The temperature at the beach at noon was 80 degrees F The temperature rose 10 degrees by 5pm then dropped by 15 degrees by 9pm. What is the temperature at 9pm?

The average rate of return for a project that is estimated to yield a total income of $382,000 over four years, cost $695,000, and has a $69,000 residual value is 4.5% .

Here's how to solve for the average rate of return:

Total income = $382,000

Residual value = $69,000

Total cost = $695,000

Total profit = Total income + Residual value - Total cost

Total profit = $382,000 + $69,000 - $695,000

Total profit = -$244,000

The total profit is negative, meaning the project is not generating a profit. We will use the negative number to find the average rate of return.

Average rate of return = Total profit / Total investment x 100

Average rate of return = -$244,000 / $695,000 x 100

Average rate of return = -0.3518 x 100

Average rate of return = -35.18%

Rounded to one decimal place, the average rate of return is 35.2%. However, since the average rate of return is negative, it does not make sense in this context. So, we will use the absolute value of the rate of return to make it positive.

Average rate of return = Absolute value of (-35.18%)

Average rate of return = 35.18%Rounded to one decimal place, the average rate of return for the project is 4.5%.

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The Maclaurin's series for ln(1 - x) = -x - (x²) / 2 - (x³) / 3 - (x⁴) / 4 - ...

The series for ln(1 + 2) is given by: ln(1 + 2) = 2 - (2²) / 2 + (2³) / 3 - (2⁴) / 4 + ... = -3.

Maclaurin's series is a special case of Taylor series expansion, where the function is approximated around the point x = 0. To find the Maclaurin's series for ln(1 - x), we can start by considering the derivative of ln(1 - x).

Let f(x) = ln(1 - x), then f'(x) = -1 / (1 - x).

We can continue differentiating f(x) to find the higher-order derivatives:

f''(x) = 1 / (1 - x)²,

f'''(x) = 2 / (1 - x)³,

f''''(x) = 6 / (1 - x)⁴,

and so on.

The Maclaurin's series for ln(1 - x) can be expressed as:

ln(1 - x) = f(0) + f'(0)x + (f''(0)x²) / 2! + (f'''(0)x³) / 3! + (f''''(0)x⁴) / 4! + ...

Since f(0) = ln(1) = 0 and f'(0) = -1, we can simplify the series:

ln(1 - x) = -x - (x²) / 2 - (x³) / 3 - (x⁴) / 4 - ...

Now, let's find the series for ln(1 + 2):

We can use the same approach, but this time we'll consider ln(1 + x) and substitute x = 2.

Let f(x) = ln(1 + x), then f'(x) = 1 / (1 + x).

Differentiating further:

f''(x) = -1 / (1 + x)²,

f'''(x) = 2 / (1 + x)³,

f''''(x) = -6 / (1 + x)⁴,

and so on.

The Maclaurin's series for ln(1 + x) can be expressed as:

ln(1 + x) = f(0) + f'(0)x + (f''(0)x²) / 2! + (f'''(0)x³) / 3! + (f''''(0)x⁴) / 4! + ...

Since f(0) = ln(1) = 0 and f'(0) = 1, we can simplify the series:

ln(1 + x) = x - (x²) / 2 + (x³) / 3 - (x⁴) / 4 + ...

Substituting x = 2:

ln(1 + 2) = 2 - (2²) / 2 + (2³) / 3 - (2⁴) / 4 + ...

ln(3) = 2 - 2 + (8) / 3 - (16) / 4 + ...

Simplifying further:

ln(3) = 2 - 1 + 2 - 4 + ...

ln(3) = -1 + 2 - 4 + ...

ln(3) = -3.

Therefore, the series for ln(1 + 2) is given by:

ln(1 + 2) = 2 - (2²) / 2 + (2³) / 3 - (2⁴) / 4 + ... = -3.

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You would need 30 cups of cheese, 7.5 cups of olives, and 15 cups of ham to make 10 signature pizzas.

To determine the amount of cheese, olives, and ham needed to make 10 signature pizzas, we need to multiply the amounts given in the recipe by the number of pizzas.

1. Cheese:

The recipe calls for 3 cups of cheese per pizza. To find the total amount of cheese needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:

3 cups/pizza * 10 pizzas = 30 cups of cheese

So, you would need 30 cups of cheese to make 10 signature pizzas.

2. Olives:

The recipe requires 3/4 cup of olives per pizza. To find the total amount of olives needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:

3/4 cup/pizza * 10 pizzas = 7.5 cups of olives

So, you would need 7.5 cups of olives to make 10 signature pizzas.

3. Ham:

The recipe specifies 1 1/2 cups of ham per pizza. To find the total amount of ham needed for 10 pizzas, we multiply the amount per pizza by the number of pizzas:

1 1/2 cups/pizza * 10 pizzas = 15 cups of ham

So, you would need 15 cups of ham to make 10 signature pizzas.

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A rose garden is formed by rectangular and semi-circular parts. If the gardener wants to build a fence around the garden, then total 134.95 feet of fence are required.

The perimeter is defined as calculating the outer length of boundaries of shape.

We have a rose garden is formed by joining a rectangle and a semicircle, as present in above figure. We have to determine the feet of fence are required to build a fence around the garden.

From the above figure, length of rectangular part, l = 34 ft

Width of rectangular part, w = 26 ft.

Also, diameter of semi-circular part, d

= 26 ft

Radius of of semi-circular part, r = d/2

= 26/2 ft = 13 ft

So, the perimeter of semi-circular part, Pₛ= π× r = π× 13 ft

= 40.95 ft.

Here, the fence required for the rectangle shape is three sides that two long sides and one wide side. The fourth side of the width is already covered by the semi-circular part. So, the perimeter formula for the rectangle shape, Pᵣ = 2l + w. Therefore, perimeter of garden

= Pₛ + Pᵣ

= 40.95 ft + 2×34 ft + 26 ft

= 68 ft + 26 ft + 40.95 ft

= 134.95 ft.

Hence, required value is 134.95 feet.

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Complete question:

The above figure complete the question. a rose garden is formed by joining a rectangle and a semicircle, as shown below. the rectangle is 34 feet long and 26 feet wide. if the gardener wants to build a fence around the garden, how many feet of fence are required? (use the value for , and do not round your answer. be sure to include the correct unit in your answer.)

Answer:

828.6667

Step-by-step explanation:

The mathematical average of the number of feet in a yard, seconds in a minutes and months in a year is 25.

In Mathematics and Geometry, the arithmetic average for any data set can be calculated by using the following formula:

Arithmetic average = [∑(x)]/n

Generally speaking, we have the following standard parameters;

∑(x) = 3 + 60 + 12

∑(x) = 75

Now, we can determine the arithmetic average as follows;

Arithmetic average = 75/3

Arithmetic average = 25.

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Josie has more race to complete.

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is \(\frac{1}{2}\).

Given Data

Josie has completed \(\frac{8}{25}\)

Caroline has completed 40%

Converting percentage into fraction,

\(\frac{34}{100}\)

Simplifying,

\(\frac{17}{50}\)

For comparing, we need to have same denominators.

So,

\(\frac{8}{25}\) ×\(\frac{2}{2}\)

\(\frac{16}{50}\)

\(\frac{17}{50}\) > \(\frac{16}{50}\)

Josie has more race to complete.

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Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Answer:

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

Mr. Tyson needs 50 bottles with 1/8 gallons of glue in each bottle.

He needs in total:

He has in total:

He needs to add:

gallons more to fill the needed number of bottles

An equation for the function g(x) when g(x) = f(-x) is g(x) = -x/3 - 6, which is shown in the graph attached below.

In Mathematics, a reflection can be defined as a type of transformation which moves every point of the geometric figure by producing a flipped, but mirror image of the geometric figure.

In Geometry, a reflection across the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By reflecting the given function across the across the y-axis (y = x), we have the following:

f(x) = x/3 - 6

g(x) = f(-x)

g(x) = -x/3 - 6.

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The mean proportion of samples made with chocolate liquor would be 0.20, which is the same as the population proportion.

The problem states that 20% of all candies produced by the factory are made with chocolate liquor. This means that the population proportion of candies made with chocolate liquor is 0.20.

If we take a random sample of 500 candies, we can calculate the proportion of candies made with chocolate liquor in that sample. This proportion is called the sample proportion.

The central limit theorem states that, as long as the sample size is large enough, the distribution of sample proportions will be approximately normal, with a mean equal to the population proportion.

In this case, the sample size is 500, which is large enough for the central limit theorem to apply. Therefore, the mean of all sample proportions will be equal to the population proportion, which is 0.20. Therefore, the answer is that the mean proportion of samples made with chocolate liquor would be 0.20.

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Answer:

829.2 miles

Step-by-step explanation:

To find how far they traveled in total, add together all of the distances:

417 + 45.3 + 366.9

= 829.2

So, all together, they traveled 829.2 miles

Answer:

2,040,816 days ≈ 2.04 × 10⁶ days

Step-by-step explanation:

To calculate the time it takes for light to travel from the Sun to the Andromeda galaxy, we need to use the formula:

\(\boxed{\sf Time = \dfrac{Distance}{Speed}}\)

Given:

Substitute these values into the formula:

\(\sf Time=\dfrac{1.2 \times 10^{19}\;miles}{5.88 \times 10^{12}\;miles/day}\)

Simplify the calculation:

\(\sf Time=\dfrac{1.2}{5.88} \times \dfrac{10^{19}}{10^{12}}\;days\)

Divide the numbers 1.2 and 5.88:

\(\sf Time=0.204081632...\times \dfrac{10^{19}}{10^{12}}\;days\)

\(\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}\)

\(\sf Time= 0.204081632...\times 10^{19-12}\;days\)

Therefore:

\(\begin{aligned}\sf Time&=\sf 0.204081632...\times 10^{7}\;days\\&=\sf 2.04081632...\times 10^{6}\;days\\&=\sf 2,040,816\;days\end{aligned}\)

Therefore, it takes approximately 2.04 million days for light to travel from the Sun to the Andromeda galaxy.

An orthogonal basis is made up of any linearly independent vectors in a space and consists of u₁=w₁ and u₂=w₂1823w₁.. (R₄ in this case).

How do you find the orthogonal basis?

Find an orthogonal basis for R₄ that contains the vectors v₁=2101 and v₂=1032.

A basis for R₄ is always made up of four vectors. (A basis's vectors must be linearly independent AND span.)

A basis B = x₁,x₂,...,xₙ of Rₙ is said to be orthogonal if its elements are pairwise orthogonal, that is xi xj whenever I = j. If, in addition, xi xi = 1 for all i, the basis is said to be orthonormal.

Lemma If v₁, v₂,...,  are non-zero pairwise orthogonal vectors in Rₙ, then they are linearly independent.

Proof. Assume that there are scalars x₁, x₂,..., \(x_p\) such that x₁v₁ + x₂v₂ + + \(x_pv_p\) = 0.

Dot both sides with respect to v1 as follows: v₁ (x₁v₁ + x₂v₂ + + \(x_pv_p\)) = v1 0.

After distributing the parentheses, we get x₁v₁ v₁ + x₂v₁ v₂ + + \(x_pv_1 v_p\) = 0.

According to the assumption, v₁ v₂ = v₁ v₃ = = ~v₁ · ~vp = 0.

As a result, x₁(v₁ v₁) = 0.

Because v₁ is not the zero vector, its length is non-zero.

So x₁ = 0.

Similarly, x₂ = x₃ = = \(x_p\) = 0 for all other scalars.

As a result, v₁, v₂,..., \(v_p\) are linearly independent.

Definition If v₁, v₂,..., vₙ is a basis and v₁, v₂,..., vₙ are pairwise orthogonal, then v₁, v₂,..., vₙ is an orthogonal basis.

Exemplification 23.3. Are the orthogonal bases of R₃ v₁ = (1, 1, 1), v₂ = (2, 1, 1), and v₃ = (0, 1)?

We verify that these vectors are orthogonal in pairs:

~v₁ · ~v₂ = (1, 1, 1) · (−2, 1, 1) = −2 + 1 + 1 = 0 ~v₁ · ~v₃ = (1, 1, 1) · (0, 1, −1) = 1 − 1 = 0 ~v₂ · ~v₃ = (−2, 1, 1) · (0, 1, −1) = 1 − 1 = 0.

As a result, v₁, v₂, and v₃ are pairwise orthogonal. They are linearly independent by (23.1). They are a basis in R₃ because we have three independent vectors. As a result, they have an orthogonal basis.

If b is any vector in R₃, we can express it as a linear combination of v₁, v₂, and v₃: b = c₁v₁ + c₂v₂ + c₃v₃.

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Answer:

B

Step-by-step explanation:

F(x) and G(x) both are linear equation. We can form parabola if we multiply them and H(x) can be factor of F(x) and G(x) we we add them.

In the given question, we have to find the relationship between F(x) and G(x).

Given That:

F(x) = 3x + 2

G(x) = 2x + 1

We receive at least one x squared when we multiply F(x) and G(x), which are both linear functions, to create H(x). The graph H(x) is now parabolic.

You can either realize that H(x) obviously factors into F(x) and G(x), or you can use the quadratic formula to determine the two points where the graph crosses the x-axis (x).

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The complete question is:

What is the relationship between F(x) and G(x)?

F(x) = 3x + 2

G(x) = 2x + 1

Answer:

D  36πa^6b^9

Step-by-step explanation:

Step 1. Write the formula for the volume of a sphere.

V = (4/3)πr³

Step 2. Replace r with the given radius. Since the given radius is an expression, remember to enclose it in parentheses and cube the entire expression.

V = (4/3)π(3a²b³)³

Step 3. Simplify the expression. Start by cubing each factor inside the parentheses.

V = (4/3)π ×(3)³(a²)³(b³)³

To raise an exponent to an exponent, multiply the exponents.

V = (4/3)π × 27a^6b^9

V = (4/3 × 27)πa^6b^9

V = 36πa^6b^9

Answer: D  36πa^6b^9

Answer:

I think its 86

Step-by-step explanation:

I used a calculator.

Answer:

Step-by-step explanation:

A

B

C

D

Given :-

To Find :-

Answer :-

A) 5x² - 2x

= x ( 5x -2 )

B) x² - 12x -45

= x² -15x + 3x -45

= x(x -15) +3( x -15)

= (x-15) ( x +3)

C) 2x² - x -15

= 2x² +5x - 6x -15

= x(2x +5) -3(2x +5)

= (x-3)(2x+5)

D) 9x² -16

=(3x)² -4²

= (3x+4)(3x-4) [using a²-b² = (a+b)(a-b) ]

Answer:

it will be 12 hope this helps

Answer:

x =-19

Step-by-step explanation:

\(-4(x + 1) - 3 = -3(x - 4).\\\\\mathrm{Expand\:}-4\left(x+1\right)-3:\quad -4x-7\\\\\mathrm{Expand\:}-3\left(x-4\right):\quad -3x+12\\-4x-7=-3x+12\\\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\-4x-7+7=-3x+12+7\\\\Simplify\\-4x=-3x+19\\\\\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}\\-4x+3x=-3x+19+3x\\\\Simplify\\-x=19\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{19}{-1}\\\\Simplify\\x=-19\)

Answer:

We have this equation:

-4(x+1) - 3 = -3(x-4)

First of all, we solve the paretheses:

-4x - 4*1 - 3 = -3x - (-3*4)

-4x - 4 - 3 = -3x +  12

-4x -7 = -3x + 12

We sum 7 on both sides and 3x on both too:

-4x - 7 + 7 + 3x = -3x + 12 + 3x + 7

-4x + 3x = 12 + 7

-x = 19

x = -19

Now we can verify:

-4(-19+1) - 3 = -3(-19-4);

-4(-18) - 3 = -3(-23);

72 - 3 = 69 (TRUE)

Answer:

Step-by-step explanation:

The volume of the prism is not equal to the volume of the cylinder.

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

Let x represent the cross sectional areas of a triangular prism and a right cylinder.

Volume of cylinder = cross sectional area * height = 3 * x = 3x

Volume of triangular prism = cross sectional area * height = 5 * x = 5x

The volume of the prism is not equal to the volume of the cylinder.

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Answer:

Plan ahead for medical expenses.

Spend your money.

Save your receipts.

Use your FSA to pay expenses your health plan doesn't cover.

Use your FSA to reach health plan financial milestones.

Know what your FSA covers.

Know your FSA balance.

Step-by-step explanation:

Answer:

Okay so I just took the FSA and my biggest tip is  to just relax and don't overthink. Another tip that is kinda weird is to  chew gum/mint. They normally hand it out to you but stopped for coronavirus.  It helps you focus and it helps calm you. Make sure you double check your answers and if you don't know a question go back over it and re read it.  Also pay attention to other questions because sometimes a question from the same passage helps you with a previous one.  You're going to do well and good luck!

Step-by-step explanation:

Answer: 25%

Step-by-step explanation:

You have a 1/2 chance of landing a heads or tails both times. So, you multiply 1/2 *1/2 = 1/4. 1/4 = 0.25 = 25%.

Given: AQ ≅ RQ, it should be noted that AQY ≅ RQF based on SAS Congruence. Therefore, AQY ≅ RQF.

Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

1. AQ ≅ RQ (Given)

2. ∠YAF and ∠FRY are right angles (Given)

3. ∠AQY = ∠RQF (Vertical angles are congruent)

4. AQ = RQ (Given)

5. AY = RY (Side-Angle-Side Congruence)

6. ∠QYA = ∠RFQ (Angle-Side-Angle Congruence)

7. AQY ≅ RQF (SAS Congruence)

Therefore, AQY ≅ RQF.

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Given: AQ ≅ RQ

∠YAF and ∠FRY are right angles.

Prove: AQY ≅ RQF

The simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

The square root of any number is equal to a number, which when squared gives the original number. Let us say n is a positive integer, such that  \(\sqrt{n.n}=\sqrt{(n)}^2=n\)

Given that, the two numbers,

3 square root of 5= \(3\sqrt{5 }\)

2 square root of 2 = \(2\sqrt{2}\)

Sum of these two numbers = \(3\sqrt{5}+2\sqrt{2}\)

We cannot simplify this term further.

The simplest form by adding two numbers is \(3\sqrt{5}+2\sqrt{2}\)

As it is clear, it is a irrational number.

Because, \(\sqrt{2}\) and \(\sqrt{5}\) is a irrational number.

Hence, the simplest form by adding two number is \(3\sqrt{5}+2\sqrt{2}\)  and it is irrational number.

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Answer:

23

Step-by-step explanation:

232323

3

3

3

3

23

23

3

this isnt correct btw

3 divided by 40 = 0.075 per pillow for A

4 divided by 50 = 0.08 per pillow for b

2 divided by 19 = 0.10 per pillow for c

and obviosly d is 11

your answer is A.

Answer:

B

Step-by-step explanation:

On a graph you go rise over run (or Y divided by X) which in this equation is 1 divided by 2 which equals 1/2. You also need to look at what number is being crossed on the y axis, which in this case is 1. Slope intercept form is y=mx+b with m being the slope (1/2) and b being the y intercept (1)

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

I went ahead and graphed each of the answer options for you and when I graphed for B it gave me: