What is the z-score if u = 89, 0 = 11.5, and x = 82?O 1.370 -0.610.790 -1.21

The function is decreasing on the interval (0, [infinity])

The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.

The derivative of h(x) is -2/sqrt(x).

For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.

For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.

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Answer:

A 54

b -156

c -100

d -4984

e 13500

f 13272

Answer:

352,000

Step-by-step explanation:

Subtract 374,000 by 22,000 and you will get 352,000 as your answer

The number 374000 is greater then 22000 by exactly 25200 amount.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, to find out by how much times the number 374000 is greater then the number 22000 we simply subtract the number 374000 by 22000 which comes out be 35200.

It should be noted that, To cross verify the answer we can add 35200 with 22000 it must be equal to 374000.

374000 - 22000 = 352000

Therefore, the number 374000 is greater then 22000 by exactly 25200 amount.

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Answer:

2,622

Step-by-step explanation:

To determine the value of \( 2x^4 + 5x \) when x = 6, plug in the value of x, them evaluate.

\( 2(6)^4 + 5(6) \)

\( 2(1,296) + 30 \)

\( 2,592 + 30 \)

\( = 2,622 \)

Answer:

the answer would be D

Step-by-step explanation:

i worked it out and thats what i came to

Answer: After investing for 10 years at 8% interest

Step-by-step explanation: your $10,000 investment will have grown to $21,589 This calculator determines the future value of $10k invested for 10 years at a constant yield of 8.00% compounded annually

The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

We have,

The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.

Therefore, we can say that:

f(x) < 0 for x < -3 and -1.1 < x < 0.9

And,

The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).

This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:

f(x) > 0 for x > -2.4

Now,

Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).

So,

The interval where f(x) is negative and greater than 0 is:

(-∞, -3) U (-1.1, 0)

Thus,

The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

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Answer:

slope=1/4

y-intercept=3

y=.25x+3

Step-by-step explanation:

slope=rise over run so

slope=1/4

y-intercept is the value of y where the line crosses the y axis..

y-intercept=3

In y=mx+b form m is slope and b is y-intercept so...

y=.25x+3

Answer:

C. Trapezoid

Step-by-step explanation:

A hexagon is a polygon with six sides, thus and six interior angles ABCDEF. After the segment AD (which is the diameter of the circle P) has been drawn, it divides the hexagon into two halves. With each half forming the shape of a trapezoid, so that ADEF is a trapezoid.

Thus, the appropriate option is C, trapezoid.

Answer:

The amount to be raised at the fund raiser is $3,333.33

Step-by-step explanation:

Here, we want to know the amount of money needed to be raised for the fundraiser

Let the amount raised be $x

Thus;

15% of $x = $500

$500 is the cost of the fund raiser

15/100 * x = 500

15x/100 = 500

15x = (100 * 500)

x = (100 * 500)/15

x = 3,333.33

The length of the diagonal of a square with a perimeter of 56 is 14√2.

A diagonal is the longest line that divides a plane shape into two equal parts.

To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.

Formula:

Where:

From the question,

Given:

Substitute the value into equation 1 and solve for a

Finally to find the length of the diagonal of the square, we use the formula below

Where:

Substitute into equation 2

Hence, the length of the diagonal is 14√2.

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Answer:

qfewwqeffwqfefewqwqreg

Step-by-step explanation:

Answer:

3.465 x 10⁸ hours

or

346,500,000 hours

Step-by-step explanation:

Distance to travel to star = 9.5 x 10¹² kilometers

1 kilometer = 0.62mile

Therefore

9.5 x 10¹² km = 9.5 x x 10¹ x 0.6 miles
= 5.89 x 10¹² miles

Speed of satellite = 17,000 mph

In scientific notation
17,000 = 17 x 10³ = 1.7 x 10⁴ mph

Time taken to reach star at distance of 5.89 x 10¹² miles

= 5.89 x 10¹² miles/1.7 x 10⁴ mph = 5.89/1.7  x 10¹²/10⁴

= 3.465 x 10¹²⁻⁴

= 3.465 x 10⁸ hours

= 346,500,000 hours

Answer:

Therefore, the roots of the given equation are x = 2, x = 1, and x = -3.

Step-by-step explanation:

This problem involves finding the zeros (or roots) of a polynomial equation, which are the values of x that make the equation equal to zero. The given equation is cubic, meaning it has a degree of 3 and can have up to three real roots.

One way to find the roots of this equation is to use the Rational Root Theorem, which states that any rational root of a polynomial equation with integer coefficients must have the form p/q, where p is a factor of the constant term (in this case 18) and q is a factor of the leading coefficient (in this case 3). However, this method only works for finding rational roots, and there may be irrational or complex roots as well.

Another method is to use a graphing calculator or software to graph the equation and visually locate the x-intercepts, which are the points where the graph crosses the x-axis and the value of y is zero. From the graph, we can see that there are three real roots: one positive, one negative, and one between -2 and -1.

A third method is to use numerical methods (such as Newton's method or the Bisection method) to estimate the roots to a desired level of accuracy. However, this method involves iterative calculations and can be time-consuming.

Without using a graphing calculator, we can try to factor the given equation by using the Rational Root Theorem. The possible rational roots are ±1, ±2, ±3, ±6, ±9, ±18 (all factors of 18 divided by all factors of 3). We can test these roots by substituting them into the equation and seeing if the result equals zero.

Testing x = 1 gives:

3(1)^3 - 2(1)^2 - 13(1) + 18 = 3 - 2 - 13 + 18 = 6, which is not zero.

Testing x = -1 gives:

3(-1)^3 - 2(-1)^2 - 13(-1) + 18 = -3 - 2 + 13 + 18 = 26, which is not zero.

Testing x = 2 gives:

3(2)^3 - 2(2)^2 - 13(2) + 18 = 3(8) - 2(4) - 13(2) + 18 = 0, which means x = 2 is a root.

Using polynomial division, we can factor out (x - 2) from the cubic polynomial to obtain a quadratic polynomial that can be factored:

(3x^3 - 2x^2 - 13x + 18) / (x - 2) = 3x^2 + 4x - 9

Factoring the quadratic gives:

3x^2 + 4x - 9 = (3x - 3)(x + 3)

Setting each factor equal to zero and solving for x gives:

3x - 3 = 0, so x = 1

x + 3 = 0, so x = -3

Answer:

I think it may be a but I am not completely sure

Step-by-step explanation:

Answer:

B and E

Step-by-step explanation:

the graph (Justine) shows the line

y = 2x

the line for Velma is

y = 4x

now we need to remember that the slope (inclination) of a line is the factor of x (so, 2 and 4 in the two line equations).

a slope is expressed as y/x and indicates how many units y changes when x changes a certain amount of units (like 1).

as described (and also confirmed by the graph) the x units are minutes, and the y units are meters.

so, as per her slope, Velma moves 4 meters in 1 minute.

and Justine moves 2 meters in 1 meter.

so, Justine is half as fast as Velma.

and therefore, Justine moves a shorter distance than Velma each minute.

Answer:

Step-by-step explanation:

B and E

The measure of the missing side length from the given figure is 11 feet.

The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection.

It is referred to as a right angle if the angle formed by two rays exactly equals 90 degrees, or π/2.

The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal.

In the given figure, assuming that all the intersecting sides meet at right angles.

So, the opposite sides are parallel to each other.

Let x be the length of missing side.

Thus, The length of missing side = Sum of length of parallel sides

Now, x= 5+6

= 11 feet

Therefore, the length of side missing is 11 feet.

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The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

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

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Answer:  y-4 = 3(x - 5)

Step-by-step explanation:

The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate,  b is the y-value form the given coordinate,  m is the slope. x and y are the variables in the function.

To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."

Given coordinate points: ​(4​,4​) and ​(5​,7​)   \(m=\frac{y-y_{1} } {x-x_{1 }}\) substitute values:

m= 7-4/5-4  becomes  m= 3/1   so the slope m = 3

To write the equation:  Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.

y - b = m(x - a)  Using the second coordinate: (5,7)

y - 7 = 3(x - 5)

The attachment shows the graph of this equation.

(The equivalent slope-intercept form for this is y = 3x - 8 )

Answer:

Y - 4 = 3(X - 4)

Step-by-step explanation:

Y2 - Y1 / X2 - X1 = M, 7 - 4 / 5 - 4 = M, 3 / 1 = M, M = 3

Y - Y1 = M(X - X1),  

Y - 4 = 3(X - 4),

Y - 4 = 3X - 12,

+4   +4

Y = 3X - 8

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

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Answer: \(6a-2\)

Step-by-step explanation:

\((4a-5)-(-2a-3)\\=4a-5+2a+3\\=6a-2\)

The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

Apply the product rule to 4a^5:

⇒ 4^3(a^5)^3

Raise 4 to the power of 3:

⇒ 64(a^5)^3

Apply the power rule and multiply exponents, (a^m)^n = a^mn:

⇒ 64a^5*3

Multiply 5 by 3:

64a^15

Therefore, The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

6 .x = 121°

Sum of all interior angles of a 7 sided polygon is 900°.

Answer:

52

Step-by-step explanation:

RTQ is 52 because if PTR is a right angle, right angles equal 90 degrees. So if PTQ is 38 degrees, we subtract 38 from 90 to get RTQ. 90-38 equals 52.

Answer:

52 degrees

Step-by-step explanation:

right angle = 90

90-38=52

So RTQ = 52 degrees

Answer:

x=81 or 1/3

Step-by-step explanation:

\(x^\log_3(x)} =81x^3\\\log_3(x^{\log_3(x)})=\log_3(81x^3)\\\(\log_3x)(\log_3x)=\log_381+\log_3x^3\\(\log_3x)^2=3\log_3x^+4\\\\Let u=\log_3x\\\\u^2-3u-4=0\\(u-4)(u+1)=0\\u=4 \\4=\log_3x\\x=3^4=81\\\\u=-1\\-1=\log_3x\\x=3^{-1}=1/3\)

Answer:

- September

Step-by-step explanation:

The temperature in Beijing, in m months after January, is given by the following equation:

\(T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

In which m is the number of months after January.

During which month in the year would the temperature reach 55°F?

We have to find m for which: T(m) = 55. So

\(T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

\(55 = 27\cos{((\frac{\pi}{6})(m-6))} + 45\)

\(27\cos{((\frac{\pi}{6})(m-6))} = 10\)

\(\cos{((\frac{\pi}{6})(m-6))} = \frac{10}{27}\)

Now, we apply the inverse cosine, on both sides of the equation, to find the value of m.

\(\cos^{-1}{\cos{(\frac{\pi}{6})(m-6)}} = \cos^{-1}{\frac{10}{27}}\)

Now, with the help of a calculator, in radians:

\(\frac{\pi}{6}(m-6) = 1.19\)

\(\pi m - 6\pi = 6*1.19\)

\(\pi m = 6*1.19 + 6 \pi\)

\(m = \frac{6*1.19 + 6 \pi}{\pi}\)

\(m = 8.27\)

8.27 months after January, since 8.27 + 1 = 9.28, it happens during the month of September.

Answer: September

Step-by-step explanation:

Edge

Answer: Yes, this is a function!

Step-by-step explanation: Here are the requirements for determining if a 2-variable equation is a function or not.

2.

Each input should correspond to only one output

. In our case, any value of x you put into this equation only gives one value of y. We can verify this graphically using a simple test called the

vertical line test.

To do this, graph the function with the x axis being the horizontal axis and the y axis being the vertical axis (this matters!) In our case, this will be a parabola opening upwards. The test says that if I can draw vertical lines through every part of the graph and each vertical line only crosses the graph once, the equation is a function. In our case, I can draw vertical lines through everywhere in a parabola and they will only cross once. This shows that we have a function!

Hope this helps!

Bye for now,

Iz

Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.