suppose you drive an old truck with a 32 gallon gas tank that gets 16 miles/gallon. if you are 75 miles from home and you have a quarter tank of gas, will you run out of gas before you get home?

Answer:

Step-by-step explanation:

Since, PN ≅ NR

RM ≅ MQ

PL ≅ LQ

QN, LR and PM are the medians and they intersect each other at point K which will be the centroid of ΔPQR.

By the property of centroid,

Point K will divide the medians in the ratio of 2 : 1

By this property,

PK : KM = 2 : 1

4 : KM = 2 : 1

\(\frac{4}{KM}=\frac{2}{1}\)

KM = 2

KQ = \(\frac{2}{(2+1)}(NQ)\)

     = \(\frac{2}{3}\times 6\)

KQ = 4

LK : RK = 1 : 2

LK : 3 = 1 : 2

\(\frac{LK}{3}=\frac{1}{2}\)

LK = 1.5

LR = LK + RK

     = 1.5 + 3

LR = 4.5

NK = \(\frac{1}{(2+1)}(QN)\)

     = \(\frac{1}{3}(6)\)

NK = 6

PM = PK + KM

PM = 4 + 2

PM = 6

using exponents, On simplifying the equation, we get =4m+8.

The PEMDAS order of operations must be followed when you want to simplify a mathematical equation without using parenthesis (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). There are no parenthesis in the expression, so you may start looking for exponents. If it does, first make that simpler.

Work simplification is to develop better work processes that boost output while cutting waste and costs.

Simplifying an expression is the same as solving a mathematical issue. When you simplify an equation, you essentially try to write it as simply as you can. There shouldn't be any more multiplication, dividing, adding, or deleting to be done when the process is finished.

Given equation,

m-(8-3m)

=m-8+3m

=4m+8

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Answer:

-1

Step-by-step explanation:

The  graph shows a function and its is the graph in option A.

The original path is reflected on the line y = x. The two functions are said to be inverses of one another if the graphs of both functions are symmetric with respect to the line y = x. This is due to the fact that (y, x) lies on the inverse function of the function if (x, y) lies on the original function.

The inverse function is shown on a graph with the use of a vertical line test. The line has a slope and travels through the origin.

Instance is the  f(x) = 2x + 5 = y. Then, is the inverse of \(g(y) = \frac{ (y-5)}{2} = x\) f(x).Reflecting over the y and x gives us the function of the inverse.

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Answer:

-12x^2+15x

Step-by-step explanation:

-3x(4x-5)

Distributive property:

-3x*4x-(-3x)*5

-3*4x^2+3*5x

Simplify:

-12x^2+15x

Answer:

80% increase

Step-by-step explanation:

Answer:

\(y - 3 = - 4(x + 2)\)

Answer:

$541

Step-by-step explanation:

1). $550 - $120 = $430 left in her bank account.

2). $430 + $200 = $630 in her bank account.

3). $630 - $89 = $541 left in her bank account.

(Withdraw means removing some of your money out of your bank account, and deposit means putting money back in your bank account)

So, therefore, after all of those transactions, Ms. Lawrence's bank account has $541.

Hope this helps! <3

Answer:

y= x + 2

Hope this helps.

The approximate temperature rise from 10:00 to 10:45 is 4 * 0.75 = 3 degrees and in condition (ii) T(10)=95,T ′ (10)=−4,T ′′ (10)=3 with a cooling trend and a decreasing rate of temperature increase is the better news for someone who dislikes hot weather.

(a) To approximate the temperature rise from 10:00 to 10:45, we can use the fact that the derivative of the temperature function, T'(t), gives us the rate of change of temperature at any given time. Since T'(10) = 4, it means that at 10:00, the temperature is increasing at a rate of 4 degrees per hour.

To find the approximate temperature rise from 10:00 to 10:45, we can multiply the rate of change by the time interval. The time interval is 45 minutes, which is equivalent to 45/60 = 0.75 hours.

Therefore, the approximate temperature rise from 10:00 to 10:45 is 4 * 0.75 = 3 degrees.

(b) The better news for someone who does not like hot weather would be condition ii: T(10) = 95, T'(10) = -4, T''(10) = 3.

In condition ii, the initial temperature T(10) is 95 degrees, which indicates that it is already quite hot. However, the negative value of T'(10) = -4 implies that the temperature is decreasing at a rate of 4 degrees per hour at 10:00, indicating a cooling trend. Additionally, the positive value of T''(10) = 3 indicates that the rate of temperature decrease is slowing down, suggesting that the cooling trend is becoming less severe.

In contrast, in condition i, although T(10) is also 95 degrees, the positive value of T'(10) = 4 indicates that the temperature is increasing at a rate of 4 degrees per hour at 10:00, which means it is getting hotter. Furthermore, the negative value of T''(10) = -3 suggests that the rate of temperature increase is decreasing, but it still implies a warming trend.

Therefore, condition ii with a cooling trend and a decreasing rate of temperature increase is the better news for someone who dislikes hot weather.

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The leading coefficient and the degree are 7 and 5

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

-6 - 12x^2 + 7x^5 + 5x

The degree is the highest power in the expression

So, we have

Degree = 5

The leading coefficient is the coefficient of the term with highest power in the expression

So, we have

leading coefficient = 7

Hence, the leading coefficient is 7

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Answer:

7

Step-by-step explanation:

9d=67-4

d=63/9

d=7

Answer:

d = 7

Step-by-step explanation:

9d + 4 = 67

9d = 67 - 4

9d = 63

9d ÷9 = 63 ÷ 9

d = 7

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Evolution can be defined as a change in a characteristic within a population over time.

Evolution refers to the process of change in inherited traits within a population of organisms over successive generations. It is driven by various mechanisms such as genetic variation, natural selection, mutation, gene flow, and genetic drift.

When there is genetic variation within a population, individuals may possess different traits or characteristics. These traits can be physical, behavioral, or physiological. Some traits may provide individuals with advantages in terms of survival and reproduction, while others may be detrimental.

Natural selection acts on this variation, favoring individuals with traits that increase their chances of survival and reproduction in a particular environment.

Over time, individuals with advantageous traits are more likely to pass on their genes to the next generation, leading to an increase in the frequency of those favorable traits in the population. This gradual change in the characteristics of a population is known as evolution.

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Answer: B

Step-by-step explanation:

LJ should corresponds with RQ but it should correspond with PR.

Answer:

B

Segment LJ and Segment RQ

Step-by-step explanation:

look at the congruence statement

JKL≅PQR

as you can see, they do not correspond with one another

and all the other statements are pairs or congruent/corresponding parts

Answer:

Ratio = 4:2

Value of the ratio = 2

The amount of club soda is 2 times the amount of white grape juice

Step-by-step explanation:

not sure of the value of the ratio though ;-;

Answer:

2 1/4

Step-by-step explanation:

I know bc its basic math

Answer:

V% = (100(x - y)/x)%

Step-by-step explanation:

We are given;

Selling price with VAT = Rs. x

Selling price without VAT = Rs. y.

Thus; VAT = Rs. (x - y)

Rate of VAT(V%) = ((x - y)/x) × 100%

= (100(x - y)/x)%

The value of the copier after 3 years and 6 months can be found by substituting t = 3.5 into the function and solving for V. The salvage value of the copier can be found by substituting t = 5 into the function and solving for V.

After 3 years and 6 months of use, the copier is worth $5,800. This can be found by substituting t = 3.5 into the function V(t)-3600t+20000: V(3.5) = 3600(3.5) - 20000 + 20000 = $5,800.

The salvage value of the copier after 5 years of use is $4,000. This can be found by substituting t = 5 into the function V(t)-3600t+20000: V(5) = 3600(5) - 20000 + 20000 = $4,000. This is the value of the copier when it is sold or replaced after 5 years of use.

The domain of the function is all real numbers because time and value can take on any real value. However, since the function is only defined for the first 5 years of use, t must be between 0 and 5.

The graph of the function is a downward-sloping line with an intercept of $20,000 on the y-axis and a slope of -3600. This means that the value of the copier decreases by $3,600 each year. At t = 0, the copier is worth $20,000, and after 5 years, it is worth $4,000. The graph is a straight line because the function is linear.

Complete Question:

The function V(t)-3600t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use. a. What is the value of the copier after 3 years and 6 months? After 3 years and 6 months, the copier is worth $ b. What is the salvage value of the copier if it is replaced after 5 years? After 5 years, the salvage value of the copier is ts c. State the domain of this function. d. Sketch the graph of this function. 20000 18000 16000 14000 12000 10000 8000 6000+ 4000 2000 4 .

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Answer:

linear

Step-by-step explanation:

you can tell its linear bc its in a straight line

hope this helps <3

The number of independent variables that must be controlled depends on the specific movement being performed and the goals of the individual performing the movement.

The number of independent variables that must be controlled when an individual completes a movement depends on the complexity of the movement and the context in which it is being performed. However, some common independent variables that are often controlled when an individual completes a movement include:

Kinematics: the position, velocity, and acceleration of the body parts involved in the movement.

Dynamics: the forces and torques acting on the body during the movement.

Environmental factors: the physical characteristics of the environment in which the movement is being performed, such as gravity, friction, and obstacles.

Cognitive factors: the mental processes involved in planning and executing the movement, such as attention, decision-making, and memory.

Feedback: the sensory information that is received during the movement, such as proprioceptive feedback from the muscles and joints, and visual feedback from the environment.

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A) The given problem can be considered as an experiment as the researcher is trying to observe the effect of a new drug on quitting smoking.

B) In this experiment, the control group is composed of the participants who received skin patches with no drugs. They are used for the comparison of the effects of the treatment.

C) The treatment group in this experiment is composed of the participants who received skin patches with the new drug. This group is used to analyze the effect of the treatment.

D) Yes, there is a placebo being used in this experiment, which is the skin patch without the new drug. It is used to evaluate the effectiveness of the new drug.

Explanation:

An experiment is a study in which the researcher changes one or more variables and observes or measures the effect of those changes on another variable. In this given problem, the researcher is trying to observe the effect of a new drug on quitting smoking. Thus, it can be considered an experiment.

The control group is a group of participants who do not receive the treatment and are used for comparison with the treatment group. In this experiment, the participants who received skin patches with no drugs acted as the control group.

The treatment group, on the other hand, is a group of participants who receive the treatment and are used to analyze the effect of the treatment. In this experiment, the participants who received skin patches with the new drug acted as the treatment group.

A placebo is an inactive substance that has no therapeutic effect but is used in studies to evaluate the effectiveness of a drug or intervention. In this experiment, the skin patch without the new drug is used as a placebo to evaluate the effectiveness of the new drug. Thus, it is being used in the given experiment.

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The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

µ = p

The standard deviation of this sampling distribution of sample proportion is:

σ = √p(1-p)/n

The information provided is:

p = 0.14

n = 41

As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.

Compute the values of P(p^ - p >0.04) as follows:

P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411

= P(Z>2.33)

= 0.990

Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990

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National income increases, causing interest rates to increase - A) demand for loanable funds shifts outward.

Expansionary fiscal policy does not increase output, it only increases interest rates - E) the IS curve shifts outwards while the LM curve is vertical.

Nominal wages grow faster than the price level - B) real wages increase.

Firms become more confident about the future - D) the demand for money decreases and interest rates decrease.

Credit cards are introduced into the economy - C) the demand for money increases.

When national income increases, it leads to an outward shift in the demand for loanable funds, resulting in increased interest rates. This is because higher national income implies a greater demand for borrowing and investment, leading to increased demand for loanable funds.

Expansionary fiscal policy, which involves increasing government spending or reducing taxes, can lead to an outward shift in the IS curve. However, if the LM curve is vertical, it indicates that the central bank is controlling the money supply to maintain a fixed interest rate. In this case, expansionary fiscal policy will only result in increased interest rates and not increase output.

When nominal wages grow faster than the price level, it leads to an increase in real wages. Real wages refer to wages adjusted for inflation. If nominal wages increase at a faster rate than prices, it means workers have increased purchasing power, resulting in an increase in real wages.

When firms become more confident about the future, it leads to a decrease in the demand for money. Increased confidence encourages investment and spending, reducing the demand for holding money as firms are more willing to invest their funds rather than hold them.

The introduction of credit cards into the economy increases the convenience of transactions and allows individuals to easily access credit. This leads to an increase in the demand for money, as individuals require more money for transactions and credit card payments.

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a) Putting 5 cos²x+4 cosx = 1 in standard quadratic trigonometric equation form:To put the equation in standard quadratic trigonometric equation form, move all the terms to the left-hand side of the equation and simplify it. Therefore, 5 cos²x + 4 cosx - 1 = 0 is the standard quadratic trigonometric equation form.b) Using the quadratic formula to factor the equation.The quadratic formula is utilized to factor the equation. For any quadratic equation of the form ax²+ bx + c = 0, the quadratic formula is x = {-b ± √(b² - 4ac)} / 2a.5 cos²x + 4 cosx - 1 = 0 is the equation that we need to factor.Now substitute a = 5, b = 4, and c = -1 in the quadratic formula.x = {-4 ± √(4² - 4(5)(-1))} / 2(5)x = {-4 ± √(16 + 20)} / 10x = {-4 ± √36} / 10x = {-4 ± 6} / 10Therefore, x = -1 or x = 1/5 are the roots of the equation. c) Solutions to the equation to two decimal places, where 0° ≤ x ≤ 360°To find the value of x between 0 and 360 degrees, we must use an inverse trigonometric function.Cosine inverse is the inverse of cosine function that gives us the angle whose cosine is a given value. Cos -1 or arccos is used to denote the inverse of cosine function. cos -1 (1/5) = 78.46 and cos -1 (-1) = 180°, because the cosine function is negative between 90° and 270°. Therefore, the solution to the equation 5 cos²x + 4 cosx - 1 = 0, where 0° ≤ x ≤ 360°, is 78.46°.

The line integral ∫F⋅dr with the lower limit \(C_{1}\) is 52/15 and ∫F⋅dr with the lower limit \(C_{2}\) is 10/3. F is not a gradient vector field. F is not conservative.

To compute the line integrals, we need to parameterize the given curves \(C_{1}\)(t) and \(C_{2}\)(t) and then evaluate the dot product between the vector field F and the tangent vector dr. Let's calculate each line integral:

For \(C_{1}\)(t) = (t, \(t^{2}\)):

The tangent vector d\(r_{1}\) = (d\(x_{1}\) , d\(y_{1}\) ) = (dt, 2t dt)

The dot product F⋅d\(r_{1}\) = (\(x^{2}\) + \(y^{2}\)) d\(x_{1}\)  + (8xy) d\(y_{1}\)

= (\(t^{2}\) + \(t^{4}\) ) dt + (8t(\(t^{2}\))) (2t dt)

= (\(t^{2}\) + \(t^{4}\) + 16\(t^{4}\) ) dt

= (17\(t^{4}\)  + \(t^{2}\)) dt

Integrating (17\(t^{4}\)  + \(t^{2}\)) with respect to t from 0 to 1:

∫(17\(t^{4}\)  + \(t^{2}\)) dt = [ (17/5)\(t^{5}\) + (1/3)\(t^{3}\) ] evaluated from 0 to 1

= (17/5) + (1/3) - 0

= 17/5 + 1/3

= 52/15

The line integral ∫F⋅dr with the lower limit \(C_{1}\) is 52/15.

For \(C_{2}\) (t) = (t, t):

The tangent vector d\(r_{2}\) = (d\(x_{2}\) , d\(y_{2}\) ) = (dt, dt)

The dot product F⋅ d\(r_{2}\) = (\(x^{2}\) + \(y^{2}\)) d\(x_{2}\) + (8xy)  d\(y_{2}\)

= ( \(t^{2}\) +\(t^{2}\)) dt + (8t(t)) dt

= (2\(t^{2}\)  + 8\(t^{2}\) ) dt

= 10\(t^{2}\)  dt

Integrating 10 \(t^{2}\)  with respect to t from 0 to 1:

∫10 \(t^{2}\)  dt = (10/3) \(t^{3}\)  evaluated from 0 to 1

= (10/3) - 0

= 10/3

The line integral ∫F⋅dr with the lower limit  \(C_{2}\) is 10/3.

To determine whether F is a gradient vector field, we need to check if its line integrals are path-independent (i.e., the line integrals are only dependent on the endpoints and not the path taken). If the line integrals are path-independent, then F is a conservative vector field and can be expressed as the gradient of a scalar potential function.

From our calculations, we observe that the line integrals for \(C_{1}\) and  \(C_{2}\) are different. Therefore, F is not a conservative vector field and cannot be expressed as the gradient of a scalar potential function.

In summary:

The line integral ∫F⋅dr with the lower limit C1 is 52/15.

The line integral ∫F⋅dr with the lower limit  \(C_{2}\) is 10/3.

F is not a gradient vector field since its line integrals depend on the path taken.

F is not conservative.

Correct Question :

Consider The Vector Field F=(\(x^{2}\)+\(y^{2}\),8xy). Compute The Line Integrals ∫F⋅dr with lower limit C1 And ∫F⋅dr with lower limit  \(C_{2}\), Where \(C_{1}\)(t)=(t,\(t^{2}\)) And \(C_{2}\)(t)=(t,t) For 0≤t≤1.  Can you decide from your answers whether or not F is a gradient vector field? Why or why not?  Is F conservative?(Yes/No)

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The resultant moment about a both forces is zero. The statement is true.

A man B exerts a force on the rope, P = 30 lb

To find:

The magnitude of force, F

Consider a statement:

"The resultant moment about A of both forces is Zero."

Diagram attached at the end of the  solution

\($ \theta=\tan ^{-1}\left(\frac{3}{4}\right) \\\)

\(& \theta=36.87^0\)

To prevent the pole from rotating, so that the resultant moment is about A = 0

We will apply the equilibrium Equation \($\sum \mathrm{M}_{\mathbf{A}}=0$\)

Here force \($P \times \sin (45)$\) and \($F \times \sin (\theta)$\) will not produce the moment at A.

Taking clockwise moment as a negative and anticlockwise moment as a positive.

\(& \mathrm{P} \times \cos (45) \times(18)-\mathrm{F} \times \cos (\theta) \times 12=0 \\\)

\(& 30 \times \cos (45) \times(18)=\mathrm{F} \times \cos (\theta) \times 12 \\\)

\($ \mathrm{~F}=\frac{30 \times \cos (45) \times(18)}{\cos (36.87) \times 12} \\\)

F = 39.77 lb

Based on the given parameters,

The magnitude of force, F = 39.77 lb

So there exists the force by considering the resultant moment about an of both forces as zero.

The statement is true.

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Let us assume a value, a for the other part of the base. thus, the length of the base of the triangle is d + a

Considering the right angle traingle containing y degrees,

opposite side = h

adjacent side = a

Tan# = opposite side/adjacent side

tan y = h/a

a = h/tany

Considering the right angle traingle containing x degrees,

opposite side = h

adjacent side = a + d

Tan# = opposite side/adjacent side

tan x = h/(a + d)

a + d = h/tanx

a = h/tanx - d

If we equate both a's, it becomes

h/tany = h/tanx - d

d = h/tanx - h/tany

Answer:

13) x=n-11

15) x=3*10

Step-by-step explanation:

I used x as the variable. The questions are pretty straightforward. They are asking you to put the terms in the description on the right side of the equation. The questions = x. That was probably confusing, but it is correct. I hope this helped!

Product of 3 and 10 and12