At a distance of 6 meters, a person with average vision is able to clearly read letters 1.0 cm high.Approximately how large do the letters appear on the retina? (Assume that the retina is 1.7 cm from the lens.)

Answer:

P=15,625

Rate=4%

Time=3 years

CI=P(1+R/100)^T

=15,625(1+4/100)^3

=15,625*1.124864

=17576 Ans

Step-by-step explanation:

hope it helps

Answer:

24

Step-by-step explanation:

6 + 8 =24. You can ignore the 1/2 because it is on both sides of the equation.

Answer:

it is 24 and 24x1/2 but you can count 1/2 as 2 which will get you to 48 division 12

The 15-year fixed rate mortgage save $ 100,800 more than in the case of the 30-year mortgage.

We must compute the total payments to be made in order to determine the amount saved by getting a 15-year mortgage rather than a 30-year mortgage.

Payments for a 30-year mortgage with a fixed rate of 4.5% are due every month in the amount of $1,020. The total payment is then determined as follows:

Total payment  = 1020 * 12* 30  = 367,200

Difference according to lone = 367,200 - 200,000

difference = $167,200

Now, the monthly payments for the 15-year mortgage at a 4% rate will be $1,480.

Then total final payment  =  1480*12*20 = $266,400

so in this case, the difference from The loan will be

266,400 - 200,000 = $66,400
Thus, we can draw the conclusion that, when comparing the two loans, the 15-year option will result in savings of $ 100,800 more than the 30-year mortgage.

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The number -17/20 belongs to the set of real numbers.

What is the set of real numbers?

The set of real numbers is made by combining the set of rational numbers and the set of irrational numbers. Real numbers include natural numbers or counting numbers, whole numbers, integers, rational numbers (fractions and repeating or terminating decimals), and irrational numbers.

All real numbers, including fractions and decimals, are part of the set of real numbers.

The set of real numbers includes all numbers that can be expressed on the number line, including positive and negative numbers, as well as all fractions and decimals.

This set is often denoted by the symbol "ℝ".

Hence, The number -17/20 belongs to the set of real numbers.

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Answer:

Angle DFC is complementary to angle BFC

Step-by-step explanation:

AD is a straight line passing line EB. DFE, EFA, AFB and BFD are right angles as the lines are perpendicular.

DFB is divided into 2 angles by the segment FC

therefore

DFC + BFC = 90 degrees

The dimensions required are 125 feet and 50 feet.

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives can be generalized to functions of several real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is (after an appropriate translation) the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables.

The total length will be x and the height will be y.

Perimeter = 500 = 2x + 5y

Total Area = A = xy

Solve for y using the equation of perimeter:

5y = 500 - 2x

y = 100 - 2x/5

Put y in the equation of the Area

A = x(100 - 2x/5)

A = -2x²/5 +100x

To find the maximum area, find the derivative:

A' = -4x/5 + 100

To maximise the area, we equate A' to zero.

A' = 0

-4x/5 +100 = 0

∴ x = 125

A'  is positive when x < 125 and A' is negative when x >125, therefore meaning that x=125 is a maximum. Since this value is a maximum, the area is maximized when the total length is 125ft.

Put x = 125 in equation of perimeter:

500 = 2(125) + 5y

500 = 250 + 5y

5y = 250

∴ y = 50 ft

Thus, the dimensions required are 125 feet and 50 feet.

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Answer:

∠ a & ∠ d

∠ b & ∠

Answer:

∠ A and ∠ D

∠ B and ∠ E

Step-by-step explanation:

At the given point, Chad has used 176 feet of light

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

Length = 55 feet

Width = 48 feet

We start by calculating the distance from the end of the width till the beginning of the length

This is represented by the following Pythagoras theorem

Distance = √(Length² + Width²)

So, we have

Distance = √(55² + 48²)

Evaluate

Distance = 73

The number of feet is then calculated as

Feet = Length + width + distance

So, we have

Feet = 55 + 48 + 73

Evaluate

Feet = 176

Hence, the total distance is 176 feet

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Prediction for the spinner will land on an even number is 54 times.

What do you mean by permutation and combination?

By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented.

There are 3 even numbers out of A total of 8 numbers.

Each spin would have a 3/8 chance of landing in an even number.

Multiply the chance of landing on even by number of spins:

144 x 3/8 = 432/8 = 54

The answer would be 54 times.

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Answer:

Step-by-step explanation:

You want the solutions to three equations, and the error in the work shown.

The correct solution is ...

  [tex]-6n+22=-4n+14\\\\22=2n+14\qquad\text{add $6n$}\\\\8=2n\qquad\text{subtract 14}\\\\\boxed{4=n}[/tex]

Cullen's error was adding 4n to one side, and subtracting 4n from the other side of the equation. (The same operation must be done to both sides.)

The correct solution is ...

  [tex]8.4y -6.8 = -3.2y +16.4\\\\11.6y-6.8=16.4\qquad\text{add $3.2y$}\\\\11.6y=23.2\qquad\text{add 6.8}\\\\\boxed{y=2}[/tex]

Seraphina's error was dividing one side of the equation by 11.6 and subtracting 11.6 from the other side. (The same operation must be done to both sides.)

The correct solution is ...

  [tex]\dfrac{7}{8}b -32 = \dfrac{3}{4}b +32\\\\\dfrac{1}{8}b-32=32\qquad\text{subtract $\dfrac{3}{4}b$}\\\\\dfrac{1}{8}b=64\qquad\text{add 32}\\\\\boxed{b=512}\qquad\text{multiply by 8}[/tex]

Jasper's error was multiplying one side of the equation by 8 and dividing the other side by 8.  (The same operation must be done to both sides.)

The angles that satisfy the given trigonometric equation are 0°, 153.5°, 333.5°

Trigonometric ratios are the ratios of sides of a right-angle triangle. The most common trigonometric ratios are sine, cosine, and tangent.

2tan^2∅ + tan∅ = 0

let k = tan∅

so that we have

2k^2 +k = 0

factorizing,

k( 2k + 1) = 0

Therefore,

k = 0, or 2k + 1 = 0

2k  = -1

k = -1/2

so k = 0 or k  = -1/2

recall that tan∅ = k

which means

tan∅ = 0 or tan∅ = - 1/2

∅ = arc(tan) 0 or arc(tan) -1/2

∅ = 0° 0r -25.6°

but tan ∅ = -1/2 at 90° to 180° and 270° to 360°

∅ = 0°, (180 - 25.55°), (360 - 25.55°)

∅ = 0°, 153.5°, 333.5°

In conclusion the angles that satisfy the equation are 0°, 153.5° and 333.5°

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The y-coordinate of the center of the circle is 1.

What is a coordinate?

In geometry, a coordinate system is a method for determining how to place points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates. A coordinate system is a framework for specifying how objects are situated in relation to one another within a specified space, such as a specific region of the earth's surface or the entire surface of the planet.

Solution Explained:

After completing the square for x and for y, you should get

(x+2)^2  +  (y-1)^2  = 21

Center (x,y) = (-2,1)

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(x + 2) is not a factor of the given polynomial f(x).

What is factor of polynomial?

A polynomial with coefficients in a specific field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.

Consider, the given polynomial

f(x)=2x^4-3x²-4x+1

We have to check that (x + 2) is a factor of polynomial or not.

Since, if (x - a) is a factor of polynomial then 'a' is a zero of polynomial.

Here if (x + 2) is a factor of f(x) then f(-2) = 0

Plug x = -2 in f(x).

⇒

f(-2) = 2(-2)^4 - 3(-2)^2 - 4(-2) + 1

      = 32 - 12 + 8 + 1

       = 20 + 9

f(-2) = 9

f(-2) ≠ 0

Hence, (x + 2) is not a factor of the given polynomial f(x).

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The graph represents the function

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6.

Option(B) is the correct answer.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.

From the given graph we can conclude that

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6

Hence, the graph represents the function

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6

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The graph represents the function

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6.

Option(B) is the correct answer.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the input values and the output values of the function. It is typically plotted in the form of a set of points on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.

From the given graph we can conclude that

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6

Hence, the graph represents the function

y = -1 if -6 < x ≤ -4

y = 0 if -4 < x ≤ -2

y = 1 if -2 < x ≤ 0

y = 2 if 0 < x ≤ 2

y = 3 if 2 < x ≤ 4

y = 4 if 4 < x ≤ 6

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Answer:no

Step-by-step explanation:

Answer: no

Step-by-step explanation: cuz u need a number thats bigger such as the numerator is bigger than the denominator

5% of $1100 = 55

Year given = 7

So, 55 × 7 = 385

She would get after 7 years all total  = (1100 + 385) = $1485

Answer:

Step-by-step explanation:

5,6

The inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let the number be 'b'. Then the statement "the sum of a number and 10.7 is at most −3.2" is written in mathematical form. Then we have

b + 10.7 ≥ −3.2

Thus, the inequality that represents the condition will be b + 10.7 ≥ −3.2. Then the correct option is C.

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The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

The value of x is 25.

The value of y is 78.

The value of z is 24.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

From the figure given we see that,

88 and y + 10 are corresponding angles.

88 = y + 10

y = 88 - 10

y = 78

Now,

3x - 7 and 2x + 18 are oposite angles.

3x - 7 = 2x + 18

3x - 2x = 18 + 7

x = 25

Now,

(y + 10) + (3x - 7) + z = 180

78 + 10 + 3 x 25 - 7 + z = 180

88 + 75 - 7 + z = 180

z = 180 - 156

z = 24

Thus,

The value of x is 25.

The value of y is 78.

The value of z is 24.

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The probability that it will rain tomorrow is 0.2. the odds that it will rain tomorrow are 2 to .  The odds that it will not rain tomorrow are to 0.8.

What is probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The probability that it will rain tomorrow is 0.2

i.e.

P(it will rain tomorrow )=0.2

Now probability that it won't rain tomorrow is,

P(it won't rain tomorrow )=1- P(it will rain tomorrow)=1-0.2=0.8

Thus

P(it won't rain tomorrow)=0.8.

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The amount of time Jim spent on the bicycle is 6.5 hours.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

Total distance, d = 255 miles,

Total time, t = 7 hours,

The speed of walking, s = 3 miles / hour,

The speed of riding bicycle, S = 39 miles/hour,

Calculate the time spent on the bicycle as shown below,

Total time = Time on bicycle + Time walking

7 = Distance on bicycle/speed + Distance of walking / speed

7 = b / 39 + w / 3

Here w is the distance by walking and b is the distance covered by bicycle,

b + w = 255 (As given)

Solve both equations,

w = 1.5 miles and b = 255 - 1.5 = 253.5 miles

Calculate the time spent on a bicycle as shown below,

The time spent on the bicycle = b / 39

The time spent on the bicycle = 253.5 / 39 = 6.5 hours

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Answer:

3 grams

Step-by-step explanation:

g(5)-2g(1)

g × 5- 2g(1)

5g - 2g×1

5g - 2g

3g

The slicing of the equation 8x - 4y = 20 for y is y = 2x - 5

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

8x-4y=20

Rewrite the above equation properly

So, we have the following representation

8x - 4y = 20

Divide through the equation by 4

So, we have the following representation

2x - y = 5

Make y the subject of the equation in the above equation

This gives

y = 2x - 5

Hence, the solution is y = 2x - 5

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The percent decrease of people who went to the pool is 25%.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

Given

In first week = 1120

In second week

Subtracting,

1120 - 105

1015

In third week,

Sum

1015 + 140

1155

In fourth week

1155 - 315

840

The percentage of fewer persons that visited the pool during these four weeks,

1120 - 840/1120

280/1120

1/4

For percentage,

1/4 × 100%

25%

The percent decrease of people who went to the pool is 25%.

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For a polynomial function statements that need to be true are different end behavior for different degree and different sign of leading coefficient.

A function that can be expressed as a polynomial is referred to as a polynomial function.

A polynomial equation's definition can be used to derive the definition.

A polynomial is typically denoted by P (x).

The degree of the variable in P(x) is its maximum power.

The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large.

Whole real numbers make up a polynomial function's domain (R).

For a polynomial function following statements to be true:

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At the end of the year, there will be $2200.in her account

A list of debit and credit entries for transactions involving a specific object (such as cash or notes payable), a certain person or business, or both. a financial period's transaction statement that displays the final balance

The most typical kinds of bank accounts are as follows: Checking accounts and Savings accounts

Silvia invests $1,000 in an account over the course of a year, contributing 10% per month.

Because there are 12 months in a year,

She puts 10% of the account each month for a year

that is 10 * 1000/100 = 100 each month she puts in her account.

so for 12months in a year 100*12 = $1200

$1200 in her account over the course of the year she has deposited

Thus, at the end of the year,

Silvia has $1000 + $1200 = $2200 in her account.

At the end of the year, there will be $2200.in her account.

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Answer:

y = 6x + 12

Step-by-step explanation:

(2, $24)

(4, $36)

(6, $48)

Find slope (y2-y1) / (x2-x1)

m = ($36 - $24) / (4 - 2)

m = 12 / 2

m = 6

Put into formula y = mx + b

y = 6x + b

Substitute values to find b (the y offset)

$24 = 6(2) + b

$24 = 12 + b

b = $12

y = 6x+12

However, a correlation between two variables does not always imply that a change in one variable is the reason for a change in the values of the other. There is a causal link between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event.

Causal relationships between variables may consist of direct and indirect effects. Direct causal effects are effects that go directly from one variable to another. Indirect effects occur when the relationship between two variables is mediated by one or more variables.

Direct and indirect effects may make up causal connections between variables. Effects that flow directly from one variable to another are referred to as direct causal effects. When one or more factors mediate the link between two variables, indirect effects result.

What are examples of causal relationships?

Causal relationships: A causal generalization, e.g., that smoking causes lung cancer, is not about an particular smoker but states a special relationship exists between the property of smoking and the property of getting lung cancer.

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Mila will receive 68 EUROS of money after the exchange of 80 US dollar.

USD is the official money currency of united states of America.. its symbol of representation is $., also value of 1 US$ =82 rupee.

Unit of money used in other countries of European union is known as euro, also value of 1 EURO=87 rupee.

According to the given data in the question,

1 USD =0.85 EURO

80 USD = 0.85*80 EURO

80 USD= 68 EURO

Hence 80USD will be converted to 68 EUROS

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