for general , the solution . act on this equation with to confirm this is the solution to the original differential equation. remember that acts only on , not . g

The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.

The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.

Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:

2/3z > 4/5 [given]

Multiply both sides by 3/2:

2/3z × 3/2 > 4/5 × 3/2

z > (4 × 3) / (5 × 2)

z > 12 / 10

Simplify further:

z > 6/5

z > 1.2

The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.

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Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.

The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).

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Answer:

x = 75

y = 15

Step-by-step explanation:

What you need to know to solve this question:

1. Angles in a triangle sum up to 180

2. Angles on a straight line add up to 180

3. A right-angle is 90

4. The triangle illustrated is a right-angle triangle

Solving for x:

According to principle 2:

x + 105 = 180

x = 180 - 105

x = 75

Solving for y:

According to principles 1 and 3:

x + y + 90 = 180

(75) + y + 90 = 180

y = 180 - 90 - 75

y = 15

The solution for the situation is [tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex]  Where y > 1, and the graph is attached below.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

The side length x (in feet) of the base,

the height y (in feet) of the inequality y > 1/2x²+ 1 and y ≤ x,

In solving this inequality, we get,

[tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex]  where y > 1

The graph of the system is attached below.

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The correct statements regarding the comparisons of the exponential functions are given as follows:

The definition of function f(x) is given as follows:

f(x) = 4(5)^x

Meaning that it has an y-intercept and an asymptote given as follows:

From the graph of function g(x), we have that:

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1. 4

2. less than

3. increase

4. negative

Got it right on Edmentum

Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.

Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.

Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.

The final value of company x sold price is; $22,000,500

The final value of company y sold price is; $21,999,500

Let the amount of sold out products in company x and company y be denoted by a

Now, we are told that sum of both the two companies salaries are $44,000,000.

Now, the sold price of company x is 1000 more than the other.

Thus;

Sold price of company y = y

Sold price of company x = 1000 + y

Thus;

1000 + y + y = 44000000

1000 + 2y = 44000000

2y = 44000000 - 1000

2y = 43,999,000

y = 43,999,000/2

y = $21,999,500

Thus;

Sold price of company x = $21,999,500 + $1000 = $22,000,500

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Answer:

1.

x = 24

m = 112

z = 44

y = 72

2.

x = 35

Step-by-step explanation:

Number 1

Finding x

- Total angle in a triangle is 180.

- QVS = triangle

180 = ∠Q + ∠V + x

180 = 73 + 83 + x

x = 180 -73 - 83

x = 24

Finding m

- Total angle in a straight line is 180

- RW is a straight line

180 = m + ∠U

180 = m + 68

m = 180 - 68

m = 112

Finding z

- Total angle in a triangle is 180.

- RUS = triangle

180 = m + x + z

180 = 112 + 24 + z

z = 180 - 112 - 24

z = 44

Finding y

- Total angle in a triangle is 180.

- RWT = triangle

180 = z + y + ∠W

180 = 44 + y + 64

y = 180 - 44 - 64

y = 72

Number 2

- Total angle in a triangle is 180.

- Total angle in a straight line is 180.

180 = (180 -120) + 85 + x

180 = 60 + 85 + x

x = 180 - 60 - 85

x = 35

The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.

A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.

Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.

We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.

Degree of freedom,

df = n - 1

df = 29 - 1

df = 28.

The critical value of t calculated from the t-distribution table is,

[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]

Then, an 80% confidence interval is,

[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]

Then, the interval is written as

55.9 - 1.80 < μ < 55.9 + 1.80

54.1 < μ < 57.7

The required interval is 54.1 < μ < 57.7.

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Answer:

every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year  

Step-by-step explanation:

Answer:

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Step-by-step explanation:

The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].

This would mean [tex]y=\frac{x}{3}-2[/tex].

Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.

[tex]x = \frac{y}{3} -2[/tex]

Then rearrange for [tex]y[/tex]:

[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]

This new equation of [tex]y[/tex] is the inverse function.

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Answer:

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

Since the triangles CAT and DOG overlap, their corresponding parts are congruent.

As we are looking for ASA congruency, we need to select two angles and the included side.

Let's review the given options, considering names of triangles and the order of vertices in those names.

A. ∠ A ≅ ∠ T  

B. CA ≅ DO

C. AT ≅ OG

D. CT ≅ DG

E. ∠ A ≅ ∠ O

F. ∠ C ≅ ∠ D

So we have corresponding angles A and C and the included side must be AC.

Looking, at the options, we can get ASA with combination of options B, E and F.

Answer:

y = -1/2 x - 1

Step-by-step explanation:

A (-2,0)

B (0,-1)

slope = (-1-0)/(0-(-2)

-1/2

y intercept = -1

y = -1/2 x - 1

Answer:

  y = e^(-1/2x -1)

Step-by-step explanation:

You want the equation for y(x), which is graphed as a straight line on a semi-log scale.

Let z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...

  z = -1/2x -1

Using z = ln(y), we can find the equation for y by taking antilogs:

  ln(y) = -1/2x -1

  y = e^(-1/2x -1)

__

Additional comment

The attached graph shows y = f(x) and the line ln(y).

Answer:

Solutions: -1, 4, and 0

Step-by-step explanation:

f= -4.5

2f - 8 ≤ 6f + 4

2 (-4.5) -8 ≤ 6 (-4.5) + 4

-9 - 8 ≤ -27 + 4

-17 ≤ -23

Not True

f= -8

2f - 8 ≤ 6f + 4

2 (-8) - 8 ≤ 6 (-8) + 4

-16 - 8 ≤ -48 + 4

-24 ≤ -44

Not true

f= -1

2f - 8 ≤ 6f + 4

2 (-1) - 8 ≤ 6 (-1) + 4

-2 - 8 ≤ -6 + 4

-10 ≤ -2

True

f= 4

2f - 8 ≤ 6f + 4

2 (4) - 8 ≤ 6 (4) + 4

8-8 ≤ 24 + 4

0 ≤ 28

True

f= 0

2f - 8 ≤ 6f + 4

2 (0) - 8 ≤ 6 (0) + 4

0 - 8 ≤ 0 + 4

-8 ≤ 4

True

Therefore the value of K is -11

A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.

Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.

Since we know the volume of the balloon, we can set up the following equation:

(4/3)πr^3 = 26*π ft^3

Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.

To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.

The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:

(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)

Plugging in the value of r that we found earlier (2.15 ft), we get:

(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min

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86

Step-by-step explanation:

a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.

b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.

Explanation:

(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.

The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.

Therefore, the joint density of Y1 and Y2 is:

f(Y1,Y2) = f(U1U2,U2)

= f(U1) x f(U2)

= 1 x 1

= 1

(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:

f(Y1) = ∫f(Y1,Y2)dY2

= ∫1dY2

 Y2 = 1

Therefore, the marginal density of Y1 is 1

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Answer:

the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.

Step-by-step explanation:

The compositions of the two given functions are:

g(f(x)) =   √(2*x + 29) - 2

f(g(x)) = √(2*x  + 25)

Here we have the two functions:

f(x) = √(2x + 29)

g(x) = x - 2

We want to find the compositions:

f(g(x))

So we just need to evaluate f(x) on g(x), we will get:

f(g(x)) = √(2*g(x) + 29)

Now we can replace g(x) there:

f(g(x)) = √(2*(x - 2) + 29)

f(g(x)) = √(2*x - 2*2 + 29)

f(g(x)) = √(2*x  + 25)

The other composition is:

g(f(x)) = f(x) - 2

g(f(x)) =   √(2*x + 29) - 2

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The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.

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Complete question

The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms

To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.

Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.

Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.

The most likely statement about the comparison of standard deviation of Test A and Test B is (a) The standard deviations found in Test A and Test B will be about the same  .

What is Standard Deviation ?

The term standard deviation is defined as a measure which shows the  variation (such as dispersion) from the mean .

it is given that in Test A 100 experimental measurements is taken , and

in Test B 400 experimental measurements is taken .

we know that standard deviation is just  square root of average of the square distance of measurements from the mean.

So , it is not affected by the number of experimental measurements .

thus , the standard deviation remain same for both the tests .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

In test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again .

Which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?

(a) The standard deviations found in Test A and Test B will be about the same

(b) The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.

(c) The standard deviation found in Test will about be four times as big as the standard deviation found in Test B

(d) The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A .

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The total Number of miles she biked, was 216.

In the given question, over 18 days, Sophia rode her bike an average of 12 miles each day.

We have to find the total number of miles she biked.

As we know that average is the sum of all numbers divide by total numbers.

As from the question, there is a total average of 18 days.

So the total number of days is 18.

The average distance of her bike for one day is 12 miles.

So we have to find the total number of miles that she biked.

We can find the total number of miles by multiplying the total number of days with the average speed of one day. So;

Total Number of Distance = Total Days × Average Speed of One Day

Total Number of Distance = 18 × 12

Total Number of Distance = 216 miles.

So, the total Number of Distance she biked, was 216 miles.

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The total perimeter of the given composite figure is; 74.55 meters

The perimeter of the given figure can be calculated by dividing the figure into two parts : One is semi-circle and second is rectangle.

To find Perimeter of rectangle :

Length of the rectangle = 18 m

Width of the rectangle = 15 m

Perimeter = (2 × Length) + Width

Perimeter = (2 × 18) + 15

Perimeter = 36 + 15

Perimeter = 51 meters

To find perimeter of semi-circle :

Radius of semi-circle = 15/2 = 7.5 m

Perimeter of semi-circle = π × radius

Perimeter = 3.14 × 7.5

Perimeter = 23.55 meter

So, Total Perimeter of the figure = 51 + 23.55

= 74.55 meter

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This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).

The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.

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The solution of the algebraic expression   (3x + 2y)³ is

[tex]\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now, algebraic expressions are of different types. They are-

Monomial, Binomial and trinomial.

Algebraic expression with only one term is called monomial

Algebraic expression with two terms are called binomial

Algebraic expressions with three terms are called trinomial.

Algebraic expressions with more than three terms are called polynomial.

Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on

Algebraic expression of degree one is called linear

Algebraic expression of degree two is called quadratic

Algebraic expression of degree one is called cubic

The given algebraic expression is  (3x + 2y)³

Now,

[tex](3x +2y)^3\\(3x)^3 + 3 \times (3x)^2 \times (2y) + 3 \times 3x \times (2y)^2 + (2y)^3\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]

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Answer:

3,4,5

Step-by-step explanation:

Because, it is the only pair that fulfill the pythagorean theorem/formula

Pythagorean formula: [tex]c^2 = \sqrt{a^2 + b^2}[/tex]

Where c is the longest side of the triangle, or the hypothenuse, and a and b is the two perpendicular side.