What is an equation in standard form of an ellipse centered at the origin with vertex (3, 0) and co-vertex (0, - 6) ?

Thus, the value of the  sine function for the given values in right angled triangle are obtained as : x = 51.0°.

Triangle angles are measured by the sine function, a trigonometric function. It is equivalent to the ratio of a side across the hypotenuse that is opposite that angle in issue.

sin Ф = opposite side/ hypotenuse

In the given right angled triangle.

sin x = 7/9

x = 51.0°

Thus, the value of the  sine function for the given values in right angled triangle are obtained as : x = 51.0°.

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Answer:

Below

Step-by-step explanation:

The equation you need to remember is:

rate X time = distance       re-arrange to

time = distance / rate         sub in the numbers given to get

time =   x / 15  hours

Answer:

52.56 square inches.

Answer:

Kyle runs 0.1 miles every minute.

Step-by-step explanation:

Answer: 9.2 degrees

Step-by-step explanation:

2.3*4=9.2

The truth table is shown.

A truth table is a table that displays all possible combinations of input values and their matching output values.

The given statement is (p∨¬q)∧(p∧q).

The truth table is:

p            q            ¬q            p∨¬q            p∧q            (p∨¬q)∧(p∧q)

0            0              1                1                   0                      0

0            1               0               0                  0                       0

1             0              1                1                    0                      0

1             1               0               1                    1                        1

Hence, the truth table for the compound statement (p∨¬q)∧(p∧q) is shown.

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The number that is an irrational number from the set of numbers is the option;

4·√5

An irrational number is a real number that cannot be expressed in the form a ratio of integers.

The number that is an irrational number from the specified number is the number that cannot be expressed as a ratio of integers.

Expressing the specified numbers as integers, we get;

-6.11 = -611/100

4·√5 = The number cannot be expressed as a ratio of integers, therefore the number 4·√5 is an irrational number

0.7 = 7/10

0.333 = 333/1000

-6/7 is a ratio of 6 and 7, and is therefore, a rational number

The irrational number is; 4·√5

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Step-by-step explanation:

70x < 350

x < 5 (divide both sides by 70)

The number of tablet computers must be strictly below 5.

Hence the next integer below 5 is 4. (A)

Answer:

Step-by-step explanation:

Let x be the number of miles you and your friend travel.We know that the cost of the bus ride is 60 cents per mile, so the total cost of the trip is 60 * x.This can be written as an equation as follows:Cost = 60 * xOr, more simply:Cost = 60xThis equation represents the relationship between the number of miles you and your friend travel and the cost of the trip. As the number of miles increases, the cost of the trip also increases at a rate of 60 cents per mile.

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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The ounces of ground sumac = 12

The ounces of ground thyme =8

From the question, we have

Let the ounces of ground sumac = x

Let the ounces of ground thyme = y

x+y=20...............(i)

1.25x+2.25y=20*1.65

1.25x+2.25y=33...............(ii)

Solving, we get

x = 12

y =8

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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Answer:

C

Step-by-step explanation:

5 x -6=-30

-30 x -2=60

Answer:

p = 20

Step-by-step explanation:

Step1 :

Multiply each value by its  frequency then  add up :

(10 × 16) + (15 × 8) + (20 × p) + (25 × 10) + (30 × 6) = 20p + 610

Step2 :

Calculate the total of the frequencies :

6 + 8 + p + 10 + 6 = p + 30

The mean is equal to

\(\frac{20p+610}{p+30}\)

Therefore

\(20.2 = \frac{20p+610}{p+30}\)

then

20.2 × (p + 30) = 20p + 610

then

20.2p + 606 = 20p + 610

Then

20.2p -  20p = 610 - 606

Then

0.2p = 4

Then

p = 4/(0.2)

  = 20

Answer:

-1 < 1

Step-by-step explanation:

-1 is smaller than 1, if we see it on a number line, we find that 1 is more towards right than -1 which means that 1 is greater than -1

Hope my answer helps :)

Answer:

50 8/63

Step-by-step explanation:

10*5=50

when multiplying fractions we have to multiply the numerators, then multiply the denominators.

2*4=8

7*9=63

hope this helps =3

sorry if im wrong

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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Answer:

Step-by-step explanation:

Let's call the total number of plants in the field "x".

7/15 of the plants have wilted, which means that 7/15 * x plants have wilted.

And we know that 105 plants have wilted, so we can set up an equation to solve for x:

7/15 * x = 105

x = 105 / 7 / 15

x = 105 × 15 / 7

x = 1575 / 7

x = 225 plants.

Answer:

59.3 °

Step-by-step explanation:

its trigonometry

so you have the

opposite side= 43.5

and the adjacent side = 24.8

if you use SOH CAH TOA you will find that to find y you need to use TOA as tou have the opposite and adjacent.

to find the angle (tan) you need to do tue opposite / adjacent

tan^-1 (43.5/25.8)

= 59.3 to 1 d.p.

you need to use tan^-1 as you are finding the missing angle

Sara should have $4,578 removed from her projected income of $124,075 for the year 2022.

Determine Sara's taxable income by subtracting the standard deduction for head of household from her projected income. According to the tax table, the standard deduction for head of household for 2022 is $18,650. Therefore, Sara's taxable income is:

$124,075 - $18,650 = $105,425

Find the tax bracket that Sara's taxable income falls into. According to the tax table, for head of household, the tax brackets for 2022 are:

10% on taxable income from $0 to $14,100

12% on taxable income over $14,100 to $54,200

22% on taxable income over $54,200 to $86,350

24% on taxable income over $86,350 to $164,900

32% on taxable income over $164,900 to $209,400

35% on taxable income over $209,400 to $523,600

37% on taxable income over $523,600

Since Sara's taxable income is $105,425, she falls into the 24% tax bracket.

Calculate the amount of taxes that Sara owes based on her tax bracket. To do this, we need to find the amount of taxable income that falls within the 24% tax bracket, and multiply it by the tax rate. According to the tax table, the amount of taxable income within the 24% tax bracket for head of household is:

$105,425 - $86,350 = $19,075

Therefore, Sara's tax liability is:

$19,075 x 0.24 = $4,578

So, Sara should have $4,578 removed from her projected income to cover her taxes for the year.

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Answer:

58

Step-by-step explanation:

9x + 22                        x = 4

9(4) + 22

36 + 22

58

Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Answer:

slice it in the middle in the top and bottom or do it corner to corner.

Step-by-step explanation:

1. have 2 braincells

2. put them toghether and think.

Answer: 0.15

Step-by-step explanation:

we have 15. Since 15 is a number out of 100, the number 100 is 3 digits. With any percent out of one hundred, it’s going to look something like this:0.23 this is 23 percent. In this case, since we have 15, this will be 0.15 or .15

Answer:

Step-by-step explanation:

Answer:

\(P(X<13.28)=P(\frac{X-\mu}{\sigma}<\frac{13.28-\mu}{\sigma})=P(Z<\frac{13.28-13}{0.2})=P(z<1.4)\)

And we can find this probability using the normal standard distribution table and we got:

\(P(z<1.4) =0.919\)

And the percentage faster than 13.28 seconds would be 91.9%

Step-by-step explanation:

Let X the random variable that represent the runtimes of a population, and for this case we know the distribution for X is given by:

\(X \sim N(13,0.2)\)  

Where \(\mu=13\) and \(\sigma=0.2\)

We want to find this probability:

\(P(X<13.28)\)

And we can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

Using this formula we have:

\(P(X<13.28)=P(\frac{X-\mu}{\sigma}<\frac{13.28-\mu}{\sigma})=P(Z<\frac{13.28-13}{0.2})=P(z<1.4)\)

And we can find this probability using the normal standard distribution table and we got:

\(P(z<1.4) =0.919\)

And the percentage faster than 13.28 seconds would be 91.9%

The value of A∩B is equal to {2,5} for the given sets.

Set theory is a field of mathematical logic that analyzes sets, which can be characterized informally as collections of objects. Although any object can be grouped into a set, set theory, as a discipline of mathematics, is largely concerned with those that are significant to mathematics in general.

Given that the two sets are,

A={1,2,3,4,5}

B={2,5,9,12}

The value of A∩B will be calculated as,

The common numbers between the two sets are 2 and 5.

A∩B = { 2 , 5 }

Therefore, the value of A∩B is equal to {2,5} for the given sets.

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