: a lan gaming center charges continuously over time on the credit card at the constant rate of $8 per hour per computer. on your birthday, you are planning to take two of your friends to the gaming center and use your credit card to pay for all three computers. a. write a rate function, f(t), representing the per hour charge applied to your credit card at time t

Answers

Answer 1

The rate function f(t) representing the per hour charge applied to your credit card at time t is $24.

To represent the per hour charge applied to your credit card at time t, we can define the rate function, f(t), as follows:

f(t) = 8 dollars/hour/computer

Since you are planning to use three computers (including yours and your two friends'), the rate function will be multiplied by 3:

f(t) = 3 * 8 dollars/hour/computer

f(t) = 24 dollars/hour/

Therefore, the rate function f(t) representing the per hour charge applied to your credit card at time t is $24.

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Related Questions

A passenger traveling by air is allowed a maximum of 20kg luggage. A man has 4 bags weighing 3.5kg , 15kg, 2kg, 1.5kg. Find the excess weight of the luggage. Express the excess weight as a percentage of the maximum weight​

Answers

Answer:

The passenger's luggage has an excess weight of 2 kg, which is 10% of the maximum weight.

Step-by-step explanation:

First, we need to find the weight (W) of the 4 bags:

\( W = 3.5 kg + 15 kg + 2 kg + 1.5 kg = 22 kg \)

Now, knowing that the maximum allowed (M) is 20 kg the excess weight of the luggage is:

\( W_{e} = W - M = 22 kg - 20 kg = 2 kg \)

We can express the excess weight in percentage as follows:

\( \% W_{e} = \frac{W_{e}}{M} \times 100 = \frac{2 kg}{20 kg}\times 100 = 10 \% \)  

Therefore, the passenger's luggage has an excess weight of 2 kg, which is 10% of the maximum weight.          

 

I hope it helps you!                      

A rectangular parking lot is 253.5 feet long and 176.5 feet wide. a 55-gallon drum of asphalt sealer covers
4,000 square feet and costs $99.50. find the cost to seal the parking lot. (sealer can only be purchased in full
drums.)

Answers

Answer:

$1,194

Step-by-step explanation:

The area of the parking lot is 253.5(176.5) which equals 44,472.75. You then divide 44,472.75 by 4000 to see how many gallons you need to cover the parking lot. The answer to that was about 11.2 and since you can only purchase full drums you have to round it up to 12 to have enough. Finally, you multiply 12 by 99.50 and get your answer.

In which interval does a root exist for this equation? tan(x) = 3x^2

PLEASE HELP

In which interval does a root exist for this equation? tan(x) = 3x^2 PLEASE HELP

Answers

The equation tan(x) = 3x^2 can be solved using numerical methods such as the Newton-Raphson method or the bisection method. However, it is not possible to find the exact solution of this equation using algebraic methods.

To determine the interval for which a root exists, you can use the intermediate value theorem.

First, observe that the left-hand side of the equation, tan(x), is undefined for x = (n + 1/2) π, where n is an integer. Thus, we can restrict our attention to the interval (-π/2, π/2) where the tangent function is continuous and strictly increasing.

Next, note that tan(0) = 0 and tan(π/6) = 1/√3 < 3/36 = 1/12. Also, as x approaches π/2 from the left, tan(x) approaches infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (0, π/6).

Similarly, tan(-π/6) = -1/√3 > -1/12, and as x approaches -π/2 from the right, tan(x) approaches negative infinity, while 3x^2 approaches infinity faster. Therefore, there exists at least one root of the equation in the interval (-π/6, 0).

Therefore, the equation tan(x) = 3x^2 has at least one root in the interval (-π/6, π/6).

Hey guys please help

Hey guys please help

Answers

True.
Angle c=anglez
Angle RHC=angle XHZ
Therefore they’re similar.
Pls mark me as the Brainliest as I really need it, thanks!

Please help with this math equation.

Please help with this math equation.

Answers

The roots of the function f ( x ) are x = 1 and x = 3

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x⁴ - 13x³ + 38x² - 23x - 3

On simplifying , we get

The possible factors of the constant term (-3) are ±1 and ±3, while the possible factors of the leading coefficient (1) are ±1.

Now, we can test these factors by substituting them into the function and checking if the result is zero:

f(1) = (1)⁴ - 13(1)³ + 38(1)² - 23(1) - 3 = 1 - 13 + 38 - 23 - 3 = 0

f(-1) = (-1)⁴ - 13(-1)³ + 38(-1)² - 23(-1) - 3 = 1 + 13 + 38 + 23 - 3 = 72

f(3) = (3)⁴ - 13(3)³ + 38(3)² - 23(3) - 3 = 81 - 351 + 342 - 69 - 3 = 0

f(-3) = (-3)⁴ - 13(-3)³ + 38(-3)² - 23(-3) - 3 = 81 + 351 + 342 + 69 - 3 = 840

From the above calculations, we can see that f(1) = f(3) = 0. This means that x = 1 and x = 3 are roots of the polynomial function

Hence , the function is solved and x = 1 and x = 3

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8840 in standard form

Answers

Answer:

8000 + 800 + 40

       or

8.84 x 10^3

greatly appreciate help :) picture below

greatly appreciate help :) picture below

Answers

Answer:

The answer is None.

Step-by-step explanation:

I took the test on FLVS and I got the answer right.

I hope this helps. I am sorry if you get this wrong.

Answer:

None. Say the obtuse angle is 100 degrees. Since the sum of all angles in a triangle cannot be bigger than 180, it's not possible because 195 (100+95) is greater than 180 degrees.

Step-by-step explanation:

You put $500 in a savings account. The account earns $15.75 simple interest in 6 months. What is the annual interest rate?

Answers

Answer:

6.3%

Step-by-step explanation:

We're gonna use the simple interest formula: A = P(1 + rt)

A = Final amount (500 + 15.75 = 515.75)

P = Starting amount (500)

r = rate (?)

t = number of years (.5 since it's been half a year)

515.75 = 500(1 + 0.5r)

Disitribute the 500 to the equation inside the parenthesis

515.75 = 500 + 250r

Subtract 500 from both sides

515.75 = 500 + 250r

- 500   - 500

15.75 = 250r

Divide both sides by 250

15.75/250 = 250r/250

r = 0.063

Two trains start at the same time from the same station and move along straight tracks that form an angle of 36

. One train moves at the rate of 45mph and the other at 52mph. How far apart are the trains at the end of 15 minutes. 7. Two observers, facing each other, are 15 km apart on a level plain. They are looking at a hot air balloon on the same vertical plane between them. They found out that the angles of elevation of the balloon with them are 48

and 61

respectively. Find the inclined distances from the balloon to each observer. 8. If the time is 8:00 am GMT, what is the time in the Philippines which is located 120

east longitude? 9. Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40

,65

and 110

10. The right spherical triangle has an angle C=90

,a=50

, and c=80

. Find side b.

Answers

6.  At the end of 15 minutes, the two trains are approximately 58.71 miles apart.

7.The inclined distances from the balloon to each observer is 16.659 km for first observer and 32.1675 km for second observer

8.  The time in the Philippines, located 120° east longitude, is 8:00 am GMT + 8 hours, which is 4:00 pm local time.

9.  The area of the spherical triangle is 15.2725 square meters.

10. Side b in the right spherical triangle is approximately 50.951°.

6. We can use the law of cosines to find the distance between the two trains after 15 minutes. The law of cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

a = 45 mph

b = 52 mph

C = 36 degrees

Converting the time to hours:

15 minutes = 15/60 = 1/4 hour

Using the formula, we can calculate the distance:

c^2 = (45 mph)^2 + (52 mph)^2 - 2 * 45 mph * 52 mph * cos(36 degrees)

c^2 = 2025 + 2704 - 4680 * cos(36 degrees)

c^2 = 4729 - 4680 * cos(36 degrees)

c^2 ≈ 3443.28

Taking the square root of both sides:

c ≈ √3443.28

c ≈ 58.71 miles

7.  Using trigonometry, we have:

tan(48°) = x / 15 (angle of elevation for the first observer)

tan(61°) = y / 15 (angle of elevation for the second observer)

Rearranging the equations, we get:

x = 15 * tan(48°)

y = 15 * tan(61°)

Calculating these values:

x ≈ 15 * 1.1106 ≈ 16.659 km

y ≈ 15 * 2.1445 ≈ 32.1675 km

8. The Earth rotates 360° in 24 hours, which means that each degree of longitude corresponds to 4 minutes of time difference.

120° * 4 minutes = 480 minutes

480 minutes / 60 = 8 hours

9. To calculate the area of a spherical triangle, we can use the formula:

Area = (A + B + C - π) * r^2

Converting the given angles to radians:

A = 40° * (π/180) ≈ 0.6981 rad

B = 65° * (π/180) ≈ 1.1345 rad

C = 110° * (π/180) ≈ 1.9199 rad

Substituting the values into the formula:

Area = (0.6981 + 1.1345 + 1.9199 - π) * 5^2

= (3.7525 - 3.1416) * 25

=0.6109 * 25

≈ 15.2725 square meters

10. In a right spherical triangle, the side opposite the right angle (side c) is the hypotenuse, and the remaining sides are labeled as a and b.

Given: C = 90°, a = 50°, and c = 80°.

To find side b, we can use the spherical Law of Sines:

sin(a) / sin(A) = sin(b) / sin(B)

Plugging in the values:

sin(50°) / sin(90°) = sin(b) / sin(80°)

Since sin(90°) = 1, we have:

sin(50°) = sin(b) / sin(80°)

Rearranging the equation:

sin(b) = sin(50°) * sin(80°)

Taking the inverse sine of both sides:

b = arcsin(sin(50°) * sin(80°))

Evaluating the expression:

b ≈ arcsin(0.7660 * 0.9848)

b ≈ arcsin(0.7546)

b ≈ 50.951°

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Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 4.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answers

The probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is derived to be 1.02.

Probability distribution of yields to maturity a year from now on a 30-year U.S. Treasury bond with a coupon of 4.0% using the table below.

We need to derive the probability distribution of the 1-year holding period return (HPR) on the bond.

First, we calculate the bond price using the current yield to maturity.

Current Yield to Maturity of Bond = 5.0%

Coupon Payment (C) = $4.00

Face Value (F) = $100.00

Therefore, Price of Bond

= PV of all cash flows

= C / YTM * [1 - 1 / (1 + YTM)n] + F / (1 + YTM)n

= $4.00 / 0.05 * [1 - 1 / (1 + 0.05)30] + $100.00 / (1 + 0.05)30

= $76.76 + $23.24

= $100.00

Therefore, the bond is selling at par value.  

To calculate the 1-year HPR,

we use the formula

HPR = (Ending Bond Price - Beginning Bond Price + Coupon Payment) / Beginning Bond Price

= (P1 - P0 + C) / P0

= (P1 / P0) - 1 + (C / P0)

= [(C1 / P1) + 1] - 1 + (C0 / P0)

= [(C1 / P1) - (C0 / P0)] + 1  

We know that Coupon Payment (C) = $4.00,

and the Par Value (F) = $100.00.

Therefore, Coupon Payment for a 1-year period,

C0

= $4.00 * 1 / 2

= $2.00,

C1 = $4.00  

Thus, we get:  

Probability,

P(YTM) YTM Bond Price C1 / P1 C0 / P0 (C1 / P1) - (C0 / P0)

HPR

= 0.05 $100.00 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.06 $94.34 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.07 $90.29 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.08 $86.48 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.10 $81.89 $4.00 $2.00 $0.02 0.02 + 1

= 1.02

The probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is given in the above table, where HPR is derived from the Yield-to-Maturity (YTM) probability distribution provided. Therefore, the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is:   Probability, P(HPR) HPR 0.02 1.02.

Therefore, the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is derived to be 1.02.

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Help me out here plz

Help me out here plz

Answers

Answer:

I think that it would be \(28^{2}\) cm

Step-by-step explanation:

8 x 7 = 56

56/2 = 28

A common at-home workout that features high-intensity cardio, strength-building exercises, and focuses on total body fitness might be:____.

Answers

A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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ANSWERS NEEDED TODAY!!!!!
1:5x=2x+24
2:4x-2+10x+14=180
3:x+4+3x+2=90

Answers

8,12,21 1.8 2.12 3.21

Just need 1 answered

Just need 1 answered

Answers

the answer would be ( -7/2 , 7/2 )

find the critical value $z^\ast$ for an 80% confidence intervals for a proportion. explain your calculation and include r code used.

Answers

The output of this code will be the critical value `z*` for an 80% confidence interval.

To find the critical value `z*` for an 80% confidence interval for a proportion, we need to use the standard normal distribution. The formula for the confidence interval for a proportion is:

```

p ± z* √(p*(1-p)/n)

```

where `p` is the sample proportion, `n` is the sample size, and `z*` is the critical value from the standard normal distribution.

We can find `z*` using the `qnorm()` function in R, which gives the inverse of the cumulative distribution function of the normal distribution. For an 80% confidence interval, we want to find the value of `z*` such that the area under the normal curve to the right of `z*` is 0.1 (since we want a two-tailed test, we need to divide the significance level of 0.2 by 2). This can be computed as follows:

```

z_star <- qnorm(0.1/2)

```

The output of this code will be the critical value `z*` for an 80% confidence interval.

Explanation:

The `qnorm()` function in R calculates the inverse of the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the probability that a standard normal random variable is less than or equal to a given value. By taking the inverse of the CDF at a given probability level, we can find the corresponding value on the standard normal distribution that has that probability to its left. For example, if we want to find the value of `z*` such that the area to the right of `z*` is 0.1, we can use the `qnorm()` function with the argument `1-0.1` (since the CDF gives the probability to the left of a value, and we want the area to the right). The resulting value is the critical value `z*` that we need for an 80% confidence interval.

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Z - 6/3 = 4

what is the answer for the variable?

Answers

Answer:

Z = 6

Step-by-step explanation:

To solve this equation, we can do the opposite of -6/3 to isolate Z and get our answer. The opposite of -6/3 is +6/3, so we add 6/3 to both sides.

Z - 6/3 = 4

  +6/3    +6/3

Z = 4 + 6/3

Z = 4 + 2

Z = 6

Hope this helps

It takes Emily (422 - 1) hours to cut 3 acres of grass. Her brother Felix can cut 1 acre of grass in (22 + 1) hours. Part A Which expression models how many acres of grass Emily and Felix can cut per hour if they work together? 0 O O O 3 4z2-1 7 22+1 3 472-1 1 22+1 172 -1 3 + 22+1 1 422 -1 3 22+1 1

Answers

The expression that models how many acres of grass Emily and Felix can cut per hour if they work together is (1/((422 - 1)/3 + (22 + 1)/1)).

To determine how many acres of grass Emily and Felix can cut per hour when working together, we need to find the combined rate at which they can cut grass.

Emily can cut 3 acres of grass in (422 - 1) hours, so her cutting rate is 3/(422 - 1) acres per hour.

Felix can cut 1 acre of grass in (22 + 1) hours, so his cutting rate is 1/(22 + 1) acres per hour.

To find the combined rate, we add their individual rates together:

Combined rate = Emily's rate + Felix's rate

Therefore, the expression that represents the combined rate of cutting grass per hour for Emily and Felix is:

(1/((422 - 1)/3 + (22 + 1)/1))

Simplifying the expression, we get the answer (1/((421/3 + 23/1))).

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Write 23 /2 as a mixed number. Give your answer in its simplest form.

Answers

Answer:

11 1/2

Step-by-step explanation:

Convert improper fraction to mixed number

23 over 2

= 11 and 1/2

23 ÷ 2 = 11 remainder 1

Answer:

11whole,1 and a half

Step-by-step explanation:

divide 23 by 2

The vertex of this parabola is at (-2,-3). When the y-value is -2, the x-value is -5. What is the coefficient of the squared term in the parabola's equation? 5 re (-2, -3)​

Answers

Answer:

The coefficient of the squared term of the equation is 1/9.

Step-by-step explanation:

We are given that the vertex of the parabola is at (-2, -3). We also know that when the y-value is -2, the x-value is -5. Using this information we want to find the cofficient of the squared term in the parabola's equation.

Since we are given the vertex, we can use the vertex form:

\(\displaystyle y=a(x-h)^2+k\)

Where a is the leading coefficient and (h, k) is the vertex.

Since the vertex is (-2, -3), h = -2 and k = -3:

\(\displaystyle y=a(x-(-2))^2+(-3)\)

Simplify:

\(y=a(x+2)^2-3\)

We are also given that y = -2 when x = -5. Substitute:

\((-2)=a(-5+2)^2-3\)

Solve for a. Simplify:

\(\displaystyle \begin{aligned} -2&=a(-3)^2-3\\ 1&=9a \\a&=\frac{1}{9}\end{aligned}\)

Therefore, our full vertex equation is:

\(\displaystyle y=\frac{1}{9}(x+2)^2-3\)

We can expand:

\(\displaystyle y=\frac{1}{9}(x^2+4x+4)-3\)

Simplify:

\(\displaystyle y=\frac{1}{9}x^2+\frac{4}{9}x-\frac{23}{9}\)

The coefficient of the squared term of the equation is 1/9.

Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, approximately how many inches are in 1 km?

Answers

Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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Giving brainly for answer correctly uwu:)<3

Giving brainly for answer correctly uwu:)&lt;3

Answers

The correct answer is A.

What is the optimal choice when pı = 3, P2 = 5 and I = 20 and utility is (a) u(x1, x2) = min{2x1, x2} (b) u(x^2 1, x^2 2) = x} + x3 (c) u(x1, x2) = In(xi) + In(x2) (d) u(x1, x2) = x x = (e) u(x1, x2) = -(x1 - 1)^2 – (x2 - 1)^2

Answers

Using the Lagrange method, the optimal choice is therefore (x1, x2) = (20/9, 4/3).

The optimal choice when pı = 3, P2 = 5 and I = 20 and utility is u(x1, x2) = min{2x1, x2} can be found using the Lagrange method .Lagrange method: This method involves formulating a function (the Lagrange function) which should be optimized with constraints, i.e. the optimal result should be produced while adhering to the constraints provided. The Lagrange function is given by: L(x1, x2, λ) = u(x1, x2) - λ(I - p1x1 - p2x2)

Where L is the Lagrange function, λ is the Lagrange multiplier, I is the budget, p1 is the price of good 1, p2 is the price of good 2.The optimal choice can be determined by the partial derivatives of L with respect to x1, x2, and λ, and setting them to zero to get the critical points. Then, the second partial derivative test is used to determine if the critical points are maxima, minima, or saddle points. The critical points of the Lagrange function L are:

∂L/∂x1 = 2λ - 2p1 = 0 ∂L/∂x2 = λ - p2 = 0 ∂L/∂λ = I - p1x1 - p2x2 = 0

Substitute the first equation into the second equation to get:λ = p2,2λ = 2p1 ⇒ p2 = 2p1,

Substitute the first two equations into the third equation to get: x1 = I/3p1,x2 = I/5p2

Substitute p2 = 2p1 into the above to get:x1 = I/3p1,x2 = I/10p1.Substitute the values of p1, p2 and I into the above to get:x1 = 20/9,x2 = 4/3.The optimal choice is therefore (x1, x2) = (20/9, 4/3).

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Which of the following describes the idea of the Laffer Curve as it is expressed mathematically?
The ratios show the relationship between the federal income tax rates and revenue
To analyze how economic policies may affect growth and stability
Aggregate supply increases when production costs decrease.
reduce the government's role in the economy

Answers

The idea of the Laffer Curve, as it is expressed mathematically, is that there is an optimal tax rate at which the government can maximize revenue. This concept is based on the idea that as tax rates increase, revenue collected by the government initially increases but eventually reaches a point at which further increases in tax rates lead to a decrease in revenue.

The Laffer Curve is used to analyze how economic policies may affect growth and stability by illustrating the trade-off between higher tax rates and revenue generation. It is often used as an argument to reduce the government's role in the economy, as increasing taxes beyond a certain point can be counterproductive.

Additionally, the Laffer Curve is related to the idea that aggregate supply increases when production costs decrease, as lower taxes can lead to lower production costs and, therefore, an increase in supply. This is a long answer that describes the various aspects of the Laffer Curve.

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Y=2x^2 + 3x+1
a.Find the x - and y-intercept
b. Where is the line of symmetry of this parábola? Write its equation
c. Find the coordinates of the vertex

Answers

For the parabola y = 2x² + 3x + 1,

a. i.  The x-intercepts are x = -1/2 and x = -1

a. ii. The y-intercept is y = 1

b. i. The line of symmetry is at x = -3/4

b. ii. The equation of the line of symmetry is x = -3/4

c.  The vertex is at (-3/4, -1/8)

What is a parabola?

A parabola is part of a conic section which is a curve.

a. i. Find the x - intercept

Given the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.

So, y = 2x² + 3x + 1

2x² + 3x + 1 = 0

2x² + 2x + x + 1 = 0

Factorizing, we have

2x(x + 1) + (x + 1) = 0

(2x + 1)(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

2x = -1 or x = -1

x = -1/2 or x = -1

So, the x-intercepts are x = -1/2 and x = -1

ii Find the y intercept?

Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.

So, y = 2x² + 3x + 1

So, y = 2(0)² + 3(0) + 1

y = 0 + 0 + 1

y = 1

So, the y-intercept is y = 1

b. i. Where is the line of symmetry of this parábola?

The line of symmetry passes through the vertex of the parabola where dy/dx = 0.

So, y = 2x² + 3x + 1

dy/dx = d(2x² + 3x + 1)/dx

= d(2x²)/dx + d3x/dx + d1/dx

= 4x + 3 + 0

= 4x + 3

So, when dy/dx = 0,we have

4x + 3 = 0

4x = -3

x = -3/4

So, the line of symmetry is at x = -3/4

ii. Write its equation

The equation of the line of symmetry is x = -3/4

c. Find the coordinates of the vertex?

Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have

y = 2x² + 3x + 1

y = 2(-3/4)² + 3(-3/4) + 1

y = 2(9/16) - 9/4 + 1

y = 9/8 - 9/4 + 1

y = (9 - 18 + 8)/8

y = (17 - 18)/8

y = -1/8

So, the vertex is at (-3/4, -1/8)

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Discuss the downsizing process in your own words and provide an
example.

Answers

Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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a rectangle's length is 5cm more than its width, if it has an area of 336 cm squared find the length

Answers

The length of the rectangle is 19 cm.

The formula for the area of a rectangle,

Area = Length x Width

Given that the area is 336 cm squared.

So, we can set up an equation,

⇒ 336 = (w + 5)w

where w represents the width of the rectangle.

Expanding this equation,

⇒ 336 = w² + 5w

Moving all terms to one side:

⇒ w² + 5w - 336 = 0

This is a quadratic equation that we can solve using the quadratic formula,

⇒ w = (-5 ± √(5² - 4(1)(-336))) / (2(1))

⇒ w = (-5 ± 23) / 2

We'll take the positive value,

⇒ w = 14

So, the width of the rectangle is 14 cm.

We also know that the length is 5 cm more than the width,

Therefore,

⇒ l = w + 5

⇒ l = 14 + 5

⇒ l = 19

Therefore, the length of the rectangle is 19 cm.

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Q 42 - The proportion of salary of An and B is 5:3 and that of their use is 9:5. On the off chance that they spare Rs. 2600 and Rs. 1800, then their livelihoods are: A-9000, 5400 B-10000, 6000 C-6000, 3600​

Answers

Answer: Let's solve this problem step by step.

First, let's assume the salaries of An and B to be 5x and 3x, respectively, where x is a common multiplier.

According to the given information, they save Rs. 2600 and Rs. 1800, respectively. Since savings come from the remaining portion of their incomes after spending, we can calculate their expenditures as follows:

For An:

Income of An = Salary of An + Savings of An

Income of An = 5x + 2600

For B:

Income of B = Salary of B + Savings of B

Income of B = 3x + 1800

Now, let's consider the proportion of their expenditures. It is given that the proportion of their expenditures is 9:5. So, we can write the following equation:

(Expenditure of An)/(Expenditure of B) = 9/5

Since expenditure is the complement of savings, we have:

[(Income of An - Savings of An)] / [(Income of B - Savings of B)] = 9/5

Substituting the previously derived expressions for income, we get:

[(5x + 2600 - 2600)] / [(3x + 1800 - 1800)] = 9/5

Simplifying the equation, we have:

5x / 3x = 9/5

Cross-multiplying, we get:

5 * 3x = 9 * 3x

15x = 27x

Subtracting 27x from both sides, we have:

0 = 12x

This implies that x = 0, which is not a valid solution. Therefore, there seems to be an error or inconsistency in the given information or equations. Please recheck the problem statement or provide additional information to help resolve the issue.


f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6​​​​​​​
where c is constant

Answers

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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x^2- 5x- 36= 0
Solve by using the quadratic formula​

Answers

Answer:

if it say this

1:x={-3,4}

2:x={9,-4}

3:x={-9,4}

4:x={-4,5}

then it would be the second answer :)

Hope you answer is right have great weekends!

- friend

Answer:

\( {x}^{2} - 5x - 36 = 0 \\ \\ {x}^{2} - 9x + 4x - 36 = 0 \\ \\ x(x - 9) + 4(x - 9) = 0 \\ \\ (x - 9)(x + 4) = 0\)

Calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall.
Answer:

Logic - BMI formula
703*(lbs/inches^2)
703(118/64^2)=703(118/4096)
703*0.0288=20.2464

Answers

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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