0.1)^{(20 - 0) }[/tex]

[tex]=(1 - 0.1)^{20}[/tex]

= 0.12157

[tex]P(X = 1) = C(20, 1) * 0.1^1 * (1 - 0.1)^{(20 - 1) }[/tex]

[tex]= 20 * 0.1 * (1 - 0.1)^{19 }[/tex]

= 0.27017

P(X ≥  2) = 1 - 0.1074 - 0.2684

P(X ≥ 2 ) = 0.60826 (approximately)

Hence, the probability that Roger Federer wins at least 2 Grand Slam titles out of the 20 competitions is approximately 0.60826, or 60.82%.

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The probability of favorable  outcomes  P(E) = 37/256

What is probability in math?

Given,

      8 coins are faced simultaneously .

total outcomes = 2 * 2 * 2* 2 * 2 * 2 * 2 * 2

                             = 2⁸

                             = 256

favorable outcomes = 6 heads + 7 heads + 8 heads

                      = ⁸C₆ + ⁸C₇  + ⁸C₈

                       = 28 + 8 + 1   = 37

the probability of favorable  outcomes =            

              P(E) = 37/256

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Using the concepts of the hypothesis test, it is found that the p-value is of 0.0007 corresponding to  ten students who  were surveyed and asked how many hours they spent playing video games.

At the null hypothesis, we test if the mean is still the same, that is, of 10.2 hours per week, thus:

H[tex]_o[/tex] = μ=10.2

At the alternative hypothesis, we test if the mean has increased, that is, if it is greater than 10.2 hours per week, thus:

H₁=μ> 10.2

Ten students were surveyed, so there are 9 df. The test statistic is t = 0.45, and it is a one-tailed test, as we are testing if the mean is greater than a value.

Thus, using a t-distribution calculator, the p-value of the test is of 0.0007.

Hence, when the ten students were surveyed and asked how many hours they spent playing video games and the test statistics is equal to 0.45,then the p-value is 0.0007

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The value of m is 8.

The amount of times a number has been multiplied by itself is shown by its exponent. The result of multiplying 8 by itself n times is represented as follows:

8 x 8 x 8 x 8 x …..n times = [tex]8^n[/tex]

Given:

[tex]$(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.[/tex]

Now, solving for m

[tex](m-4)^4[/tex] = 16

[tex](m-4)^4[/tex] = [tex]4^4[/tex]

Taking the quad root we have

m -4 = 4

m = 4+ 4

m = 8

Hence, the value of m is 8.

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Answer: 9,000 mL

Step-by-step explanation:

If you multiply 2,000 by 4, you would get 8,000 & if you multiply .5 by 2,000, you get 1,000. If you add both the totals, you would end up with a final answer of 9,000 mL.