Calculus is hard. T-T

The standard equation of the parabola is ( y + 6 )²/4 + ( x - 3 )²/b² = 1

Given data ,

Let the vertices of the parabola be V₁ ( 3 , -4 ) and V₂ ( 3 , -8 )

So , the center of the parabola is C [ ( 3 + 3 )/2 , ( -4 - 8 ) / 2 ]

C = C ( 3 , -6 )

Now , the distance between the center and one of the vertices (which is the distance from the center to either vertex).

Using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

d = √((3 - 3)² + (-4 - (-6))²)

d = 2 units

The given point is (7, -12). If this point is closer to the x-axis (horizontally) than the center of the hyperbola, then the hyperbola is horizontally oriented.

The distance between the point P ( 7 , -12 ) and center is d₂ = √52 units

Now , the equation of the parabola is

((y - k)^2 / a^2) - ((x - h)^2 / b^2) = 1

where (h, k) is the center of the hyperbola, and a and b are the distances from the center to the vertices and the foci, respectively.

Plugging in the values we found:

Center: (h, k) = (3, -6)

a = 2

Hence , the equation is ( y + 6 )²/4 + ( x - 3 )²/b² = 1

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In the given diagram, the area of the sector is 61.25 square units

The arc length is 17.5 units

From the question, we are to calculate the area and arc length for the given sector.

If  we need to determine the area of a sector when the angle is given in radians, we will use the formula

Area of sector = (1/2) × r²θ

Where θ is the angle subtended at the center (in radians)

and r is the radius of the circle

From the given information,

r = 7

θ = 2.5

Thus,

Area of the sector = (1/2) × 7² × 2.5

Area of the sector = 61.25 square units

To determine the arc length, we will use the fromula

L = rθ

where L is the arc length

r is the radius of the circle

and θ is the angle measured in radians

Thus,

The arc length = 7 × 2.5

The arc length = 17.5 units

Hence, the arc length is 17.5 units

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Answer:

A. { 3, 4, 5, 6, 7, 8, 9, 10}  

B. {4}

Step-by-step explanation:

A. { 3, 4, 5, 6, 7, 8, 9, 10}  

⇒ We didn't include 2 in this because 2 = 2, not greater than 2.

⇒ We also didn't include 11 for the same reason. 11 = 11, not less than 11.

B. First of all, this tells us that x is a natural number, i.e. x ≥ 1

The second thing it tells us is that x = 4. So the answer is {4}

(I may have misunderstood B. If I'm not correct, I'm really sorry. )

The probability of winning the bet is: 3/7 or 0.43 or 43%

The probability of winning the bet can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In the question, the odds are given as 3 to 4 in favor of winning, which means that there are 3 favorable outcomes out of a total of 3 + 4 = 7 possible outcomes.

Therefore, the probability of winning the bet is: 3/7 or 0.43 or 43%

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Using the mathematical operations of multiplication and division, Miguel must buy 5 bunches to put 3 roses in each of the 18 vases if the roses are sold in bunches of a dozen.

The number of bunches of roses that Miguel needs to buy can be determined using mathematical operations.

The mathematical operations include multiplication and division.

The total number of roses in each vase = 3

The total number of vases = 18

The total number of roses required = 54 (3 x 18)

1 dozen = 1 bunch

12 roses = 1 dozen

Dozens or bunches to buy = 4.5 (54 ÷ 12)

= 5 bunches or dozens

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Answer:

36 pounds of bananas and 16 pounds of graphs

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

q = -1/8

Step-by-step explanation:

You're trying to solve for q
32q+4=0

Subtract 4 both sides
32q=-4

Now Divide -4 by 32 (This means you have to simplify)
-4/32 = -1/8 due to the common factor of 4.

q = -1/8

Answer:

4(8q+1)

Step-by-step explanation:

32q+4

4*8q+4*1

4(8q+1)

a) At least 5,675 adults. b) When we use the results from the 2014 survey, we still need to survey at least 5,675 adults.

c) It doesn't have much of an effect on the sample size.

We are the given information

(a) To find the minimum sample size needed, we will use the formula:

n = (z² × p × (1-p)) / E²

where z is the z-score corresponding to the desired confidence level (99%), p is the estimated proportion of e-cigarette users that is 3.65% or 0.0365), and E is the 3 percentage points or 0.03.

Plugging in these values, we get,

n = (2.576² × 0.0365 × 0.9635) / 0.03²

n = 5,674.8

n = 5,675

Therefore, we need to survey at least 5,675 adults to obtain today's e-cigarette usage rate with a 99% confidence level and a margin of error of 3% points.

(b) Using the same formula as above, we get:

n = (2.576² × 0.0365 × 0.9635) / 0.03²

n = 5,674.85

n = 5,675

Therefore, even if we use the results from the 2014 survey, we still need to survey at least 5,675 adults to obtain today's e-cigarette rate with a 99% confidence level and a margin of error of 3 percentage points.

(c) The use of the results from the 2014 survey does not have much of an effect on the sample size  because the desired confidence level and margin of error are constant, and the estimated proportion from the 2014 survey is relatively close to the true proportion.

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The number of times 9.52 x 10-5 is greater than 1.7 x 10-6 is 56

From the question, we have the following parameters that can be used in our computation:

9.52 x 10-5 than 1.7 x 10-6

The number of times is the quotient of both numbers

So, we have

Times = (9.52 x 10^-5)/(1.7 x 10^-6)

Evaluate

Times = 56

Hence, it is 56 times greater

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Answer:

The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.

Step-by-step explanation:

a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.

The total number of free throws are 1625.

Given that, Julian missed 4% of the free throws he attempts in a season.

Here, the number of throw Julian missed is 65.

Let the total number of throws be x.

Now, 4% of x=65

4/100 ×x=65

0.04x=65

x=65/0.04

x=1625

Therefore, the total number of free throws are 1625.

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The values of the probabilities are P(1 and A) = 1/24, P(odd and B) = 1/8 and P(Prime and D) = 1/8

We can determine the probability of each event using basic probability rules.

Assuming the spinner and number cube are fair and equally likely:

The probability of rolling a 1 is 1/6, and the probability of the spinner landing on A is 1/4.

Therefore, P(1 and A) = (1/6) * (1/4) = 1/24.

Similarly, we have

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The sοlutiοn οf the given prοblem οf trigοnοmetry cοmes οut tο be Tan(alpha + beta) = 121/63 and cοs(alpha + beta) = (-144/221)(56/221)(-8064/48841), respectively.

Sοme claim that the fusiοn οf many fields played a rοle in the develοpment οf astrοphysics. Exact mathematical methοds can be used tο sοlve a variety οf metric prοblems οr determine a calculatiοn's οutcοme. Frοm a scientific standpοint, trigοnοmetry is the investigatiοn οf the six fundamental geοmetric calculatiοns. Numerοus οther names and abbreviatiοns are alsο used fοr them, such as sine, variance, guidance, and οthers. (csc).

Here,

The fοllοwing trigοnοmetric identities are applicable:

cοs(alpha + beta) = cοs(alpha)cοs(beta) - sin(alpha)sin(beta)

sin(alpha + beta) = sin(alpha)cοs(beta) + cοs(alpha)sin(beta)

tan(alpha + beta) = (tan(alpha) + tan(beta))/(1 - tan(alpha)tan(beta))

We can use the Pythagοrean identity tο get cοs(alpha) since we knοw frοm the given data that sin(alpha) = 15/17:

=> cοs(alpha) = √(1 - sin²(alpha)) = √(1 - (15/17)²) = 8/17

We may use the Pythagοrean identity tο get cοs(beta) because we alsο knοw that sin(beta) = 12/13.

=> √(1 - sin²(beta)) = √(1 - (12/13)2) = -5/13 fοr cοs(beta). (since beta is in quadrant II)

The values οf cοs(alpha + beta), sin(alpha + beta), and tan(alpha + beta) are as fοllοws:

=> Alpha + beta cοs = cοs(alpha)beta

=> cοs(alpha + beta) = cοs(alpha)cοs(beta) - sin(alpha)sin(beta)

=> (8/17)(-5/13) - (15/17)(12/13)

=> -144/221

=> sin(alpha + beta) = sin(alpha)cοs(beta) + cοs(alpha)sin(beta)

=> (15/17)(-5/13) + (8/17)(12/13)

=> 56/221

=> tan(alpha + beta) = (tan(alpha) + tan(beta))/(1 - tan(alpha)tan(beta))

=> (15/8 + (-12/5))/(1 - (15/8)(-12/5))

=> 121/63

=> Tan(alpha + beta) = 121/63 and cοs(alpha + beta) = (-144/221)(56/221)(-8064/48841), respectively.

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The correct linear equation that shows the relationship between the two types of wood purchased by the contractor is option A. 45(x+3)=60x.

Let's break down the problem,

The contractor purchased 45 units of expensive wood and 60 units of cheap wood for the same total price.

Let's assume that the price of the 60 units of cheap wood is x.

According to the problem, 45 units of expensive wood cost $3.00 more per unit than 60 units of cheap wood. This means that the price of the 45 units of expensive wood is (x+3).

Now, we can set up the equation,

The total cost of 45 units of expensive wood + Total cost of 60 units of cheap wood = Total cost of wood purchased

45(x+3) + 60(x) = 105(x)

Simplifying this equation, we get:
45x + 135 + 60x = 105x
105x = 135
x = 1.29

Therefore, the price of the 60 units of cheap wood is $1.29, and the price of the 45 units of expensive wood is $4.29.

Substituting the value of x in option A, we get:
45(x+3) = 45(1.29+3) = 45(4.29) = 193.05
60x = 60(1.29) = 77.4

Total cost of wood purchased = 193.05 + 77.4 = 270.45

This confirms that option A is the correct linear equation that shows the relationship between the two types of wood purchased.

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The absolute value of -13 is equal to 13.

The absolute value (also known as the modulus) of a number is the non-negative value of that number without regard to its sign.

For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.

The absolute value of a number is denoted by vertical bars on either side of the number. For instance, the absolute value of x is written as |x|.

A number is a mathematical object that is used to represent a quantity or value. Numbers can be classified into different types, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

Therefore 13 is the absolute value.

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The fraction that we need to subtract from 3/4 to get 2/3 is 1/12.

Let's use x to represent the fraction that we need to subtract from 3/4 to get 2/3.

We can set up an equation:

3/4 - x = 2/3

3/4 - x = 2/3

x = 2/3 - 3/4

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the fractions with a denominator of 12:

x = (2/3) * (4/4) - (3/4) * (3/3)

x = 8/12 - 9/12

Now we can combine the fractions:

x = -1/12

Therefore, the fraction that we need to subtract from 3/4 to get 2/3 is 1/12.

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Answer: 1

Step-by-step explanation:

Tan(45°)= 1

Answer:

1

Step-by-step explanation:

tangent of a 45 degree angle is 1

to find tangent, it is the length of the side opposite to an angle divided by the adjacent side

so the tangent of the top angle (which measures 45 degrees) is 1/1 since the adjacent and opposite sides both measure 1, therefore the tangent is 1 bc 1/1=1.

this proves that the tangent of a 45 degree angle is 1

The angle of Depression of the boat to the shark is 21°.

Angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is also the angle between the horizontal line and the line of sight.

How to determine this

To find the angle x°

Sin x° = Perpendicular/Hypotenuse

Sin x° = 6.7 m/20.6 m

Sin x° = 0.325

x° = [tex]Sin^{-1}[/tex] 0.325

x° = 21.07°

x = 21° to nearest whole number

Therefore, the angle of depression of the boat is 21°

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The simplified sum is (2x²+x-7)/[(x+4)(x-2)] of the expression (2x+3)/(x+4)+(x-1)/(x²+2x-8)

In the expression there are two fractions

To add the two fractions, we need to have a common denominator.

The denominator of the first fraction is x+4, while the denominator of the second fraction is x²+2x-8=(x+4)(x-2).

Therefore, we can write:

(2x+3)/(x+4) + (x-1)/(x²+2x-8) = (2x+3)/(x+4) + (x-1)/[(x+4)(x-2)]

Now, we can sum the fractions by finding a common denominator and adding the numerators:

(2x+3)/(x+4) + (x-1)/[(x+4)(x-2)] = [(2x+3)(x-2) + (x-1)(x+4)]/[(x+4)(x-2)]

= (2x²+x-7)/[(x+4)(x-2)]

Therefore, the simplified sum is (2x²+x-7)/[(x+4)(x-2)], which is option (C).

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Answer:

(4x + 10) cm

Step-by-step explanation:

Given:

A rectangle

l (length) = (x + 5) cm

w (width) = x cm

Find: P (perimeter) - ?

The perimeter is the sum of all side lengths (there are 2 sides of width x and 2 sides of length (x + 5)):

P = 2x + 2(x + 5) = 2x + 2x + 10 = 4x + 10

Store revenue will be maximised, if they charge 7 dollars for each movie rental.

The entire amount of money received by an organisation's operations over a predetermined period of time is the basic definition of revenue.

A company's revenue is its total revenue before any expenses are subtracted. According to the definition, revenue is the total sum of money obtained through conducting commercial activities like sales.

Let store charge x $ for each movie.

No.of rented movies per weak = 108-9x(x-z)

Total revenue = x*[108-9(x-2)]

= x*[108-9x+18]

= x*[126-9x]

= 126x-9x^2

Total revenue will be maximised when dT/dx = 0

dT/dx = 126-9*2x

= 126-18x = 0

18x = 126

x = 7$

Store revenue will be maximised, if they charge 7 dollars for each movie rental.

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your answer for h(x)=x2-1 will be 5 the photo will demonstrate how it is solved

Answer:  20% down on the $184,000 house would be $36,800.

Step-by-step explanation: To find 20% of the purchase price, we can multiply the price by 0.2 (which is the same as dividing by 5):

20% of $184,000 = 0.2 x $184,000 = $36,800

Therefore, 20% down on the $184,000 house would be $36,800.

Answer:

Theoretical probability is a mathematical concept that represents the likelihood of an event occurring based on mathematical reasoning or calculation. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes in a given situation. For example, the theoretical probability of flipping a coin and getting heads is 1/2, because there is one favorable outcome (heads) out of two possible outcomes (heads or tails).

Experimental probability, on the other hand, is based on actual observations or experiments. It is calculated by conducting an experiment and counting the number of times an event occurs, then dividing that by the total number of trials. For example, if you flip a coin 100 times and get heads 55 times, the experimental probability of getting heads is 55/100 or 0.55.

The main difference between theoretical and experimental probability is that theoretical probability is based on mathematical calculations and reasoning, while experimental probability is based on actual observations and experiments. Theoretical probability is used to predict the likelihood of an event occurring, while experimental probability is used to estimate the likelihood of an event occurring based on observed data.

In the given problem, considering the range of data,  the correct box plot is b. Therefore, option b is the correct answer in the given problem.

The range of the data is from 11 to 31, so options a, c, and d are incorrect because the whiskers extend beyond this range.

In option b, the box extends from 13 to 27, which covers the range of the data. The line in the box is at 24, which is the median score. The whiskers end at 11 and 31, which are the minimum and maximum scores, respectively. This box plot accurately represents the given data.

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Answer:

y = - 4x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 13) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-13}{0-(-2)}[/tex] = [tex]\frac{-8}{0+2}[/tex] = [tex]\frac{-8}{2}[/tex] = - 4

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - 4x + 5 ← equation of line

Answer:

Step-by-step explanation:

The answer is B, 6/10. This is because the probability of pulling out a number that is divisible by 2 or 3 is 6 out of 10.

Outcome is the result of an action, event or process. It is the final product or effect of an activity and is often used to measure the success or failure of something.

This can be calculated by dividing the number of events that meet the criteria by the total number of possible outcomes.

In this case, there are 6 numbers that are divisible by 2 or 3 (2,3,4,6,8,9) and 10 pieces of paper with numbers 1 to 10, so 6/10.

To express this probability in percentages, the answer would be 60%. This means that there is a 60% chance of pulling out a number that is divisible by 2 or 3.

This type of probability calculation is used in many situations, such as determining the probability of an event occurring in a game or determining the likelihood of something happening in a given sample size. It is important to understand how to calculate these probabilities in order to make informed decisions.

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There are a total of 1 + 3 = 4 original values that are greater than 80.

A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.

We can count the number of data values in the data set by looking at the stem-and-leaf plot. There are:

So, there are a total of 3 + 14 + 5 + 2 = 24 data values in the data set.

To find how many of the original values are greater than 80, we need to look at the last stem (9#) and the stem before that (8#). We can see that there are:

So, there are a total of 1 + 3 = 4 original values that are greater than 80.

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The estimate for the mean time spent dancing is given as follows:

27 minutes.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

In this problem, we have a grouped frequency chart, hence, using the midpoint rule, the observations are given as follows:

Hence the mean is given as follows:

M = (11 x 6 + 25 x 18 + 23 x 30 + 15 x 42 + 6 x 54)/(11 + 25 + 23 + 15 + 6)

M = 27.

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The ocean current has a bearing of S 50.3º E and a speed of 60 miles per hour.

Speed is defined as the rate of change of distance with time. It has the dimension of distance by time. Thus, the SI unit of speed is given as the combination of the basic unit of distance and the basic unit of Time. Thus, the SI unit of speed is metre per second.

We know that the SS Bigfoot is traveling on a course of N 35º W, which means its bearing with respect to due north is 35º westward. To find the ocean current's bearing and speed, we need to use the information about the captain's position after half an hour of travel.

In half an hour, the SS Bigfoot has traveled at a speed of 49 miles per hour * 0.5 hours = 24.5 miles. From the diagram, we can see that the captain's position after half an hour of travel forms a right triangle with the bay and the point where the captain started.

Let's call the point where the captain started Point A, the captain's position after half an hour Point B, and the bay Point C. We know that the distance between Point A and Point B is 24.5 miles, and the distance between Point B and Point C is 30 miles. We can use the Pythagorean theorem to find the distance between Point A and Point C:

a² + b² = c²

24.5² + 30² = c²

c ≈ 39.0 miles

So the captain is 39.0 miles from the bay after half an hour of travel.

Now we can use trigonometry to find the bearing of the ocean current. Let's call the bearing of the ocean current x. We know that:

tan x = opposite/adjacent

tan x = 30/24.5

x ≈ 50.3º

So the ocean current has a bearing of S 50.3º E.

To find the speed of the ocean current, we can use the formula:

speed = distance/time

The distance traveled by the captain is the same as the distance of the ocean current, which is 30 miles. The time it took for the captain to travel this distance is half an hour. Therefore:

speed = 30/0.5 = 60 miles per hour

So the ocean current has a speed of 60 miles per hour.

Putting it all together, the ocean current has a bearing of S 50.3º E and a speed of 60 miles per hour.

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