81a^2+5b^2
factor, but this is algebra and intro to pre-calc

Answer:

Step-by-step explanation:

[tex]\frac{15}{7} or \frac{26}{9}[/tex]

The  mean is 5.907, and the standard deviation is 0.677.

To construct a binomial probability distribution, we need the parameters n and p, where n is the number of trials and p is the probability of success in each trial.

From the provided data, it appears that we have the probability distribution for a binomial random variable X with n = 6 trials. The probabilities are as follows:

P(0) = 0.0156

P(1) = 0.0938

P(2) = 0.2344

P(3) = 0.3125

P(4) = 0.2344

P(5) = 0.0938

P(6) = 0.0156

The sum of these probabilities should be equal to 1.

Now, let's compute the mean (μ) and standard deviation (σ) using the formulas:

μ = np

σ = √(np(1 - p))

So, p = P(success)

= P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

= 0.0938 + 0.2344 + 0.3125 + 0.2344 + 0.0938 + 0.0156

= 0.9845

Now, we can calculate the mean and standard deviation:

μ = np = 6 x 0.9845 ≈ 5.907

σ = √(np(1 - p))

= √(6 x 0.9845 x (1 - 0.9845))

= 0.677

Therefore, the mean is 5.907, and the standard deviation is 0.677.

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[tex]$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$[/tex]The formula for calculating standard deviation is  [tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{n}}}[/tex], where

[tex]\sigma[/tex] is the population standard deviation, [tex]n[/tex] is the population size, [tex]x_{i}[/tex] is each value from the population, and [tex]\mu[/tex] is the population mean. We can substitute each value into the formula and simplify, which gives us our standard deviation.

[tex]$\sigma={\sqrt {\frac {(57-34)^{2}+(48-34)^{2}+(47-34)^{2}+(38-34)^{2}+(20-34)^{2}+(14-34)^{2}+(14-34)^{2}}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {(23)^{2}+(14)^{2}+(13)^{2}+(4)^{2}+(-14)^{2}+(-20)^{2}+(-20)^{2}}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {529+196+169+16+196+400+400}{7}}}$[/tex]

[tex]$\sigma={\sqrt {\frac {1906}{7}}}$[/tex]

[tex]$\sigma = \sqrt{272.285714286}$[/tex]

[tex]$\sigma \approx 16.5010822156$[/tex]

Our answer is [tex]$\sigma \approx 16.5010822156$[/tex], or, for convenience, [tex]$\sigma \approx 16.501082$[/tex], which is the most digits you'll probably need for any calculations you make.

Hope this helps!

The statement that is inconsistent with the distribution of sample means is, "The distribution of sample means tends to pile up around the population standard deviation." Therefore the correct answer is option D.

The mean sample distribution does not "pile up" around the population standard deviation. The sample means are central tendency measurements that indicate the average values from various samples. The population standard deviation, on the other hand, measures the population's dispersion or variability. The spread of sample means can vary, but it does not explicitly "pile up" around the population standard deviation.

In summary, option (D) contradicts the distribution of sample means, since the distribution does not pile up around the population standard deviation. The other options (A, B, and C) appropriately represent the sample mean characteristics.

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The correct question is-

Which statement below is not consistent with the distribution of sample means?

A) The distribution of sample means tends to pile up around the population mean.

B) The distribution of sample means tends to be approximately normal.

C) The distribution of sample means depicts the means of all the random samples of a particular sample size.

D) The distribution of sample means tends to pile up around the population standard deviation.

The probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.

To find the probability that a randomly selected point within the square falls in the red-shaded square, we need to compare the areas of the red square and the larger square.

The area of the larger square is given by the formula:

Area = side length x side length

In this case, the side length of the larger square is 3 units, so its area is:

Area of larger square = 3 x 3 = 9 square units

The area of the red square is given by the formula:

Area = side length x side length

In this case, the side length of the red square is 2 units, so its area is:

Area of red square = 2 x 2 = 4 square units

To find the probability, we divide the area of the red square by the area of the larger square:

Probability = Area of red square / Area of larger square

Probability = 4 / 9

Therefore, the probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.

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(a) The given sequence 2,4,8,..... is a geometric sequence, that is, the common ratio of the sequence is the same.

The next term, that is, the fourth term of the sequence can be found with the help of the nth term formula of G.P.(Geometric progression) which is given as

Aₙ = arⁿ⁻¹ where a is the first term and r is the common ratio.

Aₙ = (2)(2)⁴⁻¹

    = (2)(2)³

    = 16

(b) Putting n= 1,2,3,4 one by one in 2ⁿ, we have

2¹ =2

2²=4

2³=8

2⁴= 16

Now evaluating n²-n+2 by putting n=1,2,3,4

Putting n=1, we have

n²-n+2 = (1)²-1+2

            = 1-1+2=2

Putting n=2, we have

n²-n+2 = (2)²-2+2

            = 4-2+2

            =4

Putting n=3, we have

n²-n+2 = (3)²-3+2

            = 9-3+2

            = 6+2

            =8

Putting n=4, we have

n²-n+2 = (4)²-4+2

           = 16-4+2

           = 14

Now evaluating n³-5n²+10n-4 by putting n=1,2,3,4

Putting n=1,

(1)³-5(1)²+10(1)-4

= 1-5+10-4

= -4+6

= 2

Putting n=2,

(2)³-5(2)²+10(2)-4

= 8-20+20-4

= 4

Putting n=3,

(3)³-5(3)²+10(3)-4

=27-45+30-4

=8

Putting n=4,

(4)³-5(4)²+10(4)-4

=20  

c) 2ⁿ is a geometric sequence, but the other two do not have the same ratio and hence their nth term can not be found by G.P.

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Given statement solution is :- "3 and 5 - 1," the mean is 3.5, the median is 5, and there is no mode.

To find the mean, median, and mode for the given numbers, let's start by organizing the numbers in ascending order:

For "3 and 5":

Ascending order: 3, 5

Mean:

To find the mean, we sum up all the numbers and divide the total by the count of numbers.

Mean = (3 + 5) / 2 = 8 / 2 = 4

Median:

The median is the middle value in a set of numbers when they are arranged in ascending order. Since we have two numbers, the median is the average of the two middle numbers.

Median = (3 + 5) / 2 = 8 / 2 = 4

Mode:

The mode is the value that appears most frequently in a set of numbers.

In this case, there is no repeating value, so there is no mode.

For "3 and 5 - 1":

Ascending order: 2, 5

Mean:

Mean = (2 + 5) / 2 = 7 / 2 = 3.5

Median:

Median = 5 (since we have two numbers, the median is the average of the two middle numbers, which is 5 in this case)

Mode:

Again, there is no repeating value, so there is no mode.

Therefore, for "3 and 5," the mean and median are both 4, and there is no mode.

For "3 and 5 - 1," the mean is 3.5, the median is 5, and there is no mode.

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Answer:

3a units^2

Step-by-step explanation:

Area = 6ah^2 + 9a = 1/2(b1 + b2) × (4h^2 + 6)

Simplify: 6ah^2 + 9a = 2h^2(b1 + b2) × 3(b1 + b2)

Factor out b1 + b2:

6ah^2 + 9a = (2h^2 + 3)(b1 + b2)

Express sum of lengths (divide both sides by 2h^2 + 3):

(b1 + b2) = 6a^2 + 9a / 2h^2 + 3

= 3 units^2

So, the sum of the lengths is 3 units^2 (in terms of a).

An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Here, we have,

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

m represent the slope.

x and y represent the points.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 6)/(0 + 3)

Slope (m) = -1/3.

For the equation of line g, we have:

y - 6 = (x + 3)

y - 6 = -1/3(x + 3)

y = -x/3 + 1 + 6

y = -x/3 + 7

Therefore, the slope, m = -1/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At data point (1, -2), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 5

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Answer:

504 voice cracks per week
72 voice cracks per day

Step-by-step explanation:

If Danny's voice cracks every 20 minutes, we can calculate the number of times his voice cracks in a day and in a week.

Number of times his voice cracks in a day:

There are 60 minutes in an hour, so there are 60/20 = 3 intervals of 20 minutes in an hour.

Since there are 24 hours in a day, Danny's voice cracks 3 times per hour * 24 hours = 72 times in a day.

Number of times his voice cracks in a week:

Since there are 7 days in a week, we can multiply the number of times his voice cracks in a day by 7.

Danny's voice cracks 72 times per day * 7 days = 504 times in a week.

Answer:

S = π(6^2) + π(6)(9) = 90π

= about 283 cm^2

Using π = 3.14:

S = 90(3.14) = about 283 cm^2

The percent increase in Newark's population from 2010 to 2020 is 11.98%.

By comparing percent increases, the greatest percent increase occurred in the 1840s - 1850s decade with 124.83%.

To get percent increase, we have to find difference between the population in 2020 and 2010, divide it by the population in 2010, and then multiply by 100.

Population in 2010: 277,140

Population in 2020: 310,350

Percent increase = ((310,350 - 277,140) / 277,140) * 100

Percent increase = (33,210 / 277,140) * 100

Percent increase = 11.983113228

Percent increase = 11.98%.

To know decade with the greatest percent increase, we need to calculate percent increase for each decade and compare the values.

Percent increase for each decade goes as follows:

1840s to 1850s:

= ((38,864 - 17,290) / 17,290) * 100

≈ 124.83%

1850s to 1860s:

= ((71,941 - 38,864) / 38,864) * 100

≈ 85.08%

1860s to 1870s:

= ((105,059 - 71,941) / 71,941) * 100

≈ 45.87%

2010s to 2020s:

= ((310,350 - 277,140) / 277,140) * 100

≈ 11.97%

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Answer:

36.84%

Step-by-step explanation:

7 over 19 as a percentage?

We Take

(7 ÷ 19) x 100 ≈ 36.84%

So, the answer is 36.84%.

The figure ABC is not a right triangle

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

Side lentghs = (0.73 cm) (0.7 cm) (0.24 cm)

Using the Pythagorean formula, we have

Square of longest sides = Sum of the squares of the other sides

using the above as a guide, we have the following:

0.73² = 0.7² + 0.24²

Evaluate

0.5329 = 0.5476

This equation is false

Hence, ABC is not a right triangle

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The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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Answer:

57° + 108° + p = 180°

165° + p = 180°

p = 15°

a.)The expression of David's money as a fraction would be = 2/3×h

b.) The amount of money they have together would be = $40.

To determine the fraction of Henry's money that is of David's, the following steps needs to be considered.

Let d represent David's money

Let h represent Henry's money

a.) Therefore, Fraction of Henry's money that belongs to David;

d = 2/3×h ----> 1

b.) d= 60+ h----->2

Substitute d= 60+h in equation 1;

60+h = 2/3h

60= 2/3h-h

60 = -1/3h

h= 60/3

h= -20

The total amount of money they both have= 60-20 = $40

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Complete question:

1/2 of David's money is 2/3 of Henry's money.

a) Express David's $ as a fraction of Henry's $.

b) If David has $60 more than Henry, how much money to they have altogether.

The  average density of the planet is approximately 5.6g/cm³

The formula for density is expressed as;

D = m/v

Such that;

From the information given, we have that;

Volume = 1.02×10⁹ km³

Mass = 5.683 × 10²¹ kg

Convert the parameters

Volume = 1.02×10²⁴cm³

Mass = 5.683 × 10²⁴g

Substitute the values, we have;

Density = 5.683 × 10²⁴g/1.02×10²⁴cm³

Density = 5.6g/cm³

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To find the probability of picking 2 green marbles and 1 blue marble from the bag, we need to determine the number of favorable outcomes (picking 2 green marbles and 1 blue marble) and the total number of possible outcomes.

Step 1: Determine the number of green marbles:

The given information states that there are 7 green marbles.

Step 2: Determine the number of blue marbles:

The given information states that there are 3 blue marbles.

Step 3: Determine the total number of marbles:

The given information states that there are 3 blue marbles + 7 green marbles + 4 yellow marbles = 14 marbles in total.

Step 4: Calculate the probability of picking 2 green marbles and 1 blue marble:

When picking without replacement, the probability of multiple events occurring is the product of their individual probabilities.

The probability of picking the first green marble is: 7 green marbles / 14 total marbles = 7/14.

After picking the first green marble, the total number of marbles remaining is 13 (since one green marble is already picked).

The probability of picking the second green marble from the remaining marbles is: 6 green marbles / 13 remaining marbles = 6/13.

After picking the second green marble, the total number of marbles remaining is 12 (since two green marbles are already picked).

The probability of picking the blue marble from the remaining marbles is: 3 blue marbles / 12 remaining marbles = 3/12.

To find the probability of all events occurring (picking 2 green marbles and 1 blue marble), we multiply their individual probabilities:

Probability of picking 2 green marbles and 1 blue marble = (7/14) * (6/13) * (3/12) = 126/2184 = 9/156.

Therefore, the probability of picking 2 green marbles and 1 blue marble without replacement is 9/156.

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The (g.f)(x)  of the two functions is:

(g.f) (x) = 6x + 37

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To find (g.f) (x), follow the steps below:

1. Substitute the value of f(x) into the function g(x).

2. Then simplify the expression.

That is:

f(x) = 3x+18

g(x) = 2x+1

Thus, we have:

(g.f) (x) = g(f(x))

(g.f) (x) = g(3x+18)

(g.f) (x) = 2(3x+18) + 1

(g.f) (x) = 6x+36 + 1

(g.f) (x) = 6x + 37

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The probability P(Z > -1.3) in a standard normal distribution is approximately 0.9032 or 90.32%.

We have,

To find the probability P(Z > -1.3) in a standard normal distribution, you can use a standard normal table or a calculator that provides cumulative probabilities.

Using a standard normal table:

The standard normal table provides the cumulative probabilities for values between 0 and the given z-score.

Since we want to find the probability of Z greater than -1.3, which is on the left side of the mean, we need to find the complementary probability of Z less than or equal to -1.3 and subtract it from 1.

Looking up -1.3 in the standard normal table, we find the cumulative probability to be 0.0968.

The probability P(Z > -1.3) is:

P(Z > -1.3) = 1 - P(Z ≤ -1.3)

P(Z > -1.3) = 1 - 0.0968

P(Z > -1.3) ≈ 0.9032

Using a calculator:

If you have a calculator that provides cumulative probabilities for the standard normal distribution, you can directly input the value -1.3 to find the probability.

Using the calculator, you would calculate:

P(Z > -1.3) ≈ 0.9032

Therefore,

The probability P(Z > -1.3) in a standard normal distribution is approximately 0.9032 or 90.32%.

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You need to buy 29 feet of lumber to frame the outside of the sandbox.

To calculate the total amount of lumber you need to buy to frame the outside of the sandbox, you need to calculate the perimeter of the box.

The formula to calculate the perimeter of a rectangle is:

Perimeter = 2×(Length + Width)

Given that the dimensions of the sandbox are 6.3 ft. by 8.2 ft., we can substitute the values into the formula:

Perimeter = 2×(6.3 ft. + 8.2 ft.)

Perimeter = 2 × (14.5 ft.)

Perimeter = 29 ft.

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The length of AB in the triangle is 9 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, the side AB can be found as follows:

AC = 27 units

CD = 9 units

DB = 3 units

Therefore, let's find the height of the triangle. AD is an angle bisector. Angle bisector theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Using angle bisector theorem,

AC / AB =  CD / DB

Therefore,

27 / AB = 9 / 3

cross multiply

AB = 81 / 9

AB = 9 units

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Approximately 26 percentage  of the counters are yellow.

To find the percentage of counters that are yellow, we first need to determine the total number of yellow counters.

Given that there are 600 counters in total, we know that the sum of the number of blue, red, and yellow counters should equal 600.

From the information provided, we know that 5/12 of the counters are blue. We can calculate the number of blue counters as follows:

Blue Counters = (5/12) * 600 = 250

We also know that 194 of the counters are red.

So, the total number of blue and red counters is:

Blue Counters + Red Counters = 250 + 194 = 444

To find the number of yellow counters, we subtract the sum of blue and red counters from the total number of counters:

Yellow Counters = Total Counters - (Blue Counters + Red Counters) = 600 - 444 = 156

Now, we can calculate the percentage of yellow counters by dividing the number of yellow counters by the total number of counters and multiplying by 100:

Percentage of Yellow Counters = (Yellow Counters / Total Counters) * 100 = (156 / 600) * 100 ≈ 26%

Therefore, approximately 26% of the counters are yellow.

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The following table shows the number of hours 45 hospital patients slept for one night. Use the table to answer the questions:Hours of Sleep | Patients0-2 | 53-5 | 96-8 | 179-11 | 2212-14 | 10a) How many patients slept between 6 and 11 hours?A total of 22 patients slept between 6 and 11 hours.

To find out, we need to add the number of patients who slept for 6-8 hours (17) and those who slept for 9-11 hours (5). Therefore, 17+5=22.b)

The mode is the value that occurs most frequently in the data set. In this case, the mode is the number of hours that the highest number of patients slept.

From the table, we can see that 9-11 hours is the mode because 22 patients slept for that number of hours, which is more than any other number of hours.c)

The median is the middle value in the data set when the data are arranged in numerical order. In this case, we have 45 patients, so we need to find the middle value between the 22nd and 23rd patients. These patients slept for 9-11 hours, so the median is 9-11 hours.

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Answer:

  9, -2

Step-by-step explanation:

You want two numbers with a product of -18 and a sum of 7.

These are easiest if you list the factor pairs of the product. You want to choose them so their sum has the sign of the required sum.

  -18 = (-1)(18) = (-2)(9) = (-3)(6)

Sums of these factor pairs are 17, 7, 3.

The pair of numbers you want is -2 and 9.

<95141404393>

The marginal cost for the fifth unit is $50. Hence, the correct option is b. $50.

To find the marginal cost for the fifth unit, we need to calculate the change in total cost when moving from producing 4 units to producing 5 units.

Total cost consists of both fixed costs and variable costs. The fixed costs remain constant regardless of the number of units produced, so they do not contribute to the marginal cost.

Variable costs, on the other hand, increase as more units are produced. The change in variable costs from producing 4 units to producing 5 units is $150 - $100 = $50.

Therefore, the marginal cost for the fifth unit is $50.

Hence, the correct option is b. $50.

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Answer:

A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-step explanation:

The diameter of a sunflower pollen grain is [tex]3.0 * 10^{-5}[/tex] meters.

The diameter of a ginger pollen grain is [tex]1.5 * 10^{-4}[/tex] meters.

We can divide the diameter of the sunflower pollen grain by the diameter of the ginger pollen grain to compare the sizes of these grains.

This gives us:

[tex]\frac{3.0 * 10^{-5} }{1.5 * 10^{-4 }}= 0.2[/tex]

This means that a sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

So the answer is A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Answer: Your answer is B. A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-Step Explanation: Take them both and divide them (3.0*10^(-5))/(1.5*10^(-4)) Solving the equations first and that makes:

Scientific Notation 2⋅10^−1

Or expanded form 0.2

Hope it helped :D

Answer:

C

Step-by-step explanation:

(i)

given a triangle with 2 sides and the included angle known

to find the third side use the Cosine rule

a² = b² + c² - 2bc cosA

adapting the formula to describe Δ PQR

r² = p² + q² - 2pq cosR

here r = PQ, p = QR = 7.6 , q = PR = 8.4 and ∠ R = 62° , then

r² = 7.6² + 8.4² - (2 × 7.6 × 8.4 × cos62° )

  = 57.76 + 70.56 - 59.942

  = 128.32 - 59.942

  = 68.376 ( take square root of both sides )

r = [tex]\sqrt{68.378}[/tex]

  ≈ 8.27

that is PQ ≈ 8.27 cm ( to 2 decimal places )

(11)

the area (A) is then calculated as

A = [tex]\frac{1}{2}[/tex] pq sinR

  = 0.5 × 7.6 × 8.4 × sin62°

  ≈ 28.2

that is area of Δ PQR ≈ 28.2 cm² ( to 1 decimal place )

Answer:

c

Step-by-step explanation:

I think it's c I might be wrong though not sure

Answer: Total visitors =1500

Step-by-step explanation:

By rounding off each no. nearest to 100 is :

185=200, 349=300, 107=100, 355= 400. 451= 500

By adding round off  no. i.e.200+300+100+400+500= 1500

So total no. of visitors were 1500