find the product binomial expression

(3×+2) (4×+5)​

a) Consider the experiment of picking 3 tax returns at random as 3 related experiments (due to the fact that it is without replacement); then, as for the first time one selects a tax return,

As for the second time we grab a tax return, there are 69 tax returns in total and 9 of them contain errors; thus,

Similarly, as for the third picking round,

Finally, the probability of experiment a) is

Rounded to one decimal place, the probability of event a) is 65.7%

b) Similarly, in the event of all three tax returns containing errors,

Thus,

The probability of event b) is 0.2%. It is quite unusual.

c) The condition 'at least one of those containing errors' includes the cases when 1, 2, or 3 tax returns of the ones selected have errors. Notice that

Therefore,

And we found the probability of picking 3 tax returns without any errors in part a); thus,

The probability of event c) is 34.3%.

d) Analogously to part c), the probability of selecting at least one without errors is

The probability of event d) is 99.8%, and it is not improbable at all.

The frequency distribution table of the data is illustrated below.

The data we have been given represents the percentage of people who have completed 4 or more years of college education in different states. To create a frequency distribution, we need to first decide on the number of classes we want to use. In this case, we will use 7 classes.

Next, we need to determine the range of values for each class. To do this, we first find the minimum and maximum values in the data set, which are 18.9 and 37.9, respectively.

The range of values for each class will be (max value - min value) / number of classes, which in this case is (37.9 - 18.9) / 7 = 2.86.

We will start with the first class, which will include all values from 18.9 to 21.76 (the lower limit of the first class plus the range of values for each class). The next class will include values from 21.76 to 24.62, and so on, until we reach the final class which will include all values from 33.18 to 36.04 (the upper limit of the final class plus the range of values for each class).

To create the frequency distribution, we count the number of values in the data set that fall into each class. For example, the first class includes values between 18.9 and 21.76, and there are 2 values in the data set that fall into this range (21.4 and 20.0). We continue this process for each class until we have a table that shows the frequency of values in each class.

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Complete Question:

Percentage of People Who Completed 4 or More Years of College Listed by state are the percentages of the population who have completed 4 or more years of a college education. Construct a frequency distribution with 7 classes.

21.4,26.0,25.3,19.3,29.5,35.0,34.7,26.1,25.8,23.4,27.1,29.2,24.5,29.5,22.1,24,3,28.8,20,0,20.4,26.7,35.2,37.9,24.7,31.0,18.9,24.5,27.0

Answer:

Monomial, Binomial,Trinomial,Quadratic equation,Linear equations

Step-by-step explanation:

The graph that matches sine function y = 2 sin (x – π) + 2 is:

On a coordinate plane, a function has a maximum of 4 and minimum of 0. It completes one period at 2 pi. It decreases through the y-axis at (0, 2).

A graph is a pictorial representation of data. Graphs are usually plotted in a cartesian plane having x and y directions

The graph in the given problem is a graph showing sin function representing sinusoidal waves.

The given equation: y = 2 sin (x – π) + 2

substituting x = 0

y = 2 sin (0 – π) + 2

y = 2 sin (-π ) + 2  (in radians)

y = 2 * 0 + 2

y = 0 + 2

y = 2

Therefore the ordered pair is correct for the graph (0, 2)

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Answer: The answer is D (the last option)

Step-by-step explanation:

The limit is evaluated by using the series expansion of 1 - cos(2x) and 1 + 2x - e^2x. The series expansion of 1 - cos(2x) is 2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ... and the series expansion of 1 + 2x - e^2x is 2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ... Therefore, the limit of both series is 0 as x approaches 0.

The limit of 1 - cos(2x) as x approaches 0 is calculated by taking the series expansion of 1 - cos(2x), which is

2x^2 - (2/3)x^4 + (1/5)x^6 - (1/42)x^8 + ...

When x is 0, all terms in the series are 0, so the limit is 0. Similarly, the limit of 1 + 2x - e^2x as x approaches 0 is calculated by taking the series expansion of 1 + 2x - e^2x, which is

2x - (2/3)x^3 + (2/5)x^5 - (4/21)x^7 + ....

When x is 0, all terms in the series are 0, so the limit is also 0.

The limit of 1 - cos(2x) as x approaches 0 is also calculated numerically. When x is

0.0001, 1 - cos(2x) is 0.000399980.

When x is 0.00001, 1 - cos(2x) is 0.0000039998.

As x becomes closer to 0, the value of 1 - cos(2x) approaches 0. The same is true for

1 + 2x - e^2x.

When x is 0.0001, 1 + 2x - e^2x is 0.000399980.

When x is 0.00001, 1 + 2x - e^2x is 0.0000039998.

As x becomes closer to 0, the value of

1 + 2x - e^2x also approaches 0.

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Answer:

4.27

Step-by-step explanation:

1 bundle= $0.56

7bundles=o.56x7=$3.92

Tax=0.35

3.92+0.35=4.27

Answer:

ok

Step-by-step explanation:

Answer: no body

Step-by-step explanation:

thanks though :)

Given that, magnification is 3 times enlarged and virtual image. So m=+3(because +represents virtual image and 3 tells us that the height of image is 3 times that of object. Since, m=-(v/u) 3 = -(v/-10cm) v=30cm By mirror formula, 1/f = 1/v +1/u = 1/30 + 1/-10 =-2/30 f=-15cm Since R=2f=2x(-15cm)=-30cm Ans: The Radius of curvature measures -30cm

If you're talking about if someone asked a question and you just so happen to be following them, then just go to "Me" at the bottom of your screen, click "Following", choose the person who asked the question, and it will pull up their profile stuff, and once you're there click " My Questions" (in that person's profile). After that, all you have to do is choose the one you wanted to answer.

The expressions x and 15-x add back up to 15.

An example: Let x = 7 which means the remaining piece is 15-x = 15-7 = 8 feet long.

Answer: 5-x

Step-by-step explanation:

The probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

σ_sample = σ / sqrt(n)

σ_sample = 2.5 / sqrt(55)

σ_sample ≈ 0.336

Now, we can standardize the values of 17 and 18 pounds using the Z-score formula. This will tell us how many standard deviations away from the population mean these values are:

Z = (X - μ) / σ_sample

Z_17 = (17 - 17.2) / 0.336 ≈ -0.595

Z_18 = (18 - 17.2) / 0.336 ≈ 2.381

Now we will use the standard normal distribution (Z-distribution) to find the probabilities corresponding to these Z-scores. You can use a Z-table, statistical software, or an online calculator to find these probabilities.

P(Z < -0.595) = 0.2760

P(Z < 2.381) = 0.9915

To find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds, we will find the difference between the probabilities corresponding to the two Z-scores:

P(17 < X < 18) = P(Z < 2.381) - P(Z < -0.595)

P(17 < X < 18) = 0.9915 - 0.2760

P(17 < X < 18) ≈ 0.7155

So, the probability that the mean of a sample of 55 families will be between 17 and 18 pounds is approximately 71.55%.

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Answer:

x less thsn 4

Step-by-step explanation:

hope it helps

Answer: C. x less than 4

Step-by-step explanation:  X is not the variable being subtracted, and 4 is the variable being subtracted, therefore the answer is C. x less than 4 because this does not describe x - 4

if i was i your class or in bigger class i will help you

Answer:

100 but I am not sure I guess it's 100

Answer:

15

Step-by-step explanation:if you make the donminater  the same on all three equations you get 15 and 6 is drinking water so minus 6 that 9 2/5 are resting by a nearby pond so minus 6 and 1/3 i grazing the forest so minus 3 and you get zero so the answer is 15

$4,204.80

Interest is the amount of money an initial investment earns.

Simple Interest

The question states that this account has simple interest. This means that the interest is only earned on the principal (initial investment) and not compounded. For simple interest, we need to know 3 things: the principal, the rate of interest, and the time period. So, all we need to do is plug in the values we were given.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this formula, P is the principal, r is the rate as a decimal, and t is the time. Now, we can plug our values in.

So, over the course of 2 years, the account will earn $4,204.80.

Answer:

Step-by-step explanation:

\(x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b = -7\,,\ c=9\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}2\\\\x_1=\dfrac{7+\sqrt{13}}2\,,\quad x_2=\dfrac{7-\sqrt{13}}2\)

The total displacement of ostrich is equals to the 4 metre in south. So, the correct choice for answer of this problem is option (d).

Distance travelled and displacement of a body are two different things. The distance travelled by the ostrich is the sum of the distances covered in each run but the displacement is the distance from the nest and the final position of the ostrich. The ostrich runs in north direction in a straight line = 21 metre

Then, displacement after takes a turn

in south direction= 25 metre

Total distance travelled by her = 21 + 25

= 46 m

But displacement is always measured from the starting point(her nest). If we look from the starting position of the ostrich, it is 25 - 21 = 4 m away that too in the south direction, So the displacement of the ostrich is 4 m in the South direction.

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Step-by-step explanation:

Opposite to the angle = Pole

Adjacent to the angle = Shadow

Therefore tan50° = 18ft/x,

x = 18ft / tan50° = 15.1ft.

Answer:

19 1/16

Step-by-step explanation:

Answer:

305/16

Step-by-step explanation:

Simplify the following:

(5 (30 + 1/2))/8

Hint: | Express (5 (30 + 1/2))/8 as a single fraction.

(5 (30 + 1/2))/8 = (5 (30 + 1/2))/8:

(5 (30 + 1/2))/8

Hint: | Put the fractions in 30 + 1/2 over a common denominator.

Put 30 + 1/2 over the common denominator 2. 30 + 1/2 = (2×30)/2 + 1/2:

(5 (2×30)/2 + 1/2)/8

Hint: | Multiply 2 and 30 together.

2×30 = 60:

(5 (60/2 + 1/2))/8

Hint: | Add the fractions over a common denominator to a single fraction.

60/2 + 1/2 = (60 + 1)/2:

(5 (60 + 1)/2)/8

Hint: | Evaluate 60 + 1.

60 + 1 = 61:

(5×61/2)/8

Hint: | Express 5×61/2 as a single fraction.

5×61/2 = (5×61)/2:

((5×61)/2)/8

Hint: | Express ((5×61)/2)/8 as a single fraction.

((5×61)/2)/8 = (5×61)/(2×8):

(5×61)/(2×8)

Hint: | Multiply 2 and 8 together.

2×8 = 16:

(5×61)/16

Hint: | Multiply 5 and 61 together.

5×61 = 305:

Answer:  305/16

The margin of error of the random selection is 0.29

The given parameters are:

\(n = 320\) --- the sample size

\(\sigma = 2.9\) --- the standard deviation

\(\bar x = 24\) --- the mean

\(\alpha = 90\%\) --- the confidence level.

The margin of error (E) is calculated as follows:

\(E = z \times \sqrt{\frac{\sigma^2}{n}}\)

So, we have:

\(E = z \times \sqrt{\frac{3.2^2}{320}}\)

\(E = z \times \sqrt{\frac{10.24}{320}}\)

The z-value for 90% confidence level is 1.645.

Substitute 1.645 for z

\(E = 1.645 \times \sqrt{\frac{10.24}{320}}\)

\(E = 1.645 \times \sqrt{0.032}\)

Take square roots

\(E = 1.645 \times 0.1789\)

Multiply

\(E = 0.2943\)

Approximate

\(E = 0.29\)

Hence, the margin of error is 0.29

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The factored form of the function is  (x - 5)(x + 5)(x - 2)²

The given function is f(x) = x⁴ - 4x³ - 21x² + 100x - 100

Since x = 5, then use synthetic division to find the factored polynomial so we can find another root:

5    |    1    -4    -21    100    -100

    |    ↓    5      5     -80      100

          1    1     -16     20       0 ← remainder is zero so (x - 5) is a factor

Use the factored polynomial to find another root:

-5   |    1     1     -16    20

    |    ↓   -5     20   -20  

          1   -4      4      0 ← remainder is zero so (x + 5) is a factor

Now use the perfect square formula on the factored polynomial:

   x² - 4x + 4

= (x - 2)(x - 2)

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Answer:

48

Step-by-step explanation:

48/3=16 i did 3*16 to get 48  so do the opposite operation

hope this helps

The given function is f(x) = 15(1.02)^x, where x is the number of years from the date at which money is initially deposited.

This means that $15 were initially deposited into the account, and the amount grows at an annual rate of 2% (which is represented by 1.02 being raised to the power of x).

Therefore, the correct answer is: $15 were initially deposited into the account, which grows at an annual rate of 2%.

Hope I helped you...

Answer:

b = -17

Plug it in to find maybe correct answer if not sure next time.

To calculate the molar solubility and solubility in g/L of each salt, we need to use the solubility product constant (Ksp) values given for each compound.

The molar solubility is represented by "s" and the solubility in g/L is calculated using the molar mass of the compound.

(a) PbF2:

The molar solubility of PbF2 can be calculated using the Ksp value:

Ksp = [Pb2+][F-]^2 = (s)(2s)^2 = 4s^3

4.0 × 10^(-8) = 4s^3

s^3 = 1.0 × 10^(-8)

s = (1.0 × 10^(-8))^(1/3)

s ≈ 4.64 × 10^(-3)

The molar solubility of PbF2 is approximately 4.64 × 10^(-3) M.

To calculate the solubility in g/L, we need the molar mass of PbF2, which is approximately 245.19 g/mol. Using the molar solubility:

Solubility (g/L) = (molar solubility) × (molar mass)

Solubility (g/L) = (4.64 × 10^(-3) mol/L) × (245.19 g/mol)

Solubility (g/L) ≈ 1.14 × 10^(-2) g/L

(b) Ag2CO3:

Using the Ksp value: Ksp = [Ag+]^2[CO3^2-]

Let the molar solubility of Ag2CO3 be s.

Ksp = (2s)^2(s) = 8.1 × 10^(-12)

4s^3 = 8.1 × 10^(-12)

s^3 = (8.1 × 10^(-12)) / 4

s ≈ 8.02 × 10^(-4)

The molar solubility of Ag2CO3 is approximately 8.02 × 10^(-4) M.

To calculate the solubility in g/L, we need the molar mass of Ag2CO3, which is approximately 275.75 g/mol. Using the molar solubility:

Solubility (g/L) = (molar solubility) × (molar mass)

Solubility (g/L) = (8.02 × 10^(-4) mol/L) × (275.75 g/mol)

Solubility (g/L) ≈ 0.221 g/L

(c) Bi2S3:

Using the Ksp value: Ksp = [Bi3+]^2[S2-]^3

Let the molar solubility of Bi2S3 be s.

Ksp = (2s)^2(s)^3 = 1.6 × 10^(-72)

4s^5 = 1.6 × 10^(-72)

s^5 = (1.6 × 10^(-72)) / 4

s ≈ 4.0 × 10^(-15)

The molar solubility of Bi2S3 is approximately 4.0 × 10^(-15) M.

To calculate the solubility in g/L, we need the molar mass of Bi2S3, which is approximately 465.96 g/mol. Using the molar solubility:

Solubility (g/L) = (molar solubility) × (molar mass)

Solubility (g/L) = (4.0 × 10^(-15) mol/L) × (465.96 g/mol)

Solubility (g/L) ≈ 1.86 × 10^(-12) g/L

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Given:

A new type of pump can drain a certain pool in 9 hours.

An older pump can drain the pool in 11 hours.

To find:

The required time when both pumps work together to drain the pool.

Explanation:

One hour's work of the new pipe is,

One hour's work of the old pipe is,

So, one hour's work of both the pipe together is,

Therefore, the time taken to drain the pool for both the pipes together is,

Final answer:

The required time to drain the pool for both the pipes together is 4 hours 57 minutes.

The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

Answer:

7.2

Step-by-step explanation:

a good method towards percentages in multiplying both numbers in this case 48 and 15 and then lowering the product by 2 decimal places

The solution to the given question is given below:(a) f(x) = 3x^2+4/x^2+2To differentiate the given function, we will use the quotient rule of differentiation.

which is given by,(f(x)/g(x))'=[f'(x)g(x)-f(x)g'(x)]/[g(x)]2Now, putting the given values into the formula, we get,f(x) = 3x2+4/x2+2Let f(x) = 3x2+4 and g(x) = x2+2Now,f'(x) = d/dx[3x2+4] = 6xg'(x) = d/dx[x2+2] = 2xAfter substituting all the values in the quotient rule, we get,(f(x)/g(x))'=(6x(x2+2)-2x(3x2+4))/(x2+2)2=(-6x^3-8x+12x^3+16x)/[x^4+4x^2+4] = (6x^3+8x)/[x^4+4x^2+4]Hence, f'(x) = (6x^3+8x)/[x^4+4x^2+4].Therefore, the required derivative of the given function is (6x^3+8x)/[x^4+4x^2+4].(b) f(x) = (x2 - 7x)12To differentiate the given function, we will use the chain rule of differentiation which is given by, d/dx[f(g(x))] = f'(g(x)).g'(x)Now, putting the given values into the formula, we get,Let f(x) = x^12 and g(x) = x2-7xThen,f'(x) = 12x^11g'(x) = d/dx[x2-7x] = 2x-7After substituting all the values in the chain rule, we get,d/dx[f(g(x))] = f'(g(x)).g'(x) = 12(x2-7x)11.(2x-7)Therefore, the required derivative of the given function is 12(x2-7x)11.(2x-7).(c) f(x) = x^4√6x+5To differentiate the given function, we will use the product rule of differentiation which is given by, (fg)' = f'g + fg'Now, putting the given values into the formula, we get,Let f(x) = x^4 and g(x) = √6x+5Then,f'(x) = d/dx[x4] = 4x3g'(x) = d/dx[√6x+5] = 3/√6x+5After substituting all the values in the product rule, we get,(fg)' = f'g + fg' = (4x3).(√6x+5) + (x^4).(3/√6x+5)Hence, f'(x) = (4x3).(√6x+5) + (x^4).(3/√6x+5).Therefore, the required derivative of the given function is (4x3).(√6x+5) + (x^4).(3/√6x+5).

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The derivatives of the functions of the differentiation of the given functions has been calculated.

(a) The rule of differentiation applied to

f(x) = 3x²+4/x²+2 is as follows:

f'(x) = [12x(x²+2)-(6x)(4)] / [(x²+2)²]

=> f'(x) = [12x³-24x] / [(x²+2)²]

=> f'(x) = 12x(1-x²)/[(x²+2)²].

(b) The rule of differentiation applied to f(x) = (x² - 7x)^12 is as follows:

f'(x) = 12(x²-7x)^11(2x-7).

We apply the chain rule, which is the following:

[f(g(x))]' = f'(g(x)) * g'(x).(c)

The rule of differentiation applied to f(x) = x⁴√(6x+5) is as follows:

f'(x) = 4x³ * (6x+5)¹∕² + x⁴ * 1/2(6x+5)^-1/2 * 6

=> f'(x) = [24x³(6x+5) + 3x⁴(6)]/[2(6x+5)¹∕²]

=> f'(x) = [3x³(8x²+15)]/[(6x+5)¹∕²].

Thus, the differentiation of the given functions has been calculated.

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