if m FGK= 5w+7 and m FGH= 114, find W

21345 ththththththththththth

Answer:

AD = 112

Step-by-step explanation:

AD = AB + BC + CD = 25 + 37 + 50 = 112

Answer:

22.512

Step-by-step explanation:

1.014 x (10-2) = 1.014 x 8

                     = 8.112

2.4 x (10-4) = 2.4 x 6

                  = 14.4

8.112 + 14.4 = 22.512

Hope this helps :)

Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

\(\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}\)

and flows out at a rate of

\(\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}\)

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

\(\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))\)

Multiply both sides by the integrating factor, \(e^{t/180}\), and rewrite the left side as the derivative of a product.

\(e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))\)

\(\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))\)

Integrate both sides with respect to t (integrate the right side by parts):

\(\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt\)

\(\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C\)

Solve for A(t) :

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}\)

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

\(\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}\)

So,

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}\)

Recall the angle-sum identity for cosine:

\(R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)\)

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

\(R \cos(\theta) = -\dfrac{66,096,000}{32,401}\)

\(R \sin(\theta) = \dfrac{367,200}{32,401}\)

Recall the Pythagorean identity and definition of tangent,

\(\cos^2(x) + \sin^2(x) = 1\)

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

Then

\(R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}\)

and

\(\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)\)

so we can rewrite A(t) as

\(\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}\)

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

\(24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}\)

and

\(24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}\)

which is to say, with amplitude

\(2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}\)

The equation of the quadratic function is f(x) = 3(x - 2)² - 1

A quadratic function is an expression of the form f(x) = ax² + bx + c

Since we have the graph of f(x) which is quadratic, to write its function, we use the equation of a parabola in vertex form.

f(x) = a(x - h)² + k where (h, k) are the coordinates of its vertex.

Now, form the graph, the vertex is at (2, -1)

So, f(x) = a(x - 2)² + (-1)

f(x) = a(x - 2)² - 1

Also, we have the point (3, -4) on the graph. Substituting these into the equation, w ehave

f(x) = a(x - 2)² - 1

f(3) = a(3 - 2)² - 1

-4 = a(1)² - 1

-4 = a - 1

a = -4 + 1

a = - 3

So, substituting this into f(x), we have that

f(x) = 3(x - 2)² - 1

So, the equation is f(x) = 3(x - 2)² - 1

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Answer:

(4,-1)

Step-by-step explanation:

Current B Co-ordinate: (3, -4)

When you increase the y-value of the B Co-ordinate by 3, you get it as -1.

When you increase the x-value of the B Co-ordinate by 1, you get it as 4.

Hence, the B Co-ordinate after translation is (4,-1)

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Answer:

the points and where it is located

Step-by-step explanation:

To estimate the number of households in the sample that lost electricity, we can use the mean of the relevant distribution,

A) The relevant random variable is the number of households in the sample that lost electricity. Since we know that 7% of households in the city lost electricity, we can use this as the probability of any one household in the sample losing electricity. Therefore, the mean of the relevant distribution is:

Mean = np = 50 * 0.07 = 3.5 households

B) To find the standard deviation of the distribution, we use the formula:

Standard deviation = √(np(1-p))

where n is the sample size and p is the probability of success (in this case, the probability of a household losing electricity). Plugging in the values, we get:

Standard deviation = √(50 * 0.07 * (1 - 0.07)) = 1.51 households

Therefore, our estimate is that the sample will have an average of 3.5 households that lost electricity, with a standard deviation of 1.51 households.

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The study is a randomized controlled trial (RCT) study.

In an RCT study, participants are randomly assigned to either the treatment group or the control group. The treatment group receives the intervention (in this case, one of the two surgery procedures) being studied, while the control group does not receive the intervention.

The participants are then followed to observe the outcome of interest (in this case, the hours to recovery after surgery).

The goal of an RCT study is to determine if the intervention has an effect on the outcome. By randomly assigning participants to the treatment and control groups, any observed differences in the outcome between the two groups can be attributed to the intervention.

This helps to control for other factors that may influence the outcome and reduces the risk of bias in the results.

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The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.

The mean of the total length for both Alex and Brandon can be determined by multiplying the mean length of a single stick by the number of sticks required for each toy. In this case, each toy requires four 9-inch long sticks.

Mean of the total length for both Alex and Brandon: 4 sticks * 9 inches = 36 inches.

Since both Alex and Brandon have sticks with the same mean length and standard deviation, the standard deviation of the total length for both of them remains the same.

Standard deviation of the total length for both Alex and Brandon: 0.17 inches.

Therefore, The mean of the total length is 36 inches, and the standard deviation is 0.17 inches. This means that on average, the total length of the sticks will be 36 inches, and there will be a variation of approximately 0.17 inches around this mean length.

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The probability that Cody makes his first free throw or his second free throw is given by P(A or B) = 0.44 + 0.48 - (0.44 * 0.48) = 0.68.

To calculate the probability that Cody makes his first free throw or his second free throw, we can use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Since Cody's chances of making each free throw are independent, the probability that he makes his first free throw is 0.44, and the probability that he makes his second free throw given that he made the first is 0.48. Therefore, P(A) = 0.44 and P(B) = 0.48.

To determine whether the two free throws are mutually exclusive, we need to check if the events "making the first free throw" and "making the second free throw" can occur simultaneously. Since Cody can make both free throws, the events are not mutually exclusive.

Therefore, the probability that Cody makes his first free throw or his second free throw is given by P(A or B) = 0.44 + 0.48 - (0.44 * 0.48) = 0.68.

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In this case, I will consider the relationship between a person's age and their income. I believe that income is more likely to have a higher standard deviation compared to age.

1. Economic Factors: Income is influenced by economic factors such as job market conditions, economic growth, and industry trends. These factors can fluctuate over time, leading to variations in income levels. On the other hand, age progresses in a more predictable manner.

2. Career Development: Income is strongly influenced by career development, including promotions, job changes, and salary negotiations. These factors introduce a level of unpredictability, as individuals may experience significant income changes at different stages of their careers. Age, although related to career progression, follows a relatively more predictable pattern.

3. Individual Choices: Income can also be influenced by individual choices such as entrepreneurship, investment decisions, and career changes. These choices introduce a higher level of variability as they depend on personal circumstances, risk appetite, and market conditions. Age, in contrast, progresses in a more linear and predictable manner.

Considering these reasons, it is reasonable to expect that income would have a higher standard deviation compared to age. Income is influenced by various external and personal factors that can result in significant fluctuations, making it less predictable compared to the relatively more stable progression of age.

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Answer:

a=13

Step-by-step explanation:

-90=-6a-12

-6a=-78

a=13

Answer:

a=13 well as u can see the other comment already gave an explanation of y it is a=13 and i completely agree with it have a nice afternoon,night,or day to u

Step-by-step explanation:

Answer:

This is the nearest tenth already.

Answer:

276.4 rounded to the nearest tenth = 276.4

Step-by-step explanation:

round 276.4 to the nearest tenth, leaving only one number after the decimal point, then you have come to the right post.

See the attachment for more examples

Answer: x=12y/-8-3

Step-by-step explanation: image below

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

A manned spacecraft traveling at 40,000 km/hr would take approximately 164.38 years to reach Mars from Earth, based on the distance of 57.6 million km.



To calculate the time it would take for a manned spacecraft to reach Mars from Earth, we can divide the distance between the two planets by the spacecraft's speed. The distance of 57.6 million km can be converted to 57,600,000,000 km (since 1 million is equal to 1,000,000). Using the formula: Time = Distance / Speed, we can calculate the time as follows:

Time = 57,600,000,000 km / 40,000 km/hr = 1,440,000 hours.

Since we want to convert the time to years, we divide the total number of hours by the number of hours in a year. Assuming there are 24 hours in a day and 365 days in a year:

1,440,000 hours / (24 hours/day * 365 days/year) ≈ 164.38 years.

Therefore, it would take approximately 164.38 years for the manned spacecraft to reach Mars from Earth at a speed of 40,000 km/hr. None of the options provided (0.00144 yr, 1440 days, 24 days, 60 days) are accurate.

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Answer: 3/8

Step-by-step explanation:

7/8-1/2

Find common denominator which is 8 and you get that from 1/2 by multiplying 4 on the top and bottom and so you wind up with 4/8 and 7/8-4/8 is 3/8

Answer: Its D positive

Step-by-step explanation:

Answer: B pls vote branliest

Step-by-step explanation:

Answer:

$75

Step-by-step explanation:

20 - 14 = 6

6 students would pay in the second week

6 x $12.50 = $75

The teacher would collect $75 in the second week

Answer:

X>3

Step-by-step explanation:

X+9<4X

x-x+9<4x-x

9<3x

3<x

The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet. You need 11.83 minutes in the shower to use as much water as the bath.

The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet.

The amount of water used in shower = flow rate × time = 2.23 gallons/minute × 8 minutes = 17.84 gallons

Let's convert gallons to cubic feet: 1 cubic foot = 7.5 gallons

17.84 gallons = 17.84/7.5 cubic feet = 2.378 cubic feet

The volume of water used in the shower is 2.378 cubic feet. The volume of water used for taking a bath is 26.4 cubic feet.

To calculate how many minutes one would need in the shower to use as much water as the bath, divide the volume of water used in taking a bath with the amount of water used per minute in the shower as shown:

26.4/2.23=11.83 min

Therefore, one needs 11.83 minutes in the shower to use as much water as the bath.

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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Answer:

Step-by-step explanation:

If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology

The roots are 14.09, 0.30 and -0.39 to nearest hundredth.

(1) The two triangles are similar because they have equal angles.

(2)  Triangle QRS is similar to triangle QLM because they have equal angles.

(3) Both triangles are similar and the value of x is 21.

Two triangles are said to be similar if they have equal sides, equal angles or both.

The missing angles of the triangles for the question is calculated as;

Bigger triangle; missing angle = 180 - (44 + 46) = 90

Smaller triangle; missing angle = 90 - 46 = 44⁰

Both triangles are similar.

For the second question; triangle QRS is similar to triangle QLM  because angle R is equal to angle L, and also they have common angle Q, which implies that angle S must be equal to angle L.

For third question, the triangles are similar because their corresponding angles are equal.

The value of x is calculated as;

48 + 4x + (180 - (56 + 76)) = 180 (sum of angles on a straight line)

48 + 4x + 48 = 180

4x = 84

x = 84/4

x = 21

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Answer:

Ellas forman triángulos./Ellos forman triángulos.

They do form triangles.

Answer:

3/4 or 0.75

Step-by-step explanation:

\( \frac{3 }{8} + \frac{3}{8} \)

transform the equation

\( \frac{3 + 3}{8} \)

calculate

\( \frac{6}{8} \)

simplify

\( \frac{3}{4} \)

or 0.75

Angle relationships, where we're given a diagram containing 2+ parallel lines and a transversal, can tell us a lot about the angles.

The two angles indicated in the diagram measure 4x + 19 degrees and 6x + 7 degrees.

These two angles form a "Z" pattern, meaning they are on opposite sides of the transversal and opposite sides of the two parallel lines. They are alternate angles.

Alternate angles are always equal. Therefore, we can set up the following equation and solve for x:

\(4x + 19 = 6x + 7\\19 = 2x + 7\\12 = 2x\\x = 6\)

x = 6

To compute the inverse Laplace transform of L^-1 {3s + 2/s^2 - s - 12 e^-4s}, we first need to break it up into simpler terms using partial fraction decomposition. We have:

L^-1 {3s + 2/s^2 - s - 12 e^-4s}

= L^-1 {3s} + L^-1 {2/s^2 - s} + L^-1 {12 e^-4s}

= 3 δ(t) + (2 u(t) - 1) - (1 - u(t - 4)) \* 3/2 e^(4(t-4))

where δ(t) is the Dirac delta function and u(t) is the Heaviside step function.

The first term, 3 δ(t), comes from the L^-1 {3s} term, which corresponds to a constant function.

The second term, (2 u(t) - 1), comes from the L^-1 {2/s^2 - s} term, which we can decompose as:

2/s^2 - s

= 2/s^2 - 2s/s^2 + s/s^2

= 2 (1/s - 1/s^2) - s/s^2

Taking the inverse Laplace transform of each term separately gives:

L^-1 {2 (1/s - 1/s^2)} = 2 (u(t) - 1) L^-1 {-s/s^2} = -(t u(t))

Putting these together, we get: L^-1 {2/s^2 - s} = 2 (u(t) - 1) - (t u(t))

The third term, (1 - u(t - 4)) \* 3/2 e^(4(t-4)), comes from the L^-1 {12 e^-4s} term, which corresponds to an exponentially decaying function.

We use the time-shifting property of the Laplace transform to shift the function by 4 units to the right, giving: L^-1 {12 e^-4s} = 3/2 e^(4(t-4)) u(t-4)

But we want the function to be 0 for t < 4, so we subtract off the Heaviside step function u(t - 4), giving: L^-1 {12 e^-4s} = (1 - u(t - 4)) \* 3/2 e^(4(t-4))

Putting everything together, we get: L^-1 {3s + 2/s^2 - s - 12 e^-4s} = 3 δ(t) + 2 (u(t) - 1) - (t u(t)) - (1 - u(t - 4)) \* 3/2 e^(4(t-4))

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The man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

To calculate the Body Mass Index (BMI) of a person, we use the following formula:

BMI = weight (in kilograms) / height^2 (in meters)

First, we need to convert the weight from pounds to kilograms. Since 1 pound is approximately 0.4536 kilograms, the man's weight of 154 pounds is equal to 69.85 kilograms (rounded to two decimal places).

Next, we need to convert the height from inches to meters. Since 1 inch is equal to 0.0254 meters, the man's height of 70 inches is equal to 1.778 meters (rounded to three decimal places).

Now, we can calculate the BMI using the formula:

BMI = 69.85 kg / (1.778 m)^2

Calculating this expression, we find that the man's BMI is approximately 22.09 (rounded to two decimal places).

In summary, the man's BMI is approximately 22.09 based on his weight of 154 pounds and height of 70 inches.

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Answer:

78 squared feet

Step-by-step explanation:

area= base x height

so 6 x 13 = 78

and yeah

HOPE I HELPED:))

your answer is 91 square feet