i need help with 1,2,3, and 4!!

Evaluate each finite geometric series.

1/5 + 1/10 + 1/20 + 1/40 + 1/80=0.3875

What is the sum of a finite geometric series?

Given:

a=1/5

r=5/10 = 1/2

n=5

[tex]S_n=\frac{a(1-r^{n} )}{1-r} \\\\S_5=\frac{\frac{1}{5}(1-(\frac{1}{2}))^{5} }{1-\frac{1}{2} } \\\\S_5=\frac{1}{5} (\frac{31}{32} *\frac{2}{1}) \\\\S_5=\frac{1}{5} (\frac{31}{16} )\\\\S_5=0.3875[/tex]

What is a finite geometric series?

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The distance traveled in each section will be 150 meters and 350 meters.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

From a simultaneous equation for: A cyclist completes a journey of 500 m in 22 seconds, part of the way at 10m/s and the remainder at 50m/s.

Let x distance be covered with velocity 10 m/s in time t₁ and the remaining distance (500 - x) covered with velocity 50 m/s in time t₂. Then the equation will be

t₁ + t₂ = 22          ....1

Then the time t₁ will be

10 = x / t₁

t₁ = x / 10

Then the time t₂ will be

t₂ = (500 - x) / 50

Put the time in equation 1, then we have

x / 10 + (500 - x) / 50 = 22

5x + 500 - x = 1100

4x = 600

x = 150 meters

And the remaining distance will be

500 - x = 500 - 150

500 - x = 350 meters

The distance traveled in each section will be 150 meters and 350 meters.

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The statement "angles 4 and 6 are alternate interior angles" is true

Given,

The statement " Angles 4 and 6 are alternate interior angles"

Here,

∠4 and ∠6 are lie opposite sides of the the transversal and both are nonadjacent interior angles .

So, ∠4 and ∠6 are alternate interior angles

Hence, the statement "angles 4 and 6 are alternate interior angles" is true.

The complete question is:

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

Angles 4 and 6 are alternate interior angles.

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The solution of the equation (2x - 4) (x + 6) = 0  is is x = {2, -6}  (C)

The solutions of an equation means if we substitute these solutions into the variables of the equation, it will lead to the correct equality.

Suppose we have an equation in the form of:

(x - a) (x - b) = 0

This is called a factorization form. The equality will be true if either:

The given equation is:

(2x - 4) (x + 6) = 0

This equality will be correct if:

2x - 4 = 0

⇒ x = 2

or

x + 6 = 0

⇒ x = -6

Hence, the solution is x = {2, -6}  (C)

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The formula for the height of a cylinder is h = V / (π.r²) and the height of a cylinder with a volume of 36 cm³ and a radius of 3 cm is  4/π cm

Given a cylinder with a radius r and height h, then its volume is given by the formula:

      V = π.r².h

Where:

V = volume

r = radius

h = height

To find the formula for the height, divide both sides by π.r²

V : π.r² = π.r².h : π.r²

or,

           h = V / (π.r²)

The given parameters are:

V = 36 cm³

r = 3 cm

Substitute those parameters into the formula:

h = 36 / (π.3²)

h = 36 / (9π)

h = 4/π cm

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Answer:

b. Solve the inequality. Show all your work.

Step-by-step explanation:

h= V/πr² is the formula for the volume of a cylinder, V= πr²h , solved for h.

⇒ V= πr²h

⇒ V/πr² = h

⇒ h= V/πr²

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every Linear equation can be solved easily.

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Answer:

1/2(35-3(2-4)(5-8)

1/2(32(-2(-3))

1/2(32(-6))

1/2(192)

1into192/2

=96

Step-by-step explanation:

Answer: If your rounding to the second spot after the decimal it would be in the hundredths place so in case it would be 2874.29 Although I'm not sure if that's how you wanted it to be done.

Round the number 2,874.2878 to two decimal places will be 2,874.29.

The action of forming anything into a circle. Mathematics. the act of substituting a number with one that is roughly equivalent in value but has fewer digits: To the closest dollar, rounding $27.68 results in $28. a comparable procedure that identifies one of several rules.

The decimal number is given below.

⇒ 2,874.2878

Round 2,874.2878 to two decimal places.

If the third place after the decimal is more than 5, then the second place after the decimal will be increased by one.

In the third place after the decimal is 7, then the number 8 is increased by one that is 9.

Round the number 2,874.2878 to two decimal places will be 2,874.29.

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The equation in slope-intercept form is y = -3/2x + 9. Slope of the equation is - 3/2 and y - intercept is 9.

Calculate the slope (m).

Keep in mind that the slope is determined by dividing the change in y by the change in x. (rise over run).

Find the y-value of the y-intercept by solving (b).

In the formula y=mx+b, swap out m and b with their respective values.

The given equation is -

3x + 2y = 18

divide the equation by 2

3/2x + y = 9

Rearranging the equation -

y = -3/2x + 9

Comparing it with y = mx + c

so slope m = -3/2

and y - intercept = 9

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The geometric mean of a and b [tex]=\sqrt{a*b}[/tex] then the geometric mean of 8 and 18 is 12.

In Mathematics, the Geometric Mean (GM) is the average value or mean which signifies the central tendency of the set of numbers by finding the product of their values. Basically, we multiply the numbers altogether and take the nth root of the multiplied numbers, where n is the total number of data values.

The geometric mean is used in finance to calculate average growth rates and is referred to as the compounded annual growth rate.

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the result.

Geometric mean of a and b [tex]=\sqrt{a*b}[/tex]

Geometric mean of 8 and 18 [tex]$=\sqrt{8*18}[/tex]

a = 8 , b = 18  

= √144

= 12

The geometric mean of 8 and 18 is 12.

Therefore, the correct answer is option D. 12.

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The payment she gets after 22 hours of working is $187.

According to the statement

We have to find that the total amount she earned.

So, For this purpose, we know that the

Straight-time pay is the total amount of money you earn in a given pay period.

From the given information:

Sally Barrett, a banjo player for a local band, earns $8.50 per hour.What is her straight-time pay for a week in which she worked 22 hours?

Then

The amount she get as a rate per hour = $8.50

And

The time for which she works =  22 hours

Then

Pay she get after the work of the 22 hours = $8.50 * 22

Then

Pay she get after the work of the 22 hours = $8.50 * 22

Now multiply these to get the answer

Pay she get after the work of the 22 hours = $187

So, The payment she gets after 22 hours of working is $187.

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The polynomial function V to represent the volume of a round bale is  V(x) = π(x + 5)²(x + 8).

A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation, etc.

Let the dimensions of round bale is x+5 feet radius and 3 feet wide.

As we know that round bale is a shape of cylinder in which we will consider wide instead of height.

Volume of Round Bale (V) = πr²w

    V = πr²w = π(x + 5)²[(x + 5) + 3]

V(x) = π(x + 5)²(x + 8)

Hence, we got the polynomial function that represent the volume of round bale is  V(x) = π(x + 5)²(x + 8).

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Answer:The idea is to multiply by some number (10, 100, 1000, etc.) so that when we subtract the original number from the multiple, the repeating part cancels out. If we multiply by 10, we get 10x = 2

Step-by-step explanation: sorry if its wrong thats all i remember

Answer:

-23.4

Step-by-step explanation:

-0.0468 ÷ 0.002 = -23.4 (A negative divided by a negative is a positive!)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

The measurement of each angle is : m∠A = 108° , m∠B = 36° , m∠C = 36°.

In mathematics, an isosceles triangle is a triangle in which any of the two sides are equal. Or we can say that if a triangle has at least two sides of equal length then it is known as isosceles triangle. In geometry, isosceles triangle follow the property of congruency of triangles. That means in an isosceles triangle the two angles of equal sides are congruent to each other.

In the given question,

Let m∠B = m∠C = x  , where m denotes measure of angle

therefore, m∠A = 3x

According to Triangle Angle-Sum Theorem,

m∠A + m∠B + m∠C = 180

thus,

3x + x + x = 180

5x = 180

x = 36

Hence,

m∠A = 3x = 180

m∠B = 36°

m∠C = 36°

Therefore, the measure of each angle A , B and C is 180°, 36° and 36° respectively.

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There were 29 nickels and 10 dimes in the bank.

We know that:

1 dime = 5 cents

1 nickel = 10 cents.

Also, $ 3.40 = 340 cents

Let the  number of nickels be n and the number of dimes be d.

Now, we are given that:

5 dimes and 2 nickels were taken away.

So, total coins = 46 - 2 - 5 = 46 - 7

Total coins = 39

We get the equation:

n + d = 39

d = 39 - n

Now, we also know that:

5 d + 10 n = 340

d + 2 n = 68

Put the value of d, we get that:

39 - n + 2 n = 68

n = 68 - 39

n = 29

d = 39 - n

d = 39 - 29

d = 10

Therefore, we get that, there were 29 nickels and 10 dimes in the bank.

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Answer:

-0.1

Step-by-step explanation:

-1/100 = -0.01

1/10 = 0.1

-0.01/0.1 = -0.1

Answer:

Volume = 665 cm³

Step-by-step explanation:

We can calculate the volume of a cylinder using the following formula:

[tex]\boxed{\mathrm{Volume = \pi r^2 h}}[/tex],

where:

• r = radius of cylinder

• h = height of the cylinder

In the question, we are told that the diameter of the cylinder is 8.4 cm. Since the diameter is twice of radius:

[tex]\mathrm{radius = 8.4 \div 2}[/tex]

          [tex]= \bf 4.2 \: cm}[/tex]

We are also told that the height of the cylinder is 12.0 cm. Therefore, using this information, as well as the formula above, we can find the volume of the cylinder:

[tex]{\mathrm{Volume = \pi \times (4.2 \mathrm{\: cm})^2 \times 12.0 \mathrm{\: cm}}}[/tex]

            [tex]= \pi \times 17.64 \mathrm{\: cm^} \times 12.0 \mathrm{\: cm}[/tex]

            [tex]\approx \bf 665 \: cm^3[/tex]

Therefore the volume of the cube is 665 cm³.

Step-by-step explanation:

there are many construction vids if you need a visual, but first off you need to a ruler, compass and protractor. draw a straight line horizontally, leave enough space above to add the length given as vertical side.

on the straight line choose a point preferably near centre and. place compass on the point and open to any distance, on the pencil side, draw a semi circle cutting the horizontal line at two points.

label the two points a and b

place compass on point and draw a smaller curve from that point above the center then do the same on other side

remember do not change the Size the compass was opened at for drawing the curves

the two new curves you drew should intersect, using ruler, draw a straight line vertically through intersection and center point

this line can be the required length given

you will notice an inverted T shape

the angle will be 90deg on either side, measure to ensure

He typically work each day for 10 hours.

According to the question, the expression can be written as:

The time taken to stretch the fingers = (1/2)t

Similarly, the time taken to smashed toes = (1/5)t

Total time = 7 hours

Now, the final expression can be written as:

(1/2)t + (1/5)t = (7)

(7/10)t = 7

t = 10 hours

Hence, he typically work each day for 10 hours.

What is time and work?

The time and work represents the problems deals with the time either with the individual or the group of the people to complete the piece of work. And the efficiency taken by each individual.

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The Proportional relationship y = 10x is a good fit for the data.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality,

i.e., y = kx

In which k is the constant of proportionality.

For this problem, foe each value of x, the output is 10 times that, hence the constant is k = 10 and the proportional relationship y = 10x is a good fit for the data.

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Answer:

The Proportional relationship y = 10x is a good fit for the data.

Answer:

2) y= 4x+17

Step-by-step explanation:

y- y1 = m(x- x1)
y- 5 = 4 (x - (-3))
y-5= 4( x+ 3)
y-5= 4x+ 12
y= 4x+17

If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

We know that when a transversal cuts two parallel lines, then the corresponding angles are equal.

We know that parallel lines never intersect each other. When a third line is perpendicular to one of the parallel lines, then the third line must be perpendicular to another line as well.

To prove if AD is perpendicular to MN, it is also perpendicular to OP

ABN=90o

( Since AD is perpendicular to MN)

BCP=ABN=90o

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The geometrical representation of y=3 as an equation in

a) one variable is y = 3

b) in two variables is 0x + y = 3.

Based on the information illustrated, the geometrical representation of y=3 as an equation in one variable is y = 3.

Also, the geometrical representation of y=3 as an equation in two variables is:

y = 3.

0x + y = 3

0x + y - 3 = 0

Therefore, y = 3.

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Answer:

i didn't understand please write it in a clearer way so I can help

Answer: given clear information about the question

Step-by-step explanation:

What I can advise is, Please look for the "X or Y" carefully, work on it step by step!!

Using the distance formula, the distance between the pair of points R(-2,3)  and S(3,15) is 13 units

Given,

The points = R(-2,3)  and S(3,15)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}-(y_{2} -y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(3--2)^{2}+(15-3)^{2} }[/tex]

[tex]=\sqrt{5^{2}+12^{2} }\\ =\sqrt{25+144}\\ =\sqrt{169}[/tex]

=13 units

Hence, using the distance formula, the distance between the pair of points R(-2,3)  and S(3,15) is 13 units

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Answer:

x-4   IS a factor

Step-by-step explanation:

IF   x-1 is a factor    then putting   x = 1   into the equation will make it =    zero......  it does not

IF x+1  is a factor then putting x = -1   into the equation will result in = 0

     it does not

IF  x -4 is a factor , then puting in x =4 into tthe equation will = 0   it DOES !