suppose the lifetime of a particular brand of tire for cars is approximately normally distributed with a mean of 48,000 miles and standard deviation of 3,000 miles. step 1 of 2: what is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles? round your answer to 4 decimal places if necessary.

We have:tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(7/2)

To prove the equation tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) without using a calculator, we can utilize the trigonometric properties and identities to simplify the expression.

Let's start by using the addition formula for the tangent function:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

We can rewrite the given expression as:

tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2)

Using the addition formula, we can combine the first two terms:

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)((1/11 + 5/6) / (1 - (1/11)*(5/6)))

Simplifying further:

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)((11/66 + 55/66) / (1 - 5/66))

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)(66/66 / (61/66))

tan^(-1)(1/11) + tan^(-1)(5/6) = tan^(-1)(1)

Using the same approach, we can combine the remaining terms:

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)((1/3 + 1/2) / (1 - (1/3)*(1/2)))

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)((5/6) / (3/2))

tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(5/9)

Now, we have:

tan^(-1)(1/11) + tan^(-1)(5/6) + tan^(-1)(1/3) + tan^(-1)(1/2) = tan^(-1)(1) + tan^(-1)(5/9)

Using the addition formula again:

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)((1 + 5/9) / (1 - (1)*(5/9)))

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)((14/9) / (4/9))

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)(14/4)

tan^(-1)(1) + tan^(-1)(5/9) = tan^(-1)(7/2)

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Step-by-step explanation:

\( = ( - 3x - 9x) + 8 - 6 \\ = - 12x + 2\)

Answer:

A least degree polynomial, having rational coefficients and a leading coefficient of 2, with,-4, 0, 2, and 4 as the zeros of the polynomial is;

f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x

Step-by-step explanation:

The given parameters of the polynomial are;

The leading coefficient of the polynomial = 2

The zeros of the polynomial = -4, 0, 2, 4

We note that zeros of -4, and 4 gives a factor of the form, (x² - 4²)

For a zero of the polynomial equal to 0, one of the factors of the polynomial is equal to 'x'

To have a leading coefficient of 2, we can add '2' as a factor of the polynomial

Therefore, we can have the factors of the polynomial as follows;

(x² - 4²)·2·x×(x - 2) = 0

From the above equation, using a graphing calculator, we get the following possible polynomial;

(x² - 4²)·2·x×(x - 2) = 2·x⁴ - 4·x³ - 32·x² + 64·x = 0

Therefore, a polynomial, function of least degree that has rational coefficients, a leading coefficient of 2,and the zeros, -4, 0, 2, and 4 is  f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x.

The equation of g(x) include the following: D. g(x) = 4x² + 2

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

In this context, we can logically deduce that the parent function f(x) = x² was translated 2 units up and vertically stretched by 4 units in order to produce the graph of the image g(x), we have:

g(x) = 4f(x) + 2

g(x) = 4x² + 2

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Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

If A and B are 2x2 matrices, det(A)=-1,det(B)=3 then

det(AB) = -3

det(-2A) = 8

det(A^T) = -1

det(B^-1) = 1/3

det(B^4) = 81

This can be found by :

det(AB) = det(A) * det(B) = (-1) * 3 = -3

det(-2A) = (-2)^2 * det(A) = 4 * (-1) = -4

det(A^T) = det(A) = -1

det(B^-1) = 1 / det(B) = 1/3

det(B^4) = (det(B))^4 = 3^4 = 81

For det(AB) we use the property that the determinant of a product of matrices is the product of their determinants.

For det(-2A) we use the property that the determinant of a matrix multiplied by a scalar is the determinant of the matrix multiplied by the scalar raised to the power of the matrix size.

For det(A^T) we use the property that the determinant of a matrix is the same as the determinant of its transpose.

For det(B^-1) we use the property that the determinant of the inverse of a matrix is the reciprocal of the determinant of the matrix.

For det(B^4) we use the property that the determinant of a matrix raised to a power is the determinant of the matrix raised to that power.

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The value of x or length of FD int the figure is  75.

image attached below,

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

This is similarities in sides questions. To solve make equation.

JY = 42

JS = 42 + 63 = 105

JD = 50

JF = 50 + x

Using the sides,

52/105 = 50/50+x

(42)(50+x) = (50)(105)

2100 + 42x = 5250

42x = 5250 - 2100

42x = 3150

x = 3150/42

x = 75.

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Answer:

90 units

$7100

Answer:

Hope this helps!

Step-by-step explanation:

4(5) is 20 bit im not sure exactly what your other question is asking!!?

Answer:

17 / 18

Step-by-step explanation:

1/9 + 5/6 needs to be converted to a different equivalent fraction so that the denominators are the same, so;

1/9 = 2/18 and 5/6 = 15/18

2/18 + 15/18 = 17/18!

Answer:

-41

Step-by-step explanation:

The change is -2

(-2*20)-1 = -41

At t = 3, the rate οf change οf y with respect tο x is:

dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15

The prοcess οf differentiatiοn cοmpares the rate οf change οf the functiοn tο the rate οf change οf the independent variable. The οutcοme οf differentiating a functiοn is referred tο as the functiοn's derivative. It prοvides each pοint's slοpe οn the functiοn's graph.

Tο find the rate οf change οf y with respect tο x, we need tο find dy/dx at t = 3. We can use the chain rule tο express dy/dx in terms οf derivatives with respect tο t:

dy/dx = (dy/dt) / (dx/dt)

We can find dx/dt and dy/dt as follows:

dx/dt = 3t² - 6t

dy/dt = (1/2)(t² + 16\()^{(-1/2)\) * 2t

Substituting t = 3, we get:

dx/dt = 3(3)² - 6(3) = 9

dy/dt = (1/2)((3)² + 16\()^{(-1/2)\) x 2(3) = 3/5

Therefore, at t = 3, the rate of change of y with respect to x is:

dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15

So the answer is 1/15.

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Answer:

IQR = 63-54 = 9

Hope that answers your question

Step-by-step explanation:

Answer:

79

Step-by-step explanation:

2(2) - 4(2(-1)^2 + 5(-1)) + 3(-1)^2 + 8(2)^3 + 4(-1)

4 - 4 (2 - 5) + 3 + 64 - 4

4 - 4(-3) + 3 + 64 - 4

4 + 12 + 3 + 64 - 4

16 + 3 + 64 - 4

19 + 64 - 4

83 - 4

79

hope this  helps! <3

Answer:

B. k=7

Step-by-step explanation:

28/4=7

56/8=7

84/12=7

etc... good luck!

The independent variable in a relationship between two variables is the variable that is used to predict or explain the variation in the other variable.

It is the variable that is manipulated or controlled by the researcher. For example, if we are investigating the relationship between temperature and ice cream sales, temperature would be the independent variable, as we would expect changes in temperature to predict changes in ice cream sales.

On a scatter diagram, the independent variable is typically represented on the horizontal axis (x-axis) and the dependent variable is typically represented on the vertical axis (y-axis). This is because the independent variable is typically plotted along the horizontal axis, with its values placed at regular intervals, and the dependent variable is then plotted along the vertical axis, with its values plotted based on their relationship to the corresponding independent variable values.

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Answer:

E.65

Step-by-step explanation:

In linear equation,$308 is Mr. Brown leaving a a tip .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                        Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The amount of hotel bill= $140

He leaves 12% of the hotel bill as a tip for the housekeeping service.

Thus, the amount of tip= 12% of hotel bill

=12% of $140

= 12/100 * 140

= 12 * 14

=    168

Therefore, the total amount Mr. Chin pays, including tip =$140+$168 =$308

Hence, Mr. Chin pays $308, including tip

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Answer:

$4680 after one year

$4867.20 after 2 years

Step-by-step explanation:

4500 x 1.04 = 4680

4680 x 1.04 = 4867.20

The probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

Standard deviation is a statistical measurement that depicts the average deviation of each value in a dataset from the mean value. It tells you how much your data deviates from the mean value. It represents the typical variation between the mean value and the individual data points.

The formula for the probability that a truck drives between 99 and 128 miles in a day is:

\(Z = (X - \mu) /\sigma\)

where, X is the number of miles driven per day; μ is the mean of the number of miles driven per day; σ is the standard deviation of the number of miles driven per day. The value of Z for 99 miles driven per day is:

\(Z = (99 - 120) / 11 = -1.91\)

The value of Z for 128 miles driven per day is:

\(Z = (128 - 120) / 11 = 0.73\)

Using a standard normal distribution table or calculator, the probability of a truck driving between 99 and 128 miles per day is:

\(P(-1.91 < Z < 0.73) = 0.7734\)

Therefore, the probability that a truck drives between 99 and 128 miles in a day is 0.7734 rounded to four decimal places.

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In a standard game of volleyball, each team is allowed a maximum of three hits (or touches) to return the ball back over the net to the opposing team's side.

The first touch is typically a pass, also known as a bump, which is used to control and direct the ball to a teammate who is better positioned to make the second touch.

The second touch is usually a set, which is used to position the ball for the third touch, which is typically a spike or an attack to try and score a point.

However, it's important to note that a team can hit the ball fewer than three times if they manage to score a point before using all of their touches.

For example, if a player hits the ball over the net and it lands on the opposing team's side without being touched, the serving team scores a point and the play ends.

Similarly, if the opposing team manages to block the ball and it lands on the serving team's side of the court, the play also ends, and the team that successfully blocked the ball is awarded a point.

In conclusion, a team is allowed a maximum of three hits to return the ball over the net, but the number of hits can be fewer if they score a point or if the opposing team successfully blocks the ball.

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Answer:

3% of 66.7 is 2.001 or 2.00

18% of 66.7 is 12.006 or 12.01

The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.

We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).

This means that h = 1/2 and k = -1/2.

The radius of the circle is r = square 2 divided by 4.

We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.

Now we can substitute these values into the standard form equation to get:

(x - 1/2)² + (y + 1/2)² = 1/8

So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

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A cubic centimeter is 1000 times larger than a cubic millimeter because 1 centimeter equals 10 millimeters, and a volume is calculated by multiplying the length.

Width and height, so 1cm x 1cm x 1cm = 1cm3 and 0.1mm x 0.1mm x 0.1mm = 0.001mm3. A measure of volume in the metric system. One thousand boxy centimeters equal one liter. Also called cc, milliliter, and mL.  

A cubic centimeter ( symbol cm ³ or cc)(U.S. spelling boxy centimeter) is a generally used unit of volume extending the deduced SI-unit boxy meter. It corresponds to the volume of a  cell measuring 1 cm × 1 cm × 1 cm.

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A cubic centimetre is 1000 times greater than a cubic millimetre.

A volume is derived by multiplying the length, width and height.

As we know.

1 centimetre equals 10 millimetres.

Therefore 0.1mm x 0.1mm x 0.1mm = 0.001mm^3

And 1cm x 1cm x 1cm = 1cm^3.

A volumetric measurement using the metric system.

One litre is equivalent to one thousand boxy centimetres. Also known as cc, mL, and millilitre.

A cubic centimetre, often known as a boxy centimetre in the United States, is a commonly used volume measurement unit that extends the SI unit boxy metre. It is equivalent to the volume of a cell with dimensions of 1cm x 1cm x 1cm

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The multiplication of the mixed fractions =  \(\frac{44}{3}\).

We have two mixed fractions -

\(2\frac{3}{4}\) and \(5\frac{1}{3}\)

We have to Multiply them.

Consider the mixed fraction -  \(a\frac{x}{y}\).

In normal fraction, it can be written as -   \(\frac{y \times a + x}{y}\)

According to question, we have -

\(2\frac{3}{4}\) and \(5\frac{1}{3}\)

Converting them into Proper fraction, we get -

\(\frac{11}{4}\) and \(\frac{16}{3}\)

Multiplying both -

\(\frac{11}{4} \times \frac{16}{3}\) = \(\frac{44}{3}\)

Hence, the multiplication of the mixed fractions =  \(\frac{44}{3}\).

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Answer:

\( \sf \: \frac{44}{3} \)

Step-by-step explanation:

Given problem,

\( \sf \rightarrow 2 \frac{3}{4} \times 5 \frac{1}{3} \)

Let's solve the problem,

\( \sf \rightarrow 2 \frac{3}{4} \times 5 \frac{1}{3} \)

\( \sf \rightarrow \frac{11}{4} \times \frac{16}{3} \)

\( \sf \rightarrow \frac{(11 \times 16)}{(4 \times 3)} \)

\( \sf \rightarrow \frac{176}{12} \)

\( \sf \rightarrow \frac{44}{3} \)

Hence, the answer is 44/3.

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

The time dilation using the Lorentz transformation formula is presented as follows;

\(t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } \)

From the question, we have;

The spaceship's speed, v = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

\(\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8\)

The time that elapses as measured by Andrea = 8 years

Andrea's age, A, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

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The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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