Roberto deposited 860 in a new account that earns 6.5% simple interest. after 6 months, how much interest will he have earned?​

Answer:

A.) 1/16

Step-by-step explanation:

Remove parenthesis 2^-4

Use negative power rule 1/2^4

Simplify 2^4 to 16

Answer 1/16

Answer:

1/16 is the answer to that

Step-by-step explanation:

if the exponent is negative, you will bring it down with the whole number and change the sign to positive, hope this helps!! have an nice day!!

The number of ways is 1 billion.

We are asked to determine the possible number of ways of the social security number that is 9 digits if the numbers can be repeated.

In this case, using fundamental counting, there are 10 possible numbers in each digit that is from zero to nine.

Thus, the number of ways is 10*10*10*10*10*10*10*10*10 equal to 1 billion ways.

Hence the number of ways is 1 billion.

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As a result, the radian measure of the relevant center angle is around 3.07 radians.

An arc is any smooth curve that connects two locations. The length of an arc is referred to as its arc length. A graph arc is an ordered pair of neighboring vertices in a graph. An arc is defined as any segment (other than the complete curve) of a circle's circumference.

Here,

The formula for the length of an arc in a circle is given by:

Arc Length = (Central Angle / 2π) * Circumference

We know the Arc Length and the Radius of the circle, so we can find the Central Angle as follows:

Arc Length = (Central Angle / 2π) * 2π * Radius

66/5 * π = (Central Angle / 2π) * 2π * 22

66/5 * π = Central Angle * 22

Central Angle = (66/5 * π) / 22

The radian measure of an angle is equal to the ratio of the length of the arc that it intercepts to the radius of the circle. Hence, the radian measure of the central angle is given by:

Central Angle (in radians) = Arc Length / Radius

= (66/5 * π) / 22

So, the radian measure of the corresponding central angle is approximately 3.07 radians.

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Answer:

  72 cm²

Step-by-step explanation:

You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.

The area of the rectangle is ...

  A = bh

  A = (8 cm)(7 cm) = 56 cm²

The area of the triangle is ...

  A = 1/2bh

  A = 1/2(8 cm)(4 cm) = 16 cm²

The total area is the sum of the areas of the parts:

  total area = rectangle area + triangle area

  = (56 cm²) +(16 cm²) = 72 cm²

The area of the shape is 72 cm².

__

Additional comment

You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm  wide rectangle with the same base.

The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.

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Total assets is $94,000. total liabilities is $75,000, owner's equity is $19,000 and Debt-to-Equity ratio is 3.947.

Assets are the money or items which are benefitted by the company or will benefit in the future.

Liabilities are the amount or items which are obligation for the company.

From the given,

Total assets = bank account balance + inventory + accounts receivable + fixed assets

= $13,000 + $57,000 + $2,000 + $22,000

= $94,000

Total liabilities = Amount owed to video game vendors + bank loan

                        = $25,000 + $50,000

                        = $75,000

Owner's equity = Total assets - Total liabilities

                         = $94,000 - $75,000

                         = $19,000

Debt-to-Equity ratio = Total liabilities / owner's equity

                                 = 75,000 / 19,000

                                 = 3.947

Hence the required amount are found.

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Answer:

n = ^1/2

Step-by-step explanation:

z^1/2 = √z

1/2 as an exponent means square root

Answer:

A : 1704

Step-by-step explanation:

13/104 = 213/1704

The estimated number of bass in the lake is 1704 bass if the researchers in the city lake caught, marked, and released 213 basses.

The population and sample are described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

We have given that, the researchers caught, marked, and released 213 basses. Later they took a sample of 104 basses and found that 13 were marked.

Proportion = 104/13 = 8

It means 1 marked fish in every 8 fish

The number of basses in the lake = 8×213 = 1704 bass

Therefore, the estimated number of bass in the lake is 1704 bass if the researchers in the city lake caught, marked, and released 213 basses.

Hence, they took a sample of 104 basses and found that 13 were marked option A; 1704 is correct.

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due to multiple y-values for the same x-value.The given relation tt is not a function.

For a relation to be a function, each input (x-value) must have exactly one corresponding output (y-value). In the given relation tt, we have multiple entries with the same x-value but different y-values. Specifically, we have the points (6, 3) and (6, 0) in the relation. Since the x-value 6 is associated with both the y-values 3 and 0, it violates the definition of a function.
Therefore, the relation tt is not a function because it does not satisfy the one-to-one correspondence between the x-values and y-values.

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Answer:

-1.6

Step-by-step explanation:

\(-4.4y = 7.04\)

\(+4.4\)      

___________

\(y = 11.44\),  is the answer.

If you have any further questions, please reach out to me :)

Step-by-step explanation:

4 2/3 + 3 4/5 = 8 7/15

change to a common denominator:

4 10/15 + 3 12/15 = 7 22/15

reduce:

7 22/15 = 8 7/15

When the given mixed fractions are solved and tired to prove that both the sides are equal, the result will show that the given equation is correct.

A proper fraction that is less than one whole must represent the fractional portion of the mixed number. When a fraction is written properly, the top number, or numerator, must be less than the bottom number, or denominator.

A mixed fraction is one that has both a whole number and a fractional component. Additionally known as "Mixed numerals"

4 ⅔  + 3 ⅘  = 8  ⁷/ ₁₅  

¹⁴/ ₃ + ¹⁹ / ₅ = ¹²⁷ / ₁₅

⁷⁰ / ₁₅ + ⁵⁷ / ₁₅ = ¹²⁷ / ₁₅

¹²⁷ / ₁₅ =  ¹²⁷ / ₁₅

The result will demonstrate that the above equation is accurate when the given mixed fractions are solved and used to demonstrate that both sides are equal.

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The unicycle would move 2.512 meters if the wheel turns once

The wheel needs to rotate completely 40 times in order for Pierre to travel 100m

An equation is an expression that shows the relationship between two or more numbers and variables.

a) The circumference of the wheel = π * diameter = 3.14 * 80 cm = 251.2 cm = 2.512 m

The unicycle would move 2.512 meters if the wheel turns once

b) For a 100m race:

Number of wheel rotation = 100 m / 2.512 m = 39.8

The wheel needs to rotate completely 40 times in order for Pierre to travel 100m

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The next step in the series will be a circle divided into five shapes.

option D.

A series is a sequence of numbers or events that are arranged or added in a particular pattern.

From the given diagrams, the next step in the series is calculated as follows;

the first diagram is a circle divided into two shapes,

the second diagram is a circle divided into three shapes

the third diagram is a circle divided into four shapes

the fourth diagram will be a circle divided into five shapes

So the next step in the series will be a circle divided into five shapes or pentagon.

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Answer:

1. A=πr2=π·4.62≈66.4761

A≈66.48

2. A=πr2=π·22≈12.56637

A≈12.57

please mark as brainiest

Answer:

1. 66.48

2. 12.57

Step-by-step explanation:

Formula is A = ㅠr^2

The radius is that half line :))

The curve y = 8e^x has maximum curvature at the point (0, 8).there is no point where the second derivative equals zero,

To determine the point of maximum curvature on the curve y = 8e^x, we need to find the second derivative of the function and identify the point where it equals zero. The second derivative represents the rate of change of the slope, or the curvature, of the curve.

First, we find the first derivative of y = 8e^x with respect to x:

dy/dx = 8e^x

Then, we differentiate again to find the second derivative:

d²y/dx² = d(8e^x)/dx = 8e^x

Setting the second derivative equal to zero:

8e^x = 0

Exponential functions, such as e^x, are never equal to zero for any value of x. Therefore, there is no point where the second derivative equals zero, indicating that the curve y = 8e^x does not have any inflection points or points of maximum curvature.

However, we can determine the point where the curvature is the greatest by considering the graph of y = 8e^x. Since the exponential function e^x is always positive, the curve y = 8e^x is always concave up. This means that the curvature is positive throughout the curve, but there is no specific point of maximum curvature.    

In conclusion, the curve y = 8e^x does not have a point of maximum curvature but is always positively curved.  

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Overall, equations provide a mathematical representation and understanding of relationships, while tables present data points in a structured format.

When comparing an equation and a table, you can examine their characteristics, purpose, and the information they provide. Here are some points to consider when making comparisons:

Representation:

An equation represents a mathematical relationship between variables using symbols and mathematical operations. A table presents data or values in a structured format, typically organized into rows and columns.

Communication of Information:

Equations provide a concise and general representation of a relationship, allowing for predictions, calculations, and modeling. Tables present specific data points or values, providing a visual representation of how variables are related or how they change.

Variables:

Equations involve variables, which can be manipulated to explore different scenarios and analyze the relationship between quantities. Tables display specific values or data points for variables, showing how they vary or are related based on the given information.

Visualization:

Equations can express relationships symbolically and provide a mathematical understanding, but they may not offer a visual representation of data. Tables provide a visual representation of data points, allowing for a quick overview and easy comparison of values.

Flexibility:

Equations offer flexibility in terms of adjusting variables and parameters to explore different scenarios and make predictions. Tables can be easily modified or expanded by adding or removing data points to reflect new observations or additional information.

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Answer:

206 is the answer

Step-by-step explanation:

Like and give 5 star rating

Answer:

5.988

Step-by-step explanation:

Fraction : Word problems may involve fractions if we are dealing with partial values coming from a whole.

Total number of pages she read on Monday are 50 pages .

Total number of pages she read on Tuesday are 40 pages .

Operations with Fractions:

we have to remeber some important rules, making fractions similar for addition and subtraction, and applying the reciprocal for the divisor in division. The operations would depend on the analysis of the problem.

We have given in the problem that on Monday, Saumya read 1/3 of a book and on Tuesday, she read 2/5 of the remaining pages. After those, the remaining number of pages is 60

Firstly, we have to find the total number of pages the book has.

We will begin by finding the remaining fraction of pages after Saumya read on Monday. We will subtract 1/3 from 1 whole since she read from the beginning of the book.

1 − 1/3 = 2/3

Now, we know that on Tuesday, Saumya began reading with 2/3 remaining in the book. We will now find the fraction of the pages Saumya read on Tuesday. We know that it's 2/5 of the remaining pages, so it's 2/5 of 2/3

=> 2/5× 2/3 = 4/15 of the total number of pages of the book on Tuesday. So now, we will find the total fraction of the number of pages of the book that Samuya has read so far. This is so we can compare this fraction with the number of pages remaining. For this, we will add

1/3 + 4/15 = (5 + 4)/15 = 9/15

then 1 - 9/15 = (15-9)/15 = 6/15

This means that there would be another 6/15

= 2/5 of the book remaining and

that the remaining 2/5 of the book = 60 pages the total number of pages = 60/2/5

= 60×5/2 = 150

Therefore, the book has a total of 150 pages.

Total number of pages she read on Monday

= 1/3 of 150 = 50 pages

Total number of pages she read on Tuesday

= 4/15 of 150 = 40 pages

Hence, the total number of pages she read on Monday and Tuesday are 50 pages and 40 pages respectively.

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Answer:

50°

Step-by-step explanation:

BC⊥CD

Sum of interior angles of ΔABC = 180

Therefore, m∠BAC = 180 - 90 - 40 = 50

Answer:

The answer is B

Step-by-step explanation:

I took the test.

Answer:

Can I have a picture?

Step-by-step explanation:

Put it DB and I'll gladly answer!

All the angles in the given diagram are;

∠5 = 81°

∠1 = 128°

∠2 = 52°

∠3 = 47°

∠4 = 133°

We are given different angles. Thus;

52 + ∠5 + 47 = 180

This is because sum of angles on a straight line is 180°. Thus;

99 + ∠5 = 180

∠5 = 180 - 99

∠5 = 81°

∠1 = ∠5 + 47° because of the definition of corresponding angles. Thus;

∠1 = 81° + 47°

∠1 = 128°

∠2 = 52° because they are corresponding angles.

∠3 = 47° because they are corresponding angles.

∠4 = 180 - 47° because sum of angles on a straight line is 180°.

∠4 = 133°

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Using Algebraic expression solution ,

The cost of three hats is $18 .

We have given that,

A hat company charge for design fee $4 per hat .

i.e design fee of one hat = $4

total cost of 5 hats = $30

let the cost of one hat without design fee be $x and total cost of one hat is $(x+4) .

using the above statement, we get an algebraic expression,

5( x+ 4)= 30

we solve the above algebra expression,

=> 5x + 20 = 30

=> 5x = 10

=> x = 2

so, cost of a hat without design fee is $2

and total cost of one hat is $6.

we have to calculate cost of 3 hats .

cost of one hat in hat company= $ 6

cost of three hats in hat company= $(6×3)

= $18

Hence, the total cost of 3 hats is $18.

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Answer: 11.3 hours

Step-by-step explanation:

Before this question is another asking for an equation depicting this with Jordan's progress in miles (y) after a number of hours (x).

That would be y = 15x

x in the real world context would be the number of hours it would take for Jordan to finish the 170 mile bike race.

To solve this make y to be 170 and solve for x.

170 = 15x

x = 170/15

x = 11.3 hours

The amount of concrete required to make 80 pots is 0.24192 cubic meters after adding 5% of the required concrete.

Given that:External dimensions of the prism, a = 18 cmHeight of the prism, h = 16 cm Thickness of the walls, t = 3 cmNumber of pots, n = 80Wastage is 5% of the required concreteLet the side of the inner square be 'a1'. Then,a = a1 + 2t⇒ a1 = a - 2t = 18 - 2×3 = 12 cmVolume of the pot = volume of the outer prism - volume of the inner prismVolume of the outer prismVolume of the outer prism = a²hVolume of the outer prism = 18²×16 = 5184 cm³Volume of the inner prismVolume of the inner prism = a1²hVolume of the inner prism = 12²×16 = 2304 cm³Volume of the potVolume of the pot = 5184 - 2304 = 2880 cm³In m³, Volume of the pot = 2880/1000000 m³Volume of 80 such potsVolume of 80 pots = 80 × 2880/1000000 m³= 0.2304 m³Concrete required for the potsConcrete required = volume of 80 pots × (100 + 5)/100Concrete required = 0.2304 × 105/100 m³Concrete required = 0.24192 m³

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Step-by-step explanation:

an = 2n^2 - 3 · Anonymous. -1, 5, 15, 29, 47, ... an = 2 n^2 - 3.

The required nth term will be 2n² - 3 in the given quadratic sequence.

Sequences are defined as an arrangement of numbers that is in a particular order.

The first 5 terms of a quadratic sequence are following as:

-1, 5, 15, 29, 47,

We have to determine the nth term of the given sequence.

As per the given question, we have

-1, 5, 15, 29, 47,

We can rewrite the above numbers in the sequence as

first term = -1 = 2(1)²-3,

second term = 5 = 2(2)²-3,

3d term = 15 = 2(3)²-3,

4th term = 29 = 2(4)²-3,

5th term = 47 = 2(5)²-3

Similarly, nth term = 2n² - 3

Therefore, the required nth term will be 2n² - 3 in the given quadratic sequence.

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5x+7y=25

5x-2y=-65

subtract both of the equations

5x-5x=0

7y--2y= 7y+2y=9y

25--65=25+65=90

0+9y=90

9y=90

divide both sides by 9 to get y by itself

9y/9=90/9

cross out 9 and 9 which becomes 1*1*y=y

90/9=10

y=10

find x by using the substitution method

5x+7y=25

5x+7(10)=25

5x+70=25

move +70 to the other side

sign changes from +70 to -70

5x+70-70=25-70

5x=-45

divide both sides by 5 to get x by itself

5x/5=-45/5

cross out 5 and 5 then becomes 1*1*x=x

-45/5=-9

x=-9

answer:

(-9,10)

Lets do

\(\\ \sf\longmapsto \sqrt{-100}\)

\(\\ \sf\longmapsto \sqrt{-(10)^2}\)

\(\\ \sf\longmapsto \sqrt{10^2}\sqrt{-1}\)

\(\\ \sf\longmapsto 10i\)

Write in standard form

\(\\ \sf\longmapsto 10i\)

\(\\ \sf\longmapsto \boxed{0}+\boxed{10}i\)

Step-by-step explanation:

√-100

√-(10)²

√10²√-1

10i

0+10i

The correct expression  and diagram represent "three times a number" is shown in option 2.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

"three times a number"

Now,

Let a number = x

Hence, We get;

⇒  "three times a number"

⇒ 3 × x

⇒ 3x

Thus, The correct expression  and diagram represent "three times a number" is shown in option 2.

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Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

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Marcus ends up paying $37.70 for the two shirts.

To calculate the final price, we need to follow these steps:

1. Calculate the discounted price of each shirt:

  - Shirt 1: $28.99 - 30% = $20.29

  - Shirt 2: $30.29 - 30% = $21.20

2. Apply the additional 10% off the already reduced prices:

  - Shirt 1: $20.29 - 10% = $18.26

  - Shirt 2: $21.20 - 10% = $19.08

3. Calculate the total cost of the shirts before tax:

  - Total cost = $18.26 + $19.08 = $37.34

4. Add the 6% sales tax:

  - Sales tax = 6% of $37.34 = $2.24

5. Calculate the final price including tax:

  - Final price = $37.34 + $2.24 = $39.58

Therefore, Marcus ends up paying $39.58 for the two shirts. None of the provided options match the calculated amount, so none of the given options are correct.

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