b. 2/(x-2)(x-3)+2/(x-1)(3-x)+1/(1-x)(2-x)

The required solution for the hypothesis testing is shown,

The T - statistic is the ratio of the predictive value of a parameter from its hypothesized value to its standard disputable values.

n = 16, ss = 960, and [tex]\bar x = 55,[/tex]
[tex]S.D, s = \sqrt{ \ [ss/n - 1]\\s = \sqrt{960/15} \\s = 8[/tex]

The test statistic is,
[tex]t = \bar x - mu / [s /\sqrt{n} ]\\t = 55 - 50 / [8/\sqrt{16} ]\\t = 2.5[/tex]

df = n - 1 = 15 , let α = 0.05
tcrp = 2.131 [from t - table]
Since t > 2.131
The result is significant

(b)

Cohen's d = mean difference /SD
                = 55 - 50 / 8 = 0625.

Thus, the required solution for the hypothesis testing is shown,

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Hello,

I hope you and your family are doing well!

If a ticket to the circus was 10% less on a Tuesday than it was on a Saturday, then it was 90% of the Saturday ticket price. If you paid $27 each to attend Tuesday's show, then the Saturday ticket price was $27 / 0.9 = $30.

Since you bought two tickets, the total cost of attending the circus on Saturday would have been 2 * $30 =60

Therefore, your total cost would have been $60 had you attended the circus on Saturday.

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Happy Holidays and New Year!

The tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.

What is the similarity of the triangles?

When it comes to Euclidean geometry, two things are said to be comparable if they have the same shape or the same shape as each other's mirror image. One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

We have,

In ΔHIJ

∠HIJ = 64°

∠JHI = 96°

and the side are

HI = 2 unit

IJ = 5.5 unit

HJ = 5 unit

So, the third angle will according to the sum of the angles of a triangle:

∠IJH = 20°

the triangles similar to ΔHIJ are:

A) It is similar to ΔHIJ cause,

∠HIJ ≅ ∠KLM

∠IJH ≅ ∠LMK

so, the third also will be equal:

∠JHI ≅ ∠LKM

D) It is similar to ΔHIJ cause,

∠IJH ≅ ∠XZY

HI/YX = 2/4 = 1/2

HJ/YZ = 5/10 = 1/2

C) It is similar to ΔHIJ cause,

HI/UV = 2/4 = 1/2

HJ/UW = 5/10 = 1/2

IJ/VW = 5.5/11 = 1/2

Hence, the tringles ΔKLM, ΔXYZ, and ΔUVW are similar to the ΔHIJ.

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a) Histogram (figure attached)

b) The expected number of defective is equal to 0.4 syringes.

c) Probability that the batch will be accepted is equal to 0.94275.

d) The standard deviation is 0.6164.

It is a binomial distribution "DISCRETE probability distribution that encapsulates the likelihood that a value will take one of two independent values when a particular set of conditions is met. The assumptions for the binomial distribution are that each trial has a single possible outcome, each trial has an equal chance of success, and each trial is independent of the others or mutually exclusive ".

Let X be the number of syringes being defective as a binomial random variable.

We are given that in the batch, there can be assumed to be 5% defective syringes.

∴ n = 8

Probability of syringes being defective, p = 0.05

Probability of syringes being not defective , q = 1-p = 1-0.05 = 0.95

a) Histogram (figure attached)

b) We know that the formula for Expectation in binomial distribution is;

μ =n×p = 8×0.05

=0.4 syringes

Therefore, the inspector will find the expected number of defective is equal to 0.4 syringes.

c) We have to find binomial probability for that we will use the binomial probability distribution is given by:

P(X=x) = ⁿCₓpˣ (1-p)^n-x, x = 0,1,2,3 ..8

Therefore,

P(x<2) = P(X=0) + P(X=1)

= ⁸C₀(0.05)⁰(1-0.05)⁸ + ⁸C₁(0.05)¹(1-0.05)⁷

=  0.66342 + 8×0.05×0.6983

= 0.66342 + 0.27933

= 0.94275

Therefore, probability that the batch will be accepted is equal to 0.94275.

d) We first find the variance:

σ² = Var(X) = n×p×(1-p)

= 8 × 0.05 ×(1-0.05)

= 0.38

Thus, the standard deviation is

σ = [tex]\sqrt{0.38}[/tex] = 0.6164

Thus,

a) Histogram (figure attached)

b) The expected number of defective is equal to 0.4 syringes.

c) Probability that the batch will be accepted is equal to 0.94275.

d) The standard deviation is 0.6164.

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Hello,

I hope you and your family are doing well!

(a) The exponential growth model is given by the equation P(t) = P0 * r^t, where P(t) is the population t years after 2010, P0 is the population in 2010 (7420), and r is the annual growth rate (2.3%).

Substituting the given values into the equation gives us:

P(t) = 7420 * 1.023^t

This is the equation that estimates the population t years after 2010.

(b) To estimate the population of the town in 2022, we can substitute t = 12 into the equation:

P(12) = 7420 * 1.023^12

Calculating this gives us:

P(12) = 7420 * 1.023^12 = 7420 * 1.291891 = 9593.45

So the estimated population of the town in 2022 is approximately 9593

Happy to help!

Answer:

11.9988

Step-by-step explanation:

Use a calculator.

Answer:

Line 2

Step-by-step explanation:

This would represent a negative slope.  A negative slope goes down if you start on the left side and go down.

If initial sample of 458 grams of a radioactive substance decays according to the function [tex]A(t)=458e^{-0.038t}[/tex] then the half-life of the substance is 0.

Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.

Given,

An initial sample of 458 grams of a radioactive substance decays according to the function

[tex]A(t)=458e^{-0.038t}[/tex]

We need to find the half life

[tex]458=458e^{-0.038t}[/tex]

Divide both sides by 458

[tex]1=e^{-0.038t}[/tex]

Take log on both sides

[tex]log1=-0.038t[/tex]

0=-0.038t

t=0

Hence, the half-life of the substance is 0.

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Answer:

4/3

Step-by-step explanation:

you use the slope formula y^1 - y^2 over x^1 over x^2, substitute the said values and are left with the slope of 4/3 in its improper form.

Hope this helps!!! :3

Answer:

x = -2

Step-by-step explanation:

The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.

Using the above information, we can construct the equation:

3x + 2 = 2x

and solve it for x.

x = -2

The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.

We can substitute the number in the inequality to find if the inequality holds true. If the inequality holds true, it is a valid solution. This is very similar to substituting a number in an equation, in order to check if it holds.

The same holds true for others.

The value of y is 15.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

87 + 87 y = 1218 + 174

Now, Solving

87+ 87y= 1392

87y= 1392- 87

87y= 1305

y= 1305/ 87

y= 15

Hence, the value of y is 15.

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Yes, it is a proportional relationship. The relationship is distance (d) is directly proportional to time(t). The equation of the relationship is d= 65t

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other. For example, when one variable changes the other, then they are said to be in proportion. If d( distance) is directly proportional to t( time) the equation is of the form d= kt (where k is a constant).

When d =65miles and t= 1hour, k =d/t

k= 65/1= 65

for other values of d and t, k = 65

Therefore the relationship between the distance and time is a proportional relationship. And the equation of the relationship is d= 65t

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Answer:

it is 3/5

Step-by-step explanation:

cos is the adjuacent devided by hypotenuse so it is 27/45 and that is 3/5

The values of x in the given equation, x² - 5x = -4, are x = 4 and x = 1

From the question, we are to solve the given equation by factoring

The given equation is

x² - 5x = -4

To solve the equation by factoring, transfer the constant to the other side of the equation

x² - 5x + 4 = 0

Factorize the left hand side expression

x² -x -4x + 4 = 0

x(x - 1) -4(x -1) = 0

(x - 4)(x - 1) = 0

x - 4 = 0 OR x - 1 = 0

x = 4 OR x = 1

Hence, the values of x are 4 and 1

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The perimeter of the polygon is 57 meters.

A polygon is an enclosed two-dimensional shape with three or more straight sides that are connected together. It can be regular or irregular and can be made up of triangles, squares, rectangles, and other shapes. Polygons are classified by the number of sides they have, such as triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), and hexagons (6 sides). Polygons can also be classified by their internal angles, such as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees), and reflex (greater than 180 degrees). Polygons are used in many mathematical problems and can be used to represent a variety of real-world objects, such as buildings, mountains, and stars.

The perimeter of the polygon is 57 meters.

The perimeter is calculated by adding up the lengths of each side. 7m + 16m + 9cm + 15m = 57m.

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The system of equations that Tristan needs to solve is:

x*0.05 + y*0.10 = 1.40

x = 2*y

Let's define the variables:

x = number of nickels.

y = number of dimes.

Knowing that the net is $1.40 and that he has twice as many nickels as dimes, we can write:

x*0.05 + y*0.10 = 1.40

x = 2*y

That is our system of equations that Tristan can use to find the numbers of nickels and dimes.

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Step-by-step explanation:

chances of rolling 1= 1/6

chances of rolling 2=1/6

chances of rolling anything else=2/3

Answer:

(0,-5) , (3, -6) , (6, -7) ,(9, -8)

Step-by-step explanation:

I apologize for being unable to graph, but here are some of the points.

(0,-5) <-- The "y intercept"

slope is y2-y1/x2-x1, so "-1" is added to the "y" of the coordinate, and 3 is added to the "x"

(3,-6)

(6,-7)

(9,-8)

Hope this helps :)

By solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

What is the system of linear equations?

A grouping of one or more linear equation containing the same variables is known as a system of linear equations.

Here, we have

Given:  8x - 5y = 11....(1), 4x - 3y = 5...(2)

We solve equation(2) and find the value of x

4x = 5+ 3y

x = 5/4 + 3y/4

Now, we put the value of x in equation (1) and we get

8(5/4 + 3y/4) - 5y = 11

5×2 + 2×3y - 5y = 11

10 + y = 11

y = 1

Now, we put the value of y in equation(2) and we get

4x = 5+ 3(1)

4x = 8

x = 2

Hence, by solving the system of linear equations by elimination we get the value of x= 2 and y = 1.

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Answer:

Check out the image shown above/below

The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

If the vertex of the absolute function is at (h, k). Then the absolute function is given as

f(x) = | x - h| + k

The absolute function is given below.

g(x) = | x | - 8

Compare the function g(x) with the function f(x), then the vertex of the absolute function is as,

(h, k) = (0, -8)

The absolute function opens up because there is a positive sign before mode.

The vertex of the absolute function g(x) will be (0, -8). And the function opens up. Then the correct option is A.

The graph is given below.

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The first function is an odd and the second one is neither even nor odd. The correct options are (1) and (2).

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given problem can be solved as follows,

(2) The graph of the given function shows the following,

The value of the function is positive for positive x and negative for negative x.

It can be mathematically written as,

f(-x) = -f(x).

Which shows the given graph is of an odd function.

(3) The given function is f(x) = 4x³ + 2x² - x⁵.

In order to check the type of the function, find its value at the same value of x with different signs as,

f(1) = 4 × 1³ + 2 × 1² - 1⁵ = 5

And, f(-1) = 4 × -1³ + 2 × -1² - -1⁵ = -1

Since, f(1) ≠ f(-1), the function is not even.

And f(-1)  ≠ -f(1), the function is not odd.

Thus, the given function is neither even nor odd.

Hence, the first and the second functions of the given problem are odd and neither even nor odd respectively.

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Change the equations to inequalities  to modify the graph and the solutions are (-1.871, 1.5) and (1.871, 1.5)

The graph is the given parameter

From the graph, we have the following equations

f(x) = x² - 2

g(x) = -x² + 5

To modify the graph, we simply change the equations to inequalities

After the modifications in (a), we have:

f(x) >  x² - 2

g(x) ≥  -x² + 5

From the graph of the inequalities, the curves of the inequalities intersect at (-1.871, 1.5) and (1.871, 1.5)

Hence, the solutions are (-1.871, 1.5) and (1.871, 1.5)

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Answer:

6(4)-4=3(4)+8

24-4=12+8

20=20

Step-by-step explanation:

To prove x=4, substitute four into the equation

6(4)-4=3(4)+8

24-4=12+8

20=20

Therefore x=4 is proved

Answer:

(Answer in Image)

Step-by-step explanation:

6x-4=3x+8

6x-4-3x=3x+8-3x                    subtract -3x on both sides

3x-4=8                                    

3x-4+4=8+4                               add four on both sides

3x=12                                      simplify

3/3x=12/3                                       divide both sides by 3

x=4

What percentage of $680 is 490? ANSWER: 138.78%

The price is reduced from $680 to $490. What is the percentage decrease? ANSWER: 72.06%

Step-by-step explanation:

ANSWER: 138.78%

690 & 490 can be written as a fraction

which would be 680/490, how do I find the percentage?

490 and 680 can be written as a fraction

which would be 490/680, how do I find the percentage?

Answer:

Ann must pay $800 in income tax for the first $8,000 of her taxable income because 8000 * .1 = 800

Ann must pay $4,600 in income tax for the amount of her taxable income over $8,000 because (35000 - 8000) * .16 = 4600

Therefore, Ann must pay a total of $800 + $4,600 = $<<800+4600=5400>>5,400 in income tax for last year.

Answer:

$5,120 in taxes, total

Step-by-step explanation:

Ann made $35,000 in taxable income last year. Suppose the income tax rate is 10% for the first $8,000 plus 16% for the amount over $8,000. How much must Ann pay in income tax for last year?

8,000 * 10% = 800 in taxes for first $8,000

remaining: 35,000 - 8,000 = $27,000 to be taxed at 16%

27,000 * 16% = $4,320

$800 + $4,320 = $5,120 in taxes, total