Matrix, help.
So I was instructed to use a calculator rather than solving by hand, so I did try to use my TI-84 but I'm having trouble, Is it possible to solve this by hand and if so- how do I go about it? Thank you (:

1) The lower limit of the confidence Interval is: 1489.77.

The upper limit of the confidence Interval is: 1530.23

2) The lower limit of the confidence Interval is: 1478.32

The upper limit of the confidence Interval is: 15411.68

The formula to find the confidence interval is:

CI = x' ± z(σ/√n)

where:

CI is confidence interval

x' is sample mean

z is z-score at confidence level

σ is standard deviation

n is sample size

1) The parameters are:

σ = $234

x' = $1510

n = 362

z at 90% CL = 1.645

Thus:

CI = 1510 ± 1.645((234/√362)

CI = 1510 ± 20.23

CI = (1489.77, 1530.23)

2) The parameters are:

σ = $234

x' = $1510

n = 362

z at 99% CL = 2.576

Thus:

CI = 1510 ± 2.576((234/√362)

CI = 1510 ± 31.68

CI = (1478.32, 15411.68)

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The given expression is equivalent to \($(1215)^{x/5}\).

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following equation -

\($(\sqrt[5]{1215})^{x}\)

For \($\sqrt[a]{x} = x^{1/a}\)

Using the rule, we can write -

\($(\sqrt[5]{1215})^{x}\) = \($(1215)^{x/5}\)

Therefore, the given expression is equivalent to \($(1215)^{x/5}\).

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Answer:

a. 0.1971

Step-by-step explanation:

Z score is used to measure by how many standard deviations the raw score is above or below the mean. It is given by the formula:

\(z=\frac{x-\mu}{\sigma}\\ \\Where\ \mu=mean, x=raw\ score, \sigma=standard\ deviation\)

Given that:

μ = 1050 kWh, σ = 218 kWh

For x = 1100 kWh

\(z=\frac{x-\mu}{\sigma}=\frac{1100-1050}{218} =0.23\)

For x = 1225 kWh

\(z=\frac{x-\mu}{\sigma}=\frac{1225-1050}{218} =0.80\)

From the normal distribution table, P(1100 < x < 1225) = P(0.23 < z < 0.8) = P(z < 0.8) - P(z < 0.23) = 0.7881 - 0.5910 = 0.1971

Maci and 2 appointments and Logan had 3 appointments.

The linear equation that represents the total amount earned by Maci is:

Total amount earned = (amount per appointment x number of appointments)  + tips

$170 = ($60 x a) + $50

$170 = $60a + $50

$170 - $50 = $60a

$120 = $60a

a = $120 / $60

a = 2

The linear equation that represents the total amount earned by Logan is:

Profit = total revenue - total cost

Profit = (fee per appointment  x number of appointments) + amount received in tips - (rental fee x number of appointments)

$235 = ($75 x a) + $40 - ($10 x a)

$235 = $75a + $40 - $10a

$235 = $65a + $40

$235 - $40 = $65a

$195 = $65a

a = $195 / 65

a = 3

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Answer:

To find out how much the employee earns per hour, we need to divide the total earnings by the number of hours worked.

So the hourly rate would be:

68.85 ÷ 8.5 = 8.1 dollars/hour

Therefore, the employee earns $8.1 per hour.

Answer:    585.225

Step-by-step explanation:

False Reason:...This is false if (x=5)  (y=3). and denotes the requirement that both be true.

This is true: (z=8) > (x=5) The entire statement is false because it relies on the and condition rather than the OR condition.

What is an example of a Boolean expression?

A Boolean expression(named for mathematician George Boole) is an articulation that assesses to one or the other valid or misleading. Let's take a look at some examples from common speech: Pink is my favorite color. valid • I'm anxious about PC programming. False This book is a laugh-out-loud good read.

Which three Boolean expressions are there?

There are three fundamental Boolean operators: What's more, OR, and NOT.

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Answer:

25%

Step-by-step explanation:

Formula to calculate the percent change :-

Change in distance from $12 per hour to $15 per hours = 15-12=3 per hour

Previous value = $12 per hour

Now, the percent change will be :_

Hence,  the percent change for  from $12 per hour to $15 per hour= 25%

(I copied this answer from JeanaShupp from question-11653373 [no links])

Answer:

1. False

2. Not sure

3. True

Statement A

A = bh/2

34 = (10)h/2

68/10 = h

h = 6.8

FALSE The actual height of the triangle is the hypotenuse of the fake outer triangle. 6.8 is not used to calculate the area.

Statement B

A = (d1 + d2)/2

56 = (d1 + d2)/2

112 = d1 + d2

I have no idea for this one. There is no way that I know of to verify the area if I don't have at least one diagonal.  

Statement C

A = (a + b)(h)/2

24 = (7 + 9)(3)/2

48 = (7 + 9)(3)

16 = 7 + 9

16 = 16

TRUE Area of the trapezoid = 24 in².

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

<95141404393>

Answer:

The answer is 65

Step-by-step explanation:

Evaluate:

8x + 9

When x = 7

Use PEMDAS order of operations:

8x + 9

= 8(7) + 9

= 56 + 9

= 65

Hope this helps

Answer:

y=42 or h=y/42

Step-by-step explanation:

Then the constant would be the number of yards of yarn required for each hat

Answer:

Step-by-step explanation:

Volume of a cube:

V = a3

Surface area of a cube:

the area of each face (a x a) times 6 faces

S = 6a2

Face diagonal of a cube:

By the pythagorean theorem we know that

f2 = a2 + a2

Then f2 = 2a2

solving for f we get

f = a√2

Diagonal of the solid cube:

Again, by the pythagorean theorem we know that

d2 = a2 + f2

substituting f into this equation we get

d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2

solving for d we get

d = a√3

Answer:

Thank you for being so kind! X=15

Step-by-step explanation:

each expression combined is equal to 180.

so you must put 5x+9+7x-9 and solve to get 15!

Answer: 17 miles

.5hr x 10Mph + .5 x 24mph = 17 miles

Step-by-step explanation:

Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

<95141404393>

The correct answer is (C) \(\angle B \cong \angle C.\) when In the diagram below of circle O, chords AD and BC intersect at E.

What is a circle ?

A circle is a two-dimensional geometric shape that consists of all the points in a plane that are at a fixed distance from a given point, called the center.

In the given diagram, we have a circle O with chords AB, CD, AD, and BC. The chords AD and BC intersect at point E.

Based on the diagram, we can see that the opposite angles in the quadrilateral AEDC are supplementary (i.e., they add up to 180 degrees). Therefore, we have:

\(\angle A + \angle C = 180^\circ\)

Similarly, the opposite angles in the quadrilateral BEFC are supplementary. Thus,

\(\angle B + \angle C = 180^\circ\)

We can rewrite the second equation as:

\(\angle C = 180^\circ - \angle B\)

Substituting this value of \angle C into the first equation, we get:

\(\angle A + 180^\circ - \angle B = 180^\circ\)

Simplifying, we get:

\(\angle A = \angle B\)

Therefore, the correct answer is (C) \(\angle B \cong \angle C.\)

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Answer:

14.11

Step-by-step explanation:

24 divided by 1.7

Answer:

14.117

Step-by-step explanation:

that is the answer to your problem

Answer:

126.99 cm³

Step-by-step explanation:

volume of cone = ⅓πr²h ≅ 296.88 cm³

volume of empty portion = 296.88 - 169.89 = 126.99 cm³

Hello,

\(f(x) = ax + b \: \Leftrightarrow f(x) = - 2x + b\)

We have :

\( - 2 \times ( - 6) + b = 4\)

\(\Leftrightarrow \: 12 + b = 4\)

\(\Leftrightarrow \: b = 4 - 12\)

\(\Leftrightarrow \: b \: = - 8\)

\(f(x) = - 2x - 8\)

Answer:

60

Step-by-step explanation:

5 plus 4 is nine.

I based everything on how much times more it was at first, and did that times 9 for every name.

I added up how much more boxes they got in total and got 60.

Every three candy bars cost a dollar.

Divide 25 by three.  

$8.33

9 km — 1 cm

225 km — 225 : 9 = 25 cm

Answer:  To find her total balance in a year, Yaritza needs to multiply her

current balance by 1.08 in one step.

Step-by-step explanation:

- Let Yaritza has 'a' amount.

- Simple interest per year is 8 per cent

- Therefore, simple interest (SI) = (a x 8 x 1)

divided by 100 which equals to 8a divided by 100

- So, in one year the investment will be Amount + SI, i.e. (a + 8a) divided by 100

- So total amount = (100a + 8a) divided by 100 which equals to 108a

divided by 100

- So to reach to 108a divided by 100 from a, let Yaritza multiplies with 'b'

'a' multiplied by 'b' equals to 108a divided by 100

Hence, 'b' = 108 by 100 equals to 1.08

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Answer:

(f-g)(x) is given by -x^2+4x+6

Step-by-step explanation:

Answer:

\(\displaystyle f(x) = \frac{x + 3}{x - 2}\) has no relative extrema when the domain is \(\mathbb{R} \backslash \lbrace 2 \rbrace\) (the set of all real numbers other than \(2\).)

Step-by-step explanation:

Assume that the domain of \(\displaystyle f(x) = \frac{x + 3}{x - 2}\) is \(\mathbb{R} \backslash \lbrace 2 \rbrace\) (the set of all real numbers other than \(2\).)

Let \(f^{\prime}(x)\) and \(f^{\prime\prime}(x)\) denote the first and second derivative of this function at \(x\).

Since this domain is an open interval, \(x = a\) is a relative extremum of this function if and only if \(f^{\prime}(a) = 0\) and \(f^{\prime\prime}(a) \ne 0\).

Hence, if it could be shown that \(f^{\prime}(x) \ne 0\) for all \(x \in \mathbb{R} \backslash \lbrace 2 \rbrace\), one could conclude that it is impossible for \(\displaystyle f(x) = \frac{x + 3}{x - 2}\) to have any relative extrema over this domain- regardless of the value of \(f^{\prime\prime}(x)\).

\(\displaystyle f(x) = \frac{x + 3}{x - 2} = (x + 3) \, (x - 2)^{-1}\).

Apply the product rule and the power rule to find \(f^{\prime}(x)\).

\(\begin{aligned}f^{\prime}(x) &= \frac{d}{dx} \left[ (x + 3) \, (x - 2)^{-1}\right] \\ &= \left(\frac{d}{dx}\, [(x + 3)]\right)\, (x - 2)^{-1} \\ &\quad\quad (x + 3)\, \left(\frac{d}{dx}\, [(x - 2)^{-1}]\right) \\ &= (x - 2)^{-1} \\ &\quad\quad+ (x + 3) \, \left[(-1)\, (x - 2)^{-2}\, \left(\frac{d}{dx}\, [(x - 2)]\right) \right] \\ &= \frac{1}{x - 2} + \frac{-(x+ 3)}{(x - 2)^{2}} \\ &= \frac{(x - 2) - (x + 3)}{(x - 2)^{2}} = \frac{-5}{(x - 2)^{2}}\end{aligned}\).

In other words, \(\displaystyle f^{\prime}(x) = \frac{-5}{(x - 2)^{2}}\) for all \(x \in \mathbb{R} \backslash \lbrace 2 \rbrace\).

Since the numerator of this fraction is a non-zero constant, \(f^{\prime}(x) \ne 0\) for all \(x \in \mathbb{R} \backslash \lbrace 2 \rbrace\). (To be precise, \(f^{\prime}(x) < 0\) for all \(x \in \mathbb{R} \backslash \lbrace 2 \rbrace\!\).)

Hence, regardless of the value of \(f^{\prime\prime}(x)\), the function \(f(x)\) would have no relative extrema over the domain \(x \in \mathbb{R} \backslash \lbrace 2 \rbrace\).

Answer:

n < -4

Step-by-step explanation:

-n > 4

Multiply both parts by -1, remembering to switch signs.

-n(-1) < 4(-1)

n < -4

The volume of the given triangular prism is 384 cm³.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the area of the base is

Area of a rectangle = 1/2 ×Base×Height

= 1/2 ×12×4

= 24 cm²

Now the volume is 24×16

= 384 cm³

Therefore, the volume of the given triangular prism is 384 cm³.

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