3 Which of the following figures have
the same area?
2.9 cm
II
4 cm
2 cm
A. Figures I and II
C. Figures I and III
I
5.8 cm
III 3.7 cm
3.7 cm
B. Figure II and III
D. None of the above

Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  [tex](x-h)^2+(y-k)^2=r^2[/tex]   (where (h,k) is center, r is radius)

  [tex](x-4)^2+(y-7)^2=3^2[/tex]

  [tex](x-4)^2+(y-7)^2=9[/tex]     (This is the general standard form )

in expanded form,

  [tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]

  [tex]x^2+y^2-8x-14y+56=0[/tex]

Note: Unless stated either form is an acceptable answer.

The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.

If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.

The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)

It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.

Learn more about rectangle here:

https://brainly.com/question/27722891

#SPJ4

Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.

The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.

Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.

for such more questions on solubility

https://brainly.com/question/23946616

#SPJ11

Based on the given information, the scout should choose Player A if they are looking for consistency.

What are range and standard deviation?

Range is the difference between the highest and lowest scores in the set.

Standard deviation measures how spread out the scores are from the mean.

To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.

The smaller the range, the more consistent the player's scores are.

A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.

Using the data provided, we can calculate the range and standard deviation for both players:

Player A:

Range = 21 - 0 = 21

Standard deviation = 5.70

Player B:

Range = 48 - 3 = 45

Standard deviation = 10.89

From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.

To know more about the range and standard deviations visit:

brainly.com/question/14801621

#SPJ1

The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:

σ = sqrt((p*(1-p))/n)

where n is the sample size.

Substituting the values given in the question, we have:

σ = sqrt((0.5*(1-0.5))/555) = 0.0258

To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:

P(|p_hat - p| < 0.05)

where p_hat is the sample proportion.

We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:

P(|p_hat - p|/σ < 0.05/σ)

P(-0.97 < Z < 0.97)

where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:

P(-0.97 < Z < 0.97) = 0.8327

Rounding to four decimal places, we have:

P(|p_hat - p| < 0.05) = 0.8327

Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.

Learn more about  probability

https://brainly.com/question/30034780

#SPJ4

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

To learn more about sum, click here:

brainly.com/question/29034036

#SPJ4

The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion

This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.

A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.

To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:

Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)

where:

Using this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.

This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.

Read more about random samples here:

https://brainly.com/question/29444380

#SPJ1

Answer:33

Step-by-step explanation:45-12=33

The 4 in the hundredths place has a smaller value than the 4 in the tens place.

In the decimal number system, each digit to the left of the decimal point represents a power of 10, starting with 10^0 = 1 for the rightmost digit. Each digit to the right of the decimal point represents a negative power of 10, with the place value decreasing as you move farther to the right.

In the number 240.149, the 4 in the tens place represents 4 x 10 = 40. The 4 in the hundredth place represents 4/100 or 0.04, which is smaller than 40. Therefore, the 4 in the tens place has a greater value than the 4 in the hundredths place.

Hence, the value of a digit in a decimal number depends on its position relative to the decimal point. Digits to the left of the decimal point represent whole numbers, while digits to the right of the decimal point represent fractions or parts of a whole.


To know more about the decimal number system, refer here:

https://brainly.com/question/30477589#

#SPJ11

The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.

To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:

Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.

Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.

Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.

The slope formula is given by m = (y2 − y1) / (x2 − x1).

Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.

Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.

for such more question on reflection

https://brainly.com/question/26642069

#SPJ11

The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]

To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula

CI = X ± Zα/2 (σ/√n)

where

X = sample mean = 35.8

Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.

σ = sample standard deviation = 2.5

n = sample size = 40

Substituting these values into the formula, we get

CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].

Therefore, the correct option is (a) [34.7296, 36.8704]

Learn more about confidence interval here

brainly.com/question/24131141

#SPJ4

The third term of a sequence is 14. Term to term rule is square, then subtract 11. The first term of the sequence is 6.

The given information is about the third term of a sequence which is 14, and the term to term rule is square, then subtract 11.

We have to find the first term of the sequence. The sequence can be calculated using the following formula:

An = A1 + (n-1)d

Where, An is the nth term of the sequence A1 is the first term of the sequence d is the common difference between the terms of the sequence. Let's solve the problem by finding the value of the common difference between the terms of the sequence.

Using the given information, we can write: A3 = 14=> A1 + (3 - 1)d = 14=> A1 + 2d = 14 ----- (i)

Also, the term to term rule is square, then subtract 11.So, we can write, A2 = A1 + d = (A1)² - 11 ---- (ii)

Substituting the value of d from equation (ii) in equation (i),

we get: A1 + 2 [(A1)² - 11] = 14 Simplifying this equation, we get: A1² - 2A1 - 12 = 0 On solving this quadratic equation

we get: A1 = -2 or A1 = 6 Ignoring the negative value of A1, we get the first term of the sequence to be 6.

for such more question on sequence

https://brainly.com/question/7882626

#SPJ11

Answer:

8;-2

Step-by-step explanation:

8 is the x axis and -2 is the y axis

Answer:

Step-by-step explanation:

The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.

Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.

Solving these equations simultaneously, we get a = 2 and d = 3.

To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:

S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.

Find out more about arithmetic sequence

brainly.com/question/15412619

#SPJ4

There are 5²⁵ possible ways to select 25 cans of soda from 5 types, while there are [5¹⁸] (25 choose 7) possible ways to select 25 cans with at least 7 Dr. Peppers, and only [3²²] (25 choose 3) possible ways to select 25 cans with only 3 Dr. Peppers available.

(a) Since there are five types of soda and we are selecting 25 cans, we can choose any type of soda for each can. Therefore, the number of ways to select 25 cans of soda is 5²⁵.

(b) If we must include at least seven Dr. Peppers, then we can choose the remaining 18 cans from any of the five types of soda (including Dr. Pepper). We can choose 7 Dr. Peppers in (25 choose 7) ways. Therefore, the number of ways to select 25 cans of soda with at least seven Dr. Peppers is (25 choose 7) [5¹⁸].

(c) If there are only three Dr. Peppers available, then we must choose all three Dr. Peppers and select the remaining 22 cans from the four types of soda (excluding Dr. Pepper). We can choose the remaining 22 cans in 4²² ways. Therefore, the number of ways to select 25 cans of soda with only three Dr. Peppers available is 3 [4²²].

Learn more about Combinatorics here: brainly.com/question/13261685

#SPJ4

Complete question:

From an unlimited selection of five types of soda, one of which is Dr. Pepper, you are putting 25 cans on a table.

(a) Determine the number of ways you can select 25 cans of soda.

(b) Determine the number of ways you can select 25 cans of soda if you must include at least seven Dr. Peppers.

(c) Determine the number of ways you can select 25 cans of soda if it turns out there are only three Dr. Peppers available.

The option that would result in the smallest margin of error in estimating the mean salt content, u, is 95% confidence, n = 50. The correct answer is Option D.

The margin of error is the amount by which a statistic is expected to differ from the true value of the population parameter. The interval estimate is calculated with the help of a margin of error. The margin of error and the interval estimate are inversely related to each other. If we want a small margin of error, we must increase the sample size.

The confidence level is the likelihood that a population parameter will fall within a specified range of values. The confidence level is determined by the sample size and margin of error. The sample size and margin of error are directly related to each other. When the sample size is smaller, the margin of error is larger. When the sample size is larger, the margin of error is smaller.

The margin of error is the highest at a confidence level of 50%. In general, as the confidence level increases, the margin of error decreases, and vice versa. As the sample size increases, the margin of error decreases. It follows that a 95% confidence level, n = 50 would yield the smallest margin of error in estimating the mean salt content, u. Hence, option D) 95% confidence, n = 50 would result in the smallest margin of error in estimating the mean salt content, u.

Learn more about margin of error here: https://brainly.com/question/29328438

#SPJ11

The mean absolute deviation (MAD) of the given set of data is 3.875.

To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:

Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8

Mean = 8

Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:

|12 - 8| = 4

|10 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|8 - 8| = 0

|4 - 8| = 4

|2 - 8| = 6

|12 - 8| = 4

Then, we find the mean of the absolute deviations:

Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8

Mean absolute deviation = 26 / 8

Mean absolute deviation = 3.875

Therefore, the mean absolute deviation of the given set of data is 3.875.

Learn more about Mean absolute deviation:

https://brainly.com/question/447169
#SPJ4

Complete Question:

what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.

When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique

Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.

Learn more about cluster sampling technique:https://brainly.com/question/11003935

#SPJ11

0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

Learn more about probability.

brainly.com/question/30034780

#SPJ11

The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.

In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:

(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:

6⁽⁷⁻⁶⁾ = 6¹ = 6.

Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.

Find out more about exponent

brainly.com/question/30066987

#SPJ4

Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

See Below

HAVE A NICE DAY !

The probability of selecting two non-defective DVD players from a group of six is 2/5. This is based on the assumption that the selection is done without replacement.

We can use the formula for calculating probabilities of combinations:

P(not defective) = number of ways to choose 2 non-defective DVD players / total number of ways to choose 2 DVD players

Total number of ways to choose 2 DVD players out of 6 is:

C(6,2) = 6! / ([2!] [4!]) = 15

Number of ways to choose 2 non-defective DVD players out of 4 is:

C(4,2) = 4! / ([2!] [2!]) = 6

Therefore, the probability that Cecil chooses 2 non-defective DVD players is:

P(not defective) = 6/15 = 2/5

So the value of P(not defective) is 2/5.

Learn more about probability here: brainly.com/question/30034780

#SPJ4

The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.

We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.

To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:

P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96

So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.

Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.

For more such questions on Probability.

https://brainly.com/question/11234923#

#SPJ11

Answer:

Step-by-step explanation:

asdf

Answer:29160

Step-by-step explanation:

Answer:

(2, 180)

Step-by-step explanation:

w(x)=-5x^2+20x+160

a=-5 b=20

x=-20/2x(-5)

x=2

w(2)=180

2, 180

There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

We are given the boundary-value problem:

y" + 16y = 0, y(0) = 1, y(L) = 1

The characteristic equation is r^2 + 16 = 0, which has roots r = ±4i.

The general solution to the differential equation is then y(x) = c1cos(4x) + c2sin(4x).

Using the boundary conditions, we get:

y(0) = c1 = 1

y(L) = c1cos(4L) + c2sin(4L) = 1

Substituting c1 = 1 into the second equation, we get:

cos(4L) + c2*sin(4L) = 1

Solving for c2, we get:

c2 = (1 - cos(4L))/sin(4L)

Thus, the general solution to the differential equation that satisfies the given boundary conditions is:

y(x) = cos(4x) + (1 - cos(4L))/sin(4L)*sin(4x)

Now, we can answer the questions:

(a) To have precisely one nontrivial solution, we need the coefficients c1 and c2 to be uniquely determined. From the above expression for c2, we see that this is only possible if sin(4L) is nonzero. Thus, if sin(4L) ≠ 0, there exists precisely one nontrivial solution.

(b) If sin(4L) = 0, then c2 is undefined and we have a family of solutions that differ by a constant multiple of sin(4x). Hence, there are infinitely many solutions.

(c) There is no solution if the boundary conditions are inconsistent, i.e., if y(0) ≠ y(L) = 1.

To learn more about nontrivial solution visit: https://brainly.com/question/30452276

#SPJ11

Answer:

Step-by-step explanation:

a. 100 divided by 75 = 1.3333333333333333333333333333333

1.3333333333333333333333333333333 times 43 = 57.333333333333333333333333333332

round it to the nearest whole number: ≅ 57%