Does the series shown below converge or
diverge?
If convergent, find its sum.

answer:

100 text messages.

$50-$40 = $10

$10/$0.1 = 100

100 text messages

Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

As given in the question,

Total amount share by Annie and Dermot is $600.

Ratio of amount share by Annie and Dermot is 11 : 9

Let x be the amount of money.

11x + 9x = $600

⇒ 20x = $600

⇒20x/20 = $600/20

⇒x= $30

Amount received by Annie is equal to

= 11 × 30

= $330

Amount received by Dermot is equal to

= 9 × 30

= $270

Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount  received by Annie is $330 and Dermot is $270.

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Answer:

Clara ate 2/15

Step-by-step explanation:

1/5 equals 3/15

Answer:

it should be the first one, if not it’s the third

Step-by-step explanation:

In regression analysis, there is one dependent variable and there can be one or more independent variables among which a relationship has to be established.

Given that;

Regression analysis is a statistical procedure for developing a mathematical equation that describes;

Finding the variables that have an effect on an interest issue can be done with accuracy using regression analysis. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression. You must specify a dependent variable that you believe is influenced by one or more independent variables before you can do a regression analysis.

The next step is to create an extensive dataset to work with. A great technique to create this dataset is by sending surveys to your target audiences. Questions covering each of the independent variables in which you are interested should be included in your survey.

Hence, Regression analysis requires establishing a link between one or more independent variables and one dependent variable.

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Answer: 2x^2 -6x

Step-by-step explanation:

First you should distribute the x's as shown:

(x)(x)+(x)(−3)+(3)(x)+(3)(−3)+x2+−6x+9=x2+−3x+3x+−9+x2+−6x+9

Then combine Like terms:

↓x2+−3x+3x+−9+x2+−6x+9=↓

↓(x2+x2)+(−3x+3x+−6x)+(−9+9)↓

2x2+−6x

Hope this helped... :)

By using the diagram and the given angle measure we get that:

if, m∠1 = 143°

then, m∠2 = 37°

         m∠3 = 143°

         m∠4 = 37°

What is angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

What is Properties of Congruence?

       For all angles A ,

        ∠A≅∠A .

       An angle is congruent to itself.

        For any angles A  and  B ,

        if ∠A≅∠B , then ∠B≅∠A .

         Order of congruence does not matter.

        For any angles A,B,  and  C ,

        if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .

        If two angles are both congruent to a third angle, then the first two        angles are also congruent.

I assume that, this refers to two intersecting lines which form four angles.

         ∠1 + ∠2 = 180°

          143° + ∠2 = 180°

          ∠2 = 180° - 143°

          ∠2 = 37°.

         It means that,  ∠1 = ∠3 =143° (properties of congruency)

         and ∠2 = ∠4 =37° (properties of congruency).

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Answer:

164 minutes

Step-by-step explanation:

$8 + $0.06m = $17.84

To isolate the m, first bring the eight to the other side

0.06m = 9.84

then divide both sides by 0.06

m = 164

The required measure of the angle is m∠A=64°.

orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

,

Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°

Thus, the required measure of the angle is m∠A=64°.

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Answer: x = 25/6

Step-by-step explanation: yes

Answer: x=25/6

Step-by-step explanation:

combine multiplied terms into 1 fraction

5/2*+1/2x=9+7/2

5x/2+1/2x=9+7/2

combine

5x/2+1/2x=9+7/2

5x/2+1x/2=9+7/2

multiply by 1

5x/2+1x/2=9+7/2

5x/2+x/2=9+7/2

A quadrilateral is a polygon with four sides, the length of BC for the given quadrilateral will be 8.1.

A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.

In other meaning, a quadrilateral is a kind of polygon in which four sides, for example, rectangle, square, and parallelogram are quadrilateral.

As per the give quadrilateral,

In triangle ACD.

Apply Pythagoras' theorem,

BD = √(5²+7.5²) = 9.0123

In triangle BDC by cosine law,

Cos38° = ((DB)²+(DC)² - (BC)²)/(2×DB×DC)

Cos38° = (9.0123²+13²- (BC)²)/(2×9.0123×13)

Cos38° = (250.25- (BC)²)/(234.32)

(250.25- (BC)²) = 184.646

(BC)² = 65.60

BC = 8.1

Hence, "A quadrilateral is a polygon with four sides, the length of BC for the given quadrilateral will be 8.1".

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Complete question attached below ;

Step-by-step explanation:

The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit of $3,365, what is the value of c?

$3,365 = 225(75) - (165(75) + c)

$3,365 = 16,875 - 165(75) - c

$3,365 = 16,875 - 12,375 - c

$3,365 = 4,500 - c

=1,135 =  - c

c = 1,135

Answer:

10

Step-by-step explanation:

substitute x = 4 into the expression

3x - 2 = 3(4) - 2 = 12 - 2 = 10

Answer: 10

Step-by-step explanation:

4 × 3 = 12

12 - 2= 19

Hope it helps

An area 825 by 550 ft gives max area for $6600.

acc to our question-

hence, 3300 + 3300 = $6600

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Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .

In the question ,

it is given that

the amount of food that the ocicat eats in 1 day = 3/5 pound

So , the amount of food that the ocicat eats in 1 week = (3/5) × 7 = 21/5

we have to find the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed .

So ,

the number of ocicat that can eat  [tex]19\frac{1}{2}[/tex] pound of food feed = [tex]19\frac{1}{2}[/tex] ÷ 21/5

= (19*2+1)/2 ÷ 21/5

= 39/2 × 5/21

= (39 × 5)/(2 × 21)

= 195/42

= 65/14

= [tex]4\frac{9}{14}[/tex]  ocicats

since the number of ocicats cannot be in fraction ,

so number of ocicats = 4

Therefore , Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .

The given question is incomplete , the complete question is

An ocicat eats 3/5 of a pound of food daily. How many whole ocicats can a [tex]19\frac{1}{2}[/tex] -pound bag of food feed for one week?

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Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.

What is graphing method by adding ordinates?

The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.

For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.

According to the given question:

Follow these steps to graphing the function:

1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.

2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.

3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.

4. Fill in the fourth column by simply adding the second and third columns.

5. Graph y = 3x - sin 4x  by using the x-coordinates from column A and the y-coordinates from column D.

Check the attachment below for the required graph obtained after plotting the points.

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It is also called as Random  Sample experiment.

Hence, it is an random experiment.

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The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

Given that,

Jake sold 49 tickets while jeans sold 12 for the school.

In simplest form the ratio of the given case will be;

Simplest form:

A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.

The ratio we get;

→ 12/49

The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.

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Answer:

Hey, hope it helps my friend

Step-by-step explanation:

In the image

⇒ [tex]=5-(x)-(-4)\\=5-x+4\\=-x+5+4\\=-x+9[/tex]

⇒Note the negative sign has to multiply every term in the brackets!

Option A is the answer

The equation of line with undefined slope and passes through the point

(1/2, 5) will be;

⇒ x = 1/2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point = (1/2 , 5)

And, The slope = undefined

Now,

Since, We know that;

The equation of line with undefined slope and passes through the point will be;

⇒ x = a

Where, 'a' is the x - intercept.

Here, The point = (1/2 , 5)

The slope = undefined

And, The x - intercept = 1/2

So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;

⇒ x = 1/2

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The value of function is positive so the function have maximum value 30 at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value 30 at x=3.

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The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

What is a binomial distribution?

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

Formula to calculate the binomial distribution

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ

Here, we know that

Solar-heat installations successfully reduce the utility bill 60% of the time.

We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.

We have 60% = 0.6 = p and n = 10.

We have a binomial distribution: X : (10, 0.6).

We use the binomial distribution formula to calculate the probability

P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get

P(x ≥ 9) = 1 - P(x < 9)

P(x ≥ 9) = 1 - P(x ≤ 8)

P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)

P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ

P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)

P(X ≥ 9) = 1 -0.95365

P(X ≥ 9) = 0.04635

Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.

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Answer:

See below.

Step-by-step explanation:

Let the price of drinks be x and the price of candies be y.

9x + 4y = 60 --------------------(1)

10x + 2y = 57.50 --------------(2)

2(10x + 2y) = 57.50*2

20x + 4y = 115 --------------(3)

9x + 4y - 20x - 4y = 60 - 115

9x - 20x = -55

-11x = -55

11x = 55

x = 55/11

Put x = 5 in Eq. (1)

9(5) + 4y = 60

45 + 4y = 60

4y = 60 - 45

4y = 15

y = 15/4

So, the cost of one drink is $5 and the cost of one candy is $3.75.

[tex]\rule[225]{225}{2}[/tex]

Answer:

10

Step-by-step explanation:

(2w + 4) - (2w - 6)

2w + 4 - 2w + 6

2w - 2w + 4 + 6

10

I hope this helps!

Answer:

Adult is 10$ and Child is 7$.

Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.

Hope this helps!

Step-by-step explanation:

2x + 4y = 48

5x + 2y = 64

2x + 4y = 48

10x + 4y = 128

( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )

8x = 80

x = 10

2 ( 10 ) + 4y = 48

20 + 4y = 48

4y = 48 - 20

4y = 28

y = 7