The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

1.8
2
8/9

Weights of Cherry Tomatoes are likely to be closer to the mean, Option B is the correct answer.

Mean is a measure to test the central tendency of the data.

It is calculated by the sum of all the data divided by the number of data.

In the given question the data is given , the man and the mean absolute deviation calculation is also given.

Mean absolute deviation (MAD) calculates the average of the distance between the data and the mean.

More the deviation , more the data is scattered.

From the data it can be seen that MAD for the cherry tomato is 0.5 which is less than that for the grape tomatoes

and

Therefore The statement B is true.

Weights of Cherry Tomatoes are likely to be closer to the mean.

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To rewrite the expression 8x²y²z - 6x³y² + 2x³y²z² as a product by pulling out the greatest common factor, we need to identify the highest power of each variable that appears in all the terms. The greatest common factor of the given expression is 2x²y², which can be factored out.

The given expression is 8x²y²z - 6x³y² + 2x³y²z². To find the greatest common factor, we need to look for the highest power of each variable that appears in all the terms.The highest power of x that appears in all the terms is x³, the highest power of y is y², and the highest power of z is z². Additionally, there is a common factor of 2 that appears in all the terms.
Now, we can factor out the greatest common factor, which is 2x²y²:
2x²y²(4z - 3x + xz²)
By factoring out 2x²y², we have rewritten the expression as a product. The remaining factor (4z - 3x + xz²) represents what is left after factoring out the greatest common factor.Therefore, the expression 8x²y²z - 6x³y² + 2x³y²z² can be rewritten as the product 2x²y²(4z - 3x + xz²) by pulling out the greatest common factor.

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Answer:

  -3 or x > -3

Step-by-step explanation:

Using a calculator, it can be found that

Rounding to three decimal places,

Answer:

Brainliest here!

Step-by-step explanation:

3 dozen cookies = 1.5 cups

one dozen cookies= 0.5 cups

5 dozen cookies = 2.5 cups of sugar

A graph of the triangle with the vertices (-5, 0), (-5, 9), and (0, 9) is shown in the image below.

In Mathematics and Geometry, a triangle can be defined as a two-dimensional geometric shape that comprises three side lengths, three vertices and three angles only.

Generally speaking, there are five (5) major types of triangle based on the length of their side lengths and angles, and these include the following;

In this scenario, we would use an online graphing calculator to plot the given triangle with the vertices (-5, 0), (-5, 9), and (0, 9) as shown in the graph attached below.

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The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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The probability that a test taker chosen at random takes 9 minutes or more to read the article is 0.38. Rounded to four decimal places, this is 0.3800.

To find the probability that a test taker chosen at random takes 9 minutes or more to read the article, we need to calculate the integral of the probability density function f(t) from 9 to 10 (since t is between 0 and 10).
∫(9 to 10) 0.012t^2 − 0.0012t^3 dt
Using the power rule of integration, we get:
[0.004t^3 - 0.0003t^4] from 9 to 10
Substituting the limits, we get:
[0.004(10)^3 - 0.0003(10)^4] - [0.004(9)^3 - 0.0003(9)^4]
Simplifying, we get:
0.38

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Answer:

5 hrs  19.57 Minutes will be taken to prepare 1575 Bags by Ashley & her 4 friends if Ashley take 2/3 minute to prepare a bag & her each friend takes 75% Longer

Step-by-step explanation:

Ashley Takes  2/3  minute to prepare a bag

=> ashley prepare bag in 1 minute = 3/2  

Her friends takes 75%  Longer to prepare a bag

time taken by her friends =  2/3  + (75/100)(2/3)

= (2/3)( 1  + 3/4)

= (2/3)(7/4)

= 7/6  Minutes

Her one friend prepare bag in 1 minute =  6/7

Bag prepared by Ashley & her 4 friend in 1 Minute

=  3/2  +  4*6/7

=  (21 + 48)/14

= 69/14  Bag

69/14   Bag prepared in 1 minute

1 Bag prepared in    14/69   minutes

1575  bags prepared  in   1575  * 14/69

= 319.57 minutes

= 5 hrs  19.57 Minutes

Here, we want to get the cost for one pound of banana

To do this, all we have to do is to divide the cost by the number of pounds

We can infact select any of the pairs

We have the cost as;

The entire trip to the mall took 5 hours, and it was 24 miles away. Cameron biked for 2 hours and walked for 3 hours.

Cameron started biking to the mall at a speed of 9 mph. After some time, the bike got a flat so Cameron walked the rest of the way, traveling at a speed of 2 mph. The distance that Cameron biked to the mall was x, and the distance he walked to the mall was 24 - x.

Cameron traveled at two different speeds, 9 mph and 2 mph, and traveled a total of 24 miles. So the time he spent biking plus the time he spent walking was 5 hours, and we can create an equation:

Time biking + time walking = 5 hours x/9 + (24 - x)/2 = 5 hours

Multiply everything by 18 to remove the denominators:
2x + 9(24 - x) = 90
2x + 216 - 9x = 90-7x = -126x = 18
Time biking = x/9 = 18/9 = 2 hours
Time walking = (24 - x)/2 = (24 - 18)/2 = 3 hours

Therefore, Cameron biked for 2 hours and walked for 3 hours.

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Answer:

It's evident that the two angles in question are complementary, which equal up to 90 degrees. So what answer choice, added to m1 (37 degrees), equals 90 degrees? By using inverse operations, we can conclude that the answer is A because 90 - 37 = 53.

Answer:

It's evident that the two angles in question are complementary, which equal up to 90 degrees. So what answer choice, added to m1 (37 degrees), equals 90 degrees? By using inverse operations, we can conclude that the answer is A because 90 - 37 = 53.

Answer:

7.74$

Step-by-step explanation: I have no expiation its easy

Answer:

75%

Step-by-step explanation:

the question can be '12 is what percent of 16'?

we can use this proportion:  let 'd' = discount

is/of = %/100

12/16 = d/100

cross-multiply to get:

16d = 1200;  d = 1200/16

which is 75 percent

The answer for the fraction 1/4 of 100 is 25.

Given,

The fraction; 1/4

We have to find the 1/4 of 100.

Fraction;

A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions

Here,

1/4 of 100 = 1/4 x 100 = 25.

That is,

The answer for the fraction 1/4 of 100 is 25.

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The sample indicates that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

This given test is a test for single sample proportion

The test hypothesis are:

\(H_{o} :p=0.20\), null hypothesis

\(H_{1} :p\neq 0.20\), alternative hypothesis

The test statistic fallows a standard normal distribution and is given by:

\(Z=\frac{x-p}{{\sqrt{p(1-p)/n} } }\)

p=0.20

X=47 plants

Sample size, n=500

x, is the sample mean:

x=X/n=47/500

x=0.094

So, test statistic is calculated as:

\(Z=\frac{0.094-0.20}{\sqrt{0.20(1-0.20)/500} }\)

Z=-5.93

From the z-table, the p-value associated with Z=-5.93 is approximately 0

The decision rule based on p-vale, is to reject the null hypothesis if p-value is less than confidence level

In this case, the p-value is very small and less than confidence level of 0.20, we therefore reject the null hypothesis or the claim

So we conclude that the data does not provide sufficient evidence to support the claim that 20% of plants are infected.

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(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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Answer:

n=25

Step-by-step explanation:

Using the relation that describes the measure of the angle formed by two secants being equal to half of the difference of the 2 arcs (large arc-small arc) we can establish the relation;

\(10 = \frac{45 - n}{2} \)

\(20 = 45 - n\)

\( - 45 + 20 = - n\)

\( - 25 = - n\)

\(n = 25\)

To maximize revenue in a monopoly market with a demand function of p = 195 - 0.40x and a revenue function of R = px, the price that will maximize revenue is $97.50.

The revenue function is given by R = px, where p is the price per unit and x is the number of units sold. In a monopoly market, the demand function represents the relationship between price and quantity demanded.

To find the price that maximizes revenue, we need to determine the price that corresponds to the maximum point of the revenue function. The revenue function can be rewritten as R = (195 - 0.40x)x.

To find the maximum point, we can take the derivative of the revenue function with respect to x and set it equal to zero. Differentiating R with respect to x, we get dR/dx = 195 - 0.80x. Setting this derivative equal to zero, we have 195 - 0.80x = 0.

Solving for x, we find x = 243.75. Substituting this value back into the demand function p = 195 - 0.40x, we can calculate the price that maximizes revenue: p = 195 - 0.40(243.75) = $97.50.

Therefore, the price that will maximize revenue in this monopoly market is $97.50.

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Answer:

11 points

Step-by-step explanation:

Claire had 11 points  because 18-7=11

C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

Two or more expressions with an Equal sign is called as Equation.

Given that Ava scored 18 points in a basketball game.

Let Ave score be represented as A.

Ave scored seven points more than Claire.

Let C be the Claire score.

A=7+C

As given Ava scored 18 points in a basketball

so the value of A is 18

18=7+C

Now let us find the value of C

Subtract 7 from both sides

18-7 =C

11=C

Hence, C+7 =18 is the equation which can be used to find the Claire score C, the value of C is 11.

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Yes, if two angles are vertical angles, then they are congruent (have equal measures).

Vertical angles are two non-adjacent angles formed by the intersection of two lines. They are always congruent, meaning they have the same measure. This can be proven mathematically using the Vertical Angles Theorem which states that vertical angles are congruent.

If two angles are vertical angles, they are formed by intersecting lines and share a common vertex but do not share a common side. The angles are always equal in measure and are congruent. This is known as the Vertical Angles Theorem, and it can be proven mathematically. When working with geometry, understanding the properties of different angles is important to correctly solve problems and equations. By knowing that vertical angles are always congruent, we can simplify calculations and make geometric proofs easier.

In conclusion, vertical angles are always congruent, which is a fundamental concept in geometry. The Vertical Angles Theorem proves that two angles formed by intersecting lines are always equal in measure and are congruent. This knowledge is essential for solving geometry problems and is a useful tool for math students.

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There are 126 blue marbles.

Total marbles in the bag=150

There are 21 blue marbles for every 4 white marbles then the sequence will be⇒ 4+21+4+21+4+21+4+21+4+21+4+21=150

21 blue marbles appear 6 times for every 4 blue marbles

So 21×6=126 blue marbles and 4×6=24, then 126+24=150 total marbles

∴There will be a total of 126 blue marbles along with 24 white marbles among the 150 marbles.

The sample consists of three scores: 7, 8, and 9. The mean is 8, the median is 8, there is no mode, and the range is 2.

In statistics and probability, a sample refers to a subset of a population that is used to make inferences or draw conclusions about the entire population. In this case, the sample consists of the scores you obtained in 5 quizzes. The scores are as follows: 7, 8, and 9.
To analyze this sample, there are several key measures that can be calculated:
1. Mean: The mean, also known as the average, is calculated by summing up all the scores and dividing it by the number of scores. In this case, the mean can be calculated as (7 + 8 + 9) / 3 = 8.
2. Median: The median is the middle value when the scores are arranged in ascending order. In this case, since there are three scores, the median is the middle score, which is 8.
3. Mode: The mode is the score that appears most frequently in the sample. In this case, none of the scores repeat, so there is no mode.
4. Range: The range is the difference between the highest and lowest scores in the sample. In this case, the highest score is 9 and the lowest score is 7, so the range is 9 - 7 = 2.
5. Standard Deviation: The standard deviation is a measure of how spread out the scores are from the mean. It quantifies the amount of variation or dispersion in the sample. To calculate the standard deviation, you would need the full set of scores, not just the three provided.

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Answer:

x-3 =27

Step-by-step explanation:

Answer: n-3=27

Step-by-step explanation:

The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

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Answer:

5y

Step-by-step explanation:

In algebra when an unknown number (symbolized by a letter in the alphabet) is side by side with another number, it means it's multiplying.

In this context, 28% is a statistic. A statistic is a numerical measurement or summary of a sample.

In this case, the survey collected data from a sample of 2625 elementary school children, and the 28% represents the proportion of children in the sample who were classified as obese. It is a descriptive statistic that provides information about the sample but does not make inferences about the entire population of elementary school children.

The number of cars in the parking garage is a quantitative variable. Quantitative variables are those that can be measured or counted numerically. The number of cars represents a numerical count or measurement, such as 0 cars, 5 cars, or 10 cars. It provides a quantitative value that can be analyzed and compared using mathematical operations. Additionally, quantitative variables can be further categorized into discrete or continuous variables. In the case of the number of cars, it is a discrete quantitative variable because it takes on specific, distinct numerical values rather than being measured on a continuous scale.

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The probability that a randomly chosen test-taker will score between 470 and 530 is 0.2358 (or 23.58% when expressed as a percentage).

To solve this problem, we need to use the standard normal distribution formula:
Z = (X - μ) / σ
where Z is the standard score (z-score) of a given value X, μ is the mean, and σ is the standard deviation.
First, we need to convert the given values of 470 and 530 to z-scores:
Z1 = (470 - 500) / 100 = -0.3
Z2 = (530 - 500) / 100 = 0.3
Next, we need to find the probability that a randomly chosen test-taker will score between these two z-scores.

We can use a standard normal distribution table or a calculator to find the area under the curve between -0.3 and 0.3.
Using a calculator or an online tool, we find that the area under the curve between -0.3 and 0.3 is approximately 0.2358.

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When solving proportions, we set the cross products equal, and then we solve for the unknown variable.

When solving proportions, we set the cross products equal to each other and then proceed to solve for the unknown variable. A proportion is an equation that states that two ratios or fractions are equal. To solve a proportion, we first identify the two ratios involved and set their cross-products equal.

For example, consider the proportion: a/b = c/d

To solve for the unknown variable, we set the cross products (a * d) and (b * c) equal:

a * d = b * c

This equation allows us to find the value of the unknown variable by manipulating the equation through multiplication or division to isolate the variable on one side of the equation.

By setting the cross products equal, we essentially establish an equality between the two ratios, indicating that the fractions on either side of the proportion are equivalent. Solving for the unknown variable allows us to determine its value based on the relationship between the given ratios.

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Answer:

B

Step-by-step explanation:

The constant of proportionality is 5 in every column which makes it proportional.