Assume z is a standard normal random variable. Then P(–1.20 ≤ z ≤ 1.50) equals

We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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Answer:

I dont know for sure but i think its 2,3,4,5,and 6

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

375/100

Reduce to lowest term

15/4 or 3 3/4

If initial sample of 458 grams of a radioactive substance decays according to the function \(A(t)=458e^{-0.038t}\) then the half-life of the substance is 0.

Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.

Given,

An initial sample of 458 grams of a radioactive substance decays according to the function

\(A(t)=458e^{-0.038t}\)

We need to find the half life

\(458=458e^{-0.038t}\)

Divide both sides by 458

\(1=e^{-0.038t}\)

Take log on both sides

\(log1=-0.038t\)

0=-0.038t

t=0

Hence, the half-life of the substance is 0.

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Answer:

Step-by-step explanation:

i need help on that too

Answer: no she dosen't

Step-by-step explanation:

If you were to add up all three numbers

49.95+19.95+21.95=91.85

Which means she is $1.85 short to buy all of the items

G. From the origin move right 3 units,then up 6 units

H. From the origin move left 2 units,then up 11 units

J. From the origin move right 8 units, then down 10 units

K. From the origin move left 16 units, then down 20 units

L. Plot the first point at the origin then move up 5 units

M. From the origin move left 14 units and plot the next point at the origin

5 years longer then Bill, 2x5=10.

10+2=12.

12-5=7

Hoang has be there for 12 years. Bill has for 7 years.

The maximum revenue possible in this situation is 15625/A dollars, where A is the coefficient in the quadratic equation.

To find the maximum revenue possible in this situation, we can use the concept of vertex or the vertex form of a quadratic equation.

The revenue equation is given by R = -Ax^2 + 250x, where A is a constant coefficient.

The maximum revenue occurs at the vertex of the parabolic curve represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -A and b = 250. Plugging in these values, we get:

x = -250 / (2 * (-A))

= 125 / A

To find the maximum revenue, we substitute this value of x into the revenue equation:

R = -A * (125 / A)^2 + 250 * (125 / A)

= -A * (15625 / A^2) + (31250 / A)

= -15625 / A + 31250 / A

= 15625 / A

The maximum revenue is given by 15625 / A. The value of A is not specified in the question, so we cannot determine the exact maximum revenue without knowing the value of A. However, we can say that the maximum revenue increases as A decreases.

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Answer:

2/10 because if the two fraction

The equivalent fractions of 8/11 = 16/22 , 24/33 , 32/44

The equivalent fractions of 1/10 = 2/20 , 3/30 , 4/40

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the first fraction be represented as A

Now , the value of A = 8/11

Let the second fraction be represented as B

Now , the value of B = 1/10

And , the equivalent fractions of A is given by

A = 8/11 , 16/22 , 24/33 , 32/44

And , the equivalent fractions of B is given by

B = 1/10 , 2/20 , 3/30 , 4/40

Hence , the fractions are solved

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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To find arcsin, we need to use the identity:

sin(arcsin(x)) = x

Since arcsin is negative, sin(arcsin) is also negative. Therefore, we can say:

sin(arcsin) = -sqrt(1 - (cos)^2)

where (cos)^2 = 8/17

Substituting, we get:

sin(arcsin) = -sqrt(1 - (8/17))

Simplifying, we get:

sin(arcsin) = -sqrt(17/17 - 8/17)

Simplifying further, we get:

sin(arcsin) = -sqrt(9/17)

Therefore, arcsin = -sqrt(9/17)

To find arctan, we need to use the identity:

tan(arctan(x)) = x

Substituting, we get:

tan(arctan) = -8/17

Therefore, arctan = -8/17

So, arcsin is -sqrt(9/17) and arctan is -8/17.

Answer:

idek and i dont ;like how this is working!

Step-by-step explanation:

the effect of the second transformation just is:

(x - 3, y + 4) → (-3 + 4, y + 4)

Here we have a sequence of transformations, we start with a point (x, y) which we:

The second transformation is the first reflection, so we need to see what that reflection does.

First, the translation maps our point from (x, y) into (x - 3, y + 4).

Then, a reflection across the y-axis will only change the sign of the x-component of our point, so the effect of the second transformation just is:

(x - 3, y + 4) → (-3 + 4, y + 4)

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Answer:

5

Step-by-step explanation:

When taking a percent of a number, multiply the number by the percent divided by a hundred:

\(25 * \frac{20}{100}\)

You get an answer of

5

Answer:

5 students are in a club.

Step-by-step explanation:

To do 20% of 25, you must first move the % until all numbers are on the right side of the decimal.

Observe: 20% ---> 0.20 aka 0.2

Now, you must take 0.2 and multiply it by 25 to get 20% of 25.

0.2 x 25 = 5

There's your answer, 5 students in a club :)

Answer:

Step-by-step explanation:

Answer:

5.93

Step-by-step explanation:

\(Average= \frac{9+5/9+7+2/9+2+7/36+4+3/4}{4} = 5.930555\) or \(\frac{427}{72}\)

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer: y=2/3x-2

Step-by-step explanation:

Slope intercept form is: y=mx+b

m=slope

b= y-intercept

slope is 2/3

Answer:

  1,120 dollars interest will be paid by Joe in 4 years

Step-by-step explanation:

   4,000 times 7 ( 0.07 ) is 280, and 280 times 4 is 1,120

Answer:

1 1/8

Step-by-step explanation:

Answer:

EF is 109

DAB is 54.5

Step-by-step explanation:

Applying the central angle theorem, the correct statement would be:

The central angle theorem states that:

Thus:

Measure of minor arc EF = m∠ECF = 109°

m∠DAB = 1/2(109°) [m∠ECF = m∠BAD = 109°]

m∠DAB = 54.5°

Therefore, applying the central angle theorem, the correct statement would be:

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Answer:

A

Step-by-step explanation:

In the slope-intercept form (y=mx+c), the coefficient of x is the slope and c is the y-intercept.

g(x)= -6x +3

Slope= -6

y- intercept= 3

f(x)

y- intercept is the point at which the graph cuts through the y- axis, and it occurs at x= 0.

The two points on the graph are (0, 3) and (1, 1).

slope

\( = \frac{y1 - y2}{x1 - x2} \)

\( = \frac{3 - 1}{0 - 1} \)

\( = \frac{2}{ - 1} \)

= -2

y- intercept= 3

Thus, both have different slopes but the same y-intercepts.

Answer:

A

The slopes are different but the y-intercepts are the same

Step-by-step explanation:

Answer:

ghthtf

Step-by-step explanation:

tygtgg

Answer:

\(9 \sqrt{2} \)

Step-by-step explanation:

\(3 \sqrt{6} \times \sqrt{3} \\ 3 \times \sqrt{2} \sqrt{3} \times \sqrt{3} \\ 3 \times 3 \sqrt{2} \\ 9 \sqrt{2} \)

Answer:

$41.69

Step-by-step explanation:

The computation of the selling price of the each pair of slacks is as follows:

Given that

Cost = $19.36 per pair  

Markup = $22.33

As we know that  

Markup = Sell Price - Cost

So,  

Sell Price = Cost + Markup

= $19.36 + $22.33

= $41.69

Hence, the selling price is $41.69