Someone plsssssssss help

The probability that the sample mean is between 17.5 and 18.5 is approximately 0.369, rounded to three decimal places.

To find the probability that the sample mean is between 17.5 and 18.5 for a random sample of 16 smartphone owners, we need to use the properties of the normal distribution.

The population mean is 18 and the population standard deviation is 6, we can calculate the standard error of the mean using the formula: standard deviation / sqrt(sample size). In this case, the standard error is 6 / sqrt(16) = 6 / 4 = 1.5.

Next, we need to calculate the z-scores for the lower and upper limits of the sample mean range. The z-score formula is given by: (sample mean - population mean) / standard error.

For the lower limit (17.5), the z-score is (17.5 - 18) / 1.5 = -0.333.

For the upper limit (18.5), the z-score is (18.5 - 18) / 1.5 = 0.333.

Using a standard normal distribution table or a calculator, we can find the probability corresponding to these z-scores. The probability that the sample mean is between 17.5 and 18.5 is approximately 0.369, rounded to three decimal places.

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According to a report from a business intelligence company, smartphone owners are using an average of 18 apps per month. Assume that number of apps used per month by smartphone owners is normally distributed and that the standard deviation is 6. Complete parts (a) through (d) below. a. If you select a random sample of 16 smartphone owners, what is the probability that the sample mean is between 17.5 and 18.5? (Round to three decimal places as needed.)

A truth table is a table that describes the values of an input signal and the resulting output signal. The truth table can be used to determine the values of Boolean expressions by matching the input signal with the output signal.

The Boolean expressions can be derived from the truth table.In order to draw Truth Table for the given expressions and get their SOP and POS Boolean expression, we have to follow the below steps: Step 1: Truth Table for the given expressions

Truth Table for a) Y = A BC + AC + BC:

Truth Table for b) Y = (AB) + C(A + B):

Truth Table for c) Y = (A BC) A+D):

Truth Table for d) Y = A BC + (A + B)D:

Step 2: SOP (Sum of Product) and POS (Product of Sum) Boolean expression From the Truth Tables above, we can create the SOP and POS Boolean expression.

Here are the SOP and POS expressions for each of the given expressions:

a) Y = A BC + AC + BC- SOP: A B C + A C + B C- POS: (A + B) (A + C) (B + C)

b) Y = (AB) + C(A + B)- SOP: AB + AC + BC- POS: (A + C) (B + C)

c) Y = (A BC) A+D)- SOP: A B C + A D- POS: (A + D) (B + C) (A + D)

d) Y = A BC + (A + B)D- SOP: A B C + A D + B D- POS: (A + D) (B + D) (A + B)

Thus, the Truth Table for the given expressions and their SOP and POS Boolean expression are as shown above.

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Answer:

\(49. \ \dfrac{x^2}{x^2 +2 \cdot x - 8} - \dfrac{x - 4}{x + 4}\)

The above reaction can be rewritten as follows;

\(\dfrac{x^2}{x^2 +2 \cdot x - 8} - \dfrac{x - 4}{x + 4} =\dfrac{x^2}{(x + 4) \cdot (x - 2)} - \dfrac{x - 4}{x + 4} = \dfrac{x^2 + (x - 2) \cdot (x - 4)}{(x + 4) \cdot (x - 2)}\)

Which gives;

\(\dfrac{x^2}{x^2 +2 \cdot x - 8} - \dfrac{x - 4}{x + 4} = \dfrac{x^2 -(x^2 -6 \cdot x + 8) }{(x + 4) \cdot (x - 2)} = \dfrac{6 \cdot x - 8 }{(x + 4) \cdot (x - 2)}\)

\(50. \ \dfrac{x - 3}{x^2 +10 \cdot x + 25} + \dfrac{x - 3}{x + 5}\)

\(\dfrac{x - 3}{x^2 +10 \cdot x + 25} + \dfrac{x - 3}{x + 5} = \dfrac{x - 3}{(x + 5) \cdot (x + 5)} + \dfrac{x - 3}{x + 5} = \dfrac{x - 3 + (x - 3) \cdot (x + 5)}{(x + 5) \cdot (x + 5)}\)

\(\dfrac{x - 3 + (x - 3) \cdot (x + 5)}{(x + 5) \cdot (x + 5)} = \dfrac{x - 3 + x^2 + 2\cdot x - 15}{(x + 5) \cdot (x + 5)} = \dfrac{ x^2 + 3 \cdot x - 18}{(x + 5) \cdot (x + 5)}\)

\(53. \ \dfrac{5}{a^2 +9 \cdot a + 8} - \dfrac{3}{a^2 -6 \cdot a - 16}\)

\(\dfrac{5}{a^2 +9 \cdot a + 8} - \dfrac{3}{a^2 -6 \cdot a - 16} = \dfrac{5}{(a + 1) \cdot (a + 8)} - \dfrac{3}{(a - 8) \cdot (a + 2) }\)

\(\dfrac{5}{(a + 1) \cdot (a + 8)} - \dfrac{3}{(a - 8) \cdot (a + 2) } = \dfrac{5 \cdot (a - 8) \cdot (a + 2) - 3\cdot (a + 1) \cdot (a + 8)}{(a + 1) \cdot (a + 8) \cdot (a - 8) \cdot (a + 2)}\)

\(\dfrac{5 \cdot (a - 8) \cdot (a + 2) - 3\cdot (a + 1) \cdot (a + 8)}{(a + 1) \cdot (a + 8) \cdot (a - 8) \cdot (a + 2)} = \dfrac{2 \cdot a^2 -57 \cdot a -104}{a^4+3 \cdot a^3-62 \cdot a^2 -192 \cdot a - 1}\)

\(\dfrac{5}{a^2 +9 \cdot a + 8} - \dfrac{3}{a^2 -6 \cdot a - 16} = \dfrac{2 \cdot a^2 -57 \cdot a -104}{a^4+3 \cdot a^3-62 \cdot a^2 -192 \cdot a - 1}\)

\(55. \ \dfrac{2}{x^2 +6 \cdot x + 9} + \dfrac{3}{x^2 + x - 6}\)

\(\dfrac{2}{x^2 +6 \cdot x + 9} + \dfrac{3}{x^2 + x - 6} = \dfrac{2}{(x + 3) \cdot (x + 3)} + \dfrac{3}{(x+3) \cdot(x - 2)}\)

\(\dfrac{2}{(x + 3) \cdot (x + 3)} + \dfrac{3}{(x+3) \cdot(x - 2)} = \dfrac{2 \cdot(x - 2) + 3\cdot (x + 3) }{(x + 3) \cdot (x + 3) \cdot(x - 2)}\)

\(\dfrac{2 \cdot(x - 2) + 3\cdot (x + 3) }{(x + 3) \cdot (x + 3) \cdot(x - 2)} = \dfrac{2 \cdot x - 4 + 3\cdot x + 9 }{(x + 3) \cdot (x + 3) \cdot(x - 2)} = \dfrac{5 \cdot x + 5 }{(x + 3) \cdot (x + 3) \cdot(x - 2)}\)\(\dfrac{5 \cdot x + 5 }{(x + 3) \cdot (x + 3) \cdot(x - 2)} = \dfrac{5 \cdot x + 5 }{x ^3 + 4 \cdot x^2-3 \cdot x - 18}\)

\(57. \ \dfrac{x}{2 \cdot x^2 +7 \cdot x + 3} - \dfrac{3}{3 \cdot x^2 + 7 \cdot x - 6}\)

\(\dfrac{x}{2 \cdot x^2 +7 \cdot x + 3} - \dfrac{3}{3 \cdot x^2 + 7 \cdot x - 6} =\dfrac{x}{(2 \cdot x + 1) \cdot (x + 3)} - \dfrac{3}{(3\cdot x-2) \cdot (x + 3)}\)

\(\dfrac{x}{(2 \cdot x + 1) \cdot (x + 3)} - \dfrac{3}{(3\cdot x-2) \cdot (x + 3)} = \dfrac{x \cdot (3 \cdot x - 2) - 3 \cdot (2 \cdot x + 1)}{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)}\)

\(\dfrac{x \cdot (3 \cdot x - 2) - 3 \cdot (2 \cdot x + 1)}{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)} = \dfrac{ 3 \cdot x^2 - 8\cdot x - 3 }{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)}\)

\(\dfrac{ 3 \cdot x^2 - 8\cdot x - 3 }{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)} = \dfrac{ (x -3) \cdot (3 \cdot x + 1) }{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)}\)

\(\dfrac{ (x -3) \cdot (3 \cdot x + 1) }{(2 \cdot x + 1) \cdot (x + 3) \cdot (3\cdot x-2)} = \dfrac{3 \cdot x^2 - 8 \cdot x -3 }{6 \cdot x^3+ 17 \cdot x^2 + 5 \cdot x-6}\)

\(59. \ \dfrac{x}{4 \cdot x^2 +11 \cdot x + 6} - \dfrac{2}{8 \cdot x^2 + 2 \cdot x - 3}\)

Using a graphing calculator, we have;

\(\dfrac{x}{4 \cdot x^2 +11 \cdot x + 6} - \dfrac{2}{8 \cdot x^2 + 2 \cdot x - 3} = \dfrac{2 \cdot x^2 - 3 \cdot x - 4}{8 \cdot x^3+18 \cdot x^2+x - 6}\)

\(61. \ \dfrac{3 \cdot w+ 12}{w^2 + w -12} - \dfrac{2}{w - 3}\)

\(\dfrac{3 \cdot w+ 12}{w^2 + w -12} - \dfrac{2}{w - 3} = \dfrac{3 \cdot (w+ 4)}{(w + 4) \cdot (w - 3)} - \dfrac{2}{w - 3} = \dfrac{3 }{ (w - 3)} - \dfrac{2}{w - 3}\)

\(\dfrac{3 }{ (w - 3)} - \dfrac{2}{w - 3} = \dfrac{1 }{ (w - 3)}\)

\(61. \ \dfrac{3 \cdot r}{2 \cdot r^2 + 10 \cdot r +12} + \dfrac{3}{r - 2}\)

With the aid of a graphing calculator, we have;

\(\dfrac{3 \cdot r}{2 \cdot r^2 + 10 \cdot r +12} + \dfrac{3}{r - 2} = \dfrac{3 \cdot r}{2 \cdot (r+2) \cdot (r + 3)} + \dfrac{3}{r - 2}\)

\(\dfrac{3 \cdot r}{2 \cdot (r+2) \cdot (r + 3)} + \dfrac{3}{r - 2} = \dfrac{3 \cdot r \cdot (r - 2) + 3 \cdot 2 \cdot (r+2) \cdot (r + 3)}{2 \cdot (r+2) \cdot (r + 3)\cdot (r - 2) }\)

\(\dfrac{3 \cdot r \cdot (r - 2) + 3 \cdot 2 \cdot (r+2) \cdot (r + 3)}{2 \cdot (r+2) \cdot (r + 3)\cdot (r - 2) } = \dfrac{9 \cdot r^2 + 24 \cdot r + 36}{2 \cdot r^3+6\cdot r^2 - 8 \cdot r - 24}\)

Step-by-step explanation:

Answer:

3x - 5 = 2x + 6  

Step one- Subtract 2x to isolate the variable  

X – 5 = 6  

Step two- Add 5 to continue to isolate the variable  

X = 11  

Your answer is      x = 11  

Hopefully this helps! Feel free to mark brainliest!

Answer: x=11

Step-by-step explanation:

3x-5=2x+6

+5. +5

3x=2x+11

-2x -2x

x=11

Answer:

Step-by-step explanation: k=8

The quadrilateral with coordinates Q(-3,4), R(5,2), S(4,-1), and T(-4,1) is not a rectangle as adjacent sides are not perpendicular to each other.

Coordinates of the quadrilateral QRST are,

Q(-3,4), R(5,2), S(4,-1), and T(-4,1)

Quadrilateral QRST is a rectangle,

All angles are right angles.

Opposite sides are parallel and equal in length.

The slopes of the sides and the lengths of the sides.

Slope of QR

= (2 - 4)/(5 - (-3))

= -2/8

= -1/4

Slope of RS

= (-1 - 2)/(4 - 5)

= -3/-1

= 3

Slope of ST

= (1 - (-1))/(-4 - 4)

= 2/-8

= -1/4

Slope of TQ

= (4 - 1)/(-3 -(-4) )

= 3/1

= 3

Length of QR

=√((5 - (-3))^2 + (2 - 4)^2)

= √(64 + 4)

=√(68)

Length of RS

= √((4 - 5)^2 + (-1 - 2)^2)

= √(1 + 9)

= √(10)

Length of ST

= √((-4 - 4)^2 + (1 - (-1))^2)

= √(64 + 4)

= √(68)

Length of TQ

= √((-3 -(-4))^2 + (4 - 1)^2)

= √(1 + 9)

= √(10)

Slopes of opposite sides are equal .

This implies opposite sides are parallel to each other.

Opposite side lengths are also equal.

But product of the slopes of adjacent sides not equal to -1.

They are not perpendicular to each other.

Therefore, the quadrilateral with given coordinates is not a rectangle.

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The above question is incomplete , the complete question is:

Prove or disprove that the quadrilateral QRST with coordinates Q(-3,4), R(5,2), S(4,-1), and T(-4,1) is a rectangle.

Answer:

y=10(3/4)^x

10 and 3/4

Step-by-step explanation:

Answer:the mode is 2 1/2 because it repeats twice

Step-by-step explanation:repeats twice

First, we convert 1/2% to a decimal.

Similarly:

Based on the given options, the correct answer for the confidence interval is:

c. [0.2597, 0.3403]

The confidence interval represents a range of values within which we can estimate the true population parameter with a certain level of confidence. In this case, the confidence interval suggests that the true population parameter falls between 0.2597 and 0.3403.

To calculate a confidence interval, we typically need information such as the sample mean, sample standard deviation, sample size, and a desired confidence level. Without this information, it is not possible to determine the exact confidence interval.

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To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Option A with a 6-year loan at 8.5% interest compounded quarterly is the better credit option as it results in a lower total amount paid compared to Option B with a 5-year loan at 10% interest compounded annually.

What is the compound interest?

Compound interest can be regarded as the  addition of interest on the loan to the principal sum of the deposit.

Based on the given information, Option A is the better credit option.

Here's why:

Option A:

Option B:

To determine the better option, we can calculate the total amount paid for each option, which includes the principal amount (the initial loan amount) and the interest (the additional amount charged for borrowing the money).

For Option A:

Principal (P) = $12,500

Annual interest rate (r) = 8.5%

Compounding frequency (n) = 4 (quarterly)

Time (t) = 6 years

Using the formula for compound interest:

\(A = P * (1 + r/n)^{(nt)}\)

\(A = $12,500 * (1 + 0.085/4)^{(46)\\A = $12,500 * (1.02125)^{24\)

A = $16,509.63 (rounded to 2 decimal places)

For Option B:

Principal (P) = $12,500

Annual interest rate (r) = 10%

Compounding frequency (n) = 1 (annually)

Time (t) = 5 years

Using the formula for compound interest:

\(A = P * (1 + r/n)^{(nt)}\\A = $12,500 * (1 + 0.10/1)^{(15)}\\A = $12,500 * (1.10)^5\)

A = $19,379.36 (rounded to 2 decimal places)

Hence, Option A with a 6-year loan at 8.5% interest compounded quarterly is the better credit option as it results in a lower total amount paid compared to Option B with a 5-year loan at 10% interest compounded annually.

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Answer:

3/2

Step-by-step explanation:

when you plot it time is x and distance is y so go up 3 right 2

The SI base unit for measuring temperature is 4) Kelvin. Temperature is a physical quantity that measures the degree of hotness or coldness of an object or a system.

The International System of Units (SI) is a globally accepted system of measurement. In SI, temperature is measured using the Kelvin (K) scale, which is the SI base unit for temperature.

The Kelvin scale is based on the absolute zero point, which is the lowest possible temperature where all molecular motion ceases. Absolute zero is defined as 0 Kelvin (0 K). Temperature increments on the Kelvin scale are equivalent to increments on the Celsius scale, with 1 Kelvin being equal to 1 degree Celsius.

The other options listed, such as Celsius and Fahrenheit, are not SI base units for temperature but are commonly used in everyday contexts. Celsius (°C) is widely used in many countries and is based on the Celsius scale, which sets the freezing point of water at 0°C and the boiling point of water at 100°C at sea level. Fahrenheit (°F) is used mainly in the United States and a few other countries and has its freezing point at 32°F and boiling point at 212°F at sea level. However, neither Celsius nor Fahrenheit is considered an SI base unit for temperature.

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The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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A. The Hardy-Weinberg Equilibrium equation is:

1 = p^2 + 2pq + q^2

- p: the frequency of the dominant allele (S)

- q: the frequency of the recessive allele (s)

- 1: represents the total possibilities or the sum of the allele frequencies

- p^2: the frequency of the homozygous dominant genotype (SS)

- 2pq: the frequency of the heterozygous genotype (Ss)

- q^2: the frequency of the homozygous recessive genotype (ss)

B. After one generation of selection, the frequencies of S and s (p' and q') are as follows:

p' = p^2 + 0.5*(2pq) = 0.49 + 0.21 = 0.70

q' = q^2 + 0.5*(2pq) = 0.09 + 0.21 = 0.30

In this case, after one generation, the frequency of the dominant allele (S) remains the same at 0.70, while the frequency of the recessive allele (s) also remains the same at 0.30.

C. If selection were to operate in the same way for many generations, the eventual frequency of the recessive allele (s) would remain 0.30 based on the Hardy-Weinberg Equilibrium.

D. Taking into account that heterozygotes (Ss) have resistance to malaria and higher reproductive success, and SS individuals have reduced reproductive success, the frequencies of S and s after one generation of selection can be calculated as follows:

p' = 0.6(p^2) + 2pq + 0.9(q^2) = 0.6(0.49) + 0.21 + 0.9(0.09) = 0.585

q' = 0.4(p^2) + 2pq + 0.1(q^2) = 0.4(0.49) + 0.21 + 0.1(0.09) = 0.415

After one generation of selection under the new selective regime, the frequency of the dominant allele (S) is 0.585, and the frequency of the recessive allele (s) is 0.415.

E. Yes, the answer to question IC would change under this new selective regime because natural selection can affect the frequency of alleles. The selection against SS homozygotes and the advantages of heterozygotes (Ss) result in changes in the allele frequencies.

F. Sickle-cell anemia is expected to be more common in West Africa compared to Siberia. This is because malaria is a tropical disease transmitted by tropical mosquitoes, and in West Africa, where malaria is common, the heterozygotes (Ss) have higher reproductive success due to their resistance to malaria.

As a result, the frequency of the recessive allele (s) remains relatively high due to the selective advantage it provides against malaria. In Siberia, where malaria is not prevalent, there would be less selective pressure favoring the sickle cell allele.

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The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

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Answer:

50

Step-by-step explanation:

4 black cards = 5C4 = 5

2 red cards = 5C2 = 10

5 x 10 = 50

Number of ways 6-card hands having 4 black cards and 2 red cards are 50.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order.

According to the question

Number of black cards = 5 numbered 5 to 9

Number of red cards = 5 numbered 1 to 5

Number of ways to get 4 black cards = \(5C_{4}\) = 5

Number of ways to get 2 red cards = \(5C_{2}\) = 10

Number of ways 6-card hands having 4 black cards and 2 red cards

= 5 × 10

= 50

Hence, Number of ways 6-card hands having 4 black cards and 2 red cards are 50.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-6}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-3)}}} \implies \cfrac{-6 +4}{-4 +3} \implies \cfrac{ -2 }{ -1 } \implies 2\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ 2}(x-\stackrel{x_1}{(-3)}) \implies y +4 = 2 ( x +3) \\\\\\ y+4=2x+6\implies {\Large \begin{array}{llll} y=2x+2 \end{array}}\)

Answer:

No (unless it happens to have a vinculum on top of any digit image attached is an example of a vinculum)

Step-by-step explanation:

0.63 just stops at 0.63

Answer:

2x

Step-by-step explanation:

He rented 4 last week and 2 this week. He rented 2 more last week than he did this week. X stands for the cost of a rented movie. 2x. Boom roasted. (could be wrong)

Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

There are two families of functions with the same domain of f(x) = 2 · √x:

In this problem we must determine the possible functions that share the same domain of a radical function: f(x) = 2 · √x. In accordance with function theory, the domain of a function is the set of x-values such that function exists.

Radical functions of the form f(x) = a · √x has domain in the interval [0, + ∞). Another function has the same domain if it has the same interval, there are two posibilities:

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Answer:

The answer is A.

Step-by-step explanation:

they equal the same amount

I believe that C is correct!

Answer:

Yep. Answer is C

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

(x + 4)(x + 4)

x² + 4x + 4x + 16

x² + 8x + 16

Answer:

  2.5 litres

Step-by-step explanation:

You want the volume of a bottle from which 36% of its contents is poured away after it was filled to 80% full, leaving 1.28 litres.

If 36% of the contents were poured away, then (1 -36%) = 64% of the contents remained.

If the initial contents filled the bottle to 80% full, then pouring away 36% of that contents leaves the bottle filled to ...

  0.80 × 0.64 = 0.512 . . . . of its full volume

If this is 1.28 L, then the full volume is ...

  0.512·V = 1.28 L

  V = 1.28 L/0.512 = 2.50 L

The volume of the bottle is 2.5 litres.

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Given function  is ln(x) = 6 - x. We need to find the approximate solution of the given equation by using Newton's method. We have to start with x0 = 7 and find x2.

The Newton's method is given by the formula:Xn+1 = Xn - f(Xn) / f'(Xn)Where Xn+1 is the next value of x, Xn is the current value of x, f(Xn) is the value of the function at Xn, and f'(Xn) is the derivative of the function at Xn.Now, we will find the value of x2 as follows:Let us find the first derivative of the given function.

f(x) = ln(x) - 6 + xf'(x) = 1 / x + 1Now, we will substitute the given values in the Newton's formula:X1 = 7 - [ln(7) - 6 + 7] / [1 / 7 + 1]X1 = 7.14668...Similarly,X2 = X1 - [ln(X1) - 6 + X1] / [1 / X1 + 1]X2 = 6.999001...Therefore, the value of x2 is 6.999001... .It is expected that the answer will contain more than 100 words.

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