1. Sam is planning to put a square garden with an area of 225 square feet in her back yard. What will be the perimeter of the garden?

Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

Given that,

The equation f(x)=1.9(0.41)ˣ.

We have to state the initial value C, the growth or decay factor a, and percent change R for each unit increase in x.

We know that,

In order to translate their graphs over the 2D coordinate plane, I will offer the vertex form of an exponential equation for both the growth and decay functions.

In the case of growth, f(x) = a(1+r\()^{x-h}\)+k, where b = 1+r

Decay is defined as f(x)=a(1-r)(x-h\()^{x-h}\)+k, where b=1-r.

Consider the function  f(x)=1.9(0.41)ˣ.

We write as

f(x)=1.9(1-0.59)ˣ

So, initial value C is 1.9

Decay factor =0.41

Growth factor = 0.59

Therefore, Initial value C is 1.9, Decay factor =0.41 and Growth factor = 0.59 when the function f(x)=1.9(0.41)ˣ.

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The reading that separates the rejected thermometers from the others is given as follows:

1.175 ºC.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for this problem are given as follows:

\(\mu = 0, \sigma = 1\)

The 12% higher of temperatures are rejected, hence the 88th percentile is the value of interest, which is X when Z = 1.175.

Hence:

1.175 = X/1

X = 1.175 ºC.

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t < 20.

\(8 > 3 + \frac{t}{4}\)

\(8-3 > 3 + t/4-3\\ \\5 > \frac{t}{4}\)

\(5*4 > \frac{t}{4}*4\\ \\20 > t\\ \\t < 20\)

\(8 > 3 + (20)/4\\ \\8 > 3 + 5\\ \\8 > 8\)

That's correct! Hence, t < 20 is the correct answer.

Answer:  1) $300     2) $624

Step-by-step explanation:

\(\begin{array}{l||l|l}\underline{\quad \text{Item}\qquad \qquad \qquad \qquad}&\underline{\text{Income} }&\underline{\text{Expense}}\\\text{Net Pay}&5000&\\\text{Interest on Deposits}&0&\\\text{Income from Investments}&225&\\\text{Rent}&&3000\\\text{Utilities}&&250\\\text{Satellite Dish}&&175\\\text{Cell Phone Plan}&&135\\\text{Car Payment}&&385\\\text{Groceries}&&200\\\text{Insurance}&&380\\\underline{\text{Recreation}\qquad \qquad \qquad}&\underline{\qquad \quad }&\underline{400\qquad}\\\end{array}\)

TOTALS                              5225      4925

Net Cash Flow = Income - Expenses

                        = 5225 - 4925

                        = 300

*************************************************************************************

\(\dfrac{25\ hours}{week}\times \dfrac{\$8}{hour}\times 4\ weeks\times 78\%\\\\\\=25\times \$8 \times 0.78\\\\= \$624\)

I need to see the other expressions

Check the graph below

1) In the diagram, we can see the following:

2) So we can express this relation on the graph this way:

As this is a relation, we can express this by their points.

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer: x^2 +6x +2x +36 = X^2 +8x + 36

Step-by-step explanation:

Answer:

x² + 8x + 12

Step-by-step explanation:

(x × x) + (x × 6) + (x × 2) + (6 × 2)

x² + 8x + 12

good luck, i hope this helps :)

The required image of points (-4, 6) is (-6, -4) as per the given condition,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,

As the image of the point (5, -1) is mapped as, (1, 5),
Which implies a function that (x, y) mapped as (-y , x)
So for (-4, 6) mapped as (-6, -4)

Thus, the required image of points (-4, 6) is (-6, -4) as per the given condition,

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-10

Step-by-step explanation:

x = 10

x2 - 2(x + 5)

10(2) - 2(10+5)

20 - 2(15)

20 - 30

-10

Answer:

The answer is 13.33 year

Step-by-step explanation:

P = $12000

Rate = 3%

Amount = $16800

so,

I = A-P

= $16800 - $12000

= $4800

So,

T = (I × 100)/P×R

= (4800×100)/P×R

= 480000/($12000×3)

= 480000/36000

= 480/36

= 13.33 year

Step-by-step explanation: To shift the graphs up and down on the coordinate system, you need to manipulate or change the y-intercepts.

The y-intercept is just the constant term in the equation.

As long as the slopes remain the same, the graphs can be

translated up or down by changing the constant value.

Take a look at these lines graphed below.

Notice that y = x + 11 is the same as y = x + 4 but

y = x + 11 is translated 7 units down to get y = x + 4.

Answer:

yes it is

Step-by-step explanation:

why because if you divide and then subtracted what you got that would be the answer

there you go have a good day

Answer: Yes it is

Step-by-step explanation:

It is to big of a equation and it can easily be simplified

Miles has saved about $41. He wants to buy an iPod for $129 in 4 months.

So first, we need to subtract the amount that he has already saved.

Now we need to divide this amount by 4 months.

Therefore, Miles needs to save $22 each month to buy the iPod.

The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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Answer:

Let's denote:

- The number of orders Diane served as `D`

- The number of orders Sam served as `S`

- The number of orders Boris served as `B`

From the problem, we know:

1. `D + S + B = 54` (the total number of orders they served)

2. `D = S - 6` (Diane served 6 fewer orders than Sam)

3. `B = 2S` (Boris served 2 times as many orders as Sam)

We can substitute equations 2 and 3 into equation 1 to solve for the variables:

Substitute `D` and `B` in equation 1:

`(S - 6) + S + 2S = 54`

Combine like terms:

`4S - 6 = 54`

Add 6 to both sides:

`4S = 60`

Divide by 4:

`S = 15`

Now that we know `S = 15`, we can find `D` and `B` by substituting `S` into equations 2 and 3:

`D = S - 6 = 15 - 6 = 9`

`B = 2S = 2 * 15 = 30`

So, Diane served 9 orders, Sam served 15 orders, and Boris served 30 orders.

Answer:

The circumference of a circle is calculated using the formula: C = πd, where C represents the circumference and d represents the diameter of the circle.

In this case, the diameter of the circle is given as 24 inches.

Using the formula, we can substitute the values:

C = πd

C = 3.14 * 24

C ≈ 75.36 inches

Therefore, the circumference of a circle with a diameter of 24 inches (and using π = 3.14) is approximately 75.36 inches.

Step-by-step explanation:

The exact value of sin(cos⁻¹ (2/5) ) is (√21)/5.

To determine the exact value, draw a triangle in the plane with the vertex:

( 2/5, √( 1² - (2/5)² ), (2/5,0) and the origin.

The cos⁻¹(2/5) is the angle between the positive x-axis and the ray beginning at the origin and passing through ( 2/5, √( 1² - (2/5)² ).

Hence;

sin(cos⁻¹ (2/5) ) is √( 21/25 )

Now, rewrite √( 21/25 ) as (√21)/(√25 )

We can simplify the denorminator

Rewrite 25 as 5²

(√21)/(√5² )

Take the square root of √5²

(√21)/5

Therefore, the simplified form of the expression is (√21)/5.

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The scale ratio of similar sides is identical since polygon V is a scaled replica of polygon U. w = 27.

Any closed curve made up of a series of interconnected line segments lacking any intersections is referred to as a polygon in geometry.

Triangles, quadrangles, and pentagons are the most basic polygons. A two-dimensional, closed, flat or planar shape with straight sides is referred to as a polygon. Its sides are not curled. The edges of a polygon are another term for its sides. The points where both sides meet are the vertex of a polygon.

The scale ratio of similar sides is identical since polygon V is a scaled replica of polygon U.

40 ÷ 36 = 20 ÷ 18 = 30 ÷ w

40 ÷ 36 = 1.1111111

therefore 30 ÷ w = 1.111111

so W = 30 ÷ 1.11111111 = 27.000027

W = 27

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The complete question is attached below,

Answer:

8 quarts

Step-by-step explanation:

Answer: 8 quarts

Step-by-step explanation: proof with other answers

Answer:

15: 58 degrees. 16: Answer D

Step-by-step explanation:

Question 15

All you have to do for this one is to add the angle measures of 22 and 36 degrees together to get the answer of 58 degrees.

Question 16

The interior angles of a triangle will always add up to 180 degrees.

Therefore, 180 - 53 - 21 is the answer, which totals 106 degrees.

Answer:

52.6

Step-by-step explanation:

263/5=52.6

Answer:

53

Step-by-step explanation:

You must take 263 and divide it by 5

263/5 = 52.6

So, 5 times 52 = 260

BUT 5 times 53 = 265.  You would need 53 fish bowls

there is no difference in the values of Time for Idil or Sophie in that their amount will be tripled.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Idil invested $150 in an account paying an interest rate of 5.785% compounded annually. Sophie invested $150 in an account paying an interest rate of 5.625% compounded continuously.

From the general formula of compound interest:

Final value A = (1 + r/n)^nt,

where P is the principal balance

r is the interest rate

n is the number of times interest is compounded annually

t is the number of years,

For Idil,

P = 150, r = 5.782, A = 3*p = 450, and n = 1

Thus,

450 = 150 (1 + 5.785%)^t

3 = (1.05785)^t

t = 19.535 years

The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.785% per year and compounded 1 time per year is 19.535 years.

(about 19 years 6 months)

For Sophie,

P = 150, r = 5.625, A = 3*p = 450

First, convert R as a percent to r as a decimal

r = R/100

r = 5.625/100

r = 0.05625 per year,

Then, solve the equation for t

t = ln(A/P) / r

t = ln(450.00/150.00) / 0.05625

t = 19.531 years

The time required to get a total amount of $450.00 with compounded interest on a principal of $150.00 at an interest rate of 5.625% per year and compounded continuously is 19.531 years.

(about 19 years 6 months)

therefore, there is no difference in the values of Time for Idil or Sophie.

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Answer:

Step-by-step explanation:

The Conjugate Roots Theorem states that imaginary roots come in pairs. If -8i is a root of the polynomial, then so is +8i.

If both -8i and +8i are factors, we rewrite them as (x + 8i) and (x - 8i) in factored form. Since imaginary terms aren't accepted, you can FOIL these to get a quadratic with no imaginary terms.

x2 - 8ix + 8ix - 64i2

Simplify. Replace i2 with -1 because √-1 = i

x2 - 64(-1)

x2 + 64

The quadratic x2 + 64 has roots -8i and 8i. You can use the quadratic formula to verify this.

Now, let's tackle the rest of the polynomial. If x2 + 64 is a factor of the polynomial

x4 + 10x3 + 85x2 + 640x + 1344, divide it out to see what is left. I will use long division of polynomials. Note, I am using the square root symbol as a division symbol.

x2 + 10x + 21

x2 + 64 √ (x4 + 10x3 + 85x2 + 640x + 1344)

x4 + 64x2

_____________

10x3 + 21x2

10x3 + 640x

__________

21x2 +1344

21x2 + 1344

___________

0

There is no remainder, meaning x2 + 64 went in evenly. The quotient left when we divide out x2 + 64 from

x4 + 10x3 + 85x2 + 640x + 1344 is x2 + 10x + 21. Factor the quotient to get (x + 7)(x + 3).

x4 + 10x3 + 85x2 + 640x + 1344 = (x2 + 64)(x + 7)(x + 3)

You can check this factored form by FOILing out, and you should get the original polynomial.

Earth's diameter is 0.0092 times less than the sun's diameter.

The Diameter of Earth = 1.3 * 10⁴ km

The Diameter of Moon = 3.5 * 10³ km

Let the diameter of sun be x km

According to the question

The diameter of the sun is 400 times that of the moon.

x = 400 * 3.5 * 10³ km

= 14 * 10⁵ km

The Diameter of earth / diameter of sun

=  1.3 * 10⁴ / 14 * 10⁵

= 0.0092

Hence, The diameter of the Earth is 0.0092 times that of the Sun.

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Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  \(0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}\)

The proportion that shows the relationship is h/4 = 8/h

The values of a, h and b are a = 16√3, b = 16√6 and h = 4√2

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

The similar triangles

Using the right triangle/altitude similarity theorem, we have

h/4 = 8/h

Calculating the values of a, h and b

In (a), we have

h/4 = 8/h

This means that

h² = 32

So, we have

h = 4√2

For the value of (a), we have

a² = h² + 4²

So, we have

a² = 32 + 4²

a² = 48

Evaluate

a = 16√3

Next, we have

b² = 32 + 8²

b² = 96

So, we have

b = 16√6

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