How do i write an equation in slope intercept form if they give you the slope and what it has to pass through. I totally forgot how to do this

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

justification: A tangent is defined as "a straight line that touches a curve or curved surface at a point, but if extended does not cross it at that point." As you can see in the diagram, the line does not extend, which means there are two common tangents. (this is actually a diagram for two common tangents im pretty sure. wouldnt make since otherwise)

The solutions of the logarithmic equations are:

i) Ln(5x) = 7   if x = 219.32

ii) Logₓ(25) = 2    if x = 5

Here we want to solve the logarithmic equation:

Ln(5x) = 7

If we apply  the exponential function in both sides, we will get:

exp(ln5x)) = exp(7)

5x = exp(7)

x = exp(7)/5 = 219.32

The second equation is:

Logₓ(25) = 2

Remember that logₐ(x) = ln(x)/ln(a)

Then we can rewrite:

Logₓ(25) = 2

ln(25)/ln(x) = 2

ln(25)/2 = ln(x)

exp(ln(25)/2) = x

5 = x

These are the solutions.

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The vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0 is r(t) = <0, 2, 0> - t<1, -1, 0>.

To find a vector equation with parameter t for the line of intersection of the planes x + y + z = 2 and x + z = 0, we can solve the system of equations formed by the planes.
First, let's solve for y in terms of x and z from the equation x + y + z = 2. Rearranging the equation, we have y = 2 - x - z.
Now, substitute this expression for y in the equation x + z = 0. We have x + (2 - x - z) + z = 2, which simplifies to 2 - z = 2.
Solving for z, we find z = 0.
Substituting z = 0 into the equation x + z = 0, we have x = 0.
Now that we have the values of x, y, and z, we can form a vector equation for the line of intersection as follows:
r(t) =  = <0, 2 - x - z, 0> = <0, 2, 0> - t<1, -1, 0>.

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Answer:

5 quarts yellow + 2 quarts orange + 1 quart white = 8 total quarts.

To make 24 quarts you need 3 times as much, because 8 * 3 = 24.

Multiply each measurement by 3:

5 quarts yellow --> 15 quarts yellow

2 quarts orange --> 6 quarts orange

1 quart white --> 3 quarts white

Answer:

I'm not really into firm design lol I don't even know what that is, I like graphic designs like patterns and stuff.

Step-by-step explanation:

Answer:

The internal volume of the tin is 381.7 cm^3.

Step-by-step explanation:

To calculate the internal volume of the tin, we first need to find the radius and height of the tin. To do this, we need to take the average of the given minimum and maximum values for the radius and height.

The radius of the tin is the average of 3 cm and 6 cm, which is 4.5 cm.

The height of the tin is the average of 9 cm and 3 cm, which is 6 cm.

To calculate the volume of the tin, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the tin and h is the height of the tin.

In this case, the volume of the tin is V = π * 4.5^2 * 6 = 381.7 cm^3.

Therefore, the internal volume of the tin is 381.7 cm^3.

Answer:

$301.50

Step-by-step explanation:

Given that:

Stuart brought a sweater on sale for 30% discount off.

Another 25% discount off

Original price = 600

To Find:
What was the final price of a sweater?

Solve:

$600 x 30% = $180

$600 - $180 = $402 (discounted price after 30% off)

$402 x 25% = $100.50

$402-100.50 = $301.50  (discounted price after 25% off & the final price)

Hence, the final price is $301.50

Kavinsky

Answer:

0.362°

Step-by-step explanation:

hope this helps you

The value of v in the figure is 14

The angles on a straight line add up to 180 degrees.

So, we have:

4v + 90 + 34 = 180

Subtract 90 from both sides

4v + 34 = 90

Subtract 34 from both sides

4v = 56

Divide both sides by 4

v = 14

Hence, the value of v in the figure is 14

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Answer:

Step-by-step explanation:

Here the probability that you are not chosen as a president is P (not chosen as president) = 1112 .

In the question it is given that,

Total people=12

From them 1 president, 1treasurer and 1 secretary has to be chosen.

Probability (choosing 1 president) = Number of outcomes Total number of outcomes=  112 .

We have to find the probability of not chosen as a president= 1- P (Chosen as president)

P(not chosen as president)= 1-  112 =  1112.

#1234

In this instance, the likelihood that you will not be elected president is P (not chosen as president) = 11/12.

It is stated in the query that,

Total of 12 persons

A president, treasurer, and secretary must be picked from among them.

Probability = Number of outcomes while selecting one president. 112 results total were obtained.

The probability of not being selected as president must be determined:

= 1-P (Chosen as president)

P (not selected as president) =1 – 1/12

P (not selected as president)= 11/12.

Therefore, 11/12 probability against you being selected as president.

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Answer:

BD=24

Step-by-step explanation:

I assigned my unkown sides of the triangles as x and y, where x = BD and y =AD.

I used pythagoras' theorem to find expressions for the the sides of the triangles in terms of x and y.

Both expressions had the term x^2 in them, so I equated expressions of x^2

From there i rearranged to find y.

Using my value of y, I found x.

I've given you my working so I hope that helps :>

Step-by-step explanation:

the graphic shows us - the 2 end points are :

(-4, -4) and (4, -1)

the distance between these 2 points (= length of the line segment) is calculated via Pythagoras for right-angled triangles.

c² = a² + b²

c is the Hypotenuse and the distance between the 2 points. a and b are the legs of the triangle enclosing the 90 degree angle, as they are the differences between the x and the y coordinates of the points.

so,

distance² = (-4 - 4)² + (-4 - -1)² = (-8)² + (-3)² = 64 + 9 = 73

distance = sqrt(73) = length of line segment.

The mean is a measure of central tendency that represents the average value of a set of data. To find the mean of the monthly salaries of the 10 employees in the local travel office, we need to add up all the salaries and divide by the total number of employees.

So, if we add up all the salaries, we get:

1550 + 1710 + 1630 + 1000 + 1400 + 1610 + 1890 + 1300 + 2700 + 5800 = 19,940

Then, we divide this sum by the total number of employees, which is 10.

Mean = 19,940 / 10 = 1,994

Therefore, the mean monthly salary for the 10 employees in the local travel office is $1,994.

It's important to note that the mean is a useful measure of central tendency, but it can be affected by outliers. In this case, the salary of $5,800 is significantly higher than the other salaries, which may skew the mean. To get a better understanding of the distribution of salaries, it may be useful to also look at other measures such as the median and mode.
To find the mean monthly salary of the 10 employees at the local travel office, follow these steps:

1. Add up all the monthly salaries: 1550 + 1710 + 1630 + 1000 + 1400 + 1610 + 1890 + 1300 + 2700 + 5800 = 20,590.

2. Divide the total sum by the number of employees (10): 20,590 / 10 = 2,059.

The mean monthly salary of the 10 employees at the local travel office is 2,059. The mean represents the average salary of the employees, providing a general idea of the salary level at the office. In this case, the mean gives a local perspective on the financial situation of the employees within the travel office, allowing for comparisons with other companies or the industry standard.

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The test statistic for the sample mean is given byz = (x - μ) / (σ / √n)Where,x = 49, μ = 50, σ = 15, n = 55z = (49 - 50) / (15 / √55)≈ -1.24 From the z-tables, we find that the area to the left of z = -1.24 is 0.1089. This implies that the p-value = 0.1089 > α = 0.01.

Given information Random sample of 55 second-gradersSample mean score is x=49The standard deviation of test scores is σ = 15The nationwide average score on this test is 50.The school superintendent wants to know whether the second-graders in her school district have weaker math skills than the nationwide average.Level of significance (α) = 0.01Null hypothesis (H0):

The average math score of second-graders in the school district is greater than or equal to the nationwide average math score.Alternative hypothesis (Ha): The average math score of second-graders in the school district is less than the nationwide average math score.The test statistic for the sample mean is given byz = (x - μ) / (σ / √n)Where,x = 49, μ = 50, σ = 15, n = 55z = (49 - 50) / (15 / √55)≈ -1.24 From the z-tables, we find that the area to the left of z = -1.24 is 0.1089. This implies that the p-value = 0.1089 > α = 0.01.Since the p-value is greater than the level of significance, we fail to reject the null hypothesis.

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Answer:

5

Step-by-step explanation:

"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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Answer:

87.95479

Step-by-step explanation:

10.3% of 853.93 km

Expand 10.3÷100 by multiplying both numerator and denominator by 10.

\( \small \sf \frac{10.3 \times 10}{100 \times 10} = 853.93 \\ \)

\( \small \sf \frac{103}{1000} = 853.93 \\ \)

convert decimal number 853.93 to fraction 85394÷100

\(\small \sf \frac{103}{1000} = \frac{85393}{100} \\\)

Multiplying 103÷1000 and 85393÷100 by numerator times numerator and denominator times denominator.

\(\small \sf \frac{103 \times 8539 3}{1000 \times 100} \\\)

Do the multiplication in the fraction

\(\small \sf \frac{8795479}{100000} \\ \)

Divide we get

87.95479

Another way to solve it

10.3% 853.93

we know that ; % = whole no. ÷ 100

then,

10.3 ÷ 100 × 853.93

Divide the numbers

0.103 × 853.93

multiply the numbers

87.95479

Samantha works at a nursery where sh pots plants. It takes her 1-1/2 hours to pot 12 plants. So, Samantha takes7.5 minutes to pot one plant.

Samantha takes 1-1/2 hours to pot 12 plants. To find out how long it takes her to pot one plant, we need to divide the total time taken by the number of plants potted.

There are a few steps we can take to simplify the calculation. First, we can convert 1-1/2 hours to a decimal by adding 1 to 1/2, which gives us 1.5 hours. Then, we can divide 1.5 hours by 12 plants to find the time it takes to pot one plant.

1-1/2 hours = 1.5 hours

Time taken to pot one plant = 1.5 hours / 12 plants

Time taken to pot one plant = 0.125 hours per plant

Finally, we can convert hours to minutes by multiplying by 60.

0.125 hours per plant = 7.5 minutes per plant

Therefore, it takes Samantha 7.5 minutes to pot one plant.

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Question:

Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot in 1 hour? (Please give me the equation you used.)

Answer:

Suppose that we have two events, event A and event B.

Where the probability of event A is Pa, and the probability of event B is Pb.

We say that events A and B are independent if the probability of both events happening is equal to the product of the individual probabilities.

Probability of event A and B = Pa*Pb.

In this case we have:

A = missing a single flight

B = missing a single flight.

Pa = 0.19 = Pb.

And we know that the probability of missing two flights is 0.06

Let's see if this is equal to the product of the individual probabilities:

Pa*Pb = 0.19*0.19 = 0.036

So the joint probability is smaller than the one given, this means that the events are not independent and that if you miss one plane, the probability of missing the next one has a small increase.

The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

The probabilities are given as follows:

The probabilities are different, as the theoretical probability is higher.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

Out of 20 tosses, 4 resulted in heads, hence the experimental probability is given as follows:

p = 4/20

p = 1/5.

A coin is equally as likely to be heads or tails, hence the theoretical probability is given as follows:

p = 1/2.

Over a large number of trials, it is expected that the two probabilities assume close values, but for a small number of trials such as 20 it is expected for there to be differences.

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To simplify the expression secθ cosθ - cos²θ, we can use trigonometric identities to rewrite the terms in a more simplified form.

Recall the definitions of trigonometric functions:

secθ = 1/cosθ

Substitute this definition into the expression:

secθ cosθ - cos²θ = (1/cosθ) * cosθ - cos²θ

Simplify the expression:

= 1 - cos²θ

Now, we can apply the Pythagorean identity for cosine, which states that sin²θ + cos²θ = 1. By rearranging this identity, we have cos²θ = 1 - sin²θ.

Substitute cos²θ = 1 - sin²θ into the expression:

1 - cos²θ = 1 - (1 - sin²θ)

= 1 - 1 + sin²θ

= sin²θ

Therefore, the simplified expression for secθ cosθ - cos²θ is sin²θ.

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Answer:

The answer 128.57%

Step-by-step explanation:

The explanation is

Answer:

28.57%

Step-by-step explanation:

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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Statement 1 states that if a point is perpendicular to line m, the distances PA, QB, and RC are in increasing order. Statement 2 states that if line PQ is parallel to line m and vector AB is perpendicular to line m.

In statement 1, if point P is perpendicular to line m, it means that the distance PA from P to line m is the shortest. As we move along line m from P to Q, the distance QB increases. Similarly, as we move further along line m from Q to R, the distance RC further increases. Therefore, the correct order is PA < QB < RC.

In statement 2, if line PQ is parallel to line m, it means that the distances PA and QB are equal since they are perpendicular distances from points P and Q to line m, respectively. Furthermore, vector AB is perpendicular to line m, indicating that the distance RC is greater than QB. Therefore, the correct order is PA < QB < RC.

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The probability that the number of lost-time accidents occurring over a period of 7 days will be exactly 3 is 0.7295

Binomial Distribution

The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. In a Bernoulli trial, the experiment is said to be random and can only have two possible outcomes- success or failure.

In a binomial distribution the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.

Mean rate of lost time accident = 0.3 per day

probability that the number of lost-time accidents occurring over a period of 7 days will be no more than 3.

n = 7

Using binomial distribution formula :

P(x ≤3)

Probability of success (p) = 0.3

1 - p = 1- 0.3 = 0.7

nCx * p^x * (1 - p)^(n-x)

Using the binomial probability distribution calculator to save computation time :

P(x ≤3) = P(x = 0) + p(x = 1) + p(x = 2) + p(x = 3)

P(x ≤3) = 0.0403 + 0.1556 + 0.2668 + 0.2668

P(x ≤3) = 0.7295

0.7295

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The sales team must sell 8 more computers than they sold last month to receive the bonus.

Last month the sales team of Electronic Mania sold 27 computers.

If they sold 30% more computer than they sold last month, they would get a bonus.

First we find the 30 percent if 27

27 × 30/100

= 8.1

Let m be the total number of computers sold.

So, the total number of computers sold would be,

m = 27 + 8.1

m = 35.1

m ≈ 35

Therefore, they need to sell 35 computers in total.

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The derivative of the function f(x) = 5(x² - 1)  is lim x → 2[f(x) - f(2)]/(x - 2) = 20

The derivative of a function f(x) is \(\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

Since f(x) = 5(x² - 1) and we want to find its derivative, we can proceed thus.

Let x = h + 2

So,  \(\lim_{x \to 2} \frac{f(x) - f(2)}{x - 2} = \lim_{h \to 0} \frac{f(2 + h) - f(2)}{h}\)

f(x) = 5(x² - 1)

f(2) = 5[(2)² - 1]

= 5[4 - 1]

= 5(3)

= 15

f(2 + h) = 5[(2 + h)² - 1)

= 5(4 + 4h + h² - 1)

= 5(3 + 4h + h²)

= 15 + 20h + 5h²

So, f(2 + h) - f(2) = 15 + 20h + 5h² - 15

= 20h + 5h²

So, we have that

[f(2 + h) - f(2)]/h = (20h + 5h²)/h

= 20 + 5h

Now, taking the limit as h → 0, we have

= 20 + 5(0)

= 20 + 0

= 20

So,  lim h → 0[f(2 + h) - f(x)]/h = lim x → 2[f(x) - f(2)]/(x - 2) = 20

So,  lim x → 2[f(x) - f(2)]/(x - 2) = 20

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