Which of the following lines has a slope of -1/2? my options are x - 2 y = 0 - x + 2 y = 0 x + 2 y = 0

Answer:my answer is 15,490,000

Step-by-step explanation: cuz that is what rounding does

The expression or equation to represent the number of hat each shelter will receive is h = 1600 / 4

Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

To represent the amount each local shelter will receive, we can write an expression for that while the variable is present

The number of hats can be found by dividing the total number of hats collected by the number of local shelters.

Estimating the number of hats

1596 ≅ 1600

Number of hats (h) = 1600 / 4

h = 400

Each local shelter will receive 400 hats

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Answer:

x= 120-20y/9

Step-by-step explantion:

There are 75% students in class who passed the algebra test out of total 24 students.

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Here, total number of students in class is 24

students who passed the algebra test is 18

Percentage = Passed student X 100 / Total students

                   = 18 X 100 /24

                   = 0.75 X 100

                   = 75%

Thus, there are 75% students in class who passed the algebra test out of total 24 students.

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Answer:

a. 5

b. 36

c. 1/3

d. 1/6

Step-by-step explanation:

a. The answer is five because 9 people bike and 4 people walk and 9-4 is equal to 5

b. The is answer is 36 because 12 people walked, 9 people biked, 4 people walked, 6 people used a motorcycle and 5 people used a cab and 12+9+4+6+5=36

c. The answer is 1/3 because 12 people walked to school and there are 36 people in the class so 12/36 people walked to school, which can be simplified to 1/3.

d. The answer is 1/6 because 6 people used a motorcycle to go school and there are 36 people in the class so 6/36 people used a motorcycle which is equal to 1/6

There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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Answer:

1. 7.3

2. 33.3

3. 21.3

4. 31.9

5. 25.6

6. 11.0

7. 42°

8. 64°

9. 13°

10. 51°

Step-by-step explanation:

make sure if you're using a math calculator that it is in degree mode.

SIN, COS, OR TAN. SOH CAH TOA. Sin is Opposite/hypotenus.

Cos is Adjacent(next to it)/hypotenus.

Tan is Opposite/Adjacent.

~~

PROBLEM 1:

So we have 63°, 16 as hypotenus, and x as one of the legs.

1. Figure out whether it is Sin, Cos, or Tan. (It's adj and hyp. of the angle degree (63° listed so it's cos.)

2. Once you set it up, it is Cos 63°= x/16 then flip it around. which makes it 16 COS 63= X.

3. Input it into your calculator as 16cos(63, then it will give you.. 7.263847996

4. Don't forget to round to the nearest tenth, which gives you

x = 7.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 2:

Given: 39°, 27 is opposite of the °, and adj is x. So this is Tan.

1. Set it up, Tan 39° = 27/x can't solve this way so fix it.

2. rewritten as X = 27/tan39

3. round ur answer.

x = 33.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 3:

Given: 49°, adj is 14, hyp is x. So this is Cos.

1. Set up according to CAH, Cos 49=(14/x).

We can't solve it this way since the X is on the bottom. So we have to fix it!

2. Turns into X Cos 49 = 14, which then turns into X= 14/cos49.

3. Put it in your calculator as 14 DIVIDED BY cos 49. ( Put image example)

4. Round.

x= 21.3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 4:

Given: 15°, 33 hyp, adj x. Which is Cos.

1. Cos 15= x/33 and rewrite.

2. Input as 33 cos(15 into calculator = 31.875...

3. Round to tenth.

x = 31.9

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 5:

Given: 52°, 20 adj of °, and x opp of °. Will use TAN.

1. Tan 52° = x/20

2. 20 Tan(52 into calculator

3. Round

x = 25.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 6:

Given: 27°, opp of ° is 5, hyp is x. Will use Sin.

1. Write out as I have the last few times, Sin 27 = 5/x rewrite cause x can't be at the bottom.

2. Input into calculator as: 5/sin 27 which equals 11.01...

3. Round.

x = 11.0

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 7:

Given: x°, 6 as hyp, 4 opp. now we have to solve this different since we don't know the degree. Now when we input into the calculator you will press 2nd, then sin/cos/tan so it will be negative this is depending on which one ur solving for.

We will be using SIN, x is still a °.

1. Sin X = 4/6 Rewrite.

2. X= Sin^-1 (4/6)

Make sure ur sin is negative in calculator when doing this.

3. It SHOULD give you 41.81, round.

x = 42°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 8:

Given: x°, 29 opp, 14 adj. TAN.

1. Tan x°= 29/14 or..

2. X = Tan^-1(29/14) solve..

3. gives u 64.23.... round.

x = 64°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 9:

Given: x°, hyp 54, opp 12. SIN

1. Sin x°=(12/54)

2. X= Sin^-1(12/54) solve. (dont put x= into calculator.)

3. Don't Forget to round, answer unrounded: 12.839..

x = 13°

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PROBLEM 10:

Given: x°, adj 25, hyp 40. COS

1. Cos x°=25/40 rewrite.

2. X= Cos^-1(25/40) Solve.

3. Round.

X= 51°

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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Answer:

$26.53

Step-by-step explanation:

93.06-40=53.06

53.06÷2=26.53

Answer:

26.53

Step-by-step explanation:

Answer:     Part A: y= -1200x +25000 this is because it decreases 1200$ a year that is your rate of change and it started at 25000 that is your y-intercept

                  Part B:  question a would be 46000$ because that’s where the zero is which is when he bought it question b is 3000$ because that is how much the table decreases with each year

Step-by-step explanation:

just to add some more to matthewwjohnson92 great reply above.

part A

year........value

1...........25000 - 1200(1)

2...........25000 - 1200(2)

3...........25000 - 1200(3)

4...........25000 - 1200(4)

x...........25000 - 1200(x)

part B

Check the picture below.

how much lost each year? from 0 to 3 it lost 9000, so 9000/3 = 3000 per each year.

Answer:

5 3/5 or 5

Step-by-step explanation:

Because it is

Answer:

\(\frac{2}{3}\)

Step-by-step explanation:

The equation for slope is:

\(Slope = \frac{y_2-y_1}{x_2-x_1}\)

We can plug the given coordinates into the equation:

\(Slope = \frac{0-2}{-4-(-1)}=\frac{-2}{-4+1}=\frac{-2}{-3}=\frac{2}{3}\)

Answer:

2

Step-by-step explanation:

Well if 2 are red it can only be either

rrrr

or

rrrw

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

53

Step-by-step explanation:

106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.

Answer:

Option D.   \(g(x)=5(0.8)^{x}+2\)

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form \(y=a*b^x\) has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form \(y=a*b^x\) increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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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:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.

Midpoint : (6,1)

Point A : (4,8)

Point B (xb,by)

Midpoint (xm, my)=( x1+x2) /2 , ( y1+y2)/2

So:

xm= 6 = (4+xb) /2

6 = (4+xb) /2

Solve for xb

6 x 2 = 4+ xb

12 = 4+xb

12-4 = xb

8 = xb

For Yb:

my= 1 = (8+yb) /2

1 = (8+yb) /2

Solve for yb

1(2) = 8+yb

2 = 8+ yb

2-8 = yb

-6 = yb

Coordinate of B = (xb,yb) = (8,-6)

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

No solutions

Step-by-step explanation:

3x^2=y

3(-2)^2=1

Follow P.E.M.D.A.S.

3(4)=1

12=1

X= (-5)

()()())()()()()()()()()()()()

Answer:

30%

Step-by-step explanation:

30%

First, let's solve the inequality for x:

Looking at the options, the corresponding number line is option C.

Based on the temperatures displayed by Thermometer A and Thermometer B, the thermometer displaying the greater temperature is Thermometer A

The best way to find the thermometer that is displaying the greater temperature is to convert the units of temperature to a single unit so that a proper comparison can be made.

Convert Thermometer B to degrees Fahrenheit. Celsius to Fahrenheit gives:

= (1°C × 9/5) + 32

=  (22°C × 9/5) + 32

= 71.6 degrees Celsius

This means that Thermometer A is displaying the greater temperature.

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Answer:

Eduardo will get $4.03

Step-by-step explanation:

To solve this problem, first add 4.99 and 0.98 together, remember to line up the decimals

4.99

+ 0.98

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

5.97

Now take 5.97 from 10.00

first you can't take 7 from 0 so you take 1 from the tens place making 10.00 into 9.9 10, now you can take 7 from 10 which equals 3. Into the tenths place you can take 9 from 9 which is a 0. Lastly 9 - 5 is 4, adding the decimal back you get

10.00

- 05.97

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

$ 4.03

ANSWER

EXPLANATION

We want to find the expression that is equivalent to the given expression:

To do this, we have to expand the brackets.

That is:

That is the equivalent expression (Option B).