Evelyn deposited $90 in an account
earning 10% interest compounded
annually.
To the nearest cent, how much interest
will she earn in 1 year?
Use the formula B = p(1 + r)², where B is
the balance (final amount), p is the
principal (starting amount), r is the
interest rate expressed as a decimal, and t
is the time in years.

To determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

Rate of Change:

A rate of change describes how an output quantity changes relative to the change in the input quantity. The units on a rate of change are “output units per input units.”

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

[tex]\frac{\triangle y}{\triangle x} = \frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1}}[/tex]

How to determine:

Given the value of a function at different points, calculate the average rate of change of a function for the interval between two values [tex]x_{1}[/tex] and [tex]x_{2}[/tex].

Hence the answer is to determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

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The Actual Unemployment rate is 7%.

Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.

Cyclical Unemployment Rate = 1%

Natural Unemployment Rate = 6%

The Actual Unemployment rate will be:

= Cyclical Unemployment Rate + Natural Unemployment Rate

= 1% + 6%

= 7%

The unemployment is 7%.

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Answer:

Answer:The total change in the number of bushels she has for sale after 5 days is 83.125 bushelsStep-by-step explanation:The given parameters are;The initial number pf bushels the farmer has = 120 bushelsThe amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625 The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushelsThe total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 daysThe total change in the number of bushels she has for sale after 5 days = 83.125 bushels.

Step-by-step explanation:

Answer: The answer to this question would either be 8 or it would be 7.

The probability of a type I error is 0.022.

Given,

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

That is,

The probability of a type I error is 0.022.

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Answer:

1. 3  donuts

2.$76.90

Step-by-step explanation:

Answer:

u = 2

Step 1: Simplify both sides of the equation.

−7u −u +2u +11u = 10

−7u +−u +2u +11u = 10

(−7u +−u +2u +11u) = 10 (Combine Like Terms)

5u = 10

Step 2: Divide both sides by 5.

5u/5 = 10/5

Hope this helped!

Correct option is third option - " the original amount of the loan "

x value would be the time in months and y value would be the loan amount that is left.

The y-intercept is basically the point where x is 0. So, we can say the y-intercept would be when time is 0.

That's basically when the loan started and the y-value represents the full loan amount., which is $22,000.

correct option is third option -- "the original amount of the loan".

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Answer:

G. 12

Step-by-step explanation:

Step 1: Use PEMDAS to start solving

Step 2: Solve the problem

Answer:

(g.f)(-2) = -44

Step-by-step explanation:

Given:

f(x) = 3x² - 3x - 7

g(x) = -3x - 10

[tex] \rm \implies(g.f)( - 2) = [3 {( - 2)}^{2} - 3( - 2) - 7][ - 3( - 2) - 10] \\ \\ \rm \implies(g.f)( - 2) = [3 (4) + 6 - 7][ 6 - 10] \\ \\ \rm \implies(g.f)( - 2) =(12 - 1)( - 4) \\ \\ \rm \implies(g.f)( - 2) =11 \times ( - 4) \\ \\ \rm \implies(g.f)( - 2) = - 44[/tex]

Answer: 0.865 to (1dp)

Step-by-step explanation:

The common factor for the rational expression presented in this problem is given as follows:

A. (x²-1).

The rational expression in this problem is given as follows:

4/(x - 1) - 1/(x² - 1) = 6/(x - 1).

It is called a rational expression as it has the variable x in the denominator.

The common factor, which is the expression that multiplies each term, is obtained considering all the terms that are present in the denominators.

The denominators to each term of the expression are listed as follows:

Hence the two terms present in the denominators of the expression are:

(x - 1)(x + 1) = x² - 1 -> subtraction of perfect squares.

Hence option A gives the correct term.

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Answer:

17

Step by step explanation

15-6=21

38-21=17

Answer:

3rd choice

No, it is NOT a linear function because the variable x is in the denominator. x will be multiplied by y.

The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

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,

Two congruent figures.

Each figure's total sum of the angles must be 360.

The figures are congruent so the corresponding angles must be equal.

From the first figure we get,

∠A = 133 ( Corresponding angles )

∠A + ∠B + ∠C + ∠D = 360

133 + ∠B + 41 + 86 = 360

∠B = 360 - 260

∠B = 100

Now,

∠k = ∠B = 100

∠L = ∠C = 41

∠M = ∠D = 86

Thus,

The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

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Answer:

see explanation

Step-by-step explanation:

(i)

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

(k + x)² = m² + (k - x)² ← expand factors on both sides using FOIL

k² + 2kx + x² = m² + k² - 2kx + x² ( add 2kx to both sides )

k² + 4kx + x² = m² + k² + x² ( subtract k² + x² from both sides )

4kx = m² ( divide both sides by 4k )

x = [tex]\frac{m^2}{4k}[/tex]

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

(ii)

the area A of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = m and h = k - x

A = [tex]\frac{1}{2}[/tex] m (k - x) ← substitute x = [tex]\frac{m^2}{4k}[/tex]

  = [tex]\frac{1}{2}[/tex] m ( k - [tex]\frac{m^2}{4k}[/tex] ) ← distribute parenthesis

  = [tex]\frac{mk}{2}[/tex] - [tex]\frac{m^3}{8k}[/tex]  ← express as a single fraction

  =  [tex]\frac{4mk^2-m^3}{8k}[/tex] ← factor out m from each term in the numerator

  = [tex]\frac{m(4k^2-m^2)}{8k}[/tex] ← factor (4k² - m² ) as a difference of squares

  = [tex]\frac{m(2k+m)(2k-m)}{8k}[/tex]

The new coordinate after the translation of 4 point left is  (-3, -2)

Translation

Translation is done by moving the vertices of the figure the prescribed number of spaces on a coordinate plane and then drawing the new figure.

Given,

Here we have the points (1, -2).

Now, we have to translate this point by left side by 4 point.

In order to translate the given point we have to take the value of the x coordinate and then we have to subtract the translation point from it,

So, the calculation for this one is look like

Here the value of the x coordinate is 1

And now we have to subtract 4 from it,

So,

=> 1 - 4

=> -3

Therefore, the new coordinate after the translation is (-3, -2).

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Answer:

…………………………………………/,,/,,..,,.,…….

Step-by-step explanation:

Answer:.

Step-by-step explanation: .

Answer: It does not appear to show a function because the numbers are not multiples of each other

Step-by-step explanation: Hope this helps :-)

The addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.

Let a quadratic function be f(x) = 2x^2.

Let c be the positive constant.

It is now necessary to determine what will happen if we add or subtract a constant to the function.

The function f(x) = 2x^2 is a parabola opening upwards.

Now, if we add the positive constant c, then the graph of the function will shift upwards by c units and nothing will change. If we subtract the positive constant c, then the graph of the function will shift downwards by c units.

Thus, the addition or subtraction of a constant to a function will change its position in the cartesian plane. Depending on the sign of the constant, it can shift upwards or downwards.

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To see the attachment of graph of linear inequality.

Given,

In the question:

The linear inequality is given as:

y ≤ x -5

To graph the above inequality.

Now, According to the question:

What is linear inequality?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Math. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Math are polynomial inequality, rational inequality, absolute value inequality.

Hence, To see the attachment of graph of linear inequality.

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Answer: Can you check the "Recently Deleted" folder? You may find this in the "My Files" app. If this does not work, and you can confirm you have no backups whatsoever, then your photos are as good as gone. This has happened to Android devices in the past (or Samsung devices mostly) where all their media would just disappear. As far as I know, all Samsung themselves say is to restart your phone to try your luck. An app crashing or some form of corrupt media may have caused your photos to go missing. There may, however, still be a small chance that the photos are there, somewhere on your phone, you just can't find them. I advise checking the storage in "Device Care" and see if the Gallery app is using much storage. If it is, I would connect it to a PC and look through the files again.

Step-by-step explanation:

The probability of getting heads twice in a row at some point during three coin flips is 1/8.

Given info;

Assume that a fair coin has an equal chance of coming up heads or tails.

What is the likelihood that three coin flips will result in two consecutive heads at any point?

There is a three-coin flip. The potential results are;

(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)

1 is the number of successful results.

Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8

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Answer:

16

Step-by-step explanation:

p = 2j

p+j = 48

2j + j = 48

3j = 48

3/3 j = 48/3

j = 16

The smallest factor (other than 1) of 111 would be 15.

Option (A) is correct.

What is the smallest factor of a number other than 1?

A number can have a maximum of one factor, and only one has that many factors. Every other number has more than one factor.

Prime numbers have two factors, for example, 2,3,5,7,11...,2729...,2927, 9999959999, and so on. Prime numbers have only one factor the number itself.

The factors of 111 are 1, 3, 37, and 111.

for option (A), the factors of 15 are 1, 3, 5, and 15.

for option (B), the factors of 22 are 1, 2, 11, and 22.

for option (C), the factors of 28 are 1, 2, 4, 7, 14, and 28.

for option (D), the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

So if you observe all the options, the smallest factor (other than 1) of 111 would be 15.

Hence, the smallest factor (other than 1) of 111 would be 15.

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Answer:

5 days

Step-by-step explanation:

you need to make 5 3/4 into an improper fraction

(5x40)+3/4= 23/4

make all fractions have a common denominator

1/2 = 2/4    

you multiply numerator and denominator by 2 to get a denomintator of 4

23/4 ÷ 2/4

to divide a fraction you turn the second fraction into a reciprocal

2/4 in a reciprocal is 4/2

then you multiply the fractions together

23x2/2x4

simlplify to get

46/8 = 23/4

make into a mixed number by dividing by 4

5 3/4

The coordinates to the intercepts of the functions are given as follows:

c - i) Point P: P(-4,0).

c - ii) Point Q: Q(0,2).

d - i) Point P: P(-3,0).

d - ii) Point Q: Q(0,9).

The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.

For item c, the function is:

2y = x + 4.

Hence the x-intercept is obtained as follows:

x + 4 = 0

x = -4.

Then the coordinates of point P are:

P(-4,0).

For item d, the function is:

y = 3x + 9

Hence the x-intercept is obtained as follows:

3x + 9 = 0

3x = -9

x = -3.

Then the coordinates of point P are:

P(-3,0).

The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.

For item c, the function is:

2y = x + 4.

Hence the y-intercept is:

2y = 4

y = 2.

The coordinates of Q are:

Q(0,2).

For item d, the function is:

y = 3x + 9.

Hence the y-intercept is:

y = 3(0) + 9 = 9.

The coordinates of Q are:

Q(0,9).

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Answer:

x=54.5

Step-by-step explanation:

x+62+x+9=180

2x+71=180

2x+71-71=180-71(subtract 71 from both sides)

2x=109

2x/2=109/2(divide both sides by 2)

x=54.5

Answer:

x=54.5

Step-by-step explanation:

1. Combine like terms

x+62+x+9=180

2x+71=180

You can only combine the x and 62 and 9 in this equation.

2. Subtraction property of equality

2x+71=180

    -71 = -71

2x=109

Subtract 71 from both sides to isolate the variable, x.

3. Division property of equality

2x=109

/2     /2

x=54.5

Hope this helps!