Give the required elements of the hyperbola.
y²/9 - x²/4 =1
The hyperbola opens:
a. Horizontally
b. Vertically

Answer:

x = 4/9

Step-by-step explanation:

Remember when you subtract logs, you divide the numbers;

This means;

log x - log (x+4) = -1   ---------can be written as;

\(log\frac{x}{x+4} =-1\)

Eliminate the log as

\(\frac{x}{x+4} =10^{-1}\)

x/ x+4 = 1/10

10x=x+4 --------collect like terms

10x-x =4

9x = 4 ------find value of x

x= 4/9

To solve the expression (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · [18 + 3 · (13 - 9) - 5], we follow the hierarchy of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

By applying this hierarchy, we can simplify the expression step by step to find the result.

Following the hierarchy of operations, we start by simplifying expressions within parentheses and brackets.

First, within the brackets, we evaluate the expression (13 - 9) which equals 4. Therefore, [18 + 3 · (13 - 9) - 5] becomes [18 + 3 · 4 - 5].

Next, we evaluate the multiplication within the brackets: 3 · 4 equals 12. Thus, [18 + 3 · 4 - 5] simplifies to [18 + 12 - 5].

Moving outside the brackets, we proceed with addition and subtraction: 18 + 12 equals 30, and 30 - 5 equals 25. Therefore, [18 + 12 - 5] becomes 25.

After simplifying the brackets, we can now evaluate the remaining expression: (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · 25.

Within the parentheses, we perform addition: 42 + 20 equals 62. Thus, the expression becomes 62 ÷ 4 - 2 · (9 ÷ 3) - 2 · 25.

We continue by evaluating the division: 62 ÷ 4 equals 15.5. The expression now becomes 15.5 - 2 · (9 ÷ 3) - 2 · 25.

Next, we perform the division within the parentheses: 9 ÷ 3 equals 3. The expression becomes 15.5 - 2 · 3 - 2 · 25.

Finally, we evaluate the remaining multiplications: 2 · 3 equals 6, and 2 · 25 equals 50. The expression becomes 15.5 - 6 - 50.

Continuing with the subtraction, we have 15.5 - 6 equals 9.5. Therefore, the final result of the expression (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · [18 + 3 · (13 - 9) - 5] is 9.5.

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i think D hope it helps

Step-by-step explanation:

1 7/8 the least because it farther from the line than 0

Answer:

D. -1 7/8, -1 1/4, -1 1/2, 1

Answer:

The slope is 2/3

Step-by-step explanation:

y is 4 and x is 6 so it will be 4/6 then divide 2

4:2 = 2

6:2 = 3

2/3

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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the volume of the sealed balloon at 33 feet would be 3 cubic inches.

To determine the volume of the sealed balloon at 33 feet, we can apply Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure.

Boyle's Law can be expressed as:

P1 * V1 = P2 * V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

In this case, we have:

P1 = pressure at 99 feet

V1 = volume at 99 feet

P2 = pressure at 33 feet

V2 = volume at 33 feet (unknown)

Let's assume the pressure at 99 feet is P1 and the pressure at 33 feet is P2. Since we don't have specific pressure values, we'll use the relative pressure ratios between the two altitudes.

The pressure at higher altitude (99 feet) is lower compared to the pressure at lower altitude (33 feet). Therefore, P1 is less than P2. Let's assume P1 is half of P2.

Now, we can set up the equation:

P1 * V1 = P2 * V2

Let's assume V1 is 6 cubic inches. Then:

(0.5) * 6 = 1 * V2

3 = V2

Therefore, the volume of the sealed balloon at 33 feet would be 3 cubic inches.

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Answer:

Total mixture = (8x + 15y) / 100

Step-by-step explanation:

Butterfat x:

= 8% of x

= 8/100 * x

= (8 * x) / 100

= 8x / 100

Butterfat y:

= 15% of y

= 15/100 * y

= (15 * y) / 100

= 15y / 100

Total mixture = butterfat x + butterfat y

= 8x / 100 + 15y / 100

= (8x + 15y) / 100

Total mixture = (8x + 15y) / 100

Answer:

x = -8

Step-by-step explanation:

Answer:

Solution given;

2-(3x+5)=5-2x

2-3x-5=5-2x

-3-5=3x-2x

x=-8 is your answer.

Answer:

96

Step-by-step explanation:

8x6=48

48x2=96

Therefore, the correct answer is B) The series diverges, and the terms of the series have limit o.

The integral test is a powerful tool used to determine whether an infinite series converges or diverges. The integral test states that if an infinite series has a non-negative and decreasing term, then the series is convergent if and only if the corresponding integral is convergent. In the case of the series ∑n=2[infinity]1nlnn, we can apply the integral test by considering the function f(x) = 1/xlnx. This function is decreasing and positive for all x > 2. Therefore, we can integrate f(x) from 2 to infinity to obtain the integral ∫2[infinity]1/xlnx dx. Evaluating this integral, we get ln(lnx)|2[infinity], which diverges. Since the integral diverges, we can conclude that the series ∑n=2[infinity]1nlnn also diverges.

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Answer:

The correct option is (B).

Step-by-step explanation:

In this case, we need to test whether the claim made by the new brand of gym shoe is correct or not.

Claim: A new brand of gym shoe claims to add up to 2 inches to an athlete’s vertical leaps.

So, we need to test whether the average vertical leap of all the athletes increased by 2 inches or not after using the new brand of gym shoe.

The sample procedure would be to compute the average vertical leap of a group of athletes in their regular shoes (or a different pair) and the average vertical leap of a group of athletes in their new shoes.

Compare the two averages to see whether the difference is 2 inches or not.

The experimental group would be the one with the new shoes and the control group would be the one with the different pair of shoes.

Thus, the correct option is (B).

Answer:

B) Find the average vertical leap of all the athletes in their regular shoes. Give the experimental group the new shoes and the control group a different pair of shoes. Find the average vertical leap of the athletes in both groups. Compare the increases in vertical leap for each group.

Step-by-step explanation:

Answer:

Opposite interior angles of a rhombus are congruent (the same). All 4 of them equal up to 360

Total number of students in Ridgewood Junior High School are 184.

It is given in the question that:-

Number of students who brought their lunch = 46

Percent of students who brought their lunch = 25 %

We have to find the total number of students in Ridgewood Junior High School.

Let the total number of students be 4x.

Hence,

25 percent of 4x = (1/4)*4x = x = Number of students who brought their lunch

We know that 46 students brought their own lunch.

Hence, we can write,

x = 46

Hence,

Total number of students = 46*4 = 184 students.

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A car engine has an efficiency of about 30% is a true statement.

the  factual  effectiveness of a auto machine can vary grounded on  colorful factors  similar as machine size, type, and design, as well as driving conditions and  conservation.   The  effectiveness of an machine is a measure of how  important of the energy produced by the energy is converted into useful work,  similar as turning the  bus of a auto.

In an ideal situation, an machine would convert all the energy from the energy into useful work. still, due to  colorful factors  similar as  disunion and heat loss, this isn't possible.   The  effectiveness of a auto machine is  generally calculated by dividing the  quantum of energy produced by the energy by the  quantum of energy used by the machine. This is known as the boscage  thermal  effectiveness( BTE) of the machine.

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The ordered pair in the row you described would be (6,8), since we write ordered pairs in the form (x,y) and those are the x and y values in the table.

f(3) is asking "What y-value is paired with the x-value of 3?"  

f(x) = -5 is asking "What x-value is paired with the y-value of -5?"

Can you read the answers for the last two from your table?

Based on the given table, the ordered pair in the first row is (-6, 8), f(3) is -2, and f(x) = –5 when x is 4.

The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).

This is because the first column represents the input values (x) and the second column represents the corresponding output values (f(x)).

f(3) is -2.

This can be determined by finding the value of f(x) when x is 3. According to the table, when x is 3, the corresponding value of f(x) is -2.

f(x) = –5 when x is 4.

This can be determined by finding the value of x when f(x) is -5. According to the table, when f(x) is -5, the corresponding value of x is 4.

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Answer:

3.5 and 10/3

Step-by-step explanation:

just took the quiz

Answer: C.) 3.5 and D.) 10/3

Step-by-step explanation: i hope this helps :)

Answer:

Step-by-step explanation:

arc KL = 60°

arc LNK = 360° - 60°

arc NJK = 180°

angle JQN = 60°

arc JN = 60°

arc JM = 60°+55° = 115°

arc MN = 55°

arc MKN = 360° - 55° = 305°

arc JML = 180°

angle MQL = 180° - 55° - 60° = 65°

arc ML = 65°

arc LN = 55° + 65° = 120°

By comparing the boxplots, you can observe the differences in the distribution of BMI values between males and females. Look for differences in the medians, interquartile ranges, and any outliers.

To construct boxplots for the body mass index (BMI) data sets for males and females, we first need to gather the necessary information.

To create a boxplot, you need the five-number summary of the data set: minimum value, lower quartile (Q1), median, upper quartile (Q3), and maximum value. These statistics help to visualize the distribution and compare the data sets.

Once you have the five-number summary for both males and females, draw two number lines and place the respective summaries on each line. Then, construct a box around the quartiles and draw lines (whiskers) extending to the minimum and maximum values. This will create two boxplots side by side.

These differences can indicate variations in BMI between the genders.

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1. When the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

2.  The probability of detecting the change is 0.0495 or 4.95%.

To solve this problem, we'll use the concept of control limits and the sampling distribution of the sample means.

When the population mean shifts to 7.8: First, let's calculate the standard deviation of the sampling distribution, also known as the standard error (SE). The formula for SE is given by SE = σ / sqrt(n), where σ is the standard deviation of the population (1.0 ounce) and n is the sample size (47).

SE = 1.0 / sqrt(47) ≈ 0.145

Next, we need to determine the z-score corresponding to the lower and upper tails of the sampling distribution that capture 5% each. Since the total probability in both tails is 10%, each tail will have a probability of 5%. We can find the z-scores using a standard normal distribution table or calculator.

The z-score corresponding to the lower tail of 5% is approximately -1.645.

The z-score corresponding to the upper tail of 5% is approximately 1.645.

Now, let's calculate the lower and upper control limits:

Lower Control Limit (LCL) = Population Mean - (z * SE)

Upper Control Limit (UCL) = Population Mean + (z * SE)

LCL = 7.8 - (-1.645 * 0.145) ≈ 8.026

UCL = 7.8 + (1.645 * 0.145) ≈ 9.574

To find the probability of detecting the change, we need to calculate the area under the sampling distribution curve that falls beyond the control limits. In this case, we're interested in the area above the upper control limit.

Since the distribution is assumed to be normal, we can use the standard normal distribution's cumulative distribution function (CDF) to calculate this probability.

Probability of detecting the change = 1 - CDF(z-score for UCL)

Using the z-score for the upper control limit (UCL), we can calculate the probability.

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 7.8, the probability of detecting the change is approximately 0.0495 (or 4.95%).

When the population mean shifts to 8.6: We'll follow the same steps as before.

SE = 1.0 / sqrt(47) ≈ 0.145

The z-score corresponding to the lower tail of 5% is still approximately -1.645.

The z-score corresponding to the upper tail of 5% is still approximately 1.645.

LCL = 8.6 - (-1.645 * 0.145) ≈ 8.926

UCL = 8.6 + (1.645 * 0.145) ≈ 10.274

Probability of detecting the change = 1 - CDF(z-score for UCL)

Probability of detecting the change ≈ 1 - CDF(1.645) ≈ 0.0495

Therefore, when the population mean shifts to 8.6, the probability of detecting the change is also approximately 0.0495 (or 4.95%).

In both cases, the probability of detecting the change is 0.0495 or 4.95%.

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Answer:

\(\frac{5}{3} \\.3846153846\)

Step-by-step explanation:

Answer:

$64.00

Step-by-step explanation:

12.80

x5

_______

$64.00

Answer:

Help

Step-by-step explanation:

As per the regression equation, the value of intercept coefficient is 1.5707

Regression is a statistical technique used to determine the relationship between an independent variable and a dependent variable.

In this case, the regression statistics provided in table 6 show the results of estimating the model

=> Δln (Sales t) = b0 + b1Δln (Sales t −1) + εt,

where Δln (Sales t) is the change in the natural log of sales for Cisco Systems quarterly observations from 3Q:1991 to 4Q:2000.

The R-squared value of 0.0661 indicates that only about 6.61% of the variation in the change in the log of sales can be explained by the change in the log of sales from the previous quarter.

The standard error of 0.4698 indicates the average deviation between the actual and predicted change in the log of sales.

If the results show that the specification is correct, then the long-run change in the log of sales toward which the series will tend to converge can be determined by the intercept coefficient, which in this case is 1.5707.

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Therefore , the solution of the given problem of mean comes out to be value of the mean is 600.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate: Divide by how many digits there are after adding up all the digits. the total divided by the count.

Here,

Given :The sum is 600.

The average arithmetic mean of x, y and z is 50.

=>(x + y + z)/350, sox + y + z = 150

=>4x + y + 3y+z+32

=>4x+4y+4z 4x+4y+4z4(x+y+ z) 4(x+y+2)

=> 4*150 = 600

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The radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.

We are given the surface area (A) of the zorb and asked to find its radius (r) using the formula r = √(A / 4π). Let's follow these steps to solve for the radius:
1. Write down the given information:
  A (surface area) = 49.29 sq m
2. Write down the formula for the radius of a sphere:
 r = (√A / 4π)
3. Plug in the given surface area (A) into the formula:
  r = √(49.29 / 4π)
4. Calculate the value inside the square root:
  49.29 / 4π ≈ 3.923
5. Take the square root of the calculated value:
  r = √(3.923) ≈ 1.98
So, the radius of the zorb with an outside surface area of 49.29 sq m is approximately 1.98 meters.

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Answer: 3

Step-by-step explanation:

3(-1)^2

Answer: 3

Step-by-step explanation:

hope this helps

9514 1404 393

Answer:

  ∠Z = 34°

  ∠T = 56°

Step-by-step explanation:

You can solve for x using the measure of the right angle:

  90 = 3x +6

  30 = x +2 . . . . . divide by 3

  28 = x . . . . . . . . subtract 2

Then the measure of T is ...

  ∠T = 2x° = 2(28)° = 56°

  ∠Z is its complement: 90° -56° = 34°

The angle measures are ...

  m∠Z = 34°

  m∠T = 56°

To covert a fraction to it's simplest form we need to divide their numerator and denominator with the same number .

= 16/40

= 16 ÷ 4 / 40 ÷ 4

= 4/10

= 4 ÷ 2 / 10 ÷ 2

= 2/5

Since both the numerator and denominator dont have a common factor , we can say that they are in their simplest form .

Therefore , the fraction 16/40 = 2/5

The probability of winning $3,899 is 0.0001, which is a very small probability, but still possible.

To write the probability distribution for a player's winnings in the Pick 4 game, we need to consider all the possible outcomes and their probabilities.

There are a total of 10,000 possible four-digit numbers that can be drawn in the game. Since the player has to match the numbers in the exact order, there is only one winning combination for each four-digit number. Therefore, the probability of winning is 1/10,000.

To calculate the player's winnings, we need to subtract the $1 cost of playing from the $3,900 prize. Thus, the player's net winnings can be calculated as follows:

Net Winnings = $3,900 - $1 = $3,899

The probability distribution for the player's winnings can be summarized in the following table:

| Winnings (x) | Probability (P) |
|--------------|-----------------|
| $0           | 0.9999          |
| $3,899       | 0.0001          |

Note that the table shows the possible winnings (x) in ascending order, as requested. The probability of winning $0 is 0.9999, which means that the player is most likely to lose their $1 bet.

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Answer:

C

Step-by-step explanation:

\( \frac{10 + 5 + 3 + 2 +5 }{5} = \frac{25}{5} = 5\)