Jake has 4 hours before bedtime. He must spend 1 1/2 hours doing homework. The rest of the time will be spent doing puzzles. It takes Jake 3/4 hour to
complete each puzzle. Write an equation that models the number of puzzles (p) that Jake can complete before bedtime.

Answer: See attached.

Step-by-step explanation:

        This slope-intercept form equation shows us that there is a y-intercept of -7. This means that (0, -7) will be a point on the line. Next, we have a slope of positive 3. This means we will count up three units, right one unit, plot a point. Then we repeat.

Answer:

start at the y-intercept, plot some points using the slope, then connect them using a straight line.

Step-by-step explanation:

Generally you'll have an equation in slope-intercept form, which is denoted as: \(y=mx+b\)

This is a really useful form for a couple of reasons, and it has two key features. Firstly, the "m" represents the slope of the linear equation.

This makes sense the definition of slope is: \(\frac{\text{change in y}}{\text{change in x}}\)

and we can generally define the points:

\(\text{at x = 1, y = }m(1)+b\implies m+b\\\text{at x = 2, y = } m(2)+b\implies m + m + b\\\text{at x = 3, y = }m(3) + b\implies m + m + m +b\\\text{and so on...}\)

as the x value increases by 1, the change in y is the "m" value, we have one more "m" than the previous x-value, so the slope is the "m" value, which is the coefficient of the x variable.

The second key feature of slope-intercept form is the y-intercept, which is represented as "b" in this form. This also makes sense because the y-intercept is simply when the x-value is zero, and if you plug in x=0 into the equation, you're only left with the "b" value

Knowing these two things we can analyze the equation given:

\(y = 3x-7\)

since it's given in slope-intercept form, we know that slope = 3, and y-intercept = -7. We immediately know one point, which is the y-intercept, since the x-value is going to be zero at the y-intercept, so one point on the graph is: (0, -7)

now from this point we can draw the graph by going to the right one, and up three, by definition of a slope (as x increases by 1, the y-value increases by 3).

We can do something similar on the left side, except instead of right one and up three, we go left one, and down three. You may be asking why down three? Well as you go right one, you go up three, this means if you compare the previous point to the new point, the previous point is down three compared to the new point (which is to the right one), so if you were to go back, you would be going left one and down three.

Now from these points you can do the same thing to extend the line a bit, and since it's a linear equation you can connect them using a straight line.

I also attached a graph from desmos to illustrate what I was saying a bit and also show the graph.

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

me too (help)

Step-by-step explanation:

The odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

Since Jenny won a charity raffle, and her prize will be randomly selected from the 9 prizes shown below, and the prizes include 7 rings, 1 camera, and 1 headset, to find the odds against Jenny winning a headset, and find the odds in favor of Jenny winning a headset, the following calculations must be performed:

· 1 headset out of 9 total prizes

· 1/9 = headset

· 1/9 x 100 = 11.11%

· 100 - 11.11 = 88.89%

Therefore, the odds against Jenny winning a headset are 88.89% or 8 out of 9, and the odds in favor of Jenny winning a headset are 11.11% or 1 out of 9.

The probability that he receives an invitation to work in a bank given that he defends his diploma excellently is \(\mathbf{0. \overline 6}\)

The reason for the above probability value is as follows;

The known parameters are;

The probability that a graduate of the Faculty of Finance will defend the diploma excellently, P(A) = 0.6

The probability that he will defend perfectly and receive an invitation to work at a bank, P(A∩B) = 0.4

The unknown parameter is;

The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, \(\mathbf {P(B \ | \ A)}\)

The process;

\(\mathbf{ P(B \ | \ A)}\) is found using the conditional probability formula as follows;

\(\mathbf {P(B \ | \ A) = \dfrac{P(A \cap B) }{P(A)}}\)

Plugging in the values, we get;

\(P(B \ | \ A) = \dfrac{0.4 }{0.6} = \dfrac{2}{3} = 0. \overline 6\)

The probability that the student will receive an invitation from the bank given that the student defend the diploma excellent, \(P(B \ | \ A)\) = \(\mathbf {0. \overline 6}\)

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The two new wrestlers must weigh 164 pounds each in order for the median to increase by 3 pounds.

Median is used to identify the central tendency of the data and is calculated by sorting the data in order from smallest to largest and then selecting the middle value.

Since the median weight of the wrestlers increases by 3 pounds, the median of the new data set (with the two new wrestlers) must be 153 pounds.

To calculate the weights of the two new wrestlers, we need to arrange the data set in ascending order first.

When the two new wrestlers are included, the new data set looks like this: 112, 130, 142, 150, 178, 206, x, y.

The median number in this data set is the average of the third and fourth numbers, 150 and 178.

Thus, the equation is written as

(150 + 178) / 2 = 164.

We can then solve this equation to find the weights of the two new wrestlers.

150 + 178 = 328

328 / 2 = 164.

So, the two new wrestlers must weigh 164 pounds each in order for the median to increase by 3 pounds.

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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Answer:

Domain: All Real Numbers

Step-by-step explanation:

Since this function is a linear function, it will use any x-value in order to continue with being a linear function. Therefore, if the line goes on for infinity, every x-value will be used for infinity. Therefore, the domain will be All Real Numbers since every number on the x-axis has a possibility of being used.

Answer:

  3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

  0 = -16t^2 +13.4t +120

  0 = t^2 -0.8375t -7.5 . . . . divide by -16

  0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

  0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

  √7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

  t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

  (t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

Comment on the question

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

Answer:

\(2 + 12 + 24 = 38mile \: per \: hour\)

Answer:

characteristics of a Traditional economy:

A traditional economy is a system that relies on customs, history, and time-honored beliefs. Tradition guides economic decisions such as production and distribution. Traditional economies depend on agriculture, fishing, hunting, gathering, or some combination of the above. They use barter instead of money.

characteristics of a Command economy:

The government creates a central economic plan for all sectors and regions of the country. The government allocates all resources according to the central plan. The central plan sets the priorities for the production of all goods and services.

characteristics of a Free Market economy:

Private property, Freedom of choice, Motivation of self intrest, competition, limited government.

benefits of economic freedom:

It is the principles of economic freedom—free markets, rule of law, protection of private property, and open trade—that boost prosperity and reduce costs so that societies can protect their environments, improve health, and broaden access to education

benefits of competition:

Competition in America is about price, selection, and service. it benefits consumers by keeping prices low and the quality and choice of goods and services high. Competition makes our economy work.

role the government play in the US economy:

The U.S. government's role in the economy can be broken down into two basic sets of functions: it attempts to promote economic stability and growth, and it attempts to regulate and control the economy.

Step-by-step explanation:

Answer:   49.92

Step-by-step explanation: I had that question on my Exam

Answer:

error in Step 2

Step-by-step explanation:

2(x - 3) + 3x = 19

Step 1 : 2x - 6 + 3x = 19 ← simplify left side by collecting like terms

Step 2 : 5x - 6 = 19 ← add 6 to both sides

Step 3 : 5x - 6 + 6 = 19 + 6

Step 4 : 5x = 25 ← divide both sides by 5

Step 5 : x = 5

Error was made by student in Step 2 who should have added 2x and 3x, not multiplied 2 × 3

f(x) = x becomes g(x) = (1/5)x through vertical compression by a factor of 5.

Answer:

Step-by-step explanation:

We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:

x3 = 512

To solve for x, we need to take the cube root of both sides of the equation:

x = ∛512

Using a calculator or simplifying by prime factorization, we can find that:

512 = 2^9

So,

∛512 = ∛2^9 = 2^3 = 8

Therefore, there were 8 fish in the aquarium in 2016.

Answer:

Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):

x3 = 512

To solve for x, we can isolate x by dividing both sides of the equation by 3:

x = 512/3

x = 170.67 (rounded to two decimal places)

Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:

x ≈ 171

So there were 171 fish in the aquarium in 2016.

Step-by-step explanation:

The statements that are listed above that are not propositions include the following:

A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.

From the given statements,the statement that is a true proposition include the following:

The statement that is a false proposition include the following:

The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.

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Answer:

23. Similar as well as congruent triangle

25. Conguent triangle

Step-by-step explanation:

Answers:

23. Not enough information

25. Congruent (by the HL theorem)

HL = hypotenuse leg

=============================================

Explanation for problem 23.

Check out figure 1 shown below.

I have marked the given diagram with light blue and light pink to show which angles are congruent.

Because lines UN and TC are parallel, we know the following alternate interior pairs are congruent.

Therefore, we can establish one link of paired congruent angles of the triangles LNU and TCH. However, we cannot determine any other angle pairings. Why not? Because we don't know if segment UL is parallel to segment TH. If they were parallel, then we could establish something like angle LUN = angle CHT as one alternate interior pairing.

But again, we don't know if UL is parallel to TH. The arrow markers aren't shown for these segments.

Therefore, we simply don't have enough information to determine if the triangles are similar or congruent.

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

Explanation for problem 25.

Luckily this problem will provide sufficient info to prove the triangles KSR and ISR are congruent.

We start with the given info that KR = SI due to the identical tickmarks. This represents one node in the flowchart (see figure 2).

Another node is angle RKS = angle RIS because both are right angles, aka 90 degree angles.

A third node is SR = SR because of the reflexive property.

Those three nodes then feed into the final conclusion node that triangle KSR = triangle ISR. The reasoning is "HL theorem" where HL = hypotenuse leg. This theorem works for right triangles only.

Take note how I structured the proof so that it flows from top to bottom. The three nodes side by side are related so they share the same row.

There are many other ways to make the flowchart, so don't feel obligated to use this format. Use whatever works best for you.

The end behavior of the function f(n) = 3(n + 2)²(n - 3)(n - 2) is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function for this problem is given as follows:

f(n) = 3(n + 2)²(n - 3)(n - 2).

Considering the degree, the function can be interpreted as follows:

\(3n^4\)

(for the limit when the input goes to infinity we consider only the term with the highest degree).

The leading coefficient is positive and the exponent is even, hence the end behavior is given as follows:

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Answer:

Step-by-step explanation:

The number is 60:

Divide the amount and decimal of the percentage to be extracted

Case 1

\(\frac{21}{0.35} =60\)

Case 2

\(\frac{54}{0.9} =60\)

Now the 55% of this number is:

\(60(0.55)=33\)

Hope this helps

Answer: As the order quantity increases, annual ordering cost increases

Step-by-step explanation:

The Economic Order Quantity (EOQ) is simply referred to as the amount of units that should be added by a company to its inventory with each order in order to minimize total inventory costs such as order costs, holding costs, and shortage costs.

The incorrect option is that "as the order quantity increases, annual ordering cost increases". It should be noted that ordering costs are simply the expenses that are incurred in order for an order to be created and processed to a supplier. It should be noted that as the ordering quantity increases, it doesn't mean that the annual ordering costs also increase.

Approximately 1.18 hours the concentration is highest.

The given function is c(t)=100t/t² +85.

When the concentration is highest, the function becomes

100t/t² +85 =0

100/t +85=0

100+85t=0

85t=100

t=100/85

t=1.18 hours

Therefore, approximately 1.18 hours the concentration is highest.

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Transformation involves changing the location of a shape

The image of P after the transformation is: (-5,-2)

The vertices are given as:

\(\mathbf{P = (-8,6)}\)

\(\mathbf{Q = (1,-3)}\)

\(\mathbf{R = (-6,-3)}\)

The rule of reflection across line y = 2 is:

\(\mathbf{(x,y) \to (x,4-y)}\)

So, the image of P, after the reflection is:

\(\mathbf{P' = (-8,4-6)}\)

\(\mathbf{P' = (-8,-2)}\)

The rule of translation 3 units right is:

\(\mathbf{(x,y) \to (x + 3,y)}\)

So, we have:

\(\mathbf{P" = (-8 + 3,-2)}\)

\(\mathbf{P" = (-5,-2)}\)

Hence, the image of P after the transformation is: (-5,-2)

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Answer:

( x,y) = ( -2,2)

Step-by-step explanation:

I took this test

Answer:

(2, 6)

Step-by-step explanation:

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

1

Step-by-step explanation:

5(0)+1=1 because 5x0=0 then add the 1

The value of the function f (x) = 5x + 1 at x equal to zero will be 1.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given function is f (x) = 5x + 1. The value of the function at x equal to 0 will be calculated as below:-

f (x) = 5x + 1

f (0) = 5 x 0 + 1

f (0) =  0 + 1

f (0) = 1

Therefore, the value of the function f (x) = 5x + 1 at x equal to zero will be 1.

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The answer is [ all real numbers ]

The domain are the input values which makes the function defined and real.

Since we don't have any constraints or any undefined points, the domain could be literally anything. Thus proves out answer.

Best of Luck!

Answer:

Step-by-step explanation: