Select all the correct answers.
For which values is this expression undefined?
x-1/(x^2-2x-3) + 5/(2x^2+2x)

Considering the box-and-whisker plot, it is found that:

a) 25% of the students scored less than 60.

b) 25% of the students received a score greater than 85.

A box and whisker plot shows three things:

From the plot given in the graph, we have that:

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Step-by-step explanation:

Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:

  angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle

  angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant

  angle CPD = 1/2(arc CD) . . . . . . . inscribed angle

  angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent

Equating the expressions for angle A, we have ...

  1/2(arc BP) = 1/2(arc CD -arc CP)

Adding arc CP gives ...

  1/2(arc BP +arc CP) = 1/2(arc CD)

Substituting the last two equations for angles from above, this gives ...

  angle CPB = angle CPD

Hence PC bisects angle BPD.

Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

It should be noted that the Golden ratio is also called the golden mean or divine proportion.

The Golden ratio is refered to as the. most beautiful number in the universe.

It is extraordinary because it can be visualized everywhere from geometry to the human body.

In this case, quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Answer:

it mean that the patient get 7mg drug in1 hour and infour hours he get 4×7= 28mg drug

The value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if  g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

g = {(-4, 1), (0, 5), (5, -3), (8, -8)}

As we know,

If f(x) has an ordered pair (x, y) then its inverse of a function has (y, x).

g⁻¹ = {(1, -4), (5, 0), (-3, 5), (-8, 8)}

g⁻¹(5) = 0

h(x) = 3x - 10

h⁻¹(x) = (x+10)/3

h⁻¹(5) = 15/3 = 5

h(h⁻¹(5)) = 3(5) - 10

h(h⁻¹(5)) = 5

Thus, the value of g⁻¹(5) = 0, h⁻¹(x) = (x+10)/3, and the value of h(h⁻¹(5)) = 5 if  g = {(-4, 1), (0, 5), (5, -3), (8, -8)} and h(x) = 3x - 10

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Answer:

[tex]A[/tex]

Step-by-step explanation:

Indeed, the graph of [tex]f(x)[/tex] underwent only one change:

[tex]f(x) = x^3 \Leftrightarrow g(x) = f(x) - 1 = x^3 - 1[/tex].

Take a look at the attachments in order to follow the process.

The amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79

The formula for calculating the compound interest is given as:

A = P(1+r/n)^nt

Given the following parameters

25000 = P(1+0.06/12)^12(10)

25000 = P(1+0.005)^120

25000 = P (1.005)^120

25000 = 1.8194P

P =  25000/1.8194

P = $13740.79

Hence the amount he would invest today to have enough money in ten years if the investment offers an interest rate of 6.0% compounded monthly is $13740.79

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Answer:

No

Step-by-step explanation:

[tex]300 \times .9 \times 1.1 = 297[/tex]

The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

Exponential functions are trascendent expressions, these are, expressions that cannot be described algebraically, that are defined by the following expressions:

[tex]f(x) = a \cdot \left(1+ \frac {r}{100}\right)^{x}[/tex]     (1)

Where:

Exponential functions are used to represent constant continuous increases or decreases in terms of the independent variable. The sentence indicates that the increase in the value of a coin collection was exponential as such increase was continuous and constant in time. (Correct choice: A)

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Answer:

btyivh

he was so much for your support of school and I have a great day of school and I have a great day of school and I have a great day of school

The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.

We need to find the solution to the given function.

The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be at the point where the two lines intersect.

From the given graph we can see that the two functions are intersecting at (–2,–4) and (4,8).

The solution points to the system graph are (–2,–4) and (4,8). Therefore, option A is correct.

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(a) [tex]\sin(-194^{\circ})=-\sin 194^{\circ}=-(-\sin 14^{\circ})=\sin 14^{\circ}[/tex]

(b) [tex]\cos 481^{\circ}=\cos 121^{\circ}=-\cos 59^{\circ}[/tex]

(c) [tex]\tan 185^{\circ}=\tan 5^{\circ}[/tex]

(d) [tex]\sin 331^{\circ}=\sin(-29^{\circ})=-\sin 29^{\circ}[/tex]

The division of a polynomial is illustrated below.

It should be noted that a polynomial simply means an expression that consist of variables which involves the operation of addition, subtraction, etc.

The way to divide the polynomial will be:

Set up the division problem.

Determine the first term of the quotient.

Multiply the answer by the divisor.

Write it below the like terms of the dividend.

Subtract the bottom binomial from the term above it.

Bring it down and repeat the steps until you reach the last term.

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The exponential function which passes through (0,-2),(1,0),(2,2) (5,3) is negative on the interval (-∞,1) and positive on  the interval (1,∞).

Given Function f is negative on the interval (-∞,1) and positive on the interval (1,∞)

We have to find the statement for which the exponential function' s values are given.

First option is having the statement which says that exponential

function passes through points (0,-6)(0.5,-2),(1,0),(2,2) (5,3). These points are showing the domain and value of the function which is codomain.

for x=0 it has -6,

for x=1 it has 0,

for x=2 it has 2,

for x=5 it has 3.

for x=0.5 it has -2

The description says that value of function is negative in interval (-∞,1) and positive in (1,∞) which is true for option A as it has negative values of -2 for x=0 and for x=2,5 it has value of 2 and 3.

Hence the function f is an exponential function passes through  (0, minus 6), (0.5, minus 2), (1, 0), (2, 2), (5, 3).

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Answer:

D) 62.5 pounds.

Step-by-step explanation:

The volume of the swimming pool = [tex]3\times50\times25 =3750[/tex]

[tex]3750\div15 = 250[/tex] lots of 15

[tex]250\times0.25=62.5[/tex] pounds of chlorine.

Hope this helps, have a nice day!

Answer:

x>0

Step-by-step explanation:

The domain of a function is the set of x-values.

The triangle pairs that can be mapped to each other using a reflection and a translation is; Option B

Let us analyze each of the graphs;

Option A; This graph didn't use a reflection and a translation because we see that there was first a reflection across side QR and then another reflection across side AR.

Option B; This graph is correct as it made use of a reflection and a translation as seen in the attached graph.

Option C; This didn't use of a reflection and a translation because it instead carried out translation both in vertical and horizontal direction.

Option D; This carried out Translation and Rotation.

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To collect data from a number of people in a sample, use a questionnaire

Questionnaires are quantitative method used in research for information collection purpose.

This questionnaires consists of several question necessary to provide answers and solution to research questions and for the purpose of analysis. These questions can be open or closed ended questions depending on the nature of research.

Hence we can conclude that. to collect data from a number of people in a sample, use a questionnaire

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The weighted average unit cost after the October 22 purchase is $13.70.

The weighted average unit cost determines the weighted average cost of all the purchased inventory.

[(300 x 12) + (390 x 15) ] / (300 + 390)

(3600 + 5850) / 690 = $13.70

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Recall that for all t,

cos²(t) + sin²(t) = 1

Now,

x = 5 cos(t) - 7   ⇒   (x + 7)/5 = cos(t)

y = 5 sin(t) + 9   ⇒   (y - 9)/5 = sin(t)

so that substituting into the identity above, we get

((x + 7)/5)² + ((y - 9)/5)² = 1

which we can rewrite as

(x + 7)²/25 + (y - 9)²/25 = 1

(x + 7)² + (y - 9)² = 25

and this is the equation of a circle centered at (-7, 9) with radius 5.

Considering the distribution given in the table, the desired probability is:

[tex]P(-2 \leq X \leq 2) = 0.6[/tex]

The distribution is:

The values between -2 and 2(inclusive) are -2, 0 and 2, hence the desired probability is:

[tex]P(-2 \leq X \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.6[/tex]

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The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27

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

x - 3 (i.e. x = 3) and x + 9 (i.e. x = -9) are factors of f(x) = 2x³ + 17x² - 3px - 5q

Hence:

f(3) = 0

2(3)³ + 17(3)² - 3p(3) - 5q = 0  (1)

Also:

2(-9)³ + 17(-9)² - 3p(-9) - 5q = 0  (2)

Hence, p = 8, q = 27

The values of p and q in the function f(x) = 2x³ + 17x² - 3px - 5q is p = 8, q = 27

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The normal approximation is not suitable as np<5.

Given,

mean = np

It turns out that if np and nq are both at least 5, the normal distribution can be used to approximate the binomial distribution. Additionally, keep in mind that a binomial distribution has a mean of np and variance of npq.

Hence apply the mean formula and get the value for np

n= 12 and p=0.

therefore mean = np

np = n×p

np = 12×0.3×

np = 3.6

np is less than 5.

nq=?

q=1-p

q=1-0.3

q=0.7

∴nq = 12 × 0.7

nq = 8.4

nq is not less than 5

It's remarkable that the normal distribution may accurately represent the binomial distribition when n, np and nq are large.

since here only nq is greater than five and np is less than five, therefore we conclude that normal approximation is not suitable.

Hence np<5 so normal approximation is not suitable.

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Answer:

C is the correct answer.

Step-by-step explanation:

-Angle 1 is not equal to Angle 5.

-Angle 3 + Angle 5 will not equal 180 degrees, since they are corresponding angles, not supplementary angles.

Though, Angle 8 is equal to Angle 6, likewise that 7 is equal to 9. Therefore, these angles will create a 180 degrees angle. This is because if 8 and 9 are supplementary, and 7 is a corresponding angle of 9, this will make Angle 8 + Angle 7 = 180 degrees.

Answer:

$ 1021.25

Step-by-step explanation:

FV = P ( 1 + .085 * 3/12)  = 1021.25

                      3/12 = 3 months out of a year

                       .085 = decimal interest       P = 1000

The y-intercept of the continuous function in the table is (0, –6)

To determine the y-intercept coordinate, we must understand the y-intercept is a point on a graph where the line passes through the y-axis at x = 0.

With the above information in mind, we can easily obtain the y-intercept coordinate as follow:

From the the two columns given in the question, the value of y when x = 0 is -6.

Thus, the y-intercept coordinate is (0, -6)

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The product of 3x² and 2x³y + 5xy⁴ is given by the expression 6x⁵y + 15x³y⁴

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

The product of 3x² and 2x³y + 5xy⁴ is:

= 3x² * (2x³y + 5xy⁴)

= 6x⁵y + 15x³y⁴

The product of 3x² and 2x³y + 5xy⁴ is given by the expression 6x⁵y + 15x³y⁴

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A 99% confidence interval for the population proportion is; CI = (0.164, 0.194)

We are given;

Sample size; n = 4096

Number that opposed transgender students; x = 733

Thus;

Proportion; p^ = x/n = 733/4096 = 0.179

Formula for confidence interval of proportions is;

CI = p^ ± z√[p^(1 - p^)/n]

The z-value for confidence level of 99% is z = 2.576

Thus;

CI = 0.179 ± 2.576√[0.179(1 - 0.179)/4096]

CI = 0.179 ± 0.015

CI = (0.164, 0.194)

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