One out of every 5 students forgot a to bring a pencil to math class today.
Predict how many students forgot their pencil out of 120 total students.

From the above-mentioned data, it can be inferred that: When the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10 while the income effect causes the individual to change consumption of good 1 by −6.

The total effect can be calculated as the sum of both substitution and income effects. The total effect = substitution effect + income effect= 10 - 6= 4Thus, the total effect is 4.Now, to determine whether good 1 is normal or inferior, we need to consider the sign of the income effect.

If the income effect is negative, the good is inferior, and if it's positive, the good is normal.Since the income effect here is negative (-6), we can conclude that good 1 is inferior.

According to the given data, we can calculate the total effect, which is the sum of the substitution and income effects.  The substitution effect refers to the change in consumption of a good due to the relative price change, while the income effect refers to the change in consumption of a good due to the purchasing power change.  when the price of good 1 decreases, the substitution effect causes the individual to change consumption of good 1 by 10, while the income effect causes the individual to change consumption of good 1 by −6. Therefore, the total effect can be calculated as the sum of both substitution and income effects, which is 10 - 6 = 4.From the data, it can also be determined whether good 1 is normal or inferior. A good is considered normal when its income effect is positive and inferior when its income effect is negative. Since the income effect here is negative (-6), it can be concluded that good 1 is inferior.Thus, the total effect is 4, and good 1 is inferior.

The total effect is 4, and good 1 is inferior.

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The value of  \(cos^{-1}(\frac{2}{3})\) is 0.84 radian or 48.18°

Given,

\(cos^{-1}(\frac{2}{3})\)

It is an inverse trigonometric function.

Inverse trigonometric functions are also known as "Arc Functions" because they produce the length of arc required to obtain a given value of trigonometric functions. Inverse trigonometric functions are the inverse of trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are particularly useful for right angle triangles. When two sides of a right triangle are known, these six important functions are used to find the angle measure.

Thus, the value of \(cos^{-1}(\frac{2}{3})\)  using a calculator is 0.84 radian or 48.18°

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The distance between the center of the circle and the given point is 13 units.

The distance between the center of the circle (0, 0) and the given point (-5, 12) should be equal to the radius of the circle.

Using the distance formula,

d= √(-5-0)² + (12-0)²

d = √25 + 144

d = √169

d = 13 unit

Therefore, the distance between the center of the circle and the given point is 13 units.

Any point on the circle will have a distance of 13 units from the center.

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Answer: 18.4050

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Based on the information given the length of one side of the hot tub is 4. 8 ft. So the correct option is B.

The complete question is given as:-

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the centre of dilation. Square A B C D is dilated to create square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Length: Using this formula

Length=B prime C prime length/Scale factor

Where:

B prime C prime length=24 feet

Scale Factor=5

Let plug in the formula

Length=24ft/5

Length=4.8ft

In conclusion, the length of one side of the hot tub is 4. 8 ft.

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These labels describe the Body Mass Index (BMI) of an individual. BMI is a measure of body fat based on height and weight.

Labels of weight status were added, such as under 18.5 = underweight, 18.5 to 24.9 = healthy, 25 to 29.9 = overweight, 30 or higher = obese.

BMI is used to determine whether an individual is a healthy weight for their height. Under 18.5 is classified as underweight. A BMI of 18.5 to 24.9 is considered a healthy weight, 25 to 29.9 is classified as overweight, and a BMI of 30 or higher is considered obese.

It is important to note that BMI is not an exact measure of body fat, and individuals with higher amounts of muscle mass may have a higher BMI. Therefore, BMI should be used as a guide to assess overall health and not as an absolute measure of body fat.

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Answer:

65

Step-by-step explanation:

15*3+15=60

30*2+15=75

20*4+15=85

10*5+15=65

Answer:

the answer I got is x>1-y

Answer:

Step-by-step explanation:

Y = - 3x. Equation 1

x + y = - 4 equation 2

Putting value of y

x + (-3x) = - 4

x - 3x = - 4

-2x = - 4

x = - 4/-2 = 2

Putting value of x in the equation 1

Y = - 3(2)

Y = - 6

, the rule is verified.

We are given a table and we need to fit an equation that follows the pattern. We also need to describe the relationship between the two columns in words.Given table,|a|b| |5|65|6|78|8|1010|11|13|13|We see that the value of b is 13 less than the value of a. We can describe this relationship as: "The value of b is 13 less than the value of a."Hence, we can write the rule as:b = a - 13We can check this rule by substituting values from the table in the above equation as follows:When a = 5, b = 5 - 13 = -8When a = 6, b = 6 - 13 = -7When a = 8, b = 8 - 13 = -5When a = 10, b = 10 - 13 = -3When a = 13, b = 13 - 13 = 0The values of b obtained are the same as in the given table.

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Answer:

no

Step-by-step explanation:

Answer: £198.27

Step-by-step explanation:

If the probability of someone being female and voting for a candidate is 30% , then the notation for this probability is , P(Female and Voting for A) = 0.30 , the correct answer is (c) .

This notation represents the joint probability of two events: being female and voting for candidate A. It means the probability that a randomly selected person is both female and voted for candidate A is 0.30.

In Option (a) P(Female | Voting for A) = 0.30 represents the conditional probability of being female given that the person voted for candidate A. It means the probability that a person who voted for candidate A is female is 0.30.

In Option (b) P(Voting for A | Female) = 0.30 represents conditional probability of voting for candidate A given that the person is female.

It means the probability that a female person voted for candidate A is 0.30.

Therefore , the correct option is (c) P(Female and Voting for A) = 0.30  .

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The given question is incomplete , the complete question is

Suppose the probability of someone being female and voting for candidate a is 30%. What is the notation for this probability?

(a) P(Female | Voting for A) = 0.30

(b) P(Voting for A | Female) = 0.30

(c) P(Female and Voting for A) = 0.30

Answer:

-21

Step-by-step explanation:

Answer:

C) 2

Step-by-step explanation:

14 = 4x + 6

14 - 6 = 4x

8 = 4x

8/4 = x

2 = x

y-y1 = m(x-x1) — point-intercept form

Given both x1 and y1 = coordinate point.

First​ we have to find the slope by using rise over run. (y2-y1)​/(x2-x1)​ = m

The slope should be m = -4 then we substitute m-value in point-slope form.

y-y1=-4(x-x1) — new equation. After substituting slope in, we need to find the coordinate point that is part of the graph. You can use any points that are given in the picture. I will use point F or (5,0).

Then we substitute x1 = 5 and y1 = 0 in the point-slope form

y-0=-4(x-5) — point-slope form

y=-4x+20 — slope-intercept​ form..

How about we change to another coordinate point to substitute in? We can check if these points also give same equation (slope-intercept).

Let's substitute (4,4) in the equation.

y-4=-4(x-4)

y=-4x+16+4

y=-4x+20

Same answer. Meaning that all these points that are shown can be substituted in the equation and get the same slope intercept form.

Therefore, point-slope form for the graph can be

y-4=-4(x-4)

you can also change the coordinate point value.

Answer:

1

Step-by-step explanation:

We use the top formula since x = -4

g(-4) = \(\sqrt[3]{-4+5}\)

g(-4) = \(\sqrt[3]{1}\)

g(-4) =1

The factored expression of the polynomial is (x - 3)(x + 4)

The polynomial expression is given as;

x^2 + x - 12

Expand the expression

x^2 + 4x - 3x - 12

Factorize the expression

x(x + 4) -3(x + 4)

Factor out x + 4

(x - 3)(x + 4)

Hence, the factored expression of the polynomial is (x - 3)(x + 4)

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Answer:

The slope of the line, m=-80 and

The equation of the line is, \(y=-80+440\)

Step-by-step explanation:

Given that initially the hot tub is filled with 440 gallons of water.

So, at time t=0, the amount of water = 440 gallons.

Further, after 1.5 hours, the amount of water had  decreased to 320 gallons.

So, at time t=1.5 hours, the amount of water = 320 gallons.

The point (0,440) and (1.5, 320) are on the line.

So, the slope, m, of the line is

\(m=\frac{440-320}{0-1.5}=-\frac{120}{1.5}=-80\)

The equation of the line is

\(y-440=-80(x-0) \\\\\Rightarrow y-440=-80x \\\\\Rightarrow y=-80x+440\)

Hence, the slope of the line, m=-80 and the equation of the line is, \(y=-80+440\).

12.

In order to solve this system of inequalities, let's graph each inequality in the coordinate plane and then find the solution region.

To graph an inequality, first let's graph the corresponding equation, then we use the inequality symbol to determine the solution region.

Graphing the equation 3x + 3y = 1, let's determine two ordered pairs that are solution to this equation. Using x = 0 and x = 1, we have:

Now, for 2y = 11, we have the horizontal line y = 11/2.

For both inequalities, the line is not part of the solution, because the symbols are "greater than" and "lesser than", so we draw the line dashed.

Graphing both inequalities in green and blue, and the solution region in yellow, we have:

Answer:

5.5, 5¼, 5 1/5 and 5.1.

Explanation:

To list the height from greatest to least, we convert each of them to a decimal.

Therefore, the weights are: 5.1, 5.2, 5.5 and 5.25

Arranging them from greatest to least gives:

5.5, 5.25, 5.2 and 5.1 which is equivalent to: 5.5, 5¼, 5 1/5 and 5.1.

Answer:

10 , 8

Step-by-step explanation:

because those numbers match up with the x

Answer:

3.9cm= 39mm

Multiply 3.9 by 10 to convert cm into mm.

Answer:

a)25%

b)5%

Step-by-step explanation:

hope it will help goodbye

Degrees of freedom (df) refers to the number of independent pieces of information that can be used to estimate a parameter. The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from your sample data, assuming the null hypothesis is true.

However, I can still help you understand the terms and how they relate to your question.

1. Test Statistic Name: In this case, the test statistic is the t-statistic, which is used for hypothesis testing in statistics when the population standard deviation is unknown.

2. Degrees of Freedom: Degrees of freedom (df) refers to the number of independent pieces of information that can be used to estimate a parameter. In a t-test, the degrees of freedom are typically represented as "t(df)". In your example, the degrees of freedom are 45 (t(45)).

3. Test Statistic Value: This is the calculated value of the t-statistic, which you will need to compute based on the data provided. It is used to compare against the critical value or to find the p-value. You need to provide the data or information about the test to calculate this value.

4. P-value: The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from your sample data, assuming the null hypothesis is true. You will need to compute the p-value using the t-statistic value.

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The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

Related

If there’s function f(x)=3−x

is (2,a)

and (−1,b)

then how can i find the value of a and b ?

f(x)=3−x

(2,a)⟶a=f(2)=3−2=1

(−1,b)⟶b=f(−1)=3+1=4

Step-by-step explanation:

Given that f ( x ) = 2 x − 3 f(x)=2x-3 f(x)=2x−3f, left parenthesis, x, right parenthesis, equals, 2, x, minus, 3 and g ( x ) = x + 1 g(x)=x+1 g(x)=x+1g, left

The net of this figure would be a square with four equilateral triangles on each of its sides.

To create the net of this figure we must analyze its sides and the joints of each of its faces. According to the above, we can conclude that this figure is made up of four equilateral triangular faces and a square at its base. To form the net of this figure, the most appropriate thing would be to start at the base and join the sides, in this case there would be four triangles, one on each side of the square. It is very important that the triangles are equilateral and have the same dimensions so that the pyramid can be formed correctly.

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