Suppose that we sample data from a normal distribution with a mean of 40 and a standard deviation of 3. a) If our sample size is 15, what are the mean and standard deviation of

Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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Answer:

the answer is 2

Step-by-step explanation:

3(2)+6(2)=

6+12=18

Answer: 1

Step-by-step explanation:

Explanation and steps in photo

the given expressions solved by using factorization.

What is factorization of the expression ?

  To factorize an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse.

Here

4) \(x^4-36\)

=> \((x^2)^2 -6^2\)

=> \((x^2-6)(x^2+6)\)

5)64\(c^3+1\)

=> \((4c)^3+1^3\)

=> (4c+1)(\((16c^2+4c+1)\)

6)\(k^3-27\)

=> \(k^3-3^3\)

=>(k-3)(\(k^2+3k+9\))

7)\(54x^3+250y^3\)

=> 2(\(27x^3+125y^3\))

=> 2(\((3x)^3+(5y)^3\))

=> 2 ( 3x+5y)(\(9x^2+15xy+25y^2\))

8)\(3m^4-48n^2\)

=> 3(\((m^2)^2-(4n)^2\))

=> 3\((m^2-4n)(m^2+4n)\)

9)\(a^7b^2-ab^2\)

=> \(ab^2(a^6-1)\\\)

=>\(ab^2(a^3-1)(a^3+1)\)

=> \(ab^2(a+1)(a-1)(a^2-a+1)(a^2+a+1)\)

10)\(x^3y^2-343y^5\)

=> \(y^2(x^3-(7y)^3)\)

=>\(y^2(x-7y)(x^2-7xy+49y^2)\)

11)\(9y^7-144y\)

\(= > 9y(y^6-16)\\= > 9y((y^3)^2-4^2)\\= > 9y(y^3+4)(y^3-4)\)

Hence we can solve by using factorization formula.

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Answer:

3

The degree of a polynomial is the highest power of any variable in the polynomial equation.

Here the highest power is 3 of the monomial with co-efficient of 2.

Answer:

4:6 I think sorry if wrong

Step-by-step explanation:

Answer:

2 to 3. Or 2:3

Step-by-step explanation:

There are 4 triangles to every 6 squares

Their GCF is 2 so divide by 2 to get 2:3

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

In linear algebra, systems of linear equations with a unique solution can be represented by the following expression:

\(\vec A \cdot \vec x = \vec B\)      (1)

Where:

The solution of such systems is defined by:

\(\vec x = \vec A^{-1}\cdot \vec B\)

\(\vec x = \frac{1}{\det(\vec A)}\cdot adj\left(\vec A\right) \cdot \vec B\), where \(\det \left(\vec A\right) \ne 0\).

Where:

For the case of \(\vec A \in \mathbb{R}_{2\times 2}\), the inverse of \(\vec A\) is:

\(\vec A^{-1} = \frac{1}{\det \left(\vec A\right)} \cdot \left[\begin{array}{cc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right]\)     (2)

If we know that \(\vec A = \left[\begin{array}{cc}3&4\\5&2\end{array}\right]\) and \(\vec B = \left[\begin{array}{cc}1\\3\end{array}\right]\), then the solution of the system of linear equations is:

\(\vec A^{-1}= \frac{1}{(3)\cdot (2) - (5) \cdot (4)}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right]\)

\(\vec A^{-1} = -\frac{1}{14}\cdot \left[\begin{array}{cc}2&-4\\-5&3\end{array}\right]\)

\(\vec A^{-1} = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right]\)

\(\vec x = \left[\begin{array}{cc}-\frac{1}{7} &\frac{2}{7} \\\frac{5}{14} &-\frac{3}{14} \end{array}\right] \cdot \left[\begin{array}{cc}1\\3\end{array}\right]\)

\(\vec x = \left[\begin{array}{cc}\frac{5}{7} \\-\frac{2}{7} \end{array}\right]\)

By applying inverse of a matrix, we find that the solution of the system of linear equations is (x, y) = (5/7, - 2/7).

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Answer:

B

Step-by-step explanation:

3×-2+12=6 and -2×-2+2=6. You could also do it in a calculator it you want to found out if it true. But the Answer will be B

Hope this Help

The surface area of the prism is 96 cm²

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object.

The length and width of the rectangular face are 4.5 cm and 3 cm, respectively, so the area is:

4.5 cm x 3 cm = 13.5 cm²

Since there are two rectangular faces on the prism, the total area for the pair is:

= 2 x 13.5 cm²

= 27 cm²

Similarly for the another face

3 cm x 3 cm = 9 cm²

Since there are two square faces on the prism, the total area for the pair is:

= 2 x 9 cm²

= 18 cm²

The area of one of the rectangular faces that is not congruent to the first two:

= 8.5 cm x 3 cm

= 25.5 cm²

Since there are two rectangular faces that are not congruent to the first two, the total area for the pair is:

= 2 x 25.5 cm²

= 51 cm²

Now we can find the total surface area by adding the area of each pair of faces:

= 27 cm² + 18 cm² + 51 cm²

= 96 cm²

Therefore, the surface area of the rectangular prism is 96 square centimeters.

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Step-by-step explanation:

5miles=8km

so, x miles=32km

8x=160

x= 160÷8

=20miles

Answer:

x= 1 7/12

Step-by-step explanation:

x+1/2+x+2/3-x+3/4=2

1. We know that x+x-x=x

2. 1/2+2/3-3/4=6/12+8/12-9/12=5/12

3. x+5/12=2

4. x=2-5/12

x=1 7/12

Answer:

x = 1/12

Step-by-step explanation:

x+x-x = x

1/2 + 2/3 + 3/4 = 23/12

both of the above are:

23/12 +x = 2

x= 2 - 23/12

x= 1/12

Answer:

Step-by-step explanation:

if g(x)=3x-8

replace x with -2

g(-2)=3(-2)-8=-6-8=-14

Answer: Hi!

4.89 * 2.2 = 10.758 (rounded is 10.76 or 10.8)

Tip: Line up the terms vertically and multiply.

Hope this helps!

if the number of times you take the test were independent variable of the chance you fail what could that mean the difficulty of the test is consistent and unchanging.

The difficulty of the test is consistent and unchanging, making it so that the chance of failing is solely determined by the individual's performance on the test. Factors such as knowledge of the subject and the ability to focus can play a role in a person's success, but the actual chance of failing is not affected by how many times the test is taken. This means that those who fail the test will have to work harder and prepare better in order to pass it on the next attempt. Taking the test multiple times does not guarantee a higher chance of success, as the difficulty remains the same each time due to independent variable.

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The lines CD and EF in the image are not parallel for the given angle measures

Question #9

The measures of the angles are given as:

BPG = 139

GPC = 95

BQF = 110

As a general rule, the co-interior angles between a parallel, when added have a sum of 180 because they are supplementary angles.

This means that, at least 2 of the given angles must add up to 180.

So, we have:

139 + 95 = 234

139 + 110 = 249

95 + 110 = 205

None of the angles add up to 180.

Hence, the lines CD and EF in the image are not parallel for the given angle measures

Question #10

The measures of the angles are given as:

BPD = 35

APG = 115

EQA = 35

As a general rule, the co-interior angles between a parallel, when added have a sum of 180 because they are supplementary angles.

This means that, at least 2 of the given angles must add up to 180.

So, we have:

35 + 115 = 150

35 + 115 = 150

35 + 35 = 70

None of the angles add up to 180.

Hence, the lines CD and EF in the image are not parallel for the given angle measures

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The function is continuous   in D where

\($D \mathcal{D}\left\{(x, y): x > -y^6\right\}$\)

Generally, A continuous and bounded function is a function that is continuous over a finite interval, and whose range of values are within finite bounds. For example, the function f(x)=x^2 is continuous and bounded over the interval [-2,2], since it is continuous over the whole interval and the range of values is between 0 and 4.

Given that

\($F(n y)=e^{x^2 y}+\sqrt{n+y^6}$where \\\\ $e^{x^2 y}$ is cortinous everywhereAnd. \\\\\$\sqrt{n+y^6}$ is continoas if $n+y^6 > $ ?\\\\\$\Rightarrow y^6 > -n$\\\\\)

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The value of x is 200 for the given two equations x-y=80 and 3/5=y/x using the equating process.

The two equations are given as:

x - y = 80 -------- Equation 1

3/5 = y/x --------- Equation 2

First, we need to solve the equation 2. Here two terms x and y are unknown. But if we can make two equations in the terms of one variable then we can easily find the values of x and y. From equation 2, we get:

y/x = 3/5

y = 3x/5 ------ (equation 3)

Now, we can substitute this equation 3 for y into Equation 1:

x - y = 80

x - (3x/5) = 80

Multiplying both sides by 5:

5x - 3x = 400

2x = 400

x = 200

Therefore, we can conclude that the value of x is 200.

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Answer:

B! just took it!

Step-by-step explanation:

Answer:

B. f(x) = 2x2 + 2x – 4

Step-by-step explanation:

it's lit!!!

Answer:

y=2x^2+8 on a graph is smaller than y=2x^2-9 on a graph.

Step-by-step explanation:

Answer:

22.98133...

Step-by-step explanation:

30 x cos(40°)

then refine to a decimal form

Answer:

9.3 ft

Step-by-step explanation:

To start off, we can use the fact that the total area under the probability density function (PDF) must equal 1. This is because the PDF represents the probability of X taking on any particular value, and the total probability of all possible values of X must add up to 1.

So, we can set up an integral to solve for the constant c:

integral from 0 to 1 of c(1-x) dx = 1

Integrating c(1-x) with respect to x gives:

cx - (c/2)x^2 evaluated from 0 to 1

Plugging in the limits of integration and setting the integral equal to 1, we get:

c - (c/2) = 1

Solving for c, we get:

c = 2

Now that we have the value of c, we can use the PDF to find probabilities of X taking on certain values or falling within certain intervals. For example:

- The probability that X is exactly 0.5 is:

PDF(0.5) = 2(1-0.5) = 1

- The probability that X is less than 0.3 is:

integral from 0 to 0.3 of 2(1-x) dx = 2(0.3-0.3^2) = 0.36

- The probability that X is between 0.2 and 0.6 is: integral from 0.2 to 0.6 of 2(1-x) dx = 2[(0.6-0.6^2)-(0.2-0.2^2)] = 0.56

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Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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Answer:

30 x ^2 y ^2

Step-by-step explanation:

The answer is correct, we can plot both triangles on a Coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

To determine the coordinates of the vertices of the image of triangle ABC after being translated 4 units down, we need to subtract 4 from the y-coordinates of each vertex. This is because a translation is a type of transformation that moves each point of a figure a certain distance in a certain direction.

So, starting with the preimage of triangle ABC with vertices at A(-3, 3), B(0, 4), and C(-3, 0), we can find the image by subtracting 4 from the y-coordinates:

A'(-3, 3 - 4) = A'(-3, -1)

B'(0, 4 - 4) = B'(0, 0)

C'(-3, 0 - 4) = C'(-3, -4)

Therefore, the coordinates of the vertices for the image after the translation are A'(-3, -1), B'(0, 0), and C'(-3, -4).

So, the correct option is A) A′(−3, −1), B′(0, 0), C′(−3, −4).

To check if the answer is correct, we can plot both triangles on a coordinate plane and visually inspect the result. If we plot triangle ABC with vertices A(-3, 3), B(0, 4), and C(-3, 0), and then plot the image triangle A'B'C' with vertices A'(-3, -1), B'(0, 0), and C'(-3, -4), we can see that the image is a translation of the original triangle down by 4 units.

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The time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

To find the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (triple the initial deposit)

P = Principal amount (initial deposit)

r = Annual interest rate (6.1% or 0.061 as a decimal)

n = Number of times interest is compounded per year (weekly compounding means n = 52)

t = Time in years

In this case, we have:

A = 3P (triple the initial deposit)

P = P100,000

r = 0.061

n = 52

t = Time (unknown)

Substituting these values into the formula, we have:

3P = P(1 + r/n)^(nt)

Simplifying further, we get:

3 = (1 + 0.061/52)^(52t)

To isolate t, we can take the natural logarithm (ln) of both sides of the equation:

ln(3) = ln((1 + 0.061/52)^(52t))

Using the logarithmic property, we can bring down the exponent:

ln(3) = 52t * ln(1 + 0.061/52)

Now we can solve for t:

t = ln(3) / (52 * ln(1 + 0.061/52))

Using a calculator, the value of t comes out to approximately 6.12 years (rounded to two decimal places).

Therefore, the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

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