In their October 2003 issue, Consumer Reports evaluated the price and performance of 23
models of cordless phones. Computer output gives these summaries for the prices:
a. Were any of the prices outliers? Explain how you made your decision.
b. One of the manufacturers advertises a cordless phone “economy-priced at only $31.95”.
Would you consider that to be a very low price? Explain.

The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.

A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.

The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.

Given function,

f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x

f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)

=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)

f'(x)=0

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

1-4x²=0

4x²=1

x=±1/4

Given that, f(x) is decreasing function then,

f'(x)<0

((1/x)-4x)<0

(1-4x²)/x<0

1-4x²<0

1<4x²

1/4<4x²

x²>1/4

x>1/2

x∈(1/2,∞)

Hence, f(x) is decreasing on the interval x∈(1/2,∞)

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The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

The possible diagram that completes the question is added as an attachment

From the attached diagram, we have the following representation

<1 + <2 = 180 degrees --- by the theorem of supplementary angles

Also, we have the following angle measure

Given that

<1 = 86 degrees

Substitute the known values in the above equation

So, we have the following equation

86 + <2 = 180

Evaluate the like terms

<2 = 94

Also, we have

<3 = <1  --- by the theorem of vertical angles

Substitute the known values in the above equation

<3 = 86

This is so because <1 = 86 degrees

Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees

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Answer:

Step-by-step explanation:

1.) -112*-7=784

784=v+4

2.)784-4=780

v=780

Answer:

v = 12

Step-by-step explanation:

-112 = -7v -28

7v = 112 - 28

7v = 84

7/7 v = 84/7

v = 12

The money available for private investment is $250 billion dollar

What is demand curve ?

The demand curve is a graphical representation of the connection between the cost of a commodity or service and the amount that is demanded over time. The price will often be shown on the left vertical axis in a representation, and the amount needed will typically be shown on the horizontal axis.

Refer to the attachment for graph:

Once investments and government borrowing are added together, the total is = $400

if borrowing from the government is= $150

private investment

=( investment and and government borrowing) - (government borrowing )

= $400 - $150 = $250

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The required number is 1 which represents "6 times as large as 9 minus 3".

The analysis of mathematical representations is algebra, and the handling of those symbols is reasoning.

We have to determine the number that is "6 times as large as 9 minus 3".

Let the required number would be x

Translate the phrase "6 times as large as 9 minus 3" into the algebraic form :

⇒ 6 × x = 9 - 3

⇒ 6x = 6

⇒ x = 6 / 6

⇒ x = 1

Thus, the required number is 1 which represents "6 times as large as 9 minus 3".

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Answer:

Step-by-step explanation:

A is a point

AB is a line

ABC is a plane

Therefore,  ABC is a plane.

__________________

Hope this helps!

Have a great day!

4.8 × 10^4

1. Dianely's salary can be represented with the following table of values for 5 years as follows:

Year         Salary

1            $40,000

2           $42,500

3           $45,000

4           $47,500

5          $50,000

2. The equation to model Dianely's salary after n years is S = 40,000 + 2,500n.

An equation is a mathematical statement equating two or more mathematical expressions.

Equations use variables, numbers, mathematical operands, and the equation symbol (=).

Dianely's initial salary = $40,000

Salary raise per year = $2,500

Dianely's salary after n years in equation form, S = 40,000 + 2,500n.

Year         Salary

1            $40,000

2           $42,500 (40,000 + 2,500)

3           $45,000 (42,500 + 2,500)

4           $47,500 (45,000 + 2,500)

5          $50,000 ($47,500 + 2,500)

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The number of trips after the cost of the plan A and plan B is 16.

According to the question,

We have the following information:

Plan 1 charges a one-time fee of $145.00 for admission plus $5.00 every trip for parking. Plan 2 charges a one-time fee of $40.00 for parking plus $12.00 every trip for admission.

So, this will make an arithmetic progression.

The formula to find nth term of an A.P:

an = a+(n-1)d where a is the first term

Now, on left hand side, we have nth term for plan A and on the right hand side, we have the nth term for plan B because their nth term will be equal.

145+(n-1)5 = 40+(n-1)12

145+5n-5 = 40+12n-12

5n+140 = 12n+28

140-28 = 12n-5n

7n = 112

n = 112/7

n = 16

Hence, the number of trips after the cost of the plan A and plan B is 16.

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Answer:

Step-by-step explanation:

area=10×5+[(15-5)+7]/2×(10-6)

=50+(17)/2×4

=50+34

=?

Answer:

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

Answer: A

Step-by-step explanation:

The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.

The measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

According to the question,

We have the following information:

Angle CAB = 2x

Angle CBA = 3x-20

And the given triangle is a right-angled triangle which means that one of its angle is 90°.

Now, we know that the sum of three angles of a triangle is 180°.

So, we have the following expression:

2x+3x-20+90 = 180°

5x+70 = 180

5x = 180-70

5x = 110

x = 110/5

x = 22°

Now, putting the value of x in given angles:

Angle CAB = 2x

Angle CAB = 2*22

Angle CAB = 44°

Angle CBA = 3x-20

Angle CBA = 3*22-20

Angle CBA = 66-20

Angle CBA = 46°

Hence, the measure of CBA is 44° , the measure of CAB is 46° and the sum of the three interior angles of the triangle is 180°.

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Answer:

25 percent.

Step-by-step explanation:

25 divided by 100 is equal to 0.25. You then multiply that by 100 to get percent, which is 25 percent.

Hope it helps.

The value of a from the equation is a = 0.32

What is an Equation?

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.

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 data ,

Let the equation be 2 1/7 : 15a = 5/14 : 0.8

Now , on simplifying the equation , we get

15/7  : 15a = 5/14 : 0.8

Multiply by 14 on both sides of the equation , we get

( 15 x 2 ) : 15a = 5 : 0.8

30 : 15a = 5 : 0.8

So , on simplifying the equation , we get

30 / 15a = 5 / 0.8

Divide by 5 on both sides , we get

6 / 15a = 1 / 0.8

Multiply by 0.8 on both sides of the equation , we get

15a = 6 x 0.8

15a = 4.8

Divide by 15 on both sides , we get

a = 4.8 / 15

a = 0.32

Therefore , the value of a = 0.32 or a = 8 / 25

Hence , the value of a in the equation is a = 0.32

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For the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is k= -4.

As given in the question,

Given system of linear equations are as follow:

6x-12y = -7           ____(1)

2x + ky = 14         _____(2)

Form equation (1)  we have,

6x -12y = -7

⇒3 ( 2x -4y) = -7

⇒ 2x - 4y = -7 /3       ____(3)

From equation (2) and (3) we have,

2x + ky = 14

2x - 4y = - 7/3

Value of k so that the given system of equations are inconsistent is given by:

k = -4

For inconsistent there is no solution.

Therefore, for the given system of linear equations 6x-12y = -7 and 2x + ky = 14 the value of k for which linear equations are inconsistent is  k= -4.

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The trigonometric identity presented in this problem is proved trough the answer, reaching an answer 1 = 1.

The identity is presented as follows:

[tex]\csc{\beta} + 1 = \frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}}[/tex]

Then we take the right side of the denominator, and apply the subtraction of perfect squares to the denominator, as follows:

[tex]\frac{\cot{\beta}}{\sec{\beta} - \tan{\beta}} \times \frac{\sec{\beta} + \tan{\beta}}{\sec{\beta} + \tan{\beta}} = \frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}}[/tex]

The following identity relates the square of the secant and of the tangent:

[tex]\tan^2{\beta} + 1 = \sec^2{\beta}[/tex]

Hence:

[tex]\sec^2{\beta} - \tan^2{\beta} = 1[/tex]

Thus the remaining expression is:

[tex]\frac{\cot{\beta}(\sec{\beta} + \tan{\beta})}{\sec^{2}{\beta} - \tan^2{\beta}} = \cot{\beta}(\sec{\beta} + \tan{\beta})[/tex]

The equations of the cotangent, secant and tangent are given as follows:

Hence:

[tex]\cot{\beta}(\sec{\beta} + \tan{\beta}) = \frac{\cos{\beta}}{\sin{\beta}}\left(\frac{1}{\cos{\beta}} + \frac{\sin{\beta}}{\cos{\beta}}\right) = \frac{1}{\sin{\beta}} + 1[/tex]

One divided by the sine is the cosecant, as follows:

[tex]\frac{1}{\sin{\beta}} = \csc{\beta}[/tex]

Hence the simplified expression is:

[tex]\csc{\beta} + 1[/tex]

Which is equivalent to the right side of the expression, hence an identity of the format 1 = 1 is reached and the identity is proven.

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The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.

By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.

This is the z distribution given that the value of n is more than 30.

We have to make use of z when n which is the number of samples  is greater than 30.

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Probability is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of even numbers in a deck of cards.

= 5 x 4

= 20

The number of diamonds in a deck of cards.

= 4

Now,

The probability of drawing an even number from a deck of cards.

= 20 / 52

= 10/26

= 5/13

Now,

The remaining cards.

= 52 - 20

= 32

The probability of drawing diamonds after drawing the even numbers.

= Number of diamonds / remaining cards

= 4 / 32

= 1/8

Thus,

The probability of drawing an even number from a deck of cards is 5/13.

The probability of drawing an even number and then drawing a diamond out of a deck is 1/8.

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There are 284 number of students and 152 number of adults.

Two or more expressions with an Equal sign is called as Equation.

Given,

The ratio of teachers to students on a field trip is 2:13

Let x be the number of adults

If there are 132 more students than adults on the field trip, then 132+x

To find the number of adults and number of students formulate a equation as below

2/13=(x+132)/x

Apply cross multiplication

2x=13(x+132)

Apply distributive law on RHS

2x=13x+1716

11x=1716

Divide both sides by 11

x=152

x+132=152+132=284

Hence there are 284 number of students and 152 number of adults.

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By solving a linear equation, it can be calculated that

There are 4 guppies in  each family

What is a linear equation?

At first it is important to know about equation.

An equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sigh

A one degree equation is known as linear equation.

Here a linear equation needs to be solved

Let the number of guppies in each family be x

Allison has 2 aquariums.

In each aquarium she has 2 families of guppies and 3 tetras.

Total number of fishes Allison have = 2(2x + 3) = 4x + 6

Leigh has 1 aquarium with 10 tetras and 3 families of guppies.

Total number of fishes Leigh have  = 3x + 10

By the problem,

4x + 6 = 3x + 10

4x - 3x = 10 - 6

x = 4

There are 4 guppies in each family

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To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.

(12+16+10+8+14+15)/6

= 75/6

= 12.5 (answer is already rounded to nearest tenth)

The average hourly pay of person making 4500 per year is 21.63 per hour.

Given that,

we have to find what does a person making $45,000 a year make per hour on average, Assume a 52-week year and a 40-hour workweek.

To calculate this

The ratio of the sum of the values in a given set to all the values in the set is the mean value, which is the definition of the average.

We have to multiply 52-week year and a 40-hour work week.

40×52

2080

Now, divide 45000 by 2080

45000/2080

21.63

Therefore, The average hourly pay of person making 4500 per year is 21.63 per hour.

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The graph of the linear equation can be seen in the image at the end.

We start by defining the variables we will use:

x = number of weeks.

y = money that Anika has.

We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:

y = $5*x

To graph this linear equation we need to find two points on the line, if x = 0 we get:

y = $5*0 = $0

So we have the point (0, 0)

if x = 1

y = $5*1 = $5

So we have the point (1, 5)

Now we can graph these two points and connect them with a line, the graph can be seen below.

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Answer:

[tex]\frac{3}{40}=0.075[/tex]

Step-by-step explanation:

The probability of a person selected at random from this group having type AB blood is 15 out of 200 total people. Therefore:

[tex]\frac{15}{200}=\frac{3}{40}=0.075=7.5\%[/tex]

The mean age is equal to: 44.09.

The standard deviation is equal to: 10.07.

First of all, we would determine the median of each class interval as follows:

Median 1 = (25 + 34)/2 = 29.5

Median 2 = (35 + 44)/2 = 39.5

Median 1 = (45 + 54)/2 = 49.5

Median 1 = (55 + 64)/2 = 59.5

Next, we would calculate the mean age by using this mathematical expression:

Mean age = ∑fx/∑f

Substituting the given parameters into the formula, we have;

Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)

Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118

Mean age = [5,203]/118

Mean age = 44.09.

Now, we can calculate the standard deviation as follows:

Standard deviation, S = √((∑f(xi - μ)²/∑f)

Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))

Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)

Standard deviation, S = √(11,970.48/118)

Standard deviation, S = √101.5

Standard deviation, S = 10.07.

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The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Answer: A scale factor of 1/2 was applied to the first triangle to get the resulting image.

Step-by-step explanation: The initial side length of 3.4 is twice as long as 1.7, the initial triangle was reduced to half of the initial size.

Answer:

The triangle is still an equilateral triangle as before, and the only difference is that the side length is halved from 3.4 to 1.7 (3.4/2=1.7). Therefore, the scale factor is 1.7/3.4=0.5. A scale factor <1 means that the original shape is reduced. The scale factor would be a reduction.

Step-by-step explanation:

The image would be of a triangle.
Hope this helps! :))