A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

B .The results of the chi-square goodness-of-fit test, with a chi-squared statistic of 5.4 and a p-value of 0.067, Silvia cannot reject the null hypothesis that her cat is equally likely to eat first from each of the three locations at the 0.05 significance level.

Therefore, the correct answer is B: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others. It is important to note that while the p-value is relatively close to the significance level of 0.05, it does not meet the threshold for statistical significance, and the sample size may not be large enough to draw definitive conclusions about the cat's feeding preferences.

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Answer: There's not enough evidence to conclude that her cat prefers to eat first from some locations more than others.

Step-by-step explanation: Since the P-value is greater than the significance level, we can't reject the null hypothesis. In this context, the null hypothesis is that cat is equally likely to choose each of the locations. (Got it right on Khan academy)

Answer:

Hammad has made his drink stronger in taste than Julie.

Step-by-step explanation:

We need to compare the ratio of juice to lemonade in each drink.

Julie's drink has a ratio of 42ml juice to 210ml lemonade, which simplifies to 1:5.

Hammad's drink has a ratio of 30ml juice to 170ml lemonade, which simplifies to 3:17.

To compare the strength of their drinks, we need to compare the ratios of juice to lemonade. Since a higher ratio of juice to lemonade indicates a stronger taste, we can see that Hammad's drink has a stronger taste, since his ratio of juice to lemonade is higher than Julie's.

Therefore, Hammad has made his drink stronger in taste than Julie.

Answer: Please refer to the step by step explanation :)

Step-by-step explanation:

To understand how .0362 is less than .05, let’s pretend the 6 and the 2 don’t exist for right now. So, now we have .03 and .05. Since three is a lesser number than five, this has to mean .03 is less than .05. Reapplying the 6 and 2, .0362 must be less than .05.

Answer:

The answer is A

Step-by-step explanation:

thats all

Answer:

to find f(2), we need to substitute x=2 into the equation:

f(2) = 3(2)^2 - 2(2) + 4

Simplifying:

f(2) = 3(4) - 4 + 4

f(2) = 12

Therefore, f(2) = 12.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(2) = (3)(2^2) - 2(2) +4[/tex]

       [tex]= 12 - 4+ 4[/tex]

       [tex]= 12[/tex]

Based on the readings from the graph, the sequence has a next term of the 16

The missing information is attached

The readings on the graph can be represented as

1, 2, 4, 8, .....

We can see that multiplying 2 to the previous term to gives the next term

Using the above parameters, we have the following equation

Next term = 2 * Current term

The current term in the graph is 8

So, we have

Next term = 2 * 8

Evaluate

Next term = 16

Hence, the next term is 16

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The translation rule for these circles is (x+2),(y+3).

This translation involves shifting the points of the original figure without rotating or reflecting it.

In the given transformation, circle A has been transformed to circle B.

Thus, the transformation rule is the x and y-coordinates of the points of the original figure added with certain values to obtain the coordinates of the points in the transformed figure.

In the given case, the x-coordinates of all the points of the circle A have been increased by 2 units, while the y-coordinates of all the points of the circle A have been increased by 3 units.

Thus, the translation rule for these circles is (x+2),(y+3).

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The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2.

Poisson Distribution is a type of probability distribution used for independent events which occur at a known average rate within a given interval of time or space. It is used to model the number of times an event is likely to occur within a specified period of time or space. It is used in fields such as healthcare, quality control, finance, and engineering.

Coefficient of variation (CV) is a measure of relative variability or dispersion. It is a measure of the relative dispersion of a set of data points around its mean. It is calculated by dividing the standard deviation of the data points by the mean.

The coefficient of variation for a Poisson distribution with A=5 is equal to 1/A, which is equal to 0.2. This means that the relative variability of a Poisson distribution with A=5 is 0.2. This is because the standard deviation of a Poisson distribution is equal to the square root of the mean, and in this case, the mean is 5. Therefore, the standard deviation is the square root of 5, or 2.236. When divided by the mean, the coefficient of variation is 0.2.

In general, the coefficient of variation is used to compare the variability of two different datasets. A low coefficient of variation indicates that the data points are relatively close to the mean and that there is not much variability in the data. A high coefficient of variation indicates that the data points are further away from the mean and that there is a greater amount of variability in the data.

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Answer:

To evaluate 11.1x + 10.7y when x = 7 and y = 8, we simply substitute these values into the expression and simplify:

11.1(7) + 10.7(8) = 77.7 + 85.6 = 163.3

Therefore, 11.1x + 10.7y evaluates to 163.3 when x = 7 and y = 8.

Step-by-step explanation:

Answer:

reflection around the y-axis

Step-by-step explanation:

you really don't see that the picture just flipped from left to right and vice versa (around a central vertical mirror line through the black center dot) ?

to make it simple I just declare this line to be the y-axis.

Answer:

- 2 - 3 is the same thing as -2 + -3. This is because taking away 3 is the same thing as adding - 3. -2 -3 is just a more simplified version of -2 + -3.

Hope this helps!

Answer:

A = 48 cm²

Step-by-step explanation:

A = (1/2)bh

A = (1/2)(8 cm)(12 cm)

A = 48 cm²

Answer:

48cm^2

Step-by-step explanation:

8×12=96

96÷2=48cm^2

The cost of one adult ticket is $7.

The first step is to set up a pair of linear equations that represent the information in the question.

29a + 17y = 254 equation 1

21a + 22y = 213 equation 2

Where:

The elimination method would be used to solve the equations

Multiply equation 1 by 22:

638a + 374y = 5588 equation 3

Multiply equation 2 by 17:

357a + 374y = 3621 equation 4

Subtract equation 4 from equation 3

1967 = 281a

Divide both sides of the equation by 281

1967 / 281 = a

a = 7

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Answer:

It is better to buy 6 pints at $8.10

Step-by-step explanation:

To compare the cost per pint in each option, we can divide the total cost by the total number of pints.

For the first option, buying 3 pints at $3.60, the cost per pint is shown by the following:

3 pints ÷ $3.60 = $0.83 / pint

For the second option, buying 6 pints at $8.10, the cost per pint is shown by the following:

6 pints ÷ $8.10 = $0.74 / pint

Therefore, buying 6 pints at $8.10 is less expensive per pint than buying 3 pints at $3.60. Each pint when buying 3 at a time costs $0.83 whereas each pint when buying 6 at a time costs $0.74.

The graph represents a proportional relation

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

The graph

We can see that the lines pass through the origin

This means that the graph is a proportional relationship

From the graph. we have

(x, y) = (2, 400)

So, the unit rate is

Rate = 400/2

Rate = 200

The interpretation of this is that Mason's speed is 200 meters per minute

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Answer:

To determine Laars' gross earnings per pay period under different payment frequencies, we need to divide his annual salary of $90,000 by the number of pay periods in a year for each frequency.

a. Monthly: Laars will receive 12 paychecks per year, one per month.

Gross earnings per pay period = $90,000 / 12 = $7,500 per month

b. Semi-monthly: Laars will receive 24 paychecks per year, two per month.

Gross earnings per pay period = $90,000 / 24 = $3,750 per semi-monthly period (twice per month)

c. Biweekly: Laars will receive 26 paychecks per year, one every two weeks.

Gross earnings per pay period = $90,000 / 26 = $3,461.54 per biweekly period (every two weeks)

d. Weekly: Laars will receive 52 paychecks per year, one per week.

Gross earnings per pay period = $90,000 / 52 = $1,730.77 per weekly period (every week)

Therefore, Laars' gross earnings per pay period are $7,500 per month, $3,750 per semi-monthly period, $3,461.54 per biweekly period, and $1,730.77 per weekly period.

Therefore , the solution of the given problem of slope comes out to be option D 3:5 is the correct slope.

The slope of a line determines how steep it is. Gradient overflow is a condition that can occur in equations based on gradients. By dividing the total of the run (width difference) and emergence (climbing distinction) among both two points, one can calculate the slope. The fixed path problem is modelled using the equation y = mx + b with the hill variant. where slope is millimeters, a = bc, and the location of the line's y-intercept.

Here,

Given :

Vertical length = 6

and

horizontal length = 10

=> Slope: Y/X=6/10=0.6

=>  6/10 =  3/5(D)

Thus , option D 3:5 is the correct slope.

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Answer:

A

Step-by-step explanation:

Using percentage concept, we would have saved 2784.6 dollars after a year

To calculate how much you will have saved after a year, we can break down the savings for each week of each month, and then add up the total. Here's how it works:

We can use percentage to calculate how much is saved each week

In the first week of each month, you save 10% of your weekly allowance, which is 10 percent of 500 = 50 dollars.

In the second week of each month, you save 10% more than the previous week, which is 10% of (500 + 50) = 55 dollars.

In the third week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55) = 60.5 dollars.

In the fourth week of each month, you save 10% more than the previous week, which is 10% of (500 + 50 + 55 + 60.5) = 66.55 dollars.

So in total, you save 50 + 55 + 60.5 + 66.55 = 232.05  dollars per month.

Over the course of a year, you will have saved 232.05 dollars per month * 12 months = 2784.6 dollars.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -4}{2}~~~ ,~~~ \cfrac{ 2 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ -4 }{2} \right)\implies \left(-\frac{1}{2}~~,~~-2 \right)[/tex]

The correct answer is interval 2. A function is a rule that relates each element in one set, called the domain, to exactly one element in another set, called the range.

It is a mathematical expression that takes an input, performs a calculation and produces an output.

In order to determine if dy/dx>0 and d2y/dx2<0 over interval 2, we must take the first and second derivatives of the function y=f(x). The first derivative of the function is dy/dx=2x-3 and the second derivative of the function is d2y/dx2=2.

Now, if we look at the graph, we can see that the function is increasing from 0 to 3 and then decreasing from 3 to 6. This means that over interval 2, which is from 3 to 6, the first derivative, dy/dx, must be negative. This means that dy/dx<0 over interval 2.

Furthermore, the second derivative, d2y/dx2, must be negative over interval 2 since the graph is decreasing over this interval. This means that d2y/dx2<0 over interval 2.

Therefore, the correct answer is interval 2 since it is the only interval for which both dy/dx>0 and d2y/dx2<0 are true.

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In response to the query, we can state that Therefore, the Pearson correlation coefficient r for the given points is approximately -0.758.

The relationships between various variables are described by correlations. Expressions might be strong, weak, positive, or negative. 1 = Correlation does not always imply causation. Correlation is a statistical indicator of the linear relationship between two variables (that is, do they change at a constant rate).

1 6 -3 1 9 1 -3

Σx = 28

Σy = 36

n = 7

Therefore, the correlation coefficient r for the given points is approximately -0.758.

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Answer: 308.65

:) Good luck

[tex]1 \ \text{lb} = 0.45359 \ \text{kg}[/tex]

[tex]140 \ \text{kg} \times (1 \ \text{lb})\div(0.45359 \ \text{kg}) = 308.65 \ \text{lb}[/tex]

[tex]\bold{140 \ kg=308.65 \ lb}[/tex]

Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.

To show that multiplication in M_n(R) is not commutative when n > 1, we need to find two matrices A and B in M_n(R) such that AB is not equal to BA.

Let's consider two matrices A and B in M_n(R) such that:

That is, A is the n x n identity matrix, and B is the matrix with 1's on the anti-diagonal and 0's elsewhere.

Now let's compute AB and BA:

AB = [c_ij], where c_ij = Σ_k=1^n a_ik * b_kj

If i+j = n+1, then b_kj = 1 only if k = i, and a_ik = 1 only if k = j.

Therefore,

c_ij = a_i1 * b_1j + a_i2 * b_2j + ... + a_in * b_nj = a_ii * b_jj = 1 * 1 = 1

If i+j ≠ n+1, then b_kj = 0 for all k, and hence c_ij = 0.

Therefore, AB is the matrix with 1's on the anti-diagonal and 0's elsewhere, just like B.

Now let's compute BA:

BA = [d_ij], where d_ij = Σ_k=1^n b_ik * a_kj

If i=j, then a_kj = 1 only if k = i, and b_ik = 1 only if k = i. Therefore,

d_ij = b_i1 * a_1j + b_i2 * a_2j + ... + b_in * a_nj = b_ii * a_jj = 1 * 1 = 1

If i ≠ j, then a_kj = 0 for all k, and hence d_ij = 0.

Therefore, BA is the matrix with 1's on the diagonal and 0's elsewhere, just like A.

Since AB and BA are not equal for n > 1, we have shown that multiplication in M_n(R) is not commutative for n > 1.

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The survey design that we have here is not an acceptable standard survey design for research.

This survey design has limitations and may not be the most optimal way to measure student interest in classroom topics. Here are some of the reasons why:

Limited response options: By only allowing four responses, the survey restricts the range of possible responses that students can give. For instance, some students may feel that a topic is somewhat interesting, but not interesting enough to warrant a score of 6. Similarly, some students may feel that a topic is not worth studying, but not to the extreme level of giving it a score of 1. This design does not account for such nuances in student opinions.

Lack of neutral option: The survey does not include a neutral option such as "no opinion" or "undecided". This means that students who do not have a strong opinion about a topic may be forced to pick a score that does not accurately reflect their level of interest.

Lack of context: The survey does not provide any context or information about the topics being evaluated. Without such information, students may base their scores on assumptions or incomplete knowledge about the topics, which may not accurately reflect their actual level of interest.

Lack of reliability and validity: The survey's reliability and validity may be questionable. The limited response options and lack of context may lead to responses that are not reliable or valid measures of student interest.

In conclusion, while this survey design may be simple and easy to administer, it has limitations that make it less than ideal for measuring student interest in classroom topics. A more comprehensive survey design that includes a wider range of response options and provides contextual information about the topics may provide more reliable and valid results.

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Answer: Let's first calculate the number of users after one year:

Number of users after one year = 16 lakh + 50% of 16 lakh

= 16 lakh + 8 lakh

= 24 lakh

Now, we can calculate the number of users after two years by applying the same growth rate:

Number of users after two years = 24 lakh + 50% of 24 lakh

= 24 lakh + 12 lakh

= 36 lakh

Therefore, two years from now, it is expected that 36 lakh (3.6 million) students in India will be using Khan Academy.

Step-by-step explanation:

Answer:

36 Iakh Students

Step-by-step explanation:

Answer:

2520

because we need to multiply all the lengths to take out volume of piramid