Find the measure of S

Answer:

x ≤ - 5 or x ≥ 7

or, in interval notation

[ - ∞, -5] ∪ [7, ∞]

Step-by-step explanation:

From the question we get the following two inequalities
x is at most -5 ==>     x ≤ -5

x is at least 7 ==>       x ≥ 7 which can be rewritten as 7 ≤ x

This can be written as
x ≤ - 5 or x ≥ 7

In interval notation this would be
[ - ∞, -5] ∪ [7, ∞]

On the number line this would be represented as shown in the figure

Answer:

9/64

Step-by-step explanation:

\(=0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\=0.75\times \frac{0.25}{1.3}\\=0.75\times 0.1875(\left a.k.a\:\frac{3}{16}\right)\\\frac{\left(3\times 0.1875\right)}{4}\\\mathrm{\left(Clarification:\:The\:\:math\:\:above\:\:is\:\:a\:\:broken\:\:down\:version\:of\:the\:original\:problem.\right)}\\=\frac{0.5625\left(\frac{9}{16}\right) }{4}\\=0.1406\left(\frac{9}{64}\right)\)

Hope this helps!

Answer:

x = 4, -2

Step-by-step explanation:

x^2-2x=8

Move the constant term to the right side of the equation.

x^2 - 2x = 8

Take half of the coefficient of x and square it.

(-2/2)^2 = 1

Add the square to both sides of the equation.

x^2 - 2x + 1 = 8 + 1

Factor the perfect square trinomial.

(x - 1)^2 = 9

Take the square root of both sides of the equation.

x-1=\(\sqrt{9}\)
x-1=±3

Isolate x to find the solutions.

Taking positive

x=3+1=4

x=4

Taking negative

x=-3+1

x=-2

The solutions are:

x = 4, -2

Answer:

\(x = -2,\;\;x=4\)

Step-by-step explanation:

To solve the quadratic equation x² - 2x = 8 by factoring, subtract 8 from both sides of the equation so that it is in the form ax² + bx + c = 0:

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

\(x^2-2x-8=0\)

Find two numbers whose product is equal to the product of the coefficient of the x²-term and the constant term, and whose sum is equal to the coefficient of the x-term.

The two numbers whose product is -8 and sum is -2 are -4 and 2.

Rewrite the coefficient of the middle term as the sum of these two numbers:

\(x^2-4x+2x-8=0\)

Factor the first two terms and the last two terms separately:

\(x(x-4)+2(x-4)=0\)

Factor out the common term (x - 4):

\((x+2)(x-4)=0\)

Apply the zero-product property:

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

\(x-4=0 \implies x=4\)

Therefore, the solutions to the given quadratic equation are:

\(\boxed{x = -2,\;\;x=4}\)

the center is at the origin of a coordinate system and the foci are on the y-axis, then the foci are symmetric about the origin.

The hyperbola focus F1 is 46 feet above the vertex of the parabola and the hyperbola focus F2 is 6 ft above the parabola's vertex. Then the distance F1F2 is 46-6=40 ft.

In terms of hyperbola, F1F2=2c, c=20.

The vertex of the hyperba is 2 ft below focus F1, then in terms of hyperbola c-a=2 and a=c-2=18 ft.

Use formula c^2=a^2+b^2c

2

=a

2

+b

2

to find b:

\begin{gathered} (20)^2=(18)^2+b^2,\\ b^2=400-324=76 \end{gathered}

(20)

2

=(18)

2

+b

2

,

b

2

=400−324=76

.

The branches of hyperbola go in y-direction, so the equation of hyperbola is

\dfrac{y^2}{b^2}- \dfrac{x^2}{a^2}=1

b

2

y

2

−

a

2

x

2

=1 .

Substitute a and b:

\dfrac{y^2}{76}- \dfrac{x^2}{324}=1

76

y

2

−

324

x

2

=1 .

Answer:

f(36)

Step-by-step explanation:

f(3)=5(3)²-9(3)+18

f(3)=5(9)-27+18

f(3)=45-27+18

f(3)=36

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer: Period = 2 seconds

Graph is shown below

========================================================

Explanation:

1 minute = 60 seconds

We have 30 revolutions every 60 seconds, so we can write the ratio

30 rev: 60 sec

Divide both parts by 30 to turn that "30 rev" into "1 rev"

30 rev: 60 sec

30/30 rev: 60/30 sec

1 rev : 2 sec

This tells us that each full revolution takes 2 seconds. This is the period of the ferris wheel. The period is the length of each cycle.

The cyclic or periodic nature of this motion heavily implies we'll be dealing with a sine or cosine function of some kind. Let's go with sine.

Side note: cosine is really a sine function in disguise (it's just a phase shifted version of it).

---------------------

The general sine curve equation is

y = A*sin(B(x-C)) + D

where

---------------------

The wheel is 10 feet in diameter, so 10/2 = 5 is the radius. This is also the amplitude because it is the distance from the midline to either the highest point (10 ft) or lowest point (0 ft). So A = 5.

Since T = 2 is the period, this means,

B = 2pi/T

B = 2pi/2

B = pi

We don't have any phase shifts to worry about so C = 0.

The midline is D = 5 since this is halfway up

----------------------

Putting all the pieces together, we get this sine equation

y = A*sin(B(x-C)) + D

y = 5*sin(pi*(x-0)) + 5

y = 5*sin(pi*x) + 5

The graph is shown below.

x = time in seconds, y = height of the seat

The domain of the function or relation is {6, 9, -4 and 2}

The function is represented by the set of relation or ordered pairs

The ordered pairs in the relation are:

(x, y)  = (6, -3), (9, -3), (-4, 1) and (2, 1)

Remove the y values in the above domain

x = 6, 9, -4 and 2

The x values represent the domain of the function

Hence, the domain of the function or relation is {6, 9, -4 and 2}

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Answer:

The answer is 6!!

Step-by-step explanation: Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

After listing all of the factors, simply find the number that is shown in both of their factors but find the greatest number.

For example 3 is a factor that is the same but isn't the highest factor that is shown in both, it is 6! Hope this helps and Happy Halloween!!! :D

The areas of the parallelograms compare by option : A. The area of parallelograms 1 is 4 square units greater than the area of parallelogram 2.

Note that the part that is filled by a flat form or the surface of an item is called the  area.

Note that:

A₁ =  the area of parallelogram 1

A₁ = the area of parallelogram 2

l₁ = the distance between the points that is (2,6),(0,2)

l₂ = the distance between the points that is (4,0)(0,2)

b₁ = the distance between the points  that is (2,0),(0,-2)

b₂ = the distance between the points that is (2,6),(4,-6)

So

A₁ =  l₁ × b₁

=4.47 ×4.47

19.89 sq. unit

A₂= l₂×b₂

2.82 × 6.342

17.88 sq. unit

A₁-A₂ = 19.89 sq. unit - 17.88  sq. unit'

         =  2.01

Therefore, The areas of the parallelograms compare by option : A. The area of parallelograms 1 is 4 square units greater than the area of parallelogram 2.

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It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.

The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.

Substituting P = 306 in the equation, we get:

306 = 14 + 4d/9

Multiplying both sides by 9, we get:

2754 = 126 + 4d

Subtracting 126 from both sides, we get:

2628 = 4d

Dividing both sides by 4, we get:

d = 657 feet

The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.

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Answer:

The square root of ( -1 ) is i

Answer:

the square root of -1 is i

Have a nice day! :D

Step-by-step explanation:

Answer:

3.643 × 10-1

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

only x=-4 would work in the inequality

Answer:

y = 22

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the angles in the lower triangle and equate to 180°

∠ 1 + 19° + 41° = 180°

∠ 1 + 60° = 180° ( subtract 60° from both sides )

∠ 1 = 120°

∠ 1 and ∠ 2 are vertically opposite angles and are congruent , so

∠ 2 = 120°

Sum the angles in the upper triangle and equate to 180

y + 120 + 38 = 180

y + 158 = 180 ( subtract 158 from both sides )

y = 22

To calculate the distance between two points:

We apply the following formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute data and solve:

\(\bf{d=\sqrt{(6-(-3))^2+(-8-8(-8))^2 } }\\ \\ \bf{ d=\sqrt{9^2+0^2}=\sqrt{81+0} }\\ \\ \bf{d=\sqrt{81}=9 }\)

The distance between the points (−3,− 8), (6, – 8) is 9.

Answer:

(1,0)

Step-by-step explanation:

A.K.A the y and x intercepts you might need to do a little more math you get the y intercept tho

Answer:

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Step-by-step explanation:

An automobile manufacturer has given its jeep a 51.3 miles/gallon (MPG) rating.

At the null hypothesis, we test if the mean is of 51.3, that is:

\(H_0: \mu = 51.3\)

An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating.

This means that at the alternative hypothesis, we test if the mean is different of 51.3, that is:

\(H_0: \mu \neq 51.3\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

51.3 is tested at the null hypothesis:

This means that \(\mu = 51.3\)

After testing 230 jeeps, they found a mean MPG of 51.1. Assume the population variance is known to be 6.25.

This means that \(n = 230, X = 51.1, \sigma = \sqrt{6.25} = 2.5\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{51.1 - 51.3}{\frac{2.5}{\sqrt{230}}}\)

\(z = -1.21\)

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 51.1 by at least 0.2, which is P(|z| > 1.21), which is 2 multiplied by the p-value of z = -1.21.

Looking at the z-table, z = -1.21 has a p-value of 0.1131.

2*0.1131 = 0.2262

The p-value of the test is 0.2262 > 0.02, which means that the decision is to fail to reject the null hypothesis.

Answer:

7 sq rt 2

Step-by-step explanation:

must use pythagorean theorem: square of each leg = square of hypotenuse

7 squared the 7 squared = u squared

49+49=u squared

u = square root of 98, which is sq root of 49 times sq root of 2

Answer:

answer is - 95, 40, 45

Step-by-step explanation:

Since the interior angles of a triangle add up to be 180 degrees, I set up the equation like so:

(8x-1)+(3x + 4)+(3x + 9) = 180

=> 14x +12 = 180

=> 14x = 180-12

=> x = 168/14 = 12

now putting value of x = 12

we get---

8*12 -1 = 96-1 = 95

3*12 + 4 = 36+4 = 40

3*12 + 9 = 36 + 9 = 45

( Answer )

Step-by-step explanation:

To maximize profit, the Pear company needs to find the value of x that maximizes the difference between revenue and cost, which is the profit function P(x) = R(x) - C(x).

P(x) = R(x) - C(x)

P(x) = (-30x² + 189000) - (-21x² + 45000x + 21159)

P(x) = -9x² + 45000x + 157841

To find the value of x that maximizes P(x), we can use the formula x = -b/2a, where a = -9 and b = 45000.

x = -b/2a

x = -45000/(2*(-9))

x = 2500

So, the Pear company should produce and sell 2500 pPhones to maximize profit

To find the number of Phones that the Pear company should produce and sell to maximize profit, we need to use the profit function, which is:

P(x) = R(x) - C(x)

where R(x) is the revenue function and C(x) is the cost function.

Substituting the given functions, we get:

P(x) = (-30x² + 189000) - (-21x² + 45000x + 21159)

P(x) = -9x² + 104000x - 21159

To maximize profit, we need to find the value of x that maximizes P(x). To do this, we can take the derivative of P(x) with respect to x and set it equal to zero:

P'(x) = -18x + 104000 = 0

x = 5777.78

Since we can't produce a fractional number of Phones, we should round this down to 5777 Phones.

Therefore, the Pear company should produce and sell 5777 Phones to maximize profit.

Tan x = opposite side / adjacent side

opposite side: 21

Adjacent side: 28

Replacing:

Tan x = 21/28

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Answer:

x = 2.536 m

y = 2 m

Step-by-step explanation:

Considering the three sides of the rectangle and the isosceles triangle

when resolving the width and height of the rectangle to achieve the smallest possible perimeter.

step 1 :

Area of window =  xy + 1/2 xz  , perimeter = x + 2y + 2c

c = \(\sqrt{z^2 + 1/4 x^2 }\)

we are tasked with minimizing the perimeter ( p ) subject to A = 6

attached below is the detailed solution of the given problem