How to solve number 2

The expansion of the series will be 16 + 64 + 256 + 1024.

How to expand the series?

The expansion of a function into a series, or infinite sum, is known as a series expansion in mathematics. It is a technique for calculating a function that cannot be represented using just basic operators (addition, subtraction, multiplication and division).

The series is given as:

When n = 1, we have:

The series is given as S = (n=1,4)∑ [tex]4^{n+1}[/tex]

S = [tex]4^{2}+4^{3} +4^{4}+4^{5}[/tex]

S = 16 + 64 + 256 + 1024

Hence, the expansion of the series is 16 + 64 + 256 + 1024

Learn more about expansion, by the following link.

https://brainly.com/question/28062936

#SPJ4

The ratio (3 - 5)/(4 - 1) in the simplified form is -2/3.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Ratios can be divided into two categories. The part-to-whole ratio is one, and the part-to-part ratio is another. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

Mathematicians use the term "ratio" to compare two or more numbers. It serves as a comparison tool to show how big or tiny an amount is in relation to another.

The given ratio is

(3 - 5)/ (4 - 1)

When we subtract a bigger number from a smaller number, we subtract the small number from the bigger one and put the sign before the result the sign of the bigger number. So,

= - 2 / 3

So, the simplified form of (3 - 5)/ (4 - 1) is -2/3.

To know more about ratios, visit:

https://brainly.com/question/2804192

#SPJ13

Answer:

C. 34 - 16 = 18

ALSO

D. -4 - (-22)

   -4 + 22 = 18

Step-by-step explanation:

This is the REAL Question!

Which expressions have a value of 18?

Choose all answers that are correct.

A. –3 – 21 B. 7 – (–25) C. 34 – 16  D. –4 – (–22)

The positive square root, then the negative square root of each of the following numbers are:

4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.

Given,

In the question:

Find the positive square root, then the negative square root of each of the following numbers:

The numbers are given as:

16, 0.36, 25, 0.64, 1.21, 0.25, 1.44, 2500

Now, According to the question;

Square Root:

The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is \sqrt{ } ​square root of, end square root . Finding the square root of a number is the opposite of squaring a number.

We have to find the Arithmetic Square Root Method

and, Add a minus sign to the Arithmetic root.

a) [tex]\sqrt{16}[/tex] = 4

[tex]-\sqrt{16}[/tex] = -4

b) [tex]\sqrt{0.36}[/tex] = 0.6

[tex]-\sqrt{0.36}[/tex] = -0.6

c) [tex]\sqrt{25}[/tex] = 5

[tex]- \sqrt{25}[/tex] = -5

d) [tex]\sqrt{0.64}[/tex] = 0.8

[tex]-\sqrt{0.64}[/tex] = -0.8

e) [tex]\sqrt{1.21}[/tex] = 1.1

[tex]-\sqrt{1.21}[/tex] = -1.1

f) [tex]\sqrt{0.25}[/tex] = 0.5

[tex]-\sqrt{0.25}[/tex] = -0.5

g) [tex]\sqrt{1.44}[/tex] = 1.2

[tex]-\sqrt{1.44}[/tex] = -1.2

h) [tex]\sqrt{2500}[/tex] = 50

[tex]-\sqrt{2500}[/tex] = -50

Hence, The positive square root, then the negative square root of each of the following numbers are:

4, -4, 0.6,-0.6, 5,-5, 0.8, -0.8, 1.1, -1.1, 0.5, -0.5, 1.2, -1.2, 50, -50.

Learn more about Square Root at:

https://brainly.com/question/1387049

#SPJ1

Answer:

x=7

Step-by-step explanation:

Use the Distributive Property to simplify the equation.

Answer:

d

Step-by-step explanation:

angles on the circle subtended by the same arc are congruent

54° and x° are subtended by the same arc y , then

x = 54°

the measure of an inscribed angle is half the measure of its intercepted arc.

x and 54 are inscribed angles intercepted by arc y , then

y = 2 × 54° = 108°

Answer:

∠ ADC = 113° , ∠ ABC = 85°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , then

∠ ADC + ∠ ACD + ∠ CAD = 180° , that is

∠ ADC + 39° + 28° = 180°

∠ ADC + 67° = 180° ( subtract 67°  from both sides )

∠ ADC = 113°

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

DA is an angle bisector of ∠ BAC , then

∠ BAD = ∠ CAD = 28° , then ∠ BAC = 56° , then

∠ ABC + ∠ BAC + ∠ ACB = 180° , that is

∠ ABC + 56° + 39° = 180°

∠ ABC + 95° = 180° ( subtract 95° from both sides )

∠ ABC = 85°

Answer:

Why does each perfect square have two square roots?

Step-by-step explanation:

Why does each perfect square have two square roots?

Planet B has the larger mass. The mass of planet B is 50 times as large as the mass of planet A.

Mass of planet A = A = 8 * [tex]10^{23}[/tex]

Mass of planet B = B = 4 * [tex]10^{25}[/tex]

[tex]\frac{A}{B}=\frac{8 * 10^{23} }{4*10^{25} }[/tex]

    = [tex]\frac{2}{100}[/tex]

    = [tex]\frac{1}{50}[/tex]

50A = B

Hence, mass of Planet B is 50 times mass of planet B.

To learn more about mass here:

https://brainly.com/question/19694949

#SPJ1

Answer:

-11[tex]x^{2}[/tex] + 13x- 13

Step-by-step explanation:

(x - 8x² - 15) + (2 + 12x - 3x²)

(x + 12x) + (- 8x² - 3x²) + (- 15 + 2) [Combine like terms]

-11[tex]x^{2}[/tex] + 13x- 13

The probability density function is P(x) = 0 for x < 300 or x >480.

A probability density function, also known as the density of a continuous random variable, is a function whose value can be interpreted as providing a relative likelihood that the value of the random variable would be close to that sample in the sample space at any given sample in the sample space.

A.  the probability density function will be 1/(480-300) = 1/180 for 300=x=480

thus,  P(x) = 0 for x < 300 or x >480

B. the probability that the driving time will be less than or equal to 435 seconds is given by,

P(x= 435) = (1/180)(435-300) = 135/180 = 0.75.

C. the expected driving time will be the mean of intervals,

(300 + 480)/2 = 390
D. variance will be computed as (1/12)(480-300)² = 2700

E. standard deviation is calculated as √2700 = 51.96

know more about standard deviation here: https://brainly.com/question/16555520

#SPJ4

The ratio of malts to shakes is 6:11.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

In this case, in the ice cream shop ,there are 11 shakes sold for every 6 malts .

The ratio of malts to shakes will be:

= Number of malts / Number of ice cream

= 6/11

= 6:11

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

A rate of 3.76% per year for 30 years requires an initial principal investment of $281.95 to yield a total return of $600.00,

These considerations include the total amount you borrow from the bank, the loan's interest rate, and the time frame for finishing your mortgage repayment. You should use the following formula to calculate your mortgage:

M = P [i(1 + i)n] / [(1 + i)n - 1].

The first step is to convert R percent to r a decimal, which is 3.76%/100 or 0.0376 per year.

Our equation is solved as follows:

M = 600 / (1 + (0.0376 30)) = 281.95488721805 P = $281.95

A rate of 3.76% per year for 30 years requires an initial principal investment of $281.95 to yield a total return of $600.00,

To learn more about mortgage refer to:

https://brainly.com/question/22598793

#SPJ1

y = 3.12 + 61.02s

slope = 61.02

y intercept = 3.12

y intercept occurs when x = 0

correct option is the fourth option

Answer:

?

Step-by-step explanation:

If we take any sample from population the mean of sample is approximately population mean always sample mean of 100 babies is 3500.

Statistics is a science concerned with developing and studying methods of collecting, analyzing, interpreting, and presenting empirical data. Statistical research is applicable to virtually all scientific disciplines, and research challenges in various scientific disciplines motivate the development of new statistical methods and theories. Statisticians use a variety of mathematical and computational tools to develop methods and study the theory behind methods. His two basic ideas in the field of statistics are uncertainty and variability. Science (or life in general) often encounters situations where the outcome is uncertain.

Sample mean is unbiased estimator of population mean.

so , if we take any sample from population the mean of sample is approximately population mean always.

therefore, sample mean of 100 babies is 3500.

learn more about statistics here:

brainly.com/question/20982963

#SPJ4

The percentage increase in the price of a technology stock is 1.69%.

According to the question,

We have the following information:

The price of a technology stock was $9.45 yesterday. Today, the price rose to $9.61.

We know that following formula is used to find the percentage increase:

Percentage increase = 100*(final price- initial price)/initial price

Percentage increase for the technology stock = 100*(9.61-9.45)/9.45

Percentage increase for the technology stock = 100*0.16/9.45

Percentage increase for the technology stock = 16/9.45

Percentage increase for the technology stock = 1.69%

Hence, the percentage increase in the price of a technology stock is 1.69%.

To know more about percentage increase here

https://brainly.com/question/15510398

#SPJ1

The percentage increase in the cost of oranges is 20%

A % is a quantity or ratio stated as a fraction of 100 in mathematics (from the Latin per centum, "by a hundred"). The abbreviation "pct.", "pct.", and occasionally "pc" are also used to indicate it, but the percent sign, "%," is more frequently employed. There is no unit of measurement for a %; it is a dimensionless number (pure number).

The symbol for "%" developed from the progressive reduction of the Italian term per cento, which means "for a hundred." It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.

Given that the oranges at the grocery store went from $0.75/ib to $ 0.90/ib

=(0.90-0.75)/0.75

=0.15/0.75

=0.2

% increase= 0.2*100

=20%

Therefore, the percentage increase in the cost of oranges is 20%

To know more about percentage, visit:

https://brainly.com/question/16797504

#SPJ13

Answer: So the division between two persons is 1/6 and 1/2.

Step by step: First Person = 1*4/24= 4/24 = 1/6 (0.16)

Second Person = 3*4/24 = 12/24= 1/2 (0.5)

Answer: the division between two persons is 1/6 & 1/2.

Step-by-step explanation:

Just divide

The graph of the given equations is (see in attachments). The roots are (-3,-2,3)

From the question, we have

x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12

The roots are (-3,-2,3)

Graph:

A graph is an organized visual representation of any data in mathematics. The relationship between the variable quantities is depicted on the graph. In a graph theory, the set of items that are somehow connected to one another is represented by a graph. The vertices or nodes of the objects are essentially mathematical notions, and the edges between the nodes represent the relationships between the nodes. In mathematics and statistics, there are various types of graphs that are used to visually display data. The study of points and lines is known as graph theory. It is a branch of mathematics that focuses on the investigation of graphs. The mathematical truth is shown visually in this picture. Relationships are studied using graph theory.

To learn more about graph visit: https://brainly.com/question/17267403

#SPJ1

Answer:

A on edge

Step-by-step explanation:

because i said so

The number is -2. By using the concept of Linear Equation we get the number -2 as Answer of this question.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Let the number be ‘x’

So According to the Question,

The number that is 11 times less than 21 which results in seven times of the number decreases by 29 can be written in the numerical form as

11x – 21 = 7x- 29

11x – 7x = -29+21

4x = -8

x = -8/4

x = -2

So that’s how we got the value of the x = -2

To know more about Linear Equation, click here :

https://brainly.com/question/2030026

#SPJ4

Answer:

their would be 1,060 that they sold

Answer:

hink of sea level as 0 , and the elevation above sea level as positive, while the elevation below sea level is negative. Then determine the distance between them as if the two values are on a number line.

20617 feet

Step-by-step explanation:

The inequality that shows the maximum weight capacity of the elevator is w≤ 2500

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.

To represent the weight limit for the elevator using inequality, we can write it out as

w ≤ 2500

This shows that the weight must not exceed 2500 pounds

Learn more on inequality here;

https://brainly.com/question/25275758

#SPJ1

With the help of the given equation, we know that the automobile is worth $12528.15 after four years.

So, the equation of depreciation: y = A(1 - r)∧t

The current value is y.

A is the initial cost.

r is the depreciation rate.

t is the time in years, and

In four years, we must ascertain the present value.

Now,

y = $24000(1 - 0.15)⁴

y = 24000(0.85)⁴

y = 24000 × 0.52200625

y = 12528.15

Therefore, with the help of the given equation, we know that the automobile is worth $12528.15 after four years.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ4

Complete question:
The general equation for depreciation is given by y = A(1 – r)t, where y = current value, A = original cost, r = rate of depreciation, and t = time, in years. The original value of a car is $24,000. It depreciates 15% annually. What is its value in 4 years? $

By using normal distribution, it is obtained that  the probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128

What is normal distribution?

Normal distribution is a continuous type probability distribution whose probability density function is

[tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}[/tex]

where,  z = [tex]\frac{x - \mu}{\sigma}[/tex]

[tex]\mu[/tex] is the mean and [tex]\sigma[/tex]  is the standard deviation

For x = 29.8, z = [tex]\frac{29.8-30}{0.75}[/tex] = -0.27

For x = 30.2, z = [tex]\frac{30.2-30}{0.75}[/tex] = 0.27

so, P(29.8 < x < 30.2) = P(-0.27 < z < 0.27)

= 2 [tex]\times[/tex] P(z < 0.27)

= 2 [tex]\times[/tex] 0.1064

= 0.2128

Probability that a car has a gas mileage of between 29.8 and 30.2 miles per gallon is 0.2128

To learn more about normal distribution, refer to the link-

brainly.com/question/4079902

#SPJ4

Answer:

(x-4)^2  [I assume the (z+4)² option was mistyped.  Who wants zzzzzzzzz?]

Step-by-step explanation:

x² − 8x+16

Lok for a pattern that would allow us to fill in the missing numbers in

(x+a)*(x+b)

We know that a and b must equal +16 when multiplied together.  We also know their sum must be -8.  

a*b = 16

a+b = -8

Is there anything that ties these numbers together?  The number 4 comes to mind:  8 and 16 are known to be friendly to 4.  We need the sum to be -8, so lets make the 4 negative and put it into both expressions.

(-4)+(-4) = -8  YES

(-4)*(-4) = 16  YES

Assinging -4 to both a and b produces the factored expression:

(x-4)*(x-4) = x² − 8x+16    YES

All of the ways to write this time are:

.A.

10 minutes before 7

.D.

50 minutes after 6

.E.

6:50

What is a Clock?

This is a device or timepiece used to tell or measure time. It is a 24-hour measurement instrument. it reads in am(the morning time) and pm (afternoon/night time).

The morning time starts at the midnight (1 am) and ends in the mid-day(12 noon). The afternoon time starts mid-day (1 pm) and ends at the midnight(12 midnight).

Hence, 12mid night -11 in the morning is designated am. 12 noon- 11 pm in the night is designated pm.

Learn more about time on

https://brainly.com/question/12706984

#SPJ1

The circle with radius=7.95 is larger when a 100-unit long line is split in half.

A circle is a shape produced by all points in a plane that are a certain distance from the center. It is the curve drawn by a point traveling in a plane so that its distance from a specified point remains constant. The radius is the distance between any two points on a circle and the center. Typically, the radius must be positive. A degenerate instance is a circle with radius r=0. Except when otherwise noted, this article is about circles in Euclidean geometry, specifically the Euclidean plane.

A circle, in instance, is a fundamental closed curve that divides the plane into two regions: interior and exterior.

The perimeter of larger circle is 50 units

Therefore, 2πr=50

Radius=7.95

The perimeter of smaller circle is 25 units

Therefore, 2πr=35

Radius=3.97

The circle with radius=7.95 is larger.

To know more about circle, visit:

https://brainly.com/question/11833983

#SPJ1

The length of line segment is 10 units.

Writing the start and end points of line segment in (x, y) axis. First point = (-5, 5) and second point = (3, -1).

To calculate the line segment the formula to be used is -

d = ✓([tex] x_{2}[/tex] - [tex] x_{1}[/tex] )² + ([tex] y_{2}[/tex] - [tex] y_{1}[/tex] )²

Keep the values in formula

d = ✓(3 - (-5))² + (-1 - 5)²

d = ✓(3 + 5)² + (-6)²

Performing subtraction and addition based on sign

d = ✓8² + 36

Taking square on Right Hand Side of the equation

d = ✓64 + 36

Performing addition on Right Hand Side of the equation

d = ✓100

Taking square root on Right Hand Side of the equation

d = 10 units

Hence, the distance is 10 units.

Learn more about line segment -

https://brainly.com/question/2437195

#SPJ4