Please help if possible. Thank you!

Answer:

1) not diverges

2)not diverges

3) diverges

4)not diverges

Step-by-step explanation:

In geometric series, If the |r|<1 then the series is convergent and if |r|>1 then the series is divergent

Where r is the ratio between the consecutive terms of series.

1) 3/5 + 3/10 +3/20 + 3/40 ......

in the above geometric series

r= (3/10) / (3/5)

 = 1/2

 = 0.5

As |r|= 0.5 < 1, so the series will not diverge

2) -10+4-8/5 + 16/25 -......

in the above geometric series

r= (4) / (-10)

 = -2/5

 = -0.4

As |r|= 0.4 < 1, so the series will not diverge

3) ∑ 2/3(-4)^(n-1)

in the above geometric series

r= -4

As |r|= |-4| = 4 > 1, so the series will diverge

4) ∑ (-12)(1/5)^(n-1)

in the above geometric series

r=1/5

 = 0.2

As |r|= 0.2 < 1, so the series will not diverge !

Answer:

Its C!!!!!!!!!!

Step-by-step explanation:

Answer:

2 cows and 5 chickens.

Step-by-step explanation:

NOTE: This will be solved using simultaneous equations.

Let x = cows and y = chickens

1. form two equations

4x + 2y = 18 ... (1)

x + y = 7 .... (2)

2. make y (or x) the subject of one equation

x + y = 7

y = 7 - x ... (3)

3. Substitute (3) into (1)

4x + 2( 7 - x) = 18

4. solve for x

4x + 14 - 2x = 18

2x = 4

x = 2

5. Now substitute x value into equation (2)

x + y = 7

2 + y = 7

y = 5

∴ cows (x) = 2

chickens (y) = 5

The number of cows is 2 and that of chickens are 5

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, There are 7 animals in a farmer's field. ​Some are cows and some are chickens. ​The farmer counts 18 legs in all.

This will be solved using system of equations.

Let x = cows and y = chickens

4x + 2y = 18 ... (1)

x + y = 7 .... (2)

x + y = 7

y = 7 - x ... (3)

4x + 2(7 - x) = 18

4x + 14 - 2x = 18

2x = 4

x = 2

2 + y = 7

y = 5

Hence, the number of cows are 2 and that of chickens are 5

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Answer:

A. 0.7

Explanation:

B is irrational

I have no idea was c and d so that leads to A because it’s terminated

Answer:0.7

Step-by-step explanation:

A pex quiz

To calculate the new discounted price, $49.95×.60=$29.97

Answer:

The required expression is [tex]0.40\times 49.95[/tex].

Step-by-step explanation:

Consider the provided information.

The price for a pair of sandals is $49.95 in June.

In August the price is 60% less.

After getting 60% discount customer need to pay only 40% of the price.

This can be written as:

[tex]40\% \times 49.95[/tex]

[tex]\frac{40}{100}\times 49.95[/tex]

[tex]0.40\times 49.95[/tex]

Hence, the required expression is [tex]0.40\times 49.95[/tex].

Answer:

j=90 B=34 C=108

Step-by-step explanation:

if you know that the value of B=34 and the value of A= 38 and the sum of angles of the triangle =180 therefore C=180-(34+38)=108

Answer:

Check attached graph

Step-by-step explanation:

Given equation is .

Now we need to graph the given equation .

To graph that we can find two points then join them by a straight line.

We are free to plug any number for x say x=0 and x=2

plug x=0

Hence first point is (0,-2).

plug x=2

Hence first point is (2,0).

Now graph both points and joint them to get final graph as shown below.

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Answer:

The answer in the procedure

Step-by-step explanation:

we have

[tex]\pi=3.14[/tex]

[tex]r=1\ units[/tex]

[tex]h=2\ units[/tex]

case a) If the expression is

[tex]\pi r^{2} h[/tex]

then

substitute

[tex](3.14)(1)^{2} (2)=6.28\ units^{3}[/tex]

Round to the nearest whole number

[tex]6.28=6\ units^{3}[/tex]

case b) If the expression is

[tex](1/3)\pi r^{2} h[/tex]

then

substitute

[tex](1/3)(3.14)(1)^{2} (2)=2.09\ units^{3}[/tex]

Round to the nearest whole number

[tex]2.09=2\ units^{3}[/tex]

Answer:

A

Step-by-step explanation:

The amount that David must have in the bank would be $783243.6

An annuity is a series of payments made at equal period of time.

We need to apply the formula for determining present annuity. It is expressed as

PV = R[1 - (1 + r)^- n]r

Where, PV represents the present value of the investment.

R represents the regular payments made(could be weekly, monthly)

r = represents interest rate/number of interval payments.

n is the total number of payments made.

From the information given;

r = 1.5/100 = 0.015

n = 30 years

R = $32,635.15

Therefore,

PV = 32635.15[1 - (1 + 0.015)^- 30]/0.015

PV = 32635.15[1 - (1.015)^- 30]/0.015

PV = 32635.15[1 - 0.64]/0.015

PV = 32635.15[0.36]/0.015

PV = 32635.15 × 24

PV = $783243.6

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Answer:

The solutions are

[tex]x=-8\\x=-1[/tex]

Step-by-step explanation:

We must solve the equation:

[tex]x^2+9x+8=0[/tex]

To solve the equation we can use the factoring method.

To factor the expression, look for two numbers that when you add them, get the result 9 and when multiply them, get the result 8.

You can verify that the numbers that meet this requirement are: 8 and 1.

Then the polynomial factors are:

[tex](x + 8) (x + 1)[/tex]

So

[tex]x^2+9x+8=(x + 8) (x + 1) = 0[/tex]

Then

[tex]x+8= 0[/tex]   or  [tex]x+1 =0[/tex]

[tex]x=-8[/tex] or  [tex]x= -1[/tex]

Answer:

x = -1 or x = -8

Step-by-step explanation:

It is given the function

x² + 9x + 8 = 0

To find the solution of given function

x² + 9x + 8 = 0

By using splitting method we can write,

x² + x + 8x + 8 = 0

x(x + 1) + 8 (x + 1) = 0

(x + 1)(x + 8) = 0

x+ 1 = 0   or x + 8 = 0

x = -1 or x = -8

Answer:

radius = circumference / (2 * PI)

radius = 5.8378033126

Circle Area = PI * radius^2

Circle Area = PI * 5.8378033126^2

Circle Area = PI * 34.0799475167

Circle Area = 107.07 square units

Step-by-step explanation:

a=180-142=38 degree

b= 180-38-88=54 degree

c=b (since the two lines are parallel to each other) therefore c=54 degree

See the attached picture:

Answer: Hope this helps, and hopefully this is what you needed!

1 7/16 = 23/16

11 5/9 = 104/9

30 5/9 = 275/9

10 10/13 = 140/13

24 3/5 = 123/5

129 1/2 = 259/2

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

The range is the difference between the largest value and the smallest value in the data set.

minimum value = 21 and maximum value = 61

range = 61 - 21 = 40

Answer: Range of the data set would be 40.

Step-by-step explanation:

Since we have given the data set as follows:

21,23,28,28,52,54,56,56,57,60,61,61.

We need to find the range of the data set.

As we know the formula for "Range":

Range = Highest number - Lowest number

Range = 61-21

Range = 40

Hence, range of the data set would be 40.

The answer is B.

For an expression to be a polynomial term, any variables in the expression must have whole number powers.

-3/x isn’t a polynomial term because the variable is in the denominator.

Answer:

D

Step-by-step explanation:

it only consists of one term.

i believe the answer is D.) 1 over 8

Explanation: 4 is one of the 8 numbers so it would be a 1 over 8 chance.

Answer:8 inches

Step-by-step explanation:304/38 = 8 inches

Answer:

False

Step-by-step explanation:

If both lines are linear, they can only have 0, 1 or infinite solutions. If one was a quadratic function, they would intercept twice.

Answer:

2x² - 2x + 7

Step-by-step explanation:

Given

(8x² + 9) - (6x² + 2x + 2) ← distribute by - 1

= 8x² + 9 - 6x² - 2x - 2 ← collect like terms

= (8x² - 6x²) - 2x + (9 - 2)

= 2x² - 2x + 7

Answer:

2x² - 2x + 7

Step-by-step explanation:

Ape-x

Answer:

[tex]7\sqrt[3]{x^2}[/tex]

Step-by-step explanation:

The rule of exponents that dictates this to be solved is:

[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]

The power of 2/3 is on "x", NOT 7, so we use this property to write it as:

[tex]x^{\frac{a}{b}}=\sqrt[b]{x^a} \\7x^{\frac{2}{3}}=7\sqrt[3]{x^2}[/tex]

third answer choice is right,  [tex]7\sqrt[3]{x^2}[/tex]

Answer:

b or the second one top to botton

Step-by-step explanation:

trust

Answer:

its will just add 25 to the total amount of money she got in the cards.

Step-by-step explanation:

For this case we make a rule of three to determine the initial amount of euros:

1 euro ----------------> 1.3687 dollars

x ------------------------> 250 dollars

Where "x" represents the amount of euros equivalent to 250 dollars.

[tex]x = \frac {250 * 1} {1.3687}\\x = 182.655074158[/tex]

Thus, Phelan received 182.655074158 euros.

If I spend 150 euros, we have:

[tex]182.655074158-150 = 32.655074158[/tex]

Now, we make the conversion to know the amount of dollars equivalent:

1 euro ----------------> 1.3687 dollars

32,655074158 ------------------------> y

Where "y" represents the amount of dollars:

[tex]y = \frac {32.655074158 * 1.3687} {1}\\y = 44,695[/tex]

So, Phelan has 44,695 dollars

Answer:

$ 44,695

Answer:

No

Step-by-step explanation:

we have the number

[tex]7,027[/tex]

we know that

[tex]7,027=7*1,000+2*10+7*1[/tex]

so

The value of the first 7 is equal to

[tex]7*1,000=7,000[/tex]

The value of the second 7 is equal to

[tex]7*1=7[/tex]

therefore

[tex]7,000/7=1,000[/tex]

The value of the first 7 is one thousand times greater than the second 7

The answer is no

Answer:

5/6

Step-by-step explanation:

The ratio is:

45 / 54

Or, reduced:

5 / 6

The ratio of boys to girls in the senior class of the school is 45:54.

The question is asking to find the ratio of boys to girls in a senior class. Since the class has 45 boys and 54 girls, the ratio is typically written in the simplest form as 'boys: girls'. The given figures are in simplest form because they do not have a common factor other than 1. Therefore, the ratio of boys to girls in the senior class is 45:54.

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Answer:

Step-by-step explanation:

tan α=9÷(21/2)=18/21=6/7

α=arc tan(6/7)≈40.6°

Answer:

5

Step-by-step explanation:

The expression 9 - z evaluates to 5 when z = 4. This is calculated simply by substituting 4 into the equation in place of z, and then performing the subtraction.

The question is asking you to evaluate the expression 9 - z when z = 4. The term 'evaluate' in mathematics means to calculate the numerical value of. So this is a straightforward substitution problem. You take the value of z (which is 4) and substitute it into the equation in place of z. So, the equation becomes 9 - 4, which equals 5.

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Check the picture below.

so we have 3 rectangles and 1 semicircle.

let's recall that the area of a circle = A = πr², so then the area of a semi-circle is πr²/2.

let's get the area of all figures, sum them up, and that's the area of the composite.

[tex]\bf \stackrel{\textit{top rectangle}}{(2\cdot 5)}+\stackrel{\textit{middle rectangle}}{(4\cdot 11)}+\stackrel{\textit{bottom rectangle}}{(9\cdot 2)}+\stackrel{\textit{semicircle}}{\cfrac{25\pi }{2}} \\\\\\ 10+44+18+12.5\pi \implies 72+12.5\pi \qquad \approx\qquad 111.27[/tex]

Answer:

x=13

Step-by-step explanation:

x+2x=3x

-6+9+-19=-16

3x-16=23

+16     +16

3x=39

divide by 3 on both sides.

x=13

Answer:

Option A true is the answer.

Step-by-step explanation:

The given circle there are two arcs AB and CD.

Angles formed by these arcs at the center arc 30°

Formula of length of arc = r × θ

where r = radius of the circle

and θ = angle formed by arc at the center.

mAB = OA × (30°) [ By formula ]

similarly mCD = DC × (30°)

Since OA = OC = r (radii of the circle )

So mAB = mCD

Therefore, statement is true.

Option A true is the answer.

Answer:true

Step-by-step explanation:

Answer:

The mass of the cylinder is [tex]149\ g[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=7/2=3.5\ in[/tex] ----> the radius is half the diameter

[tex]h=1.5\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=(3.14)(3.5)^{2}(1.5)[/tex]

[tex]V=57.70\ in^{3}[/tex]

step 2

Find the mass

we know that

The density is equal to the mass divided by the volume

[tex]D=m/V[/tex]

Solve for the mass

[tex]m=D*V[/tex]

substitute the values

[tex]m=(2.58)*(57.70)=149\ g[/tex]

Answer:

2441 grams

Step-by-step explanation:

convert 7 and 1.5 inches into centimeters (2.54 centimeters per inch) so now you use half of 8.89 (7 * 2.54 = 2441) multiplied by 3.81

you find the area of the cylinder first by using [tex]\pi r^2*h[/tex] which should give you 945.97219

then plug it into the density formula, 2.58= mass/945.97219

that should give you mass=2440.61

and if you round it to the nearest gram, it's 2441

**THIS IS THE CORRECT ANSWER**

Answer:

[tex]y=-1,869.5x+27,995[/tex]

Step-by-step explanation:

Let

x-----> the time in years

y----> value of Zachary’s car in dollars

[tex]A(0,27,995), B(10,9,300)[/tex]

step 1

Calculate the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{9,300-27,995}{10-0}=-1,869.50[/tex]

step 2

Find the equation of the line

The equation of the line into slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=-1,869.50[/tex]

[tex]b=27,995[/tex]  -----> the y-intercept is the point A

substitute

[tex]y=-1,869.5x+27,995[/tex]

The linear equation to represent the value of Zachary's car after x years since its purchase is y = -1869.5x + 27995.

To write a linear equation to represent the value of Zachary's car after x years since its purchase, we need to determine the slope and y-intercept. The initial value of the car is $27,995, and after 10 years it depreciates to $9,300. The slope (m) can be calculated as (9300 - 27995) / (10 - 0) = -1869.5. The y-intercept (b) is the initial value, which is $27,995. Therefore, the linear equation that represents the value of Zachary's car is y = -1869.5x + 27995.

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