A line T, is tangent to the curve y = x² at the point A(1,1), and crosses the x axis at (0.5, 0). Point A is joined to point P (also on the curve y = x²) by the chord AP.
a) calculate the gradient of the tangent T.
b) calculate the gradient of the chord AP when P has coordinates:
i) (2,4)
ii) (1.5, 2.25)
iii) (1.1, 1.21)
iv) (1.01, 1.0201)
v) ( (1+h), (1+h)^2)
c) comment on the relationship between your answers to parts a and b

Answer:

324 ft

Step-by-step explanation:

\(v=\sqrt{2gh}\)

\(v^2=(\sqrt{2gh})^2\)

\(v^2=2gh\)

\(\frac{v^2}{2g}=\frac{2gh}{2g}\)

\(\frac{v^2}{2g}=h\)

\(\frac{144^2}{2(32)}=h\)

\(\frac{20736}{64}=h\)

\(324=h\)

The probability that a student has been to the United Kingdom or Japan is 0.66.

This can be calculated using the following formula:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, P(A) is the probability that a student has been to the United Kingdom, P(B) is the probability that a student has been to Japan, and P(A and B) is the probability that a student has been to both the United Kingdom and Japan.

Therefore, the probability that a student has been to the United Kingdom or Japan is:

P(A or B) = 0.28 + 0.52 - 0.14 = 0.66

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Answer:

Step-by-step explanation:

Solving for x,

This way, we can conlcude that:

The volume v of the solid obtained by rotating the region bounded by the given curves is 486π.

x = 2✓3y

x > 0

y = 9

Volume = √ 9S0 (2✓3y)2dy

= π 9S0 4✓(3y) dy

= π 12 (9²/2

= 6π (81)

= 486π

The volume is 486π.

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The  \(13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)  equation can be used to calculate the surface area of the triangular prism.

It is given that the triangular prism net showing in the figure with dimensions.

It is required to find which equation can be used to find the surface area of the triangular prism net.

It is defined as the area of 3-dimensional geometry surfaces area sum which is occupying the outer area of the object.

We know the area of a rectangle = length × width

Area of the top rectangle = 13×10

Area of the middle rectangle = 12×10

Area of bottom rectangle=  5×10

The formula for finding the area of a triangle:

\(\rm A=\frac{1}{2} \times bh\)

Area of right triangle = \(\rm \frac{1}{2} \times 5 \times12\)

Area of left triangle = \(\rm \frac{1}{2} \times 5 \times12\)

The surface area = Area of top+ Area of middle+ Area of bottom+ Area of    

                                a right triangle+ Area of the left triangle  

\(=13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)

Thus, the \(13\times10+12\times10+5\times10+\rm \frac{1}{2} \times 5 \times12+\rm \frac{1}{2} \times 5 \times12\)  equation can be used to calculate the surface area of the triangular prism.

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Answer: p = (-1/3)x + 700

Step-by-step explanation:

To find the equation of the line that relates the price of the recliners to the number sold, we need to use the two given data points: (p=300, x=600) and (p=275, x=675).

We know that the equation of a line in slope-intercept form is y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept. The slope formula is (y2-y1)/(x2-x1).

In this case, the dependent variable is the price (p) and the independent variable is the number of recliners sold (x). So we want to find the equation p = mx + b.

First, we need to find the slope (m) of the line. The slope is given by:

m = (change in p) / (change in x)

m = (275 - 300) / (675 - 600)

m = -25 / 75

m = -1/3

Next, we can use one of the given data points and the slope to find the y-intercept (b) of the line. Let's use the point (300, 600):

600 = (-1/3) * 300 + b

600 = -100 + b

b = 700

Therefore, the equation that relates the price of the recliners to the number sold is:

p = (-1/3)x + 700.

The statement says that if the result is even integer (like 2, 4, 6, ...) then x and y also are. If we want to disprove that, we need to look for a even integer that have x and/or y not even integer.

All alternatives but c have even integers as result, but only d show x and y odd integers.

So, "d" clearly disproves the statement, because they show that the sum of two odd integers (1 and 3) results in an even integer (4), which contradicts the statement.

Answer:

PROOF FOR THE "PROVE" SECTION:

As linear pairs, angle 2 and 3 are supplementary to each other. Angle 1 is equal to angle 2, as they are both same-side interior angles. Therefore, angle 1 and angle 3 are also supplementary.

Filling in the missing blanks:

S1. Angle 1, Angle 2, Angle 3

S2. Angle 1 and Angle 2

R3. Congruent (___)

R5. supplementary angles

S7. Angle 1 = Angle 2, so Angle 1 can be substitued in for Angle 2 in any equation, and Angle 2 can be substitued for Angle 1 in any equation as well (they can replace each other, like x=y & y=x or a=b & b=a)

Hope this helped! Have a great day (pls mark brainliest)!!

Answer:

1

-7x

Step-by-step explanation:

the rule of indices states that any thing raised to power of - 1 is 1 over the number. (e.g: 8^ -1 = 1/8 or 7^ -2 = 1/7²

therefore;

(-7x)‐¹ = 1

-7x

please remark brainliest

Answer:

- \(\frac{1}{7x}\)

Step-by-step explanation:

using the rule of exponents

\((a)^{-1}\) = \(\frac{1}{a}\) , then

\((-7x)^{-1}\) = - \(\frac{1}{7x}\)

Validation of the model and answering the question "what are my options" occur in the design phase of the IDC (Intelligence, Design, and Choice) framework.

The IDC framework is a decision-making process that consists of three phases: Intelligence, Design, and Choice. Each phase corresponds to a specific set of activities and objectives.

In the intelligence phase, the focus is on gathering information, identifying the problem or decision to be made, and understanding the factors and variables involved. This phase involves data collection, analysis, and exploration to gain insights and knowledge about the problem domain.

In the design phase, the emphasis is on developing and evaluating potential options or solutions to address the problem or decision at hand. This phase involves creating models, prototypes, or simulations to represent the problem and exploring different alternatives.

Validation of the model is an important aspect of this phase to ensure that the proposed solutions align with the problem requirements and objectives.

The question "what are my options" is a fundamental question that arises during the design phase. It implies the exploration and generation of various possible choices or solutions that can be evaluated and compared.

Therefore, the design phase of the IDC framework encompasses the activities of validating the model and answering the question "what are my options." It involves refining and testing potential solutions to make informed decisions in the subsequent choice phase.

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Answer:

the answer is {x| 1<x<3}

Answer:

# 3

Step-by-step explanation:

right side is x>1

left side is  x<3

Step-by-step explanation:

amount=$300

rate=13.5

time=5 years

interest =(300×13.5×5)/100=$202.5

Answer:

Part A: $55.50

Part B: 52 hamburgers(sorry if I am wrong for part b but I think it is right)

Step-by-step explanation:

Part A:     $14.50 x 3= $43.50  +         24 x $0.50= $12=        

 ($ earned per hrs  x hrs worked)+  ($ per hamburger sold x times amount)

Hence $43.50 + $12= $55.50.

Part B:        $14.50 x 6.5 = $94.25                           $120 - $94.25= $25.75

 ($ earned per hrs  x hrs worked x x hrs worked)   ($ earned - $ earn from shif

 $25.75/0.50=51.5 (51.5 rounded to nearest burgers is 52 burgers)

Hence answer is 52 burgers.

Please rate Good and mark Brainliest

Thank You

Answer:

A F B J C

Step-by-step explanation:

The center of the data in the dot plot comes to be 3.

0 has 3 dots

1 has 2 dots

2 has 5 dots

3 has 4 dots

4 has 1 dot

5 has 6 dots.

Let us arrange these data in ascending order

0,0,0,1,1,2,2,2,2,2,3,3,3,3,4,5,5,5,5,5,5

Number of observations = 21

The Median is the middle number when observations are arranged in either ascending or descending order. Median is more informative than average.

So, the median will be the middle data = 11th data

11th data = 3 so median =3

Hence, the center of the data in the dot plot comes to be 3.

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Answer:10 adult and 20 children

Step-by-step explanation:

The two inequalities for the given situation are x+y>30 and 15x+9y≤360.

Given that, a hairstylist charges $15 for an adult haircut at nine dollars for a child haircut she wants to earn at least $360.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of adults be x and the number of child be y.

So, x+y>30

Now, 15x+9y≤360

⇒ 3(5x+3y)≤360

⇒ (5x+3y)≤120

From the graph we can see that, two graphs intersecting at (15, 15)

Therefore, the two inequalities for the given situation are x+y>30 and 15x+9y≤360.

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To find the hypotenuse of a right triangle using trigonometry, we can utilize the Pythagorean theorem and the trigonometric ratios of sine, cosine, or tangent. Here's a step-by-step explanation:

1. Identify the right triangle: Ensure that the triangle has a right angle, which is a 90-degree angle.

2. Label the sides: Identify the two sides of the right triangle that are not the hypotenuse. These sides are typically referred to as the adjacent side and the opposite side.

3. Choose the appropriate trigonometric ratio: Depending on the information you have, select the appropriate trigonometric ratio that relates the sides you know.

- If you have the adjacent side and the hypotenuse, use cosine: cosθ = adjacent/hypotenuse.

- If you have the opposite side and the hypotenuse, use sine: sinθ = opposite/hypotenuse.

- If you have the opposite side and the adjacent side, use tangent: tanθ = opposite/adjacent.

4. Substitute the known values: Plug in the values you have into the trigonometric equation and solve for the unknown side (hypotenuse).

5. Apply the Pythagorean theorem: If you don't have the hypotenuse directly but know the lengths of both the adjacent and opposite sides, you can use the Pythagorean theorem, which states that the sum of the squares of the two legs (adjacent and opposite sides) is equal to the square of the hypotenuse. The formula is a² + b² = c², where c represents the hypotenuse.

6. Simplify and calculate: After substituting the known values into the equation, simplify and solve for the hypotenuse.

By following these steps and applying the appropriate trigonometric ratio or the Pythagorean theorem, you can find the length of the hypotenuse in a right triangle using trigonometry.

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Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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The required equation represents the total interest, T, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10 is (T) = 100 × 0.1 × 10.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
interest =  Principal×rate×time

Amount = Principal [1 + rate×time]

Here,
From the given data, the total interest, T, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10.

Interset (T) = 100 × 0.1 × 10

Thus, Option B is correct.

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Answer: Game 2.

Step-by-step explanation: The points double more than the last game by a lot, it's genuinely safe to say that game 2 solos enough to win over this entire argument.

The weight of food packed in certain containers is a random variable with a mean of 16 0z. and a standard deviation of 0.6 oz. If 36 packages are randomly selected, the probability that the mean will be greater than 16.2 oz is 2.28%.

Given that the weight of food packed in containers is a random variable with a mean (µ) of 16 oz. and a standard deviation (σ) of 0.6 oz, we want to find the probability that the mean weight of a sample of 36 packages (n) will be greater than 16.2 oz.
Step 1: Calculate the standard error (SE) of the sample mean.
SE = σ / √n = 0.6 / √36 = 0.6 / 6 = 0.1
Step 2: Calculate the z-score for 16.2 oz.
z = (sample mean - population mean) / SE = (16.2 - 16) / 0.1 = 2
Step 3: Find the probability that the mean weight will be greater than 16.2 oz.
To find the probability for a z-score of 2, we can look it up in a standard normal (z) table or use a calculator that provides the area to the left of the z-score.
Using the table or calculator, we find the area to the left of the z-score 2 is approximately 0.9772. Since we are looking for the probability of the mean weight being greater than 16.2 oz, we want the area to the right of the z-score. To find this, subtract the area to the left from 1:
1 - 0.9772 = 0.0228
So, the probability that the mean weight of the 36 packages will be greater than 16.2 oz is approximately 0.0228 or 2.28%.

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Answer:

5m + 37 = 79.50

Step-by-step explanation:

Answer:

its option A

Step-by-step explanation:

Answer:

Part A: Jillian added 7+3 first rather than multiplying 3*16 b/c multiplication comes before addition

Part B:

7 + 3 * (10 - 6) ^2

7+ 3 * (4)^2

7+3 * 16

7 + 48

55

Step-by-step explanation:

Answer:

Part A:

Jillian's error was that they added the 7 and the 3 to get 10 and then multiplied by 16. Jillian should have multiplied the 3 and the 16 first and then added 7. This is because multiplication comes before addition in PEMDAS.

Part B:

7+3×(10-6)^2

7+3×(4)^2

7+3×16

7+48

55

Step-by-step explanation:

PEMDAS

Answer:

1/5

Step-by-step explanation:

brainly plzzzz

Answer:

\(0.2= \frac{1}{5}\)

Step-by-step explanation:

When changing a decimal to a fraction, think of the decimal "out of 1." In mathematical terms, "out of" generally suggests division.

For example on this question, think of 0.2 as 0.2 out of 1, which would be shown as   \(\frac{0.2}{1}\)

To more easily simplify this, multiply both the top and bottom by 10:

\(\frac{0.2}{1}\) · \(\frac{10}{10}\)

You are able to do this because  \(\frac{10}{10}\)  is equal to  1  and multiplying by number and  1  results in the same number.

Then you get \(\frac{2}{10}\) . Both  2  and  10  are divisible by  2 :

\(\frac{2}{2} = 1\) and \(\frac{10}{2} = 5\)

So the final answer is \(\frac{1}{5}\)

0y-2=x cuz desmos is op

Answer:

x = -2

Step-by-step explanation:

This line has an undefined slope, so the line's linear equation will be in the form of x = a, where a is the x-intercept.

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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Answer:

Match each example of figurative language with its interpretation. Match Term Definition “He watches from his mountain walls, And like a thunderbolt he falls.” A) These lines contain a hyperbole that creates a vivid image. “As long as I live, I'll hear waterfalls and birds and winds sing. I'll interpret the rocks, learn the language of flood, storm, and the avalanche.” B) The passage of prose contains a metaphor that shows how we are all connected. “I'm only a child yet I know we are all part of a family, five billion strong, in fact, 30 million species strong and we all share the same air, water and soil.” C) These lines contain alliteration, which creates rhythm. “I have seen flocks streaming south in the fall so large that they were flowing over from horizon to horizon in an almost continuous stream all day long.” D) These lines give human abilities such as singing and language to nature. “O if we but knew what we do When we delve or hew—Hack and rack the growing green!” E) These lines use a simile to show the power of nature. Question 5(Multiple Choice Worth 5 points)

Step-by-step explanation:

Match each example of figurative language with its interpretation. Match Term Definition “He watches from his mountain walls, And like a thunderbolt he falls.” A) These lines contain a hyperbole that creates a vivid image. “As long as I live, I'll hear waterfalls and birds and winds sing. I'll interpret the rocks, learn the language of flood, storm, and the avalanche.” B) The passage of prose contains a metaphor that shows how we are all connected. “I'm only a child yet I know we are all part of a family, five billion strong, in fact, 30 million species strong and we all share the same air, water and soil.” C) These lines contain alliteration, which creates rhythm. “I have seen flocks streaming south in the fall so large that they were flowing over from horizon to horizon in an almost continuous stream all day long.” D) These lines give human abilities such as singing and language to nature. “O if we but knew what we do When we delve or hew—Hack and rack the growing green!” E) These lines use a simile to show the power of nature. Question 5(Multiple Choice Worth 5 points)

Answer:

7

Step-by-step explanation:

Answer:

Multiply the first equation by 5 and the second equation by 2. Then add.

Multiply the first equation by 2 and the second equation by 5, then subtract.

Step-by-step explanation:

Given

\(- 2x + 5y = -15\)

\(5x + 2y = -6\)

Required

Steps to solve using elimination method

From the list of given options, option 2 and 3 are correct

This is shown below

Option 2

Multiply the first equation by 5

\(5(- 2x + 5y = -15)\)

\(-10x + 25y = -75\)

Multiply the second equation by 2.

\(2(5x + 2y = -6)\)

\(10x + 4y = -12\)

Add

\((-10x + 25y = -75) + (10x + 4y = -12)\)

\(-10x + 10x + 25y +4y = -75 - 12\)

\(29y = -87\)

Notice that x has been eliminated

Option 3

Multiply the first equation by 2

\(2(- 2x + 5y = -15)\)

\(-4x + 10y = -30\)

Multiply the second equation by 5

\(5(5x + 2y = -6)\)

\(25x + 10y = -30\)

Subtract.

\((-4x + 10y = -30) - (25x + 10y = -30)\)

\(-4x + 25x + 10y - 10y= -30 +30\)

\(21x = 0\)

Notice that y has been eliminated

Answer:

How many solutions does the system have?

✔ exactly one

The solution to the system is

(

⇒ 0,

⇒ -3).

Step-by-step explanation:

the next two parts

Perks A Lot has both a higher median and a higher mean value, indicating that it typically sells more coffee per hour than Wide Awake. Perks A Lot, with a median value of 5.75 gallons i.e. A.

What exactly is a median?

In statistics, the median is a measure of central tendency that represents the middle value of a data set. To find the median, the data set must first be arranged in order from smallest to largest (or largest to smallest).

If the data set has an odd number of values, then the median is the middle value. For example, in the data set 2, 5, 7, 8, 10, the median is 7 because it is the middle value.

If the data set has an even number of values, then the median is the average of the two middle values. For example, in the data set 3, 4, 6, 9, the median is (4+6)/2 = 5.

Now,

To compare the data and determine which shop typically sells the most amount of coffee per hour, we need to calculate the measures of central tendency for each set of data.

For Perks A Lot:

Median: To find the median, we need to order the data and find the middle value. Ordering the data gives us:

2.5, 3, 3.5, 4.5, 5.5, 6, 7, 8, 9, 9.5, 10

The middle value is 5.75, so the median for Perks A Lot is 5.75 gallons.

Mean: To find the mean, we need to sum up all the values and divide by the number of values. Summing up the values gives us 63.5, and dividing by 11 (the number of values) gives us a mean of approximately 5.77 gallons.

For Wide Awake:

Median: Ordering the data gives us:

2.5, 3, 4, 4, 5, 6, 6.5, 10, 15

The middle value is 4.5, so the median for Wide Awake is 4.5 gallons.

Mean: Summing up the values gives us 49, and dividing by 9 gives us a mean of approximately 5.44 gallons.

Based on these calculations, we can see that Perks A Lot has both a higher median and a higher mean value, indicating that it typically sells more coffee per hour than Wide Awake. Therefore, the correct answer is: Perks A Lot, with a median value of 5.75 gallons.

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a. The missing probability value is 0.4.

b. E(X) = 1.4.

c. Var(X) = 0.56 and σx = 0.75.

d. E(Z) = 2.27, Var(Z) = 2.56, and σz = 1.60.

The given probability distribution of the random variable X shows the probabilities associated with each possible outcome. To find the missing probability value, we know that the sum of all probabilities must equal 1. Therefore, the missing probability can be calculated by subtracting the sum of the probabilities already given from 1. In this case, 0.1 + 0.2 + 0.3 = 0.6, so the missing probability value is 1 - 0.6 = 0.4.

To find the expected value or mean of X (E(X)), we multiply each value of X by its corresponding probability and then sum up the results. In this case, (0 * 0.1) + (1 * 0.2) + (2 * 0.3) + (3 * 0.4) = 0.4 + 0.2 + 0.6 + 1.2 = 1.4.

To calculate the variance (Var(X)) of X, we use the formula: Var(X) = Σ[(X - E(X))^2 * P(X)], where Σ denotes the sum over all values of X. The standard deviation (σx) is the square root of the variance. Using this formula, we find Var(X) = [(0 - 1.4)² * 0.1] + [(1 - 1.4)^2 * 0.2] + [(2 - 1.4)² * 0.3] + [(3 - 1.4)² * 0.4] = 0.56. Taking the square root, we get σx = √(0.56) ≈ 0.75.

Now, let's consider the new random variable Z = 1 + (2/3)X. To find E(Z), we substitute the values of X into the formula and calculate the expected value. E(Z) = 1 + (2/3)E(X) = 1 + (2/3) * 1.4 = 2.27.

To calculate Var(Z), we use the formula Var(Z) = (2/3)² * Var(X). Substituting the known values, Var(Z) = (2/3)² * 0.56 = 2.56.

Finally, the standard deviation of Z (σz) is the square root of Var(Z). Therefore, σz = √(2.56) = 1.60.

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