PLEASE TRY TO HELP I'M STRUGGLING
Write an equation of the line containing the given point and perpendicular to the given line:
​(6​, -9​); 7x+4y=3

Answer:  The required solution is [tex]y=50e^{0.1386t}.[/tex]

Step-by-step explanation:

We are given to solve the following differential equation :

[tex]\dfrac{dy}{dt}=ky~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

where k is a constant and the equation satisfies the conditions y(0) = 50, y(5) = 100.

From equation (i), we have

[tex]\dfrac{dy}{y}=kdt.[/tex]

Integrating both sides, we get

[tex]\int\dfrac{dy}{y}=\int kdt\\\\\Rightarrow \log y=kt+c~~~~~~[\textup{c is a constant of integration}]\\\\\Rightarrow y=e^{kt+c}\\\\\Rightarrow y=ae^{kt}~~~~[\textup{where }a=e^c\textup{ is another constant}][/tex]

Also, the conditions are

[tex]y(0)=50\\\\\Rightarrow ae^0=50\\\\\Rightarrow a=50[/tex]

and

[tex]y(5)=100\\\\\Rightarrow 50e^{5k}=100\\\\\Rightarrow e^{5k}=2\\\\\Rightarrow 5k=\log_e2\\\\\Rightarrow 5k=0.6931\\\\\Rightarrow k=0.1386.[/tex]

Thus, the required solution is [tex]y=50e^{0.1386t}.[/tex]

Answer:

[tex]\frac{1}{5}\ln(2)=k[/tex]

Solution without isolating [tex]y[/tex]:

[tex]\ln|y|=\frac{1}{5}\ln(2)x+\ln(50)[/tex]

Solution with isolating [tex]y[/tex]:

[tex]y=50 \cdot 2^{\frac{1}{5}x}[/tex]

Step-by-step explanation:

[tex]\frac{dy}{dx}=ky[/tex]

We will separate the variables so we can integrate both sides.

Multiply [tex]dx[/tex] on both sides:

[tex]dy=ky dx[/tex]

Divide both sides by [tex]y[/tex]:

[tex]\frac{dy}{y}=k dx[/tex]

Now we may integrate both sides:

[tex]\ln|y|=kx+C[/tex]

The first condition says [tex]y(0)=50[/tex].

Using this into our equation gives us:

[tex]\ln|50|=k(0)+C[/tex]

[tex]\ln|50|=C[/tex]

So now our equation is:

[tex]\ln|y|=kx+\ln(50)[/tex]

The second condition says [tex]y(5)=100[/tex].

Using this into our equation gives us:

[tex]\ln|100|=k(5)+\ln(50)[/tex]

[tex]\ln(100)=k(5)+\ln(50)[/tex]

Let's find [tex]k[/tex].

Subtract [tex]\ln(50)[/tex] on both sides:

[tex]\ln(100)-\ln(50)=k(5)[/tex]

I'm going to rewrite the left hand side using quotient rule for logarithms:

[tex]\ln(\frac{100}{50})=k(5)[/tex]

Reducing fraction:

[tex]\ln(2)=k(5)[/tex]

Divide both sides by 5:

[tex]\frac{\ln(2)}{5}=k[/tex]

[tex]\frac{1}{5}\ln(2)=k[/tex]

So the solution to the differential equation satisfying the give conditions is:

[tex]\ln|y|=\frac{1}{5}\ln(2)x+\ln(50)[/tex]

Most likely they will prefer the equation where [tex]y[/tex] is isolated.

Let's write our equation in equivalent logarithm form:

[tex]y=e^{\frac{1}{5}\ln(2)x+\ln(50)}[/tex]

We could rewrite this a bit more.

By power rule for logarithms:

[tex]y=e^{\ln(2^{\frac{1}{5}x})+\ln(50)}[/tex]

By product rule for logarithms:

[tex]y=e^{\ln(2^{\frac{1}{5}x} \cdot 50)}[/tex]

Since the natual logarithm and given exponential function are inverses:

[tex]y=2^{\frac{1}{5}x} \cdot 50[/tex]

By commutative property of multiplication:

[tex]y=50 \cdot 2^{\frac{1}{5}x}[/tex]

Answer:$864

Step-by-step explanation:

Since Mohammad makes a payment of $96 monthly, the amount paid by Mohammad for 9months will be 9×$96 that's $96 in 9places

9 × $96 = $864

Answer:

24

Step-by-step explanation:

This problem solution involves permutation to calculate number of arrangements of flags. The reason of using permutation in this scenario is that it is mention in the statement that flags are hanging in a particular order and when order is concern we use permutation. According to permutation definition nPr=n!/(n-r)! and so, the unique signals that are made by using 4 flags are 4P3=4!/(4-3)!=24. Here n=total number=4 and r=number chosen=3.

Final Answer:

The correct answer is D. 24.

Explanation:

To solve this problem, we will calculate the number of permutations of 4 distinct flags taken 3 at a time because the order of the flags matters and no flag can be used more than once in a single signal.
The formula for permutations of n items taken k at a time is given by:
P(n, k) = n! / (n - k)!
Where n! represents the factorial of n, which is the product of all positive integers up to n.
In our case, we have n = 4 flags, and we want to take k = 3 flags to form a signal.
First, we evaluate 4 factorial (4!):
4! = 4 × 3 × 2 × 1 = 24
Now, we need to evaluate the factorial of (4 - 3), which is (1!):
1! = 1
Using the permutation formula, we find the number of unique signals:
P(4, 3) = 4! / (4 - 3)!
P(4, 3) = 24 / 1! (since (4 - 3)! is 1!)
P(4, 3) = 24 / 1
P(4, 3) = 24
Therefore, there are 24 unique signals that can be made using 4 different flags.
The correct answer is D. 24.

Answer:

the appropriate conclusion is that

The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.

Step-by-step explanation:

Since the p-value is small, it indicates statistically significant results. This means that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014.

The samples provide evidence of a statistically significant difference in the starting salaries between chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014, as indicated by the p-value of 0.0142, which is below the 0.05 significance level.

Detailed explanation:

The journalist's question concerns whether there is a significant difference in the starting salaries of chemical engineering and electrical engineering graduates at the University of Texas at Austin for the academic year 2013-2014. The test statistic is t = 2.4693 with a p-value of 0.0142.

The samples provide evidence that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014. This conclusion is reached because the p-value is less than the common significance level of 0.05, thus we reject the null hypothesis, which states that there is no difference in starting salaries between the two groups.

Hence the final answer is that there is a statistically significant difference between the starting salary of chemical engineering and electrical engineering graduates at the University of Texas at Austin for 2013-2014

Hence the first option is correct

Answer:

Alex has driven Total of 1400 miles.

Step-by-step explanation:

Given:

Miles Driven by Alex = 588 miles

Percentage mile driven by Alex = 42%

Solution:

Let the total miles driven by Alex be 'x'.

And given that 42% of the total miles he drive for work, which is 588 miles.

That means x multiplied with 42% is equal to 588.

So framing the above sentence in equation form, we get;

[tex]x\times 42\% =588[/tex]

Now we have to remove the percentile.

For this we have to divide 42 by 100, then we get;

[tex]x\times\frac{42}{100} = 588[/tex]

Multiplying by 100 on both side, using Multiplication Property we get;

[tex]x\times\frac{42}{100}\times 100 = 588\times 100\\\\42x=58800[/tex]

Dividing both side by 42 using Division Property we get;

[tex]\frac{42x}{42}=\frac{58800}{42}\\\\x= 1400 \ miles[/tex]

Hence Alex has driven Total of 1400 miles.

Answer: 1,400

Step-by-step explanation:%

100

=  

part

whole

42

100

=  

588

x

42x = 58,800

x = 1,400

Step-by-step explanation:

Let t be the height of pole.

Given that the tree is 5 feet shorter than a pole.

Height of pole = t + 15

Also given that the pole is 3 times as tall as the tree.

Height of pole = 3t

So we have

              t + 15 = 3t

                 2t = 15

                   t = 7.5 feet

Height of tree = 7.5 feet

The question asks how tall a tree is if it is 15 feet shorter than a pole which is three times its height. The height of the tree can be found by setting up an equation to represent the problem and then solving for the height of the tree, which is 7.5 feet.

The subject of this question is a mathematical problem dealing with a tree and a pole with their heights related to one another. In the problem, we know that the pole is 15 feet taller than a tree and the pole is also 3 times as tall as the tree. We can set that up as an equation and solve for the height of the tree.

Let's call the height of the tree as 'T' and then, because the pole is three times the height of the tree, we can call the pole's height as '3T'. The problem tells us that the pole is also 15 feet taller than the tree, so we can express the pole's height as 'T + 15' as well.

Now we have two ways to express the pole's height: '3T' and 'T + 15'. We can set those equal to each other and solve for 'T'.

3T = T + 15

Subtract 'T' from both sides to get:

2T = 15

Then divide both sides by 2 and you get T = 7.5. Therefore, the tree is 7.5 feet tall.

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Answer: the total price of the necklace is $91.8

Step-by-step explanation:

The original Price of the necklace at Jared is is $99. It is on sale for 10% off. This means that there is a discount on the original price. The discount is 10/100 × 99 = $9.9

The new price of the necklace at Jared is the original price - the discount. It becomes

99 - 9.9 = $89.1

If there is a 3% tax on the discounted price, the amount of tax would be 3/100×89.1 = $2.673

The total cost of the necklace will be new cost + the amount of tax. It becomes

89.1 + 2.673 = $91.8

Answer:

Step-by-step explanation:

The id attribute requires a unique string to identify the element.

Among the options provided, the attribute of the "an" element that indicates the media type of a linked document is:

C) type="mime-type"

In HTML, when creating links to external resources or documents, the "an" element is typically represented by the "a" anchor tag. This tag often uses the 'type' attribute to specify the media type of the linked document.

For instance, if you have an anchor tag (<a>) linking to a document like a stylesheet, image, or script, you can specify the media type using the 'type' attribute. The 'type' attribute helps the browser interpret the linked document's format or MIME (Multipurpose Internet Mail Extensions) type. An example might look like:

<a href="url_to_linked_document" type="text/css">Link Text</a>

In this example, 'type="text/css"' indicates that the linked document is a CSS file (text/css MIME type), which helps browsers understand how to handle the resource being linked. Therefore, option C) type="mime-type" is the attribute used to indicate the media type of the linked document.

Complete Question:

Identify an attribute of the "an" element that indicates the media type of z linked document.

A) rel-"type"

B) hrefland="lang"

C) type="mime-type"

D) href="url"

Answer:

1) [tex]np\geq 5[/tex]

2) [tex]nq = n(1-p)\geq 5[/tex]

Other conditions that are important are:

3) n is large

4) p is close to 1/2 or 0.5

Step-by-step explanation:

1) Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

2) Solution to the problem

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n, p)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

In order to apply the normal apprximation we need to satisfy these two conditions:

1) [tex]np\geq 5[/tex]

2) [tex]nq = n(1-p)\geq 5[/tex]

Other conditions that are important are:

3) n is large

4) p is close to 1/2 or 0.5

Answer:

26%

Step-by-step explanation:

For similar questions check the following link for flash cards:

https://quizlet.com/207660833/chapter-16l23-25-flash-cards/

The question is about the incidence of mental illness among homeless adults in shelters. The specific percentage is not provided, but the rate is recognized as high, indicating the need for mental health resources to effectively address homelessness.

The question you've asked is related to the prevalence of mental illness among homeless adults residing in shelters. A specific percentage is not given, but it is commonly understood that a significant percentage of the homeless population does struggle with mental illness. However, it is essential to note that the exact percentage can vary due to different factors, such as location, available resources, and demographics. Hence, this information accentuates the need for mental health resources in addressing and alleviating homelessness.

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Answer:

154.2g

Step-by-step explanation:

This is quite straightforward, what we need to add the masses together.

113g + 114g + 27.2g = 154.2g

The total weight of the smartphone, screen protector, and heavy duty phone case is 254.2 grams.

Given that the smartphone weighs 113 g, the screen protector weighs 27.2 g, and the heavy duty phone case weighs 114 g, the total weight (in gram) of the phone, screen protector, and case would simply be the sum of these weights. In this case, we take 113 g + 27.2 g + 114 g which results in 254.2 g as the total weight. Therefore, if you use both a screen protector and a heavy duty case to protect your phone, the total weight would be 254.2 g.

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Final answer:

Jim will not have enough money to buy the car after 2 years with a bank account that pays 9.8% interest compounded continuously. The other bank offering 10% interest compounded semiannually is a better deal as Jim will have enough money to buy the car.

Explanation:

To determine if Jim will have enough money to buy a car that costs $12,160 after 2 years with a bank account that pays 9.8% interest compounded continuously, we can use the formula for compound interest:

A = P * e^(rt)

where A is the ending amount, P is the principal (initial amount), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the number of years. Plugging in the values, we have:

A = $10,000 * e^(0.098*2) = $10,000 * e^0.196 ≈ $11,961.34

Therefore, Jim will not have enough money to buy the car.

To determine if the other bank offering 10% interest compounded semiannually is a better deal, we can use the same formula:

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

where n is the number of times interest is compounded per year. Plugging in the values, we have:

A = $10,000 * (1 + 0.10/2)^(2*2) = $10,000 * (1 + 0.05)^4 = $10,000 * 1.05^4 ≈ $12,265.63

Therefore, the other bank is a better deal as Jim will have enough money to buy the car.

Answer:

0.55 is the probability that Lions will score less than 3 goals.

Step-by-step explanation:

We are given the following in the question:

Number of goals(x):         0         1           2         3          4

             Probability:      0.05     0.15     0.35     0.30     0.25

We have to find the probability that Lions will score less than 3 goals.

[tex]P(X<x) = \displaystyle\sum_{X=0}^{X=x-1}P(x_i)\\\\P(x<3)=P(x=0)+P(x=1)+P(x=2)\\P(x<3)=0.05 + 0.15 + 0.35=0.55[/tex]

0.55 is the probability that Lions will score less than 3 goals.

Final answer:

The probability that the Lions soccer team will score less than 3 goals in a game is 0.55 or 55%.

Explanation:

To find the probability that the Lions soccer team scores less than 3 goals in a game, we need to add up the probabilities of scoring 0, 1, and 2 goals. From Exhibit 5-3, the probability of scoring 0 goals is 0.05, 1 goal is 0.15, and 2 goals is 0.35.

The total probability of scoring less than 3 goals is the sum of these probabilities:

P(0 goals) = 0.05

P(1 goal) = 0.15

P(2 goals) = 0.35

Thus, P(score < 3 goals) = P(0 goals) + P(1 goal) + P(2 goals) = 0.05 + 0.15 + 0.35 = 0.55.

Therefore, the probability that the Lions will score less than 3 goals in a given game is 0.55 or 55%.

Option A

[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

[tex]cos 3x = cos(x + 2x)[/tex]

We know that,

[tex]\cos (a+b)=\cos a \cos b-\sin a \sin b[/tex]

Therefore,

[tex]\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x[/tex]  ---- eqn 1

We know that,

[tex]\sin 2 x=2 \sin x \cos x[/tex]

[tex]\cos 2 x=\cos ^{2} x-\sin ^{2} x[/tex]

Substituting these values in eqn 1

[tex]\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex]  -------- eqn 2

We know that,

[tex]\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x[/tex]

Applying this in above eqn 2, we get

[tex]\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)[/tex]

[tex]\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}[/tex]

[tex]\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x[/tex]

Therefore,

[tex]\cos 3 x=\cos x-4 \cos x \sin ^{2} x[/tex]

Option A is correct

Answer:V(x) = 6x³ + 4x² - 12x - 8

Step-by-step explanation:

The shoe box can either be cube shaped or cubiod shaped. The volume of the box is length × breadth × height

Since Area = Length × Breadth

Volume = Area × Height

V(x) = A(x) × H(x)

A(x) = 2x² - 4

H(x) = 3x + 2

V(x) = (2x² - 4)(3x + 2)

V(x) = 6x³ + 4x² - 12x - 8

Answer:

estimate a population proportion

Step-by-step explanation:

The choices are missing in the question, correct question is:

In a January 2017 Washington Post-ABC News poll, respondents were asked “There is a proposal to offer nearly 140 billion dollars in tax cuts for private companies if they pay to build new roads, bridges and transportation projects. The companies then could charge tolls for people to use these roads, bridges and transportation. Do you support or oppose this proposal?” Of the 1005 people polled, 66 percent of those surveyed said they oppose the above proposal. An objective of this study is to ________ .

a. test a claim about a population mean

b. estimate a population mean

c. test a claim about a population proportion

d. estimate a population proportion

Population proportion estimate will give the percentage of people who support or oppose the proposal of 140 billion dollars in tax cuts for private companies so that they build charge tolled new roads, bridges and transportation projects.

People are asked "Do you support or oppose this proposal?", this shows that the purpose of the study is to estimate a population proportion.

The Washington Post-ABC News poll aimed to calculate public opinion on a policy proposal regarding tax cuts and infrastructural developments paid by private companies. The majority of respondents opposed the proposal signifying its unpopularity among the surveyed population. However, results from this single poll may not represent wider public sentiment.

The question pertains to a public policy proposal. In a Washington Post-ABC News poll from January 2017, participants were asked to indicate their support or opposition to a proposition concerning tax cuts and infrastructure development funded by private companies. The question revolves around an actual policy proposal that could have impacts on the economy and society. The study's objective in this case is to gauge public opinion on the proposal, which could be used to inform policy decisions or strategies by politicians, businesses, or advocacy groups.

The fact that 66 percent of the 1005 people polled opposed the proposal suggests a majority of the respondents were not in favor of the plan. In recognizing such data and understanding its implications, it is important to remember that this is just one poll and may not necessarily represent the broader public's views.

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Answer:

option B

Step-by-step explanation:

given,

sample of person interviewed 110

people voted for A = 67

percentage of the person voted for A = [tex]\dfrac{67}{110}[/tex]

                                                                 = 0.609

now, for all the people

   = 0.609 x 9570

   = 5829 people

now compensating the error

+ 4 % = 1.04 x 5829 = 6062 people

- 4 % = 0.96 x 5829 = 5596 people

so, the range of people voted for candidate A is

5596 to 6062 People

Hence, the correct answer is option B

The price of one burger is Rs 40 and a cup of ice cream is Rs 20.

Step-by-step explanation:

Let,

Price of one burger = x

Price of cup of ice cream = y

According to given statement;

x = y+20      Eqn 1

x+2y=80      Eqn 2

Putting value of x from Eqn 1 in Eqn 2

[tex](y+20)+2y=80\\y+20+2y=80\\3y=80-20\\3y=60[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3}=\frac{60}{3}\\y=20[/tex]

Putting y=20 in Eqn 1

[tex]x=20+20\\x=40[/tex]

The price of one burger is Rs 40 and a cup of ice cream is Rs 20.

Keywords: linear equation, substitution method

Learn more about linear equations at:

LearnwithBrainly

The price of a cup of ice cream is Rs 20, and the price of a burger is Rs 40, determined by setting up equations based on the given cost relationship and total cost.

To find the price of a burger and a cup of ice cream, let's use the information given in the problem. Let B represent the cost of a burger, and I represent the cost of a cup of ice cream. We are told that a burger costs Rs 20 more than a cup of ice cream, so we can write this as B = I + 20. Additionally, we know that the total cost of a burger and two ice creams is Rs 80, which can be represented as B + 2I = 80. Now we can substitute the first equation into the second one to find the cost of each item.

Step 1: Substitute B = I + 20 into B + 2I = 80.

Returns: (I + 20) + 2I = 80

Step 2: Combine like terms.

Returns: 3I + 20 = 80

Step 3: Subtract 20 from both sides.

Returns: 3I = 60

Step 4: Divide both sides by 3.

Returns: I = 20

Now we know that a cup of ice cream costs Rs 20, and from the first equation, a burger costs Rs 20 more than the ice cream, so:

Returns: B = I + 20 = 20 + 20 = Rs 40

The price of a burger is Rs 40, and the price of a cup of ice cream is Rs 20.

Answer:

Step-by-step explanation:

I would divide the answer in two parts

part A

If the given equation is correct, then the equation has no answer

Process

let y = 0 then 5x^2 + 2 = 0. We subtract 2 from both sides 5x^2= -2.

Now we divide each side by 5 and apply square root property

x^2=-2/5  --> x=square root(-2/5). Therefore, the equation has no solution. Complex solution.

Part B

If the given equation is not correct (the exercise is badly copied), then the correct exercise would be 5x^2+3x-2=0

We can solve the polynomial using quadratic formula, and we will obtain

x=-1 and x=2/5.

So the answer X cannot be integer.

Answer:  d. 58

The height of the plant in June 1st is 58 centimeters.

Step-by-step explanation:

Given : On August 1st, a plant was 79 centimeters tall.

In June of that year it grew 12 centimeters, then 9 more centimeters in July.

Order of Month = June → July → August

Then , the height of the plant on June 1st would be

Height in August 1st - Height grew in June - height grew in July

= 79-12-9  centimeters

= 67-9 centimeters

= 58  centimeters

Therefore , the height of the plant in June 1st = 58 centimeters

Hence, the correct answer is d. 58

Answer:

On a unit circle, the point that corresponds to an angle of [tex]0^{\circ}[/tex] is at position [tex](1, \, 0)[/tex].

The point that corresponds to an angle of [tex]90^{\circ}[/tex] is at position [tex](0, \, 1)[/tex].

Step-by-step explanation:

On a cartesian plane, a unit circle is

The circle crosses the x- and y-axis at four points:

Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.

When the angle is equal to [tex]0^\circ[/tex], the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be [tex](1, \, 0)[/tex].

To locate the point with a [tex]90^{\circ}[/tex] angle, rotate the [tex]0^\circ[/tex] segment counter-clockwise by [tex]90^{\circ}[/tex]. The segment would land on the positive y-axis. In other words, the [tex]90^{\circ}[/tex]-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be [tex](0, \, 1)[/tex].

Answer:

Angle of 0º: (1,0)

Angle of 90º: (0,1)

Step-by-step explanation:

A unit circle has a radius of 1.

Therefore, the points on the x- and y-axis are as follows:

    Angle of 0º: (1,0)

    Angle of 90º: (0,1)

    Angle of 180º: (-1,0)

    Angle of 270º: (0,-1)

    Angle of 360º [have now circled back to an angle of 0º]: (1,0)

Answer:

Step-by-step explanation:

For the first one, revenue - cost = profit.  We have equations for revenue and profit, so filling in:

[tex]-.3x^2+150x-cost=-.5x^2+250x-300[/tex]

Let's add cost to both sides to make it positive and bring everything on the right over to the left and combine like terms:

[tex].2x^2-100x+300=cost[/tex]

For the second one:

P(x)*T(x) = [tex](x^2-3x-7)(3x)[/tex]

Distribute the 3x into everything inside the parenthesis to get

[tex]3x^3-9x^2-21x[/tex]

For the second part of that problem, C(x)*P(x) = [tex](x-4)(x^2-3x-7)[/tex]

Distribute the x into everything first to get:

[tex]x^3-3x^2-7x[/tex]

The distribute the -4 into everything to get:

[tex]-4x^2+12x+28[/tex]

Combine the like terms and put everything together to get

[tex]x^3-7x^2+5x+28[/tex]

Answer:

Step-by-step explanation:

Had all received popcorn, the bill would have been 40×$1.75 = $70. The bill was $13.50 more than that. Each hot dog purchased in place of popcorn adds $0.50 to the bill, so the number of hot dogs must be ...

  $13.50/$0.50 = 27

Of course, the remainder of the 40 items were popcorn, so 13 bags of popcorn.

27 hot dogs and 13 bags of popcorn were purchased.

Answer:

Increase savings to 25 percent and decrease clothing to 10 percent

Step-by-step explanation:

i got it right

Zoe should increase her savings to 25% of her income and reduce non-essential expenses like clothing to save for a car more quickly.

To assist Zoe in saving money for a car quickly after moving in with a roommate and having her rent reduced to 25% of her salary, she should adjust her budget to allocate more towards savings.

The most effective strategy for this goal would be to:

Specifically, increasing savings to 25% of her income and decreasing clothing expenses to 10% is an advisable option.

She should avoid increasing expenses in non-essential categories like entertainment or gasoline if her goal is to save for a car as quickly as possible.

Answer:

  31,536,000

Step-by-step explanation:

There are 3600 seconds in an hour and 24 hours in a day, so ...

 (3600 s/h)(24 h/da) = 86400 s/da

Then in 365 days, there are ...

  (365 da)(86400 s/da) = 31,536,000 s

_____

No rounding is needed.

There are 31,536,000 seconds in a year. This is calculated by multiplying 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 365 days in a year.

To calculate the number of seconds in a year, start with the known values of time:

We multiply all these values together to get the number of seconds in a year.

60 seconds/minute * 60 minutes/hour * 24 hours/day * 365 days/year = 31,536,000 seconds/year

To give the answer to the nearest 1000 seconds, we would round it to 31,536,000.

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Answer: 0.0055

Step-by-step explanation:

Let [tex]\overline{x}[/tex] denotes the sample mean amount  that can has.

We assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.1 oz.

i.e. [tex]\mu=12[/tex] and [tex]\sigma=0.1[/tex]

sample size : n= 8

Then, the probability that a sample of 88 cans will have a mean amount of at least 12.09:

[tex]P(\overline{x}\geq12.09)=1-P(\overline{x}<12.09)\\\\=1-P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{12.09-12}{\dfrac{0.1}{\sqrt{8}}})\\\\=1-P(z<2.5456)\ \ [\because z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-0.9945\ \ [\text{By z-table}]\\\\=0.0055[/tex]

Hence, the required sample size = 0.0055

Answer:

Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.

Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.

Step-by-step explanation:

Given:

Number of Miles for Mrs Allan car = 224 miles

Number of gallons of gas required = 8

We need to find the number of gallons of gas required for 560 miles for Mrs. Allan's car.

First we will find, in 1 gallons how many miles does Mrs Allan's Car drives.

For 8 gallons = 224 miles

So for 1 gallons = Number of miles in 1 gallon of gas

By using Unitary method we get;

Number of miles in 1 gallon of gas = [tex]\frac{224}{8}= 28\ miles[/tex]

Now we know that;

for 28 miles = 1 gallon of gas is required.

So for 560 miles = Number of gallon of gas required in 560 miles.

Again by using Unitary method we get;

Number of gallon of gas required in 560 miles = [tex]\frac{560}{28}= 20\ gallons[/tex]

Hence Mrs. Allan's Car will use 20 gallons of gas for 560 miles trip.

Also Given:

Number of Miles for Mrs Owen's car = 210 miles

Number of gallons of gas required = 6

We need to find the number of gallons of gas required for 560 miles for Mrs. Owen's car.

First we will find, in 1 gallons how many miles does Mrs Owen's Car drives.

For 6 gallons = 210 miles

So for 1 gallons = Number of miles in 1 gallon of gas

By using Unitary method we get;

Number of miles in 1 gallon of gas = [tex]\frac{210}{6}= 35\ miles[/tex]

Now we know that;

for 35 miles = 1 gallon of gas is required.

So for 560 miles = Number of gallon of gas required in 560 miles.

Again by using Unitary method we get;

Number of gallon of gas required in 560 miles = [tex]\frac{560}{35}= 16\ gallons[/tex]

Hence Mrs. Owen's Car will use 16 gallons of gas for 560 miles trip.

Answer:

Step-by-step explanation:

The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...

  tan(24°) = (building height)/(500 ft)

  building height = (500 ft)tan(24°) ≈ 222.61 ft

__

Similarly, the height to the top of the flagpole is ...

  total height = (500 ft)tan(27°) ≈ 254.76 ft

The length of the flagpole is the difference of these heights:

  flagpole length = 254.76 ft -222.61 ft = 32.15 ft

The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.

The height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet, according to the principle of trigonometry using tangent function.

The question deals with a mathematical concept called trigonometry. Specifically, we will use the tangent function. Tangent of an angle in a right triangle is the ratio of the side opposite to the angle over the side adjacent to the angle.

Let's denote H as the height of the building and F as the length of the flagpole. We know that Tan(24°) = H / 500 and Tan(27°) = (H+F) / 500. Now we can solve these two equations to find H and F.

First, calculate H. Using the first equation, H = Tan(24°) * 500 ≈ 250.37 feet.

Next, calculate H+F. Using the second equation, H+F = Tan(27°) * 500 ≈ 274.73 feet.

Then, calculate F by subtracting H from the second result. So F = 274.73 - 250.37 = 24.36 feet.

Therefore, the height of the building is approximately 250.4 feet, and the length of the flagpole is approximately 24.4 feet.

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Answer:

JH = 8, GH = 12, and GJ = 10.6

Step-by-step explanation:

According to Midsegment Theorem, a segment that connects the midpoints of two sides of a triangle is half the length of the third side.

GH = ½ DE

JH = ½ DF

GJ = ½ EF

DE is 24, so GH = 12.

JH is half of DF.  Since G is the midpoint of DF, DG is also half of DF.  So JH = DG = 8.

GJ is half of EF.  Since H is the midpoint of EF, HE is also half of EF.  So GJ = HE = 10.6.