What the meaning of statement this?

Answer:

oo = infinity btw

Decreasing: (-oo, 1)

It is going down in that interval

Answer:

[tex]2y+11x=9[/tex]

Step-by-step explanation:

[tex](1+y)^2-y^2=-11x+10\\1+2y+y^2-y^2=-11x+10\\1+2y=-11x+10\\2y=-11x+9\\2y+11x=9[/tex]

Recall the standard form of a linear equation is [tex]Ax+By=C[/tex].

The graph of the function [tex]y = \sqrt{x} - 3[/tex] is given by the image presented at the end of the answer.

The function for this problem is defined as follows:

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

The parent function is defined as follows:

[tex]y = \sqrt{x}[/tex]

The subtraction by 3 means that the function was translated 3 units down.

The function is [tex]y = \sqrt{x} - 3[/tex]

More can be learned about translations at brainly.com/question/28174785

#SPJ1

Answer:

10

Step-by-step explanation:

d = √[(x_2 - x_1)² + (y_2 - y_1)²]

d = √[(2 - 8)² + (10 - 2)²]

d = √[(-6)² + 8²]

d = √(36 + 64)

d = √100

d = 10

Answer: 10

Step-by-step explanation:

Podemos escribir las relaciones como:

a = 7x

b = 5x

c = 8x

Sustituyendo las expresiones anteriores en la ecuación a+b+c=80, obtenemos:

7x + 5x + 8x = 80

20x = 80

x = 4

Sustituyendo el valor de x en las expresiones de a, b y c:

a = 7(4) = 28

b = 5(4) = 20

c = 8(4) = 32

Por lo tanto, c - b = 32 - 20 = 12

In mathematics, a horizontal asymptote is a horizontal line that a function approaches as the input values (usually x) approach positive or negative infinity. It describes the behavior of a function as its input values become extremely large or small.

For a rational function, which is a function expressed as the ratio of two polynomials, the degree of the numerator and denominator determines the existence and location of horizontal asymptotes. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y = 0).

If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

For example, consider the function [tex]f(x) = (3x^2 + 2x + 1) / (2x^2 + 5)[/tex]. In this case, both the numerator and denominator have a degree of 2. Therefore, the horizontal asymptote is the ratio of the leading coefficients: y = 3/2.

Horizontal asymptotes help understand the long-term behavior of functions and are useful for graphing and analyzing mathematical models in various fields, including economics, physics, and engineering.

For more such questions on asymptote

https://brainly.com/question/4138300

#SPJ8

To give the same value for money as Zak's idea of putting 50% more pet food into each box without changing the price, Sara needs to reduce the price by 33.33% (approximately).

Let's consider the original price of the box of pet food as P and the original amount of pet food in each box as F.

In Zak's idea, the new amount of pet food in each box would be 1.5F (50% more than the original amount), while the price remains the same (P).

In Sara's idea, the amount of pet food in each box remains unchanged (F), but the price needs to be reduced to maintain the same value for money.

To find the price reduction percentage, we need to determine the ratio of the new price (P') to the original price (P) that would make the value for money equivalent to Zak's idea.

Since the amount of pet food is the same, we can set up the equation:

1.5F / P = F / P'

Cross-multiplying and simplifying, we get:

1.5F * P' = F * P

1.5P' = P

P' = P / 1.5

Now, to find the percentage reduction, we subtract the new price from the original price and divide by the original price, multiplied by 100:

Percentage reduction = ((P - P') / P) * 100

                  = ((P - P / 1.5) / P) * 100

                  = (P / 3P) * 100

                  = 100 / 3

                  ≈ 33.33%

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

for such more questions on price

https://brainly.com/question/29023044

#SPJ8

Step-by-step explanation:

To find the unit rate in kilometers per minute, we need to divide the distance traveled (52/2 kilometers) by the time taken (23/4 minutes).

52/2 kilometers = 26 kilometers

23/4 minutes = 5.75 minutes

So, the unit rate in kilometers per minute is:

26 kilometers / 5.75 minutes = 4.52 kilometers per minute (rounded to two decimal places)

The unit rate of the car that travels 5 2/5 km in 2 3/4 mins is 1.96 km/min.

Distance travelled by a car = 5 2/5 km = 5.4 km

Time travelled = 2 3/4 mins = 2.75 mins

The unit rate in km/min = 5.4/2.75

The unit rate in km/min = 1.96 km/min.

Happy to help, have a great day! :)

The equations of the trigonometric identities, indicates that the possible values of x are;

a) -π/2, π/6, 5·π/6, and 3·π/2

b) 0, π/6, 5·π/6, and π

c) -π/3, -π/6, π/6, and π/3

d) -2.46670, 2.46670

e) 0, π/6, π/3, π, and 5·π/3

Trigonometric identities are equations involving trigonometric functions that are true for the values of the input variable.

a) -sin²(x) = cos(2·x) from [-π, π]. The identity cos(2·x) = 1 - 2·sin²(x) indicates that we get;

-sin²(x) = 1 - 2·sin²(x)

Therefore;  sin²(x) = 1/3

sin(x) = ±√(1/3)

The solution are therefore; -π/2, π/6, 5·π/6, and 3·π/2

b) 3·tan(x) = 2·sin(2·x) from [0, 2·π]. The identity sin(2·x) = 2·sin(x)·cos(x), indicates that we get, 3·tan(x) = 4·sin(x)·cos(x)

Dividing both sides of the above equation by cos(x), we get;

3·sin(x)/cos²(x) = 4·sin(x)

3/cos²(x) = 4

cos²(x) = 3/4

cos(x) = √3/2

The possible solutions are; x = 0, π/6, 5·π/6, and π

c) sec(x)·cos(3·x) = 0 from [-π/2. π/2]. The equation is equivalent to cos(3·x)/cos(x) = 0, which indicates; cos(3·x) = 0

The possible solution are; x = -π/6, -π/3, π/6, and π/3

d) 1 - cos(x) = 2 - 2·sin²(x) from (-π, π). The identity sin²(x) + cos²(x) = 1, indicates that we get; 1 - cos(x) = 3 - 2·cos²(x)

2·cos²(x) - cos(x) + 1 - 3 = 0

2·cos²(x) - cos(x) - 2 = 0

Solving, we get; cos(x) = (1 ± √(17))/4

x = arccos((1 + √(17))/4 and x = arccos((1 - √(17))/4

x ≈ -2.46670, and x ≈ 2.46670

e) 4·cos⁴(x) - 5·cos²(x) + 1 = 0 from [0, 2·π). The equation can be expressed as a quadratic equation of the form;

4·y² - 5·y + 1 = 0, where, cos²(x) = y, which using an online tool, we get;

y = 1, and y = 1/4

Therefore; cos²(x) = 1, and cos²(x) = 1/4

cos(x) = 1, and cos(x) = 1/2

The solutions within the domain are; x = 0, π/6, π/3, π, 5·π/3

The possible trigonometric identities in the question, obtained from a similar question on the website are;

a) -sin²(x) = cos(2·x) from [-π, π]

b) 3·tan(x) = 2·sin(2·x) from [0, 2·π]

c) sec(x)·cos(3·x) = 0 from [-π/2. π/2]

d) 1 - cos(x) = 2 - 2·sin²(x) from (-π, π)

e) 4·cos⁴(x) - 5·cos²(x) + 1 = 0 from [0, 2·π)

Learn more on trigonometric identities here: https://brainly.com/question/29297432

#SPJ1

Answer:

Area of the shaded region= 4 units

Step-by-step explanation:

width (x-axis)= 3-1 = 2

length (y-axis) = 2-0 = 2

Area of rectangle= Length × Width

= 2 × 2 = 4

Answer:

pi 13

Step-by-step explanation:

in terms of pi, meaning you dont do 3.142 x diameter, you just write it as pi diameter.

I know i write it like this due to calculation being pi diameter for circumference.

diameter =

[tex]2 \times radius[/tex]

The answer is:

Work/explanation:

We calculate circumference by using the following formula

C = 2πr

where

c = circumference;

π = pi;

r = radius of the circle.

Diagram:

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 6.5\ m}\end{picture}[/tex]

Now plug in the data; remember to express the answer in terms of pi.

C = 2 × 6.5 × π

C = 13 π

Answer:

See below

Step-by-step explanation:

When [tex]-\frac{\pi}{2} < \theta < \frac{\pi}{2}[/tex], the x-coordinate of the rotated point will be positive since they cover Quadrants I and IV, both of which have positive x-values.

When [tex]\frac{\pi}{2} > \theta > \frac{3\pi}{2}[/tex], the x-coordinate of the rotated point will be negative since they cover Quadrants II and III, both of which have negative x-values.

The x-coordinate of the rotated point will be equal to cosθ since both of these values depend on the angle of θ.

cos(90°) = 0, cos(180°) = -1, and cos(270°) = 0

This is why referring to a unit circle is crucial in understanding this material.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

For more such questions on ratio of the sides

https://brainly.com/question/31529028

#SPJ8

The reconciled cash balance at July 31 for ABC Company is Br. 4,784.64.

To reconcile the bank statement balance with the ledger balance of ABC Company, we need to consider the following adjustments:

The deposit of Br. 410.90 made after banking hours on July 31 should be added to the bank statement balance.

The erroneously charged check of Br. 79 should be deducted from the bank statement balance.

The outstanding checks that have not yet been paid by the bank need to be deducted from the ledger balance.

These checks are:

Check No. 801, dated June 15, for Br. 100.00

Check No. 888, dated July 24, for Br. 10.25

Check No. 890, dated July 27, for Br. 294.50

Check No. 891, dated July 30, for Br. 205.00

The incorrectly charged check of Br. 210, which should be Br. 120, needs to be deducted from the bank statement balance.

The proceeds from the collection of the interest-bearing note receivable from David, amounting to Br. 500, should be added to the bank statement balance.

The interest earned on the average account balance during July, Br. 24.75, should be added to the bank statement balance.

The returned check of Br. 10, recorded as Br. 100 in the check register, needs to be deducted from the bank statement balance.

The bank fee of Br. 5.00 charged for handling the collection of the note receivable should be deducted from the bank statement balance.

The check from customer John, amounting to Br. 50.25, which was charged as a non-sufficient fund (NSF) item, needs to be deducted from the bank statement balance.

The service charge of Br. 12.70 for the month of July should be deducted from the bank statement balance.

The erroneous recording of check number 875, recorded as Br. 58 instead of Br. 85, should be deducted from the ledger balance.

By considering these adjustments, we can reconcile the bank statement balance and the ledger balance of ABC Company, determining the correct cash balance at July 31.

For similar question on cash balance.

https://brainly.com/question/13225323  

#SPJ8

B alone can finish the work in 15 days.

Let's assume that B takes x days to finish the work alone.

If A takes 5 days less than B to finish the work, then A takes (x - 5) days to finish the work alone.

We are given that A and B working together can finish the work in 6 days.

Using the concept of work rates, we can set up the following equation:

1/(x - 5) + 1/x = 1/6

To solve this equation, we can find a common denominator:

(x + x - 5)/(x(x - 5)) = 1/6

Simplifying the equation:

[tex](2x - 5)/(x^2 - 5x) = 1/6[/tex]

Cross-multiplying:

[tex]6(2x - 5) = x^2 - 5x[/tex]

[tex]12x - 30 = x^2 - 5x[/tex]

Rearranging the equation:

[tex]x^2 - 17x + 30 = 0[/tex]

Factoring the quadratic equation:

(x - 2)(x - 15) = 0

Setting each factor equal to zero:

x - 2 = 0   or   x - 15 = 0

Solving for x:

x = 2   or   x = 15

We discard the solution x = 2 since it suggests that B can complete the work in two days, which contradicts the fact that A takes five days fewer than B.

Therefore, B alone can finish the work in 15 days.

Learn more about word problems at https://brainly.com/question/21405634

#SPJ1

The best measure of spread to compare data sets depends on the data's nature and the analysis goals. For categorical data, the mode is appropriate. For numerical data, measures like standard deviation, range, or interquartile range (IQR) are commonly used.

In order to determine the best measure of spread to compare the data sets, we need to understand the characteristics of the data and the specific goals of the comparison.

If the data sets are categorical and consist of non-numeric values, such as different types of cakes, using the mode would be appropriate. The mode represents the most frequently occurring value and provides insight into the dominant categories within the data sets.

However, if the data sets are numerical, measures such as standard deviation, range, and interquartile range (IQR) are commonly used to analyze the spread of the data.

The standard deviation measures the dispersion of values around the mean. It provides a measure of the average deviation from the mean, making it useful when the data follows a roughly normal distribution.

The range is the simplest measure of spread, representing the difference between the maximum and minimum values in the data sets. It provides a quick indication of the overall spread, but it is sensitive to outliers.

The interquartile range (IQR) is the range between the first quartile (25th percentile) and the third quartile (75th percentile) of the data. It is resistant to outliers and provides a measure of the spread of the middle 50% of the data.

To determine the best measure of spread, you need to consider the characteristics of your data and the specific context of your analysis. There is no universally "best" measure, as it depends on the nature of the data and the purpose of the comparison.

In summary, the best measure of spread to use for comparing the data sets could be the standard deviation, range, or interquartile range (IQR), depending on the nature of the data and the goals of the comparison.

For more question on mode visit:

https://brainly.com/question/14532771

#SPJ8

The type of number that is irrational is a real number that cannot be expressed as a simple fraction or ratio of two integers.

An irrational number cannot be written in the form a/b, where a and b are integers and b is not equal to zero.

These numbers have non-repeating, non-terminating decimal representations.

Some examples of irrational numbers include the square root of 2 (√2), pi (π), and Euler's number (e).

Irrational numbers are infinitely non-repeating and cannot be represented by a finite decimal or fraction.

Their decimal expansions go on forever without settling into a repeating pattern. This property makes them distinct from rational numbers, which can be expressed as fractions or decimals that repeat or terminate.

The proof of a number being irrational often involves showing that there is no rational number that can represent it.

For instance, the square root of 2 cannot be expressed as a fraction, as it is a non-repeating decimal.

Irrational numbers are crucial in various mathematical fields and have significant applications in geometry, calculus, and number theory.

for such more questions on fraction

https://brainly.com/question/78672

#SPJ8

Answer:

Step-by-step explanation:

Rotation symmetry can be also defined as radial symmetry.  This is because no matter how many degrees you turn a figure or shape, it will still be the same figure/shape.

See attachment for an example.

Hope this helps! :)

Answer:

Step-by-step explanation:

1 oz = $1152

1 oz = 28 grams

0.1 oz = 2.8 grams

21/2.8 = 7.5

0.1 x 7.5 oz = (2.8 x 7.5)grams

0.75 oz = 21 grams

75% of 1152 is 864

So,

0.75 oz = $864

Answer:

Step-by-step explanation:

The net price factor for the CDs purchased by Hard Blues Music is approximately 0.91258.

The complement of the trade discounts provided by the wholesaler must be calculated.

The trade discounts of 4/3/2 signify price reductions of 4% for the initial discount, 3% for the subsequent discount, and then 2% for the third discount.

Let's perform a step-by-step analysis of the net price factor:

Second discount: 3% off the purchase price following the first reduction

Discount amount = 3% * $29,760 = $892.80

Price after the second discount = $29,760 - $892.80 = $28,867.20

Third discount: 2% off the price after the second discount

Discount amount = 2% * $28,867.20 = $577.34

Price after the third discount = $28,867.20 - $577.34 = $28,289.86

Now, let's calculate the net price factor by dividing the final price by the list price:

Net Price Factor = Price after discounts / List price

= $28,289.86 / $31,000

≈ 0.91258

So, the net price factor for the CDs purchased by Hard Blues Music is approximately 0.91258.

Learn more about net price factor here :

brainly.com/question/28985127

#SPJ1

The graph that represents the solution of y ≤ x² - 1 and x > y² - 3 is option D.The graph that represents the solution of y ≤ x^2 – 1 and x > y^2 – 3 is D.

In order to solve the given inequality y ≤ x² - 1 and x > y² - 3, we need to follow these steps:Firstly, we will rewrite the given inequality in standard form as y² - x + 3 ≤ 0 and x² - y - 1 ≥ 0.Then we need to find the solutions of the above two inequalities. By solving these two inequalities we get the region which is common to both the inequalities and we can plot it on the graph paper.In the first inequality y² - x + 3 ≤ 0, the coefficient of x is negative which means the parabola will be open downwards.

On plotting the parabola we can observe that it passes through (0, -3) and (-2, -1). Also, we can see that it intersects the x-axis at x = 3. Therefore, the solution to the inequality y² - x + 3 ≤ 0 is the region below the parabola including the boundary.In the second inequality x² - y - 1 ≥ 0, the coefficient of y is negative which means the parabola will be open downwards. On plotting the parabola we can observe that it passes through (0, -1) and (-2, 1). Also, we can see that it intersects the y-axis at y = -1.

Therefore, the solution to the inequality x² - y - 1 ≥ 0 is the region above the parabola including the boundary.Now, we need to find the common region between the two solutions obtained above. The common region will be the solution to the inequality y ≤ x² - 1 and x > y² - 3. By observing the graphs we can see that the common region is the shaded region inside the first parabola and outside the second parabola.The correct option is D.

For more such questions on graph

https://brainly.com/question/19040584

#SPJ8

The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

Learn more about quotient on:

brainly.com/question/27862246

#SPJ1

The percentage of the world population that is in the U.S. is approximately 4.3%.

To find the percentage of the world population that is in the U.S., we need to divide the population of the U.S. by the world population and then multiply the result by 100.

Let's calculate the percentage:

Percentage = (U.S. population / World population) * 100

Given that the U.S. population is approximately 310 million and the world population is approximately 7.2 billion, we can substitute these values into the equation:

Percentage = (310 million / 7.2 billion) * 100

To perform the calculation, we need to convert the populations to the same units. Let's convert 310 million to billion:

310 million = 310 / 1000 billion

          = 0.31 billion

Now, let's substitute the converted values:

Percentage = (0.31 billion / 7.2 billion) * 100

Simplifying the equation:

Percentage = 0.04305555556 * 100

          = 4.305555556

Rounding the result to the nearest tenth of a percent, the percentage of the world population that is in the U.S. is approximately 4.3%.

Therefore, approximately 4.3% of the world population is in the U.S.

for more such question on population visit

https://brainly.com/question/30396931

#SPJ8

The coordinates of the vertex of the parabola are (3, -7). The focus of the parabola is located at (3, -3). The equation of the directrix is y = -11.

The given equation of the parabola is in the form (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus/directrix.

Comparing the given equation with the standard form, we can see that the vertex is at (3, -7).

The coefficient 4p in this case is 16, so p = 4. Since the parabola opens upward, the focus will be p units above the vertex. Therefore, the focus is located at (3, -7 + 4) = (3, -3).

To find the directrix, we need to consider the distance p below the vertex. Since the parabola opens upward, the directrix will be p units below the vertex. Hence, the equation of the directrix is y = -7 - 4 = -11.

In summary, the coordinates of the vertex are (3, -7), the focus is located at (3, -3), and the equation of the directrix is y = -11.

for such more questions on parabola

https://brainly.com/question/29635857

#SPJ8

Answer:

Median: 7.42

Step-by-step explanation:

The median is the number in the middle of a set of numbers.

Numbers: 4.7, 8.51, 6.5, 7.42, 9.64, 7.2, 9.3

Order from least to greatest: 4.7, 6.5, 7.2, 7.42, 8.51, 9.3, 9.64

Median: 7.42

Out of the 225 people surveyed, 135 said they shop online, 27 said they always get their order delivered, and 54 said they had loyalty cards.

To calculate the number of people who said they shop online, we can use the percentage given. If 60% of the 225 people surveyed said they prefer to shop online, we can find the number by multiplying the total number of people surveyed by the percentage:

Number of people who shop online = 225 * 0.60

Number of people who shop online = 135

Therefore, 135 people said they shop online.

To find the number of people who have shopping delivered, we need to calculate 20% of the number of people who shop online:

Number of people with shopping delivered = 135 * 0.20

Number of people with shopping delivered = 27

Hence, 27 people said they always get their order delivered.

Now let's calculate the number of people who had loyalty cards. First, we need to find the number of people who said they go in-store to shop. This is 40% of the total surveyed:

Number of people who go in-store to shop = 225 * 0.40

Number of people who go in-store to shop = 90

Out of these 90 people, only 60% said they had loyalty cards:

Number of people with loyalty cards = 90 * 0.60

Number of people with loyalty cards = 54

Therefore, 54 people said they had loyalty cards.

For more such question on surveyed. visit :

https://brainly.com/question/15723299

#SPJ8

The variance (y^2) is determined by the z-scores and remains constant regardless of the values of x and μ.

Given:

Probability of x > 82.9: P(x > 82.9) = 0.1922

Mean of the normal distribution: μ = 72.4

We need to find the value of the variance (y^2).

Standardize the random variable x.

We need to find the z-score corresponding to the value x = 82.9 in order to determine the area under the standard normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

Since x follows a normal distribution with mean μ = 72.4, we can rewrite the formula as:

z = (82.9 - 72.4) / σ

Determine the z-score corresponding to the given probability.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to a probability of 0.1922. Let's denote this z-score as z1.

Find the z-score associated with the complement of the given probability.

Since we need to find P(x > 82.9), we subtract the given probability from 1 to find the probability of the complement event. Let's denote this complement probability as 1 - 0.1922 = 0.8078.

Using the standard normal distribution table or a calculator, find the z-score that corresponds to a probability of 0.8078. Let's denote this z-score as z2.

Apply the properties of the standard normal distribution to find the variance (y^2).

Since the z-scores for the given probability and its complement are z1 and z2, respectively, we can write:

z1 = (82.9 - 72.4) / σ

z2 = (x - 72.4) / σ

To find the variance (y^2), we need to solve for σ^2 in the equation above.

Solve for the variance (y^2).

Rearranging the equation for z1, we have:

σ = (82.9 - 72.4) / z1

Similarly, rearranging the equation for z2, we have:

σ = (x - 72.4) / z2

Since both equations represent the same standard deviation, we can equate them:

(82.9 - 72.4) / z1 = (x - 72.4) / z2

Substituting the values of z1 and z2, we get:

(82.9 - 72.4) / z1 = (x - 72.4) / z2

Substituting the given values, we have:

(82.9 - 72.4) / z1 = (82.9 - 72.4) / z2

Simplifying the equation, we get:

z2 = z1

Therefore, the variance (y^2) is determined by the z-scores and remains constant regardless of the values of x and μ.

for such more question on variance

https://brainly.com/question/9304306

#SPJ8

The ratio of total cholesterol to HDL cholesterol can be found by dividing the total cholesterol by the HDL cholesterol. So, the patient's ratio of total cholesterol to HDL cholesterol is:185 mg/dl ÷ 40 mg/dl = 4.625 mg/dl (dividing both numerator and denominator by 5)⇒ 37/8 (after simplification).

Thus, the patient's ratio of total cholesterol to HDL cholesterol is 37/8

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1