on a family road trip mr.peters travels 130 miles in 2 hours . at this rate,how many miles will he travel in 30 minutes

In given word problem Andre has more money than Elena after four weeks.

What is word problem?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Here,

Initial investment of Andre= $50

She add $5 per week for next 4 weeks , then

=> 4×5 = $20

Then total savings of Andre = $50+$20=$70.

Now Initial investment of Elena = $5

She adds $10 for each 4 weeks then

=> 10×4=$40.

Now total savings of Elena = $40+$5=$45.

Here $70>$45.

Hence after 4 weeks Andre has more money than Elena.

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Answer:

Ans: Rs 181.44.

Step-by-step explanation:

The midpoint of the line segment is (-1, -1).

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

It is obtained by averaging the x-coordinates and averaging the y-coordinates of the endpoints of the segment.

Given endpoints

A(− 4, −5) and B(2, 3)

Midpoint of the line segment formula:

Midpoint of a Line Segment : Its x value is halfway between the two x values · Its y value is halfway between the two y values.

Midpoint \(= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2})\)

Midpoint = \((\frac{-4+2}{2} ,\frac{-5+3}{2} )\)

Midpoint = \((\frac{-2}{2}, \frac{-2}{2} )\)

Midpoint = (-1, -1)

The midpoint of the line segment is (-1, -1).

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Answer:

0.80 m/s

Step-by-step explanation:

rate = 40 m / 50 s = 0.8 m/s

Answer: log2-log6=-log3

Step-by-step explanation:

\(\displaystyle\\log2-log6=\\\\log\frac{2}{6} =\\\\log\frac{2(1)}{2(3)}=\\\\log\frac{1}{3} =\\\\log3^{-1}=\\\\-log3\)

Answer:

B on edge $71.72

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Step-by-step explanation:

Answer: B.

Step-by-step explanation:

edge 2023

The minimum sample size needed is 93.

Given:

A political researcher takes a survey of 300 randomly selected registered voters in atlanta, and each person was asked who they plan on voting for in the 2020 mayoral election. 101 said they plan on voting for candidate a, 184 said they plan on voting for candidate b, and 15 were unsure or plan to vote for another candidate. In question 8, the political researcher estimated p, the population proportion of all registered voters in atlanta who plan to vote for candidate a, with a 95% confidence interval. The researcher now wants to estimate p with a margin of error of 3%.

here

n = 101

p = 0.5

e = 5%=0.05

z score at 95% = 1.96

\(n'=\frac{n}{1+\frac{z^2*p(1-p)}{e^2} }\)

On submitting and solving using calculator

n = 93

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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The equivalent ratios table is:

Toss     Dollars  

5             2

30           12

45           18

See the diagram in the attachment that shows the plotted points.

Equivalent ratios are ratios that have the same value when they are compared together.

For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.

Create an equation that models equivalent ratios that can be used to complete the table if:

x = toss

y = dollars

Therefore, given that 30 toss equals $12,

Constant of proportionality, k = y/x = 12/30

k = 2/5.

Plug in the value of k into y = kx:

y = 2/5x.

Therefore:

2 dollars (y = 2), will give:

2 = 2/5(x)

x = 10/2

x = 5 toss

45 tosses (x = 45) will need:

y = 2/5(45)

y = 18 dollars

The equivalent ratios table would be:

Toss | Dollars  

5           2

30        12

45         18

The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.

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Answer:

296, 288, 280, 240

Step-by-step explanation:

y = -8x + 296 is a linear equation by which you're plugging the x values of 0,1,2,7 into it to get a y value.

y = 296 when x = 0,

y = 288 when x = 1,

y = 280 when x = 2,

y = 240 when x = 7.

Cheers!

Answer:

90π in²

Step-by-step explanation:

  r = 3 in

  h = 10 in

     \(\sf \boxed{\text{\bf Surface area of cylinder =$\pi r^2h$}}\)

                                                   \(= \pi 3*3*10\\\\= 90 \pi \ in^2\)

In this question it is given that the radius of a cylinder is 3 inches. The height of the cylinder is 10 inches. We are asked to calculate the surface area of the cylinder in terms of π .

Radius = 3 inches

Height = 10 inches

We know,

\( \star \: \small \boxed{\rm{ Surface \: area \: of \: a \: cylinder = πr²h}}\)

Substituting the values we get

\( \small\sf{ Surface \: area \: of \: a \: cylinder = π × 3² × 10}\)

\( \small\rm{ Surface \: area \: of \: a \: cylinder = π × 3 \times 3 × 10}\)

\( \small\rm Surface \: area \: of \: a \: cylinder = π × 90\)

\( \small\sf{ Surface \: area \: of \: a \: cylinder = \bf{90 π \: inches²}}\)

Answer: (5,7)

Step-by-step explanation:

We want to find the image of a point after a given translation.

The image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

First, we can define how a general translation T(a, b) affects a general point (x, y).

It will add a units to the x-value and b units to the y-value, then we have:

T(a,b)[(x, y)] = (x + a, y + b).

Now we just need to apply the translation:

T(3, -4) to the point (-5, 2)

It gives:

T(3, -4)[(-5, 2)] = (-5 + 3, 2 + (-4)) = (-2, -2)

So the image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)

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Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

Answer:

The answer is D

Step-by-step explanation:

If and Then are italicized

So our final solutions on the given interval are theta = 153.4 degrees and theta = 333.4 degrees.

An equation is a mathematical statement that uses an equal sign (=) to show that two expressions are equal. It typically contains variables, constants, and mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations are commonly used in various fields of mathematics, as well as in physics, chemistry, engineering, and many other scientific disciplines.

Here,

To solve the equation tan(theta) = -1/2, we first need to find the angle whose tangent is -1/2. We can do this by using the inverse tangent function (also known as arctan or tan^-1) on a calculator or by using the reference angles for tangent.

Using a calculator, we get theta = -26.6 degrees or theta = 153.4 degrees.

To find all solutions on the given interval 0(degrees) < theta < 360 degrees, we need to add 360 degrees to each solution that is less than 0 degrees and subtract 360 degrees from each solution that is greater than 360 degrees.

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The most appropriate model to represent the data in the table is (d)

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

The table of values

In the above table of values, we can see that

To show as the number of miles change by day

A linear or line graph has to be plotted

Hence, the most appropriate model to represent the data is (d)

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The probability that a child was living with just one parent is 0.322

The probability that a randomly selected child in a country was living with his or her mother as the sole parent was 0.242

P(mother as sole parent) = 0.242

The probability that a randomly selected child in a country was living with his or her father as the sole parent was 0.080

P(father as sole parent) = 0.080

P(A U B) = P(A) + P(B) - P(A∩ B)

P(living with just one parent) = P(mother as sole parent) + P(father as sole parent)

P(living with just one parent)  = 0.242 + 0.080 = 0.322

Therefore, the probability that a child was living with just one parent is 0.322

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Answer:

292 lines of code

Step-by-step explanation:

1.) Multiply.    25 times 5 = 125

2.) Multiply previous answer by 2 (because he wrote twice as much).             125 times 2 = 250

3.) Add 42 to previous answer.    250 + 42 = 292

The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

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Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

The probability of getting tails on the coin and an even number on the number cube is 1/4

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The sample space of a coin is:

S = {H, T}

The sample space of a die is:

S = {1, 2, 3, 4, 5, 6}

The above means that:

A coin has 2 faces, one of which is the tail.

So, we have:

P(Tail) = 1/2

A number cube has 6 numbers, 3 or which are even.

So, we have

P(Even) = 3/6

The required probability is

P = P(Tail) * P(Even)

This gives

P = 1/2 * 3/6

Evaluate

P = 1/4

Evaluate the quotient

P = 0.25

Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25

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Answer: (4,3)

Step-by-step explanation: double the midpoint then subtract the endpoint from the midpoint to get (4,3)

A vector with the representation provided by the directed line segment AB for A(-2,-2), B(5,3) is <7,5> and for A(4,0,-2), B(4,2,1) is <0, 2, 3>.

a) The vector representation of a directed line segment AB with initial point A(-2, -2) and terminal point B(5, 3) is given by the difference of their position vectors: a⃗ = b⃗ − a⃗ = <5-(-2), 3-(-2)> = <7,5>.

The equivalent representation starting at the origin can be drawn as shown in the attached figure:

b) The vector representation of a directed line segment AB with initial point A(4, 0, -2) and terminal point B(4, 2, 1) is given by the difference of their position vectors: a⃗ = b⃗ − a⃗ = <4-4, 2-0, 1-(-2)> = <0, 2, 3>.

The equivalent representation starting at the origin can be drawn, as shown in the attached figure.

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A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. the dimensions that will minimize the amount of paper used is that should be 12 inches wide by 6 inches tall.

The margins are 2 inches at the top and bottom and 3 inches at each side. The margins are then added to the two 150s, making a total width of 12 inches and a total height of 6 inches. This is the minimum amount of paper that can be used for the poster.   In order to minimize the amount of paper used, it is important to consider the size of the margins.

The margins should be kept as small as possible in order to maximize the amount of space available for the printed material. Generally speaking, a margin of 1 inch is sufficient for most printed materials. If a larger margin is necessary, then the overall dimensions of the poster should be adjusted accordingly.

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The total number of peaches is given by the equation A = 25 peaches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of peaches be represented as A

Now , the equation will be

The percentage of peaches that equals 7 peaches = 28 %

Substituting the values in the equation , we get

28 % of A = 7   be equation (1)

On simplifying the equation , we get

( 28 / 100 ) x A = 7

Multiply by 100 on both sides of the equation , we get

28A = 700

Divide by 28 on both sides of the equation , we get

A = 700/28

A = 25 peaches

Therefore , the value of A is 25 peaches

Hence , the number of peaches is 25 peaches

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Answer:

3 1/3

Step-by-step explanation:

To solve this problem, we need to find the proportion of bulbs that have a life less than 700 hours. We can do this by finding the probability that a randomly selected bulb has a life less than 700 hours and then converting that probability to a percentage.

Since the distribution is symmetric about the mean, we can assume that it is approximately normal. We can then use the normal distribution to find the probability that a randomly selected bulb has a life less than 700 hours.

To do this, we need to standardize the value 700 hours by subtracting the mean and dividing by the standard deviation:

z = (700 - 900) / 50 = -2

This means that 700 hours is 2 standard deviations below the mean. We can use a standard normal table (or a calculator) to find the probability that a randomly selected bulb has a life less than 700 hours:

P(x < 700) = P(z < -2) = 0.0228

This probability is very small, so we can convert it to a percentage by multiplying by 100:

0.0228 * 100 = 2.28%

Therefore, at most 2.28% of the bulbs are expected to fail to last even 700 hours.

A percentage is a figure or ratio that in mathematics represents a portion of one hundred. It is one of the ways to indicate a dimensionless relationship between two numbers; other ways include ratios, fractions, and decimals. The symbol "%" is frequently written after the number to represent percentages.

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