prove the following equalities using mathematical induction: a. ∑ ― 1 = 1 ( 1 i(i 1)) = 1 ― 1/, ≥ 2.

Answer:

Step-by-step explanation:

400x2% of that amont would equal 800

The value of fraction in simplest form is, 1/1296.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

⇒ 1/6 with an exponent of 4.

Now, We can simplify as;

⇒ (1/6)⁴

⇒ 1 / 6⁴

⇒ 1/ 6×6×6×6

⇒ 1 / 1296

Thus, The value of fraction in simplest form is, 1/1296.

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She used 7.90 paint with white paint on her bedroom walls.

To solve such problems we must know about fractions and subtraction.

Fraction

A fraction is a way to describe a part of a whole, the amount of white paint Jane used is 7.4 pints.

Given to us,

Total paint used my Jane = 8.3 pints = 83/10 pints,

the amount of blue paint = 2/5 pints,

Amount of white paint

amount of white paint = Total paint used - the amount of blue paint

=83/10-2/5

=83/10-2*2/5*2

=83/10-4/10

=79/10

=7.9pints

Hence, the amount of white paint Jane used is 7.9pints.

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The unsigned binary equivalent of the following unsigned decimal integer value 12 is 1100

An integer is a whole number that can be positive, negative, or zero. An unsigned integer is a non-negative integer that only represents positive values or zero.

To convert an unsigned decimal integer to its equivalent binary representation, you'll need to understand the basic concepts of binary and the process of converting decimal to binary.

Here we have to consider the unsigned decimal integer value 12.

To convert it to binary, start by determining the largest power of 2 that is less than or equal to 12, which is

=>  2³ = 8.

Write a 1 in the binary place corresponding to 2³ and subtract 8 from 12 to get 4.

=> 12 - 8 = 4

Then, determine the largest power of 2 that is less than or equal to 4, which is

=> 2² = 4.

Write a 1 in the binary place corresponding to 2² and subtract 4 from 4 to get 0.

=> 4 - 4 = 0

The binary equivalent of 12 is 1100.

Complete Question:

what is the unsigned binary equivalent of the following unsigned decimal integer value 12?

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Filling in the chart below with the interest and maturity future value is as follows:

Purpose               Principal  Interest Term (Days)  a) Interest  b) Maturity

Wedding Dress  $250.00      6%       75 days           $3.10          $253.10

College Books   $360.50     3.5%    180 days          $6.28         $366.78

The future value represents the compounded present value.

Compounding involves the interest of subsequent months computed on the accumulated interest.

The future value can be computed using an online finance calculator.

N (# of periods) = 75 days

I/Y (Interest per year) = 6%

PV (Present Value) = $250

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $253.10

Total Interest = $3.10

N (# of periods) = 180 days

I/Y (Interest per year) = 3.5%

PV (Present Value) = $360.50

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $366.78

Total Interest = $6.28

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He must anticipate drawing a red tile. 30 times minimum.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given this, Alex placed 8 blue tiles and 12 red tiles in a container. He plans to draw a tile, record its color, and replace it in the container before drawing another.

Let X be the number of times a red tile is drawn from the container

Number of red tiles = 12

Total tiles = 12 + 8 = 20

p = P(randomly drawing a red tile) = 12/20 = 0.6

n = 50 number of draws or trials

Since Alex replaces the tile before he draws the next tile, we can model

the distribution of X according to Binomial Distribution

Thus, X ~ Binomial with n = 50 and p = 0.6

The Expected value of a binomial variable is E(X) = np

E(X) = n * p

= 50 * 0.6

= 30

therefore,  he should expect to draw a red tile At least 30 times.

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Answer: $50

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the expressions in the correct sequence to prove ...

  z + z + z + z = 4z

The multiplicative identity property tells you z × 1 = z. Anything multiplied by 1 is unchanged. This lets us replace z in the original expression by z·1 in every case.

The distributive property tells you that multiplication distributes over addition. This means ...

  z ·1 + z · 1 + z · 1 + z · 1 = z · (1 + 1 + 1 + 1)

The properties of addition and the set of integers tell us that ...

  1 + 1 + 1 + 1 = 4

so we can replace the indicated sum by its value:

  z · (1 + 1 + 1 + 1) = z · 4

The commutative property of multiplication says a product is the same if the operands are in a different order:

  z · 4 = 4·z = 4z

This is the last step in showing z + z + z + z = 4z.

The correct order of tiles is shown in the attachment.

<95141404393>

Answer:

4.5

Step-by-step explanation:

2 time 4.5 is 9

Answer: x=4.5

Step-by-step explanation:

2x=9

2*x=9, now flip the 2, and make it division.

x=9/2

x=4.5

Answer: The 4th option

Step-by-step explanation:

4 cm x 3cm is 12 cm. 2 cm x 5 cm is 10 cm.

Answer:

Step-by-step explanation:

solve what's in the parenthesis.

1,204-299=905

so....

905/1

answer is: 905.

if you would like, use a website called Desmos graphing calculator.

its a calculator of all subjects, and it graphs.

There are 200 teachers in a school.

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100, also defines a fraction or a ratio in which the value of the whole is always 100

Given information is

25 % of the teachers teach basic math, there are 50 basic math teachers

To calculate how many teachers are there in the school.

Let the total number of teachers =c

Number of basic maths teacher=50

Percentage of teachers of basic math = 25

According to question

25% of x=50

0.25*x=50

x=200

Hence the total number of teachers is 200

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The number of silver and gold medals won is given as follows:

75.

The number of silver and gold medals is obtained applying the proportions in the context of this problem.

The percentage equivalent to silver and gold medals is given as follows:

20 + 30 = 50%.

Hence half the number of medals was either silver or gold, thus the number is given as follows:

0.5 x 150 = 75 meddals.

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well, 100% - 20% = 80%, so the discounted price is really 80% of the original 20 bucks, what's 80% of 20?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 20}}{\left( \cfrac{80}{100} \right)20}\implies \text{\LARGE 16}[/tex]

To do this you would do

$20 times (20/100) to get $20*(.20) = $4 which is the discounted price.

%(Percent) means "a specified amount in or for every hundred." In this case 20 for every 100.

Answer:

D

Books Cost

10

$122.50

11

$134.75

12

$147

Step-by-step explanation:

The table format is all messed up but I was able to figure out the numbers.

Since 10 books cost $122.50, each book must cost $122.50/10 = $12.25

For 1 book => 10 x $12.25 = $122.50

For 11 books => 11 x $12.25 = $134.75

For 12 books => 12 x $12.25 = $147

Answer choice is D which perfectly fits the numbers

Kylar is a lifeguard at a swimming pool, The total number of hours in a single shift done by Kylar is 3 hours.

Let the total number of hours in a single shift be = A

Now , The total length of equal shifts Skylar worked last week = 3 3/4 shifts

The total length of equal shifts Skylar worked last week = 15 / 4 shifts

The total number of hours Skylar worked in the week = 11 1/4 hours

The total number of hours Skylar worked in the week = 45 / 4

Now , the equation will be

Total length of equal shifts Skylar worked last week is equal to total number of hours Skylar worked in the week.

So ,

Total length of one shift of Skylar = total number of hours Skylar worked in the week / Total length of equal shifts Skylar worked last week

On substituting the values in the equation , we get

Total length of one shift of Skylar A = ( 45/4 ) / ( 15/4 )

On simplifying the equation , we get

A = ( 45/4 ) / ( 15/4 )

A = 45 / 15

A = 3 hours

Therefore, The total number of hours in a single shift done by Kylar is 3 hours.

Complete question: Skylar is a lifeguard at a swimming pool. Last week, they worked 3(3)/(4) equal -length shifts, because rain closed the pool early one day. Those shifts totaled 11(1)/(4) hours of work. How long is a single shift?

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Answer:

The answer is c. 30 cm, 40 cm, 50 cm. This set of measures could not be the side lengths of a right triangle, as it does not satisfy the Pythagorean theorem. The Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the square of the hypotenuse (50 cm) is not equal to the sum of the squares of the other two sides (30 cm and 40 cm).

Step-by-step explanation:

The solution to the inequality 5/w > 4/45 is given as follows:

w < 56.25.

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable. The difference is that the solution is composed by infinity values in a range of values, instead of a finite number of values.

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The simplified exponential expression is given as follows:

48x^13y^7.

The first term of the numerator is (4x²y)², hence, applying the power of power rule, it is given as follows:

(4x²y)² = 16x^4y². (apply the power of 2 to each factor).

The square root is equivalent to an exponent of 1/2, hence the power of power rule is also applied as follows:

square root (9x^6y²) = 3x³y.

At the denominator, we have that the term has a negative exponent, hence it is moved to the numerator, thus:

(x³y²)² = x^6y^4.

Now the expression is given as follows:

16x^4y² times 3x³y times x^6y^4

The multiplication of the coefficients is given as follows:

16 x 3 x 1 = 48.

For the variables x and y, we keep the bases and add the exponents, hence:

Hence the simplified expression is given as follows:

48x^13y^7.

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Average rate of change for the given function is 2.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that the graph is a line. So the function is linear.

Average rate of change of a linear function is equal to the slope of the given function, and it will be a constant at any two points on the line.

We have two points from the line (-2, -3) and (1, 3).

Slope of a line with two points (x, y) and (x', y') is,

slope = (y' - y) / (x' - x)

Slope of the given function with two points (-2, -3) and (1, 3) is,

Slope = (3 - -3) / (1 - -2) = 6/3 = 2

Average rate is same value from x = 1 to x = 2.

Hence the average rate of change is 2 for the given function.

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The value of the logarithmic expression is (b) 0

From the question, we have the following parameters that can be used in our computation:

log₉(1ˣ)

The logarithmic rule log(1^b) = 0 can be used to evaluate log(1^x) base 9:

log₉(1ˣ)

This is true because

Since 1^x = 1, no matter what the value of x is,

Then log(1^x) base 9 = x = 0.

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The required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The sample size is given as,
n = p × q × (Z/E)²

Assume the estimate for population proportion,
p = 0.5

Now,
q = 1 - p
q = 1 - 0.5
q = 0.5

Confidence level = 99%

Z value = 2.58
The margin of error,
E = 0.02

The sample size is given as,
Substitute the value in equation 1.
n = 0.5×0.5×(2.58/0.02)²

n = 4160

Thus, the required sample need if they plan to create a 99% confidence interval but still maintain their accuracy is 4160.

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Step-by-step explanation:

I cannot see the diagram at the bottom, so I cannot tell you a correct answer

F(x, y, y', y",..., y(n-1)) is the expression for the function f.

1. Rewrite the given differential equation as y (n) = f (x, y, y', y",..., y (n 1)).

2. Identify y as the dependent variable, y', y",..., y(n-1), as the derivatives of y up to order n-1. X is the independent variable.

3. The right-hand side of the equation, f(x,y,y',y",...,y(n-1)), provides the expression for the function f.f(x,y,y',y",...,y(n-1)) is the expression for the function f, where x is an independent variable, y is the dependent variable, and y', y",...,y(n-1) are y's derivatives up to order n-1. The right-hand side of the equation provides the expression for the function f when the differential equation is written as y (n) = f (x, y, y', y",..., y (n 1)). Consequently, f is a function of x, y, y', y",..., and y. (n-1). The differential equation is resolved using this expression for f.

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The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

The bottleneck time is the longest time it takes to complete any task in the assembly line. In this case, the longest time needed is 10, which is the last station. This means that all the other tasks must be completed within 10 seconds in order for the entire assembly line to proceed.

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

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If f′ is growing, the f graph is concave up on the interval. In the event that f′ is decreasing, the f graph is concave down on the interval. This has been obtained by using the concept of derivatives.

What are derivatives?

In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

Assume that f is differentiable on interval I.

If f′ is increasing, the f graph is concave up on I. In the event that f′ is decreasing, the f graph is concave downward on I. The graph of f is considered to have no concavity if f′ is constant.

Hence, concave up is when f' is increasing and when it is decreasing, it is concave down.

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2 is the fifth root of 32.

Using the problem as a starting point, we may write the equation as x5=32 x 5 = 32. This equation has to have a solution. The log function can be used to both sides of the equation. Therefore, the right response is 2.

A. In mathematics, the term "root" refers to a number that, when multiplied by itself, equals the original number.. Because 49 is created by multiplying 7 by itself twice in this instance, we refer to 7 as the square root of 49. Since 333=27, the cube root of 27 is 3.

[tex]\sqrt[5]{32}[/tex]

[tex]\sqrt[5]{2*2*2*2*2}[/tex]

= 2

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If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , then the value of xy is (a) 1  .

The values of x and y are solutions to two equations:

⇒ y = x²   ....equation(1)

⇒ 2y + 6 = 2(x + 3)    ....equation(2)

To find the value of xy, we first need to find the values of x and y which satisfy both equations.

We can put value of y from the equation(1) into the equation(2) :

⇒ 2y + 6 = 2(x + 3)

⇒ 2x² + 6 = 2(x + 3)

⇒ 2x² + 6 = 2x + 6

⇒ 2x² - 2x = 0

⇒ 2x(x - 1) = 0

that means either "2x=0"   or "x-1=0" ;

⇒   x = 0  or x = 1 .

when x = 1  , we have y = (1)² = 1 .

So , the product is = 1 × 1 = 1 .

Therefore , the value of xy is (a) 1  .

The given question is incomplete , the complete question is

If (x,y) is a solution to equations y = x²  and  2y+6 = 2(x+3) , what is the value of  xy ?

(a) 1

(b) 2

(c) 3

(d) 9

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