the sum of the perimeter of an equilateral triangle and a square is 10 find the dimensions of the triangle and the square that produce a minimum total area

Expected value of the mean = 50 (the population mean)

The expected value of the mean for a sample size of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated using the central limit theorem.

According to the central limit theorem, the expected value of the mean of a sample from a population approaches the population mean as the sample size increases. In other words, as the sample size becomes larger, the sample mean becomes a more accurate estimate of the population mean.

In this case, the expected value of the mean of a sample of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated as follows:

Expected value of the mean = 50 (the population mean)

It is important to note that the expected value of the mean is equal to the population mean, regardless of the sample size. The central limit theorem states that the sample mean approaches the population mean as the sample size increases, but for a sample size of 4, the expected value of the mean is still equal to the population mean.

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The order of the quadrants in a Cartesian plane goes in a counterclockwise direction. The correct option is C

Quadrants is the axes of a two-dimensional Cartesian system divide the plane into four infinite regions, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I coordinates are I, II , III and IV .

Therefore, Quadrant is an instrument used to measure angles up to 90°. Different versions of this instrument could be used to calculate various readings such as longitude and latitude.

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The exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

Given, the terminal side of contains the point p(9, 12).

Each trigonometric function must have an exact value, which we must determine.

A line segment drawn from the origin to the point should have a length of r.

r = √x2 + y2

Here, x = 9 and y = 12

r = √(9)2 + (12)2

= √81 + 144

= √225

r = 15

sin θ = y/r = 12/15 = 4/5

cos θ =x/r = 9/15 = 3/5

tan θ = y/x = 12/9 = 4/3

cosec θ = 1/sin θ = 5/4

sec θ = 1/cos θ = 5/3

cot θ = 1/tan θ = 3/4

Consequently, each trigonometric function's precise values are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

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The full question:

The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.

The rule shows the input and output of the reflection is, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The new coordinate of A' = (- 5, - 1)

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

Parallelogram ABCD is shown. A is at (-5, 1), B is at (-4, 3). C is at (-1, 3) . D is at (-2, 1).

We know that;

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The reflection of point (x, y) across the x-axis is (x, -y).

Hence, The new coordinate of A' is,

⇒ (- 5, 1) = (- 5, - 1)

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Using the ALEKS calculator , 13.1 would roughly equal 172, rounded to the closest hundredth.

When necessary, ALEKS offers a calculator so that users may determine the difference. Instead of using your own calculator, just utilize ALEKS'. For the calculator to produce most accurate assessment results, it must only be used in the manner specified by ALEKS.

Reviewers believed that Khan Academy and ALEKS better satisfy their needs as a business. Reviewers believed that Open Courseware is the best choice when considering the level of continuing product support. Our evaluators liked the approach of Online Courses over ALEKS for feature releases and roadmaps.

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The exponential model that’s the point shown in the table is 8.00 * 0.10ˣ.

An exponential model is a mathematical function that describes the growth or decay of a quantity over time, where the rate of change is proportional to the current value of the quantity. It takes the form y = ab^x, where a is the initial value, b is the growth factor (b > 1 for growth, 0 < b < 1 for decay), and x is the time or independent variable.

To find the exponential model that fits the points shown in the table, we can use the least-squares method. This method involves finding the line of best fit that minimizes the sum of the squares of the differences between the observed y values and the estimated y values from the model.

For an exponential model of the form y = abˣ, the least-squares method requires taking the natural logarithm of both sides to obtain the equation ln(y) = ln(a) + xln(b). This equation has the form of a linear equation, y = mx + b, where m = ln(b) and b = ln(a). We can then use the least-squares method to find the line of best fit for this equation and solve for m and b.

Given the points (0,8) and (3,1), we can use the following calculations to find m and b:

ln(8) = m0 + b

ln(1) = m3 + b

Solving the system of equations, we obtain:

m = -2.3026

b = 2.3026

Therefore, the exponential model that fits the points is:

y = [tex]e^{b} *e^{m * x}[/tex]

y = [tex]e^{2.3026} *e^{-2.3026 * x}[/tex]

Rounding the exponent to four decimal places, we get:

y = 8.00 * 0.10ˣ

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The equation of the parabolas are

y = (x - 2)(x + 2)

y = (x - 2)(x + 2) -4

The graph is attached below.

What is a coordinate grid?

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

Assume the x-intercepts are 2 and -2.

The equation of a parabola whose x-intercepts a and b is y = (x-a)(x-b)

The equation of a parabola is

y = (x-2)(x-(-2))

y = x² - 4 .....(i)

The vertex of the parabola is (0,4).

The parabola's maximum or minimum value is the vertex's y-coordinate.

Thus replace - 4 with -8 of equation (i)

y = x² - 8

Puttin x = 0 in equations (i) and (ii)

y(0) = -4

y(0) = -8

Puttin x = 1 in equations (i) and (ii)

y(1) = -3

y(1) = -7

Puttin x = -1 in equations (i) and (ii)

y(-1) = -3

y(-1) = -7

The points on y = x² - 4 are (0,-4), (1,-3), and (-1,-3).

The points on y = x² - 8 are (0,-8), (1,-7), and (-1,-7).

Plot the points and join them.  

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Solving the provided question we can say that the  quadratic equation is  [tex]x^2+4x-21[/tex] answer is x = -5 and 1

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the  quadratic equation is

[tex]x^2+4x-21[/tex]

answer is x = -5 and 1

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The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

We only count one ordered pair by substituting 2 for 60 in this case. We count four ordered pairs by doing with 4.

We got 7 pairings from 6 people. I add 8 to get 12, thus. the difference between neighboring phrases by moving on and doing so (1,3,3,5,5,...).

We believe that if 2n were substituted for 60, we would find 1+3+3+5+5+7+7.... where n words will be present.

So, 1+3+3+5+5... 29+29+31 = 16*30 = 480 is our response.

The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

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The full question:

Find the number of ordered pairs $(x,y)$ of positive integers that satisfy the following equation

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]

Check attached images 1 and 2.

[tex]\frac{d}{dx} =y'\\ \\y'=(3*\frac{1}{3})x^{3-1} +2*x^{2-1} -(1*3)x^{1-1} \\ \\y'=x^{2} +2x-3[/tex]

Use the quadratic formula.

Check attached image 3.

a = 1

b = 2

c = -3

[tex]x_{1} =\frac{-(2)+\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =1\\ \\x_{2} =\frac{-(2)-\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =-3[/tex]

Quick analysis. This results tell us that the minimun and maximum points different that infinity of the original function ([tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]) are located in points x = 1 and x = -3. Now, we need to discover who's the maximum point and who's the minimum. For this, evaluate both point in the original function.

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(x)=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(1)=\frac{1}{3}(1)^{3} +(1)^{2} -3(1)\\\\ =\frac{1}{3}+1-3 \\\\ =\frac{1}{3} +\frac{3}{3}-\frac{9}{3} \\ \\=\frac{1+3-9}{3} \\ \\=-\frac{5}{3}[/tex]

[tex]f(-3)=\frac{1}{3}(-3)^{3} +(-3)^{2} -3(-3)\\ \\=\frac{1}{3}(-27) +(9)-(-9)\\ \\=\frac{-27}{3} +9+9\\ \\=-9+9+9\\ \\=9[/tex]

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

Check out the graph (attached image 4) to better understand the method used for this solution.

Note. See that the "x" coordinates where the function has maximum and minimum points are the exact same "x" coordinates where the derivative touches the "y" axis, that's why we calculated the roots of the derivative and then evaluated in the original function.

After solving the value of E(x^2 + 3) is 11.7.

The distribution of x is:

x            f(x)              x^2             x^2·f(x)

1             0.2               1                    0.2

2            0.3               4                    1.2

3             0.1               9                    0.9

4             0.4              16                   6.4

We have to determine the value of E(x^2 + 3).

We can write it as

E(x^2 + 3) = E(x^2) + 3...........(1)

As E(x^2) = Sum of x^2·f(x)

E(x^2) = 0.2 + 1.2 + 0.9 + 6.4

E(x^2) = 8.7

Now putting the value of E(x^2) in equation 1, we get

E(x^2 + 3) = 8.7 + 3

E(x^2 + 3) = 11.7

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The complete question is:

Let x have the following distribution:

x            1         2         3         4

f(x)        0.2     0.3      0.1      0.4

Find E(x^2 + 3) (write it up to first decimal place).

The new length of the longer side after application of a scale factor of 1/4 is; 7.125 ft

A scale factor is defined as the ratio between the scale of a given original object and a new object. This will be indicative of its' representation but of a different size. Thus, it could represent an enlargement or a reduction.

Now, we are given that the length of the sides are;

Length of longer sides = 28.5 cm

Length of shorter side = 16.5 cm

Thus, if the scale factor is 1/4, then it means that;

New length of longer side = 1/4 * 28.5

New length = 7.125 ft

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Therefore , the solution of the given problem of angles comes out to be 41.92 angles is the correct option.

In Euclidean space, an angle is indeed a construction comprised of two beams that split at the apex & vertex, which are located in the middle of the angle. The side of loops are the name given to these rays. A combination of two rays may result in an angle that is within the planes in that they are located. Two planes can be combined to form an angle as well. They are referred to as dihedral angles. Two line rays with end points can be arranged in a variety of ways to create styles in two dimensions.

Here,

Given :

=>  speed = 35 feet per second

=> time = 0.8 second

=> height = 9 feet

Distance covered slantly = 0.8 * 35 = 28 feet

=> Sin x = 9/28

=> x =  Sin⁻¹(9/28)

=> x = 41.92

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Step-by-step explanation:

A whole can be divided into many parts and the number of parts will depend on the unit of measurement we use to divide it.

A whole can be divided into fifty equal parts, each of which is called a "fiftieth." So, one whole would be equal to 50 fiftieths.

1 whole = 50 fiftieths

Alternatively, we can say that one fiftieth is equal to 1/50th of a whole. This can be represented as a decimal or a fraction.

1 fiftieth = 1/50th of a whole = 0.02 (decimal)

The statements that are true are:

1. f(2) = 0 , therefore (x-2) is a factor

2. (x+3) is a factor of f (x) because f (x) divided by (x+3) has a remainder of 0.

3. x-7) is a factor of f(x).

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying. To factor polynomials, we generally make use of the following properties or identities; along with other more techniques.

The polynomial x³- 6x2 - 13x + 42 has three factors.

The first factor is found by by representing x by 2 i.e f(2) = 2³-6(2)²-13(2)+42

this will give 0

therefore if x= 2

then x-2 =0

when x-2 is used to divide the polynomial it gives a quadratic equation x²-4x-21. This will give a factor (x+3) and (x-7)

Therefore the factors of the polynomial are( x-2)(x+3) and( x-7)

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The fourth term a₄ of the sequence is 15

The definition of the function is given as

a₁= 6

aₙ = aₙ₋₁ + 3

The above definitions imply that we simply add 3 to the previous term to get the current term

Using the above as a guide,

so, we have the following representation

a₂ = 6 + 3

a₂ = 9

Also, we have

a₃ = 9 + 3

a₃ = 12

Lastly, we have

a₄ = 12 + 3

Evaluate the equation

a₄ = 15

Hence, the value of a₄ is 15

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Complete question

Sequence and series:

If a_1=6 and a_n=a_{n-1}+3, then find the value of a_4

Answer:

hxxu u uu u. yy h gghchcvhhvuvuvuvuvhcuchchcjvj jvjcjcjcchhchcjcjc

Step-by-step explanation:

g g g g g. gg g

The degrees of freedom equals 7.

The test statistic will be 2.55

The critical value will be 1.89.

From the information, they randomly sample 20 individuals and administer a 30 item true or false psychological test designed to measure depression and the scores that are greater than 20 indicate significant levels of depression.

The degree of freedom will be:

= n - 1

= 8 - 1

= 7

The test statistic will be:

= 22.25 - 20 /2.49 ✓8

= 2.55

The critical value will be 1.89.

Based on the information, it should be noted that we will fail to reject the null hypothesis.

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Answer:

[tex]y = 10.5[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} y = 13\\[/tex]

We transpose

[tex]y =\frac{13X4}{5}[/tex]

[tex]y = \frac{52}{5}[/tex]

[tex]y = 10.5[/tex]

The account balance when they retire is $13,221.96

The formula for compound interest is:

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

where:

A = the future value of the investment/loan, including interest

P = the principal investment/loan amount

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years the money is invested/borrowed for

A is the account balance when they retire

P = $7,500, r = 3.2% = 0.032, n = 1, t = 58-40 = 18 years

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

A = 7,500(1 + 0.032/1)^(1*18)

A = 7,500(1 .032)¹⁸

A = $13,221.96

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Answer:

5 5/8

Step-by-step explanation:

2 2/3=8/3

8/3x=15

x=15*3/8

x=5 5/8

Answer:

Step-by-step explanation:

67267642qwu62we2q[tex]x^{2} \alpha we2qe\pi qeqe\beta \beta \left \{ {{y=2} \atop {x=2}} \right. \int\limits^a_b {x} \, dx x_{123} \alpha \pi \\ \\ \\ \\ \neq x^{2} \alpha \sqrt[n]{x} \sqrt[n]{x} x^{2}[/tex]e5427856418548248e654815

The expected value of each warranty sold is the amount of $15.

A written guarantee of a product's integrity and the maker's duty for the repair or replacement of damaged parts.

As per the question, the required solution would be as:

The expected cost of a failed product without a warranty is :

= $100 x (6/100)

= $100 x 0.006

Apply the multiplication operation,

= $0.6.

The expected cost of a failed product with a warranty is :

= $100 x 0.006 + $15 = $15.6.

So the expected value of each warranty sold is :

= $15.6 - $0.6

Apply the subtraction operation, we get

= $15.

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The required cost of the extended warranty is given as $115, as pe the given condition.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
The original warranty period but within 2 years of the purchase, with a replacement cost of $100.  They offer a 2-year extended warranty for $15,
Expected value = 100 + 15 = $115

Thus, the required cost of the extended warranty is given as $115, as per the given condition.

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The required number word that is one more than fourteen is "fifteen."

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the number system when we add 1 to the number 14, what we get is 15 in words it is fifteen
So,
one + fourteen = fifteen

Thus, the required number word that is one more than fourteen is "fifteen."

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The comparison of the fractions are

15/24 < 16/24, 3/18 < 4/18 and 14/24 <15/24

Fraction 1

Here, we have

5/8 and 2/3

The LCM of 8 and 3 is 24

So, the pair is

15/24 and 16/24

When compared, we have

15/24 < 16/24

Fraction 2

Here, we have

1/6 and 2/9

The LCM of 6 and 9 is 18

So, the pair is

3/18 and 4/18

When compared, we have

3/18 < 4/18

Fraction 3

Here, we have

7/12 and 5/8

The LCM of 12 and 8 is 24

So, the pair is

14/24 and 15/24

When compared, we have

14/24 <15/24

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Answer:

4.2 yrs hope this helped. :)

Step-by-step explanation:

Answer: Here are the evaluations of the expression 46 + (-2k) for the given values of k:

For k = 3: 46 + (-2 * 3) = 46 - 6 = 40

For k = 23: 46 + (-2 * 23) = 46 - 46 = 0

For k = -2: 46 + (-2 * -2) = 46 + 4 = 50

So, the evaluated expressions are 40, 0, and 50 respectively.

Step-by-step explanation:

Answer:

Step-by-step explanation:

P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.5 - 0.3 = 0.8.

Answer:

129

Step-by-step explanation:

516/4 = 129

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