Consider the following.
x = 5 cos(θ), y = 6 sin(θ), −π/2 ≤ θ ≤ π/2
(a) Eliminate the parameter to find a Cartesian equation of the curve.
(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Answer:

3/2

1x = 12

Step-by-step explanation:

See attachment

Answer:

Step-by-step explanation:

hello

15

Answer:

1/9 = 3^-2

1/8 = 2^-3

9 = 3²

8 = 2³

The scale factor of a dilation is the ratio between the lengths of corresponding sides of the original and dilated figures. If the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.

The scale factor is a number that is used to compare two measurements of the same object or design. It is the ratio between the two measurements, and is used to determine the size difference between the two. Scale factors can be used to scale objects up or down in size.

In other words, the scale factor is the multiplier used to stretch or compress the original figure. In Patrick's case, the scale factor can be determined by comparing the lengths of the corresponding sides of the original and dilated figures. For example, if the length of the top side of the original figure is 5 units and the length of the top side of the dilated figure is 10 units, then the scale factor is 2.

Since the dilation is on a coordinate plane, Patrick can also find the scale factor by comparing the coordinates of the original figure and the dilated figure. For example, if the coordinates of one of the vertices of the original figure are (2, 4) and the coordinates of one of the corresponding vertices of the dilated figure are (4, 8), then the scale factor is 2.

The scale factor of the dilation in Patrick's science project is an important concept and can be found by comparing the lengths of the corresponding sides of the original and dilated figures or by comparing the coordinates of the original and dilated figures.

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Answer:

80°

Step-by-step explanation:

in my opinion X= 80 digress

Answer:x-5.50=20

Step-by-step explanation:

The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

\(n = (Z^2 × p × (1-p)) / E^2\)
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

\(n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2\)
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

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Complete Question:

List five different vocabulary words that could be used to describe each given expression.

\((a)\ a - d + c\)

\((b)\ 20 - 3c\)

\((c)\ \frac{b}{d + 2}\)

Answer:

(a) Vocabulary words: sum, difference, total, subtract, add

(b) Vocabulary words: product, difference, subtract, times, less than

(c) Vocabulary words: quotient, sum, add, divide, ratio

Step-by-step explanation:

\((a)\ a - d + c\)

The word problem of this is:

The addition of c to the difference between a and c

Keywords: addition and difference

Vocabulary words: sum, difference, total, subtract, add

\((b)\ 20 - 3c\)

The word problem of this is:

The difference between 20 and the product of 3 and c

Keywords: difference and product

Vocabulary words: product, difference, subtract, times, less than

\((c)\ \frac{b}{d + 2}\)

The word problem of this is:

The quotient of \(b\ and\ the\) sum of d and 2

Keywords: quotient and sum

Vocabulary words: quotient, sum, add, divide, ratio

Answer:

jamel brother has 48.00 dollors

Step-by-step explanation:

Answer: He has 32$ 24 divided by 6 is 4 multiply 4 by 8 and you get 32

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Jennifer has 48 nickels, which means she has 144 quarters.

Let's call the number of nickels Jennifer has "n".

Since Jennifer has three more dimes than nickels, she has n + 3 dimes.

And since she has three times as many quarters as nickels, she has 3n quarters.

We can start by figuring out the total value of the nickels and dimes in terms of cents:

n * 5 cents + (n + 3) * 10 cents = 750 cents

Expanding the right side of the equation and solving for n:

5n + 10n + 30 cents = 750 cents

15n + 30 cents = 750 cents

15n = 720 cents

n = 48

So Jennifer has 48 nickels, which means she has 3 * 48 = 144 quarters.

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Answer:

Fixed ratio is a schedule of reinforcement

Step-by-step explanation:

When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

Population Mean:

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

In testing for the differences between the means of two independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are: n1 + n2 - 2.

population variance:

Population variance is a measure of how spread out a group of data points is. Specifically, it quantifies the average squared deviation from the mean.

Therefore When testing the difference between two population means, the sample variances are pooled to estimate the population variance when The population variances are assumed equal but unknown.

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Answer:

4 bags.

Step-by-step explanation:

1/10 is already good, but you need to multiply 2/5 by 2 to get 4/10, and then it's self-explanatory from there

Answer:

m∠a = 60°

Step-by-step explanation:

Hi there,

Before answering this question, you should know that the sum of all the angles in a triangle will always be 180°. Therefore, we can write this equation to find the value of ∠a :

70° + 50° + m∠a = 180°

Solve for m∠a

120° + m∠a = 180°

m∠a = 60°

Hope this answer helps. Cheers.

A ratio describes a relationship between two or more quantities. When mixing colors, ratios are often used to determine the ratio of different colors required to achieve a desired hue. Ratios can be expressed in 1:, 2:3,.. etc.

Ratios affect the appearance of paint colors. In this scenario, Can A has a higher percentage of red than can B. This means that the shade of pink you get with Can A is likely to be darker and more red due to the higher concentration of red.

Can B, on the other hand, has a lower percentage of red, suggesting that the resulting pink hue is lighter and less red than can A.  

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Answer:

H = 58, I = 71, J = 51

Step-by-step explanation:

Set all angles equal to 180

3x - 2 + 4x - 9 + 3x - 9 = 180

Then combine like terms

10x - 20 = 180

      + 20  + 20

10x = 200

/10     /10

x = 20

Then plug in for each angle

3 (20) - 2 = 58

4 (20) - 9 = 71

3 (20) - 9 = 51

The APY for 8% compounded quarterly is 2.02% and for 6% compounded continuously is 6.18%.

APY refers to the Annual Percentage Yield of an investment. It reflects the total interest received by an individual on a yearly basis when their investment is compounded annually.

The question has asked to calculate APY for money invested at 8% compounded quarterly and 6% compounded continuously.

Let's calculate APY for both cases:APY for 8% compounded quarterly:

First, let's calculate the quarterly interest rate, i = 8% / 4 = 0.02APY = (1 + i / n ) ^ n - 1, where n is the number of times compounded annually

Therefore, APY for 8% compounded quarterly is:APY = (1 + 0.02 / 4 ) ^ 4 - 1= 0.0202 x 100 = 2.02%

Therefore, the APY for 8% compounded quarterly is 2.02%APY for 6% compounded continuously:

For continuous compounding, the formula for APY is given by:APY = e ^ r - 1, where r is the interest rate

Therefore, APY for 6% compounded continuously is:

APY = e ^ 0.06 - 1= 0.0618 x 100 = 6.18%

Therefore, the APY for 6% compounded continuously is 6.18%.

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Answer:99

Step-by-step explanation:

Answer:

4: 1,4, 2,2

6: 1,6,2,3

Step-by-step explanation:

So it is basically 2

Answer:

12, 24, 36

Step-by-step explanation:

multiples of the number 4 is 4, 8, 12, 16, 20, 24...

multiples of 6 are 6, 12, 18, 24, 30, 36

AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects are said to be congruent if they are identical in shape and size, and can be superimposed onto one another. The symbol used to represent congruence is ≅. Congruence applies to various geometric objects, such as triangles, rectangles, circles, and more. When two objects are congruent, they have all corresponding angles equal and all corresponding sides equal in length.

Step 1: Statement: \($\angle DBE = \angle EBC$\)

Reason: Given that overline BE bisects \($\angle DBC$\)

Step 2: Statement: \($\angle DBC + \angle EBC = 180^\circ$\)

Reason: Angle sum property of a straight line.

Step 3: Statement: \($\angle ABC + \angle EBC = 180^\circ$\)

Reason: Angles on a straight line sum to \(180^\circ$, and $\overline{BE} || \overline{AC}$\) implies that \(\angle ABC$ and $\angle EBC$\) are co-interior angles.

Step 4: Statement: \($\angle ABC = \angle DBC$\)

Reason: From step 2 and step 3, \($\angle ABC + \angle EBC = \angle DBC + \angle EBC = 180^\circ$\). Thus, \($\angle ABC = \angle DBC$\).

Step 5: Statement: \($\triangle ABE \cong \triangle CBE$\)

Reason: By the angle-angle-side congruence criterion, since \($\angle DBE = \angle EBC$\) (from step 1) and \($\angle ABC = \angle DBC$\) (from step 4), and \($\overline{BE}$\) is common to both triangles.

Step 6: Statement: \($AB = BC$\)

Reason: By step 5, \($\triangle ABE \cong \triangle CBE$\), so corresponding sides are congruent, including \($\overline{AB} \cong \overline{BC}$\).

Therefore, AB is congruent to BC given BE bisects DBC and BE is parallel to AC is proved .

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Answer:

the correct answer is 30

Answer:

x = 4

Step-by-step Explanation:

\(\triangle LMO \sim \triangle NMO \ \rm{(AA \ Similarity)} \\ \\ \rm \implies 12x - 5 = 43 \\ \\ \rm \implies 12x = 43 + 5 \\ \\ \rm \implies 12x = 48 \\ \\ \rm \implies x = \frac{48}{12} \\ \\ \rm \implies x = 4\)

The line is the best fit of the scattered plot because the line passes through a balance point and is close to most of the data.

A scatter plot also known as scatter chart or scatter graph uses dots to represent values for two different numeric variables.

In a simpler term, scatter plots are the graphs that present the relationship between two variables in a data-set

The variables represented in the scattered plot is score and time of the talent competition.

The score is the dependent variable while the time(h) is the independent variable.

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Therefore, yes the line is the best fit because the line passes through a balance point and is close to most of the data.

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Answer:

c

Step-by-step explanation:

The major plate motion rates range from less than 10 mm/y to more than 100 mm/y. The fastest plate is the Pacific Plate, followed by the Australian and Nazca Plates. The North American Plate is one of the slowest, with average rates ranging from around 1 cm/y in the south to nearly 4 cm/y in the north.

Plates move as rigid bodies, it may appear surprising that the North American Plate can move at different rates in different locations. Plates move in a rotational fashion, as explained. For example, the North American Plate rotates counter-clockwise, while the Eurasian Plate rotates clockwise.

There are three types of plate boundaries: divergent, convergent, and transform (moving side by side). Before we discuss processes at plate boundaries, it is critical to note that there are no gaps between plates.

The plates are made up of crust and the lithospheric part of the mantle, and despite moving in different directions all the time, there is never a significant amount of space between them.

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