write an equation of a line perpendicular to y = 7 and passes through the point (3, -1).

That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.

carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.

the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.

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Answer:y=-2x+6

Step-by-step explanation:

y=-2x+6

Your question asks for the linear approximations (L(x)) and estimated y-values at x=1.2 for four different functions: f(x)=x², f(x)=ln(x), f(x)=cos(x), and f(x)=3√x.

1. For f(x)=x², L(x)=2x-0.44, and the estimated y-value at x=1.2 is 1.76.
2. For f(x)=ln(x), L(x)=x-0.2, and the estimated y-value at x=1.2 is 1.
3. For f(x)=cos(x), L(x)=-0.017x+1.051, and the estimated y-value at x=1.2 is 1.031.
4. For f(x)=3√x, L(x)=0.5x+1, and the estimated y-value at x=1.2 is 1.6.

To find L(x) and the estimated y-value at x=1.2 for each function, follow these steps:
1. Calculate the derivative of each function.
2. Evaluate the derivative at the given x-value to find the slope.
3. Use the point-slope form to find L(x).
4. Plug x=1.2 into L(x) to find the estimated y-value.

By following these steps for each function, you can find their linear approximations and the estimated y-values at x=1.2.

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Answer:

Reflect shape A on the line y=-1

Step-by-step explanation:

None needed you get full marks from the sentence above :)

Answer:

0.0000000091

..............

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

Step-by-step explanation:

70p/5=14

14*4=56*10=560p

14*3=42*20=840p

840+560+70=1470

=1470p or (£14.70)

The total value of money in the jar is 270p.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

The number of 5p, 10p, and 20p coins in a jar are in the ratio 7:4:3.

That means,

Number of 5p coins are 5x, 10p coins are 4x and 20p coins are 3x.

And 5p coins are worth 70p.

That means, x = 70p/5p

x = 14

So,

The total worth of coins are,

= 70p + 80p + 120p

= 270p

Therefore, the worth of the coins are 270p.

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Answer:

  $12

Step-by-step explanation:

You want to know the amount that has a tax of $0.72 when the tax rate is 6%.

The tax is computed by multiplying the price by the tax rate.

  tax = price × (tax rate)

  $0.72 = price × 0.06

  price = $0.72/0.06 = $(72/6) = $12

The original price of the bracelet is $12.

The implementation of the minimum wage would lead to a decrease in both consumer surplus and producer surplus, while also causing a deadweight loss due to the decrease in employment.

1. Consumer Surplus (CS): Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. In this case, the increase in the minimum wage would result in a decrease in consumer surplus. This is because some consumers who were previously able to hire workers at the market-clearing wage of $4 per hour would now have to pay a higher wage of $5 per hour. As a result, their surplus would decrease.

2. Producer Surplus (PS): Producer surplus is the difference between the price at which producers are willing to sell a good or service and the price they actually receive. In this case, the increase in the minimum wage would lead to a decrease in producer surplus. Employers who were previously able to hire workers at $4 per hour would now have to pay a higher wage of $5 per hour. As a result, their surplus would decrease.

3. Deadweight Loss (DWL): Deadweight loss is the loss of economic efficiency that occurs when the equilibrium is not achieved due to market distortions. In this case, the implementation of the minimum wage would result in a deadweight loss. The decrease in employment from 600 workers to 500 workers indicates that some workers who were previously willing to work at $4 per hour would no longer be employed at the higher wage of $5 per hour. This loss of employment represents a decrease in economic efficiency and results in deadweight loss.

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The ratio for sin A, written as a fraction in simplest form, is 3 / (2√3).

The sine function is a mathematical function that takes an angle as its input and returns the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle

In a right triangle, the sine of an angle A is defined as the ratio of the length of the side opposite to angle A to the length of the hypotenuse. Therefore, we have:

sin A = Opposite / Hypotenuse

Substituting the given values, we get

sin A = CB / AB = 8√3 / 16 = √3 / 2

To simplify this fraction further, we can multiply both the numerator and denominator by √3:

sin A = (√3 / 2) × (√3 / √3) = 3 / (2√3)

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The given question is incomplete, the complete question is:
Which is the ratio for sin A, written as a fraction in simplest form?

Answer:

5/90

Step-by-step explanation:

5/90 is the answer

Answer:

A - 5

Step-by-step explanation:

1 mile in the morning + 1 mile in the afternoon = 2 miles per day

10 miles / 2 miles = 5

The probability of rolling a 1 on the first roll and a 6 on the second roll is 1/36.

Since each roll is independent of the other, the probability of the first roll being a 1 and the second roll being a 6 is the product of the probabilities of each event happening separately.

The probability of rolling a 1 on the first roll is 1/6, and the probability of rolling a 6 on the second roll is also 1/6. Therefore, the probability of both events occurring is:

1/6 × 1/6 = 1/36

So the probability of rolling a 1 on the first roll and a 6 on the second roll is 1/36.

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Answer:

3)6 , 4)5 , 5)11 , 6)5 , 7)-14 , 8)8

Step-by-step explanation:

The probability that the selected pool has a ph level not considered safe is approximately 0.22 (or 22%). This can be calculated using the cumulative probability of a normal distribution with a mean of 7.5 and a standard deviation of 0.2.

1. Calculate the z-score for the lower limit of 7.2: (7.2 - 7.5) / 0.2 = -1.5

2. Calculate the z-score for the upper limit of 7.8: (7.8 - 7.5) / 0.2 = 1.5

3. Calculate the cumulative probability of the lower limit: P(-1.5) = 0.0668

4. Calculate the cumulative probability of the upper limit: P(1.5) = 0.9332

5. Calculate the probability that the selected pool has a ph level not considered safe: P(not safe) = 1 - (P(1.5) - P(-1.5)) = 0.22

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Answer:

The Forth Answer

Step-by-step explanation:

I Think That Is correct

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

Answer:

s and t and u and t

Step-by-step explanation:

the sides of the triangle should be the same

Answer:

600

Step-by-step explanation:

To determine how well Daniel must score on Exam B in order to do equivalently well as he did on Exam A, we can use the concept of standard scores or z-scores. A z-score indicates how many standard deviations away from the mean a score is.

First, we need to convert Daniel's score on Exam A to a z-score:

z = (18 - 28) / 5 = -2

This tells us that Daniel's score on Exam A is 2 standard deviations below the mean.

We can then use this z-score to find Daniel's equivalent score on Exam B. To do this, we can use the formula:

x = z * σ + μ

Where x is the equivalent score on Exam B, z is the z-score from Exam A, σ is the standard deviation of Exam B, and μ is the mean of Exam B.

x = (-2) * 40 + 700

x = 600

Therefore, Daniel must score 600 on Exam B in order to do equivalently well as he did on Exam A.

Keep in mind that this calculation assumes that the scores on each exam are normally distributed, which may or may not be the case. It also assumes that the two exams are of similar difficulty, which also may not be the case.

a) two representatives be picked in 5850 ways so that one is a mathematics major and the other is a computer science major. b) one representative be picked in 343 ways who is either a mathematics major or a computer science major.

Product Rule: If one event occurs in m ways and a second event occurs in n ways, the number of ways the two events occur in the sequence is m×n ways.

Sum Rule: If an event occurs either in m ways or in n ways (non-overlapping), the number of ways the event can occur is m+n ways.

according to the question,

Mathematics majors =18 and Computer science majors = 325

A. We need to use the product rule because the first event is picking up a Mathematics major and the second event is picking up a computer science major.

= 18 x 325

= 5850

B. Here sum rule is applicable because the event is picking up a mathematics major or a computer science major.

= 18 + 325

= 343

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(complete question)

there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a mathematics major or a computer science major.

Answer:

20%

Step-by-step explanation:

To find the percentage of students who prefer walking, we need to divide the number of students who prefer walking (65) by the total number of students (300), and then multiply by 100 to get the percentage:

(65/300) x 100 = 21.67%

Rounding to the nearest whole number, we get:

About 22% of the students prefer walking.

So the closest option is 20%.

Using Z-score formula,

z-score value of marks obtained by Robert in nationwide maths test is

Z-score : In statistics, The Z-score is the number of standard deviations by which the raw score value is above or below the observed or measured mean. Raw scores above the average have positive z-scores and scores below the average have negative z-scores . It is also known as standard score .

Mathematically, Z = (X - μ)/σ

where, Z---> standard score

X ---> raw score

μ --> population mean

σ ---> standard deviations we have given that,

population mean (μ) = 57

Standard deviations of sample (σ) = 10

raw score value ( X) = 85

putting all the values in above formula we get,

Z = (85 - 57)/10 = 28/10 = 2.8

Hence, Z-score value for marks obtained by Robert in maths test is 2.8 ..

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1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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Answer:

-0.7 is the answer to your question

Answer:

Answer:

-0.7 is the answer to your question

Step-by-step explanation:

Answer:

3^3

Step-by-step explanation:

Exponents

9^3 can be rewritten as

3^2 ^3

Using exponent rules a^b^c = a^ (b*c)

3^2^3 = 3^6

3^6 / 3^3

We know that a^b / a^c = a^(b-c)

3^6 / 3^3  = 3^(6-3) = 3^3

Answer:

2nd answer is correct

Step-by-step explanation:

We know that,

\( \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} \)

Accordingly, let us solve it now.

\( \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} \)

The we need to find a function f(x) that satisfies the above conditions and whose integral is easy to evaluate.

The answer is (B) diverges.

The answer is (A) converges.

Let's use the integral test to determine the convergence of the following series:

Find the integrand and integrate it.

The integral test states that if f(x) is a positive, continuous, and decreasing function on [1, infinity) such that the series ∑n=1 to infinity of f(n) converges, then the series ∑n=1 to infinity of a(n) also converges, where a(n) = f(n) for all n.

Integrating f(x) from c-1 to infinity, we get:

Integrating f(x) from 1 to infinity, we get:

Compare the sum to the integral.

Since f(x) is positive and decreasing, we can use the integral test to compare the series to the integral.

If the integral converges, then the series converges as well.

If the integral diverges, then the series diverges as well.

The integral ln(11) - ln(c+9) diverges as c approaches infinity, so the series diverges as well.

Since f(x) is positive and decreasing, we can use the integral test to compare the series to the integral.

If the integral converges, then the series converges as well.

If the integral diverges, then the series diverges as well.

The integral ln(10) - ln(1+1/10) converges.

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(a) The function f(x) = 1/x, defined on the interval (0,1]. (b) It is not possible to have a continuous function defined on a closed interval with a range equal to an open interval. (c) the function f(x) = arctan(x), defined on the interval (-∞, +∞). (d) It is not possible to have a continuous function defined on all of ℝ with a range equal to ℚ

(a) It is possible to have a continuous function defined on an open interval with a range equal to a closed interval. An example of this is the function f(x) = 1/x, defined on the interval (0,1]. The range of this function is [1, +∞), which is a closed interval.

(b) It is not possible to have a continuous function defined on a closed interval with a range equal to an open interval. This violates the Intermediate Value Theorem, which states that a continuous function on a closed interval takes on every value between its minimum and maximum. Therefore, the range of a continuous function on a closed interval will always be a closed interval or a single point.

(c) It is possible to have a continuous function defined on an open interval with a range equal to an unbounded closed set different from ℝ. An example of this is the function f(x) = arctan(x), defined on the interval (-∞, +∞). The range of this function is the closed interval [-π/2, π/2], which is unbounded but different from ℝ.

(d) It is not possible to have a continuous function defined on all of ℝ with a range equal to ℚ (the set of rational numbers). This is because the set of rational numbers is dense in ℝ, meaning that between any two rational numbers, there are infinitely many irrational numbers. A continuous function cannot "jump" over irrational numbers, so its range would necessarily include both rational and irrational numbers, making it impossible for the range to be ℚ alone.

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The area of the triangle is 6 square units.

Once you have the points they make a 3-4-5 triangle.

The two legs are 3 and 4, so the hypotenuse has to be 5.

Or you could use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5

then find area

A=1/2bh

1/2(3*4)

6

Thus, the area of the triangle is 6 square units.

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