Graph the following functions and determine where F(x) = G(x). State the x values only. Select all that apply.

a. 6.767
b. 0
c. 2.922
d. -2

The difference between the 92% confidence interval and the 98% confidence interval is that the 98% confidence interval for the population mean is wider than the 92% confidence interval for the population mean.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is given as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Increasing the confidence level, the value of z is increased, hence the margin of error is also increased and thus the 98% confidence interval for the population mean is wider than the 92% confidence interval for the population mean.

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Answer:

15.

Step-by-step explanation:

Given: simplify 3³- 3²-3

First, write the equation:

3³- 3²-3

Then using BODMAS, complete the 'power of' numbers:

27 - 9 - 3

Then subtract 27 from 9:

18 - 3

Finally subtract 18 from 3:

= 15

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hope it helps! :)

Step-by-step explanation:

To determine the domain and range of (g f) (x), we first need to find the composition of the functions f(x) and g(x):

(g f) (x) = g(f(x)) = g(2/(x^2-1)) = 2/(x^2-1) + 1

The domain of f(x) is all real numbers except x = -1 and x = 1, since these values would make the denominator equal to zero. Therefore, the domain of (g f) (x) is also all real numbers except x = -1 and x = 1.

To find the range of (g f) (x), we can start by finding the range of f(x). Since the denominator of f(x) is always positive (except at x = -1 and x = 1), the range of f(x) is all real numbers except 0.

When we add 1 to f(x), we shift the range of f(x) up by 1 unit. So, the range of (g f) (x) is all real numbers except 1.

Therefore, the domain of (g f) (x) is all real numbers except x = -1 and x = 1, and the range of (g f) (x) is all real numbers except 1.

Option B

Answer: Diagram (B)

We have a total number of balls in the urn =9

Let us denote the red ball as R = 4

Answer:521.32

Step-by-step explanation:

.3 represents your tenths

the 2 in .32 represents your hundredths

to round, you look at the number next to your two on the right which is 1

since 1 is less than 5 you leave it the same and eliminate the rest of the numbers that follow it

Therefore , the solution of the given problem of trigonometry comes out to be forms an angle with the horizontal of about 11.71 degrees.

A relationships between cubic splines and triangle maths  astrophysics is believed to have been created when the various fields came together. Many metric problems can be solved or the results of their calculation can indeed be determined with the help of precise mathematical methods. Trigonometry is the study of six basic trigonometric calculations. .

Here,

The tangent function, which is referred to as the ratio of the opposite side (the height drop) to the adjacent side, can be used to determine the angle that Highland Drive forms with the horizontal (the horizontal distance).

The angle's tangent in this situation can be written as:

=> tan(θ) = adjacent/opposite = 14.2/70

We can use a computer to determine that the angle's tangent is roughly 0.2029.

By taking the inverse tangent (also referred to as the arctangent) of this number, we can determine the angle itself:

=> 11.71 degrees are equal to theta = arctan(0.2029)

Highland Road thus forms an angle with the horizontal of about 11.71 degrees.

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13/4 is the value of x in function .

What exactly are function and example?

A function is a type of rule that produces one output from one input.   This is illustrated by the equation y=x2. You only get one output for y if you enter anything for x.

                        Considering that x is the input value, we would state that y is a function of x.

f(x) = {  5;  x< 1 }

        { -1/2x + 4 ; x≥ 1 }

 f(4) =  { -1/2  * 4 + 4 }

         =  { -2 + 4 }

         = { 2 }

f( -10) =  { -1/2 * -10 + 4 }

         =  { 5 + 4 }

          = 9

f(0) = { -1/2 * 0 + 4 }

       = { 0 + 4}

        = 4

f(-5) = ( -1/2 * - 5 + 4 )

        = 5/2 + 4

         = 13/4

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The cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Let's use the variables r and p to represent the cost per foot of redwood and pine, respectively.

From the first purchase, we can set up the following system of equations:

50r + 90p = 292 (equation 1)

90r + 70p = 406 (equation 2)

To solve for r and p, we can use the method of substitution. Solving equation 1 for r, we get:

r = (292 - 90p) / 50

Substituting this expression for r into equation 2, we get:

90[(292 - 90p) / 50] + 70p = 406

Multiplying both sides by 50 to clear the fraction, we get:

162 - 27p + 70p = 4060

Combining like terms, we get:

43p = 3898

Dividing both sides by 43, we get:

p = 90.65

So the cost per foot of pine is $90.65.

To find the cost per foot of redwood, we can substitute this value of p into equation 1 and solve for r:

50r + 90(90.65) = 292

50r = 2118.5

r = 42.37

So the cost per foot of redwood is $42.37.

Therefore, the cost per foot of redwood is $42.37, and the cost per foot of pine is $90.65.

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Answer:

28

Step-by-step explanation:

you add up all the numbers and divide by the number of numbers there is

16+50+14+20+40=140

140/5=28

Solving the equation by completing the square gives the solution as;

x = (6, -10)

The equation we are given to complete the square is;

x² + 4x = 60

Add half the square of half of the coefficient of x to both sides to get;

x² + 4x + (4/2)² = 60 + (4/2)²

x² + 4x + 4 = 64

Writing left hand side as a perfect square gives;

(x + 2)² = 64

Taking square root of both sides gives;

x + 2 = ±8

x = -2 ± 8

x = (6, -10)

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Answer:

D

Step-by-step explanation:

2ft×6ft=12ft

12ft÷2=6

6×2=12ft for the two triangles

6×4=24ft for the rectangle

24ft+12ft= 36 square feet

so it's D 36 square feet

Answer:

[tex]\huge\boxed{\sf 36 \ ft.\²}[/tex]

Step-by-step explanation:

Given that,

Base = 2 + 4 = 6 ft.

Height = 6 ft.

= Base × Height

= 6 × 6

[tex]\rule[225]{225}{2}[/tex]

The value of the expression 1 / 3x² when x equals 6 is 1/108.

Given the expression in the question;

1 / 3x²

When x = 6, value of expression = ?

The expression 1 / 3x² is a mathematical formula that involves the variable "x".

When we substitute x = 6 into the expression, we are asked to calculate the value of the expression when x is equal to 6.

To evaluate the expression, we simply substitute x = 6 into the expression and simplify:

1 / 3x²

Plug in x = 6

1 / 3(6)²

Raise 6 to the power of 2 and get 36

= 1/(3 × 36)

= 1/108

Therefore, the value of the expression is is 1/108.

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Answer:

164

Step-by-step explanation:

Answer:

each of the other sides is 2√2 = 2.8284

Step-by-step explanation:

A 45°- 45°-90° triangle is also known as a right isosceles triangle because two of the legs are the same as two of the angles are the same at 45°

If a is the length of one of the legs then the hypotenuse, h,  which is the longest side is given by the equation

[tex]h = \sqrt{a^2 + a^2}\\\\h = \sqrt{2a^2}\\\\h = a \sqrt{2}[/tex]

Or, dividing by √2 on both sides,

[tex]\dfrac{h}{\sqrt{2} }= a[/tex]

Given h = 4

[tex]a =\dfrac{ 4}{\sqrt{2}} = \dfrac{2\cdot2}{\sqrt{2}} = 2\sqrt{2} \quad\quad\quad(since $\dfrac{2}{\sqrt{2}}$ = \sqrt{2}})[/tex]

a = 2√2 = 2.8284

So each of the other sides is 2√2 = 2.8284

Answer:

6:36

this is when you time both by 2.

The ratio is equivalent to 3:18 is 7:42.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Ratio = 3:18

        = 1:6

1. 6:21

= 3:7

2. 5:20

= 1:4

3. 7:42

= 1:6

4. 12:2

= 6:1

Hence, the ratio is equivalent to 3:18 is 7:42.

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The total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.

Cost is the amount of money that must be paid for goods or services. It can refer to the price of a single item, the total expense of a purchase, or the amount of money paid for a particular service. Cost is an important factor in calculations such as profit, budgeting, and pricing. It is also a factor in determining the value of goods and services when comparing different providers.

The total cost of 3 computers, 6 printers, and 30 CD's would depend on the type of products you are looking to purchase. Computers will vary in price depending on the make and model, as well as the features included. For example, a basic laptop might cost anywhere from $200 to $400, while a high-end gaming laptop could cost upwards of $2,000. Similarly, printers also vary in price depending on the features and type, ranging from $50 to $500. CDs can cost anywhere from $0.50 to $7.00 each, depending on the type and quality.

Therefore, the total cost of 3 computers, 6 printers, and 30 CD’s will depend on the specific combinations of each type of product. However, as an estimate, you can expect to pay anywhere from $1,000 to $4,000 depending on the quality of the products you purchase.

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The largest portion of the yard they can fence in with 90 feet of fencing has an area of 2025/π  feet².

Explain area of circular portion?

The area of a circular portion is the amount of space within the boundary of the circular shape. It is given by the formula A = πr², where r is the radius of the circle.

Now,

To determine the area of the largest portion of the yard, we need to find the radius of the circular portion.

The circumference of a circle is 2πr. Since they have 90 feet of fencing, we can write:

90 = 2πr

Solving for r, we get:

r = 45/π

The area of the circular portion is given by the formula A = πr². Substituting r, we get:

A = π(45/π)² = 2025/π  feet²

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Answer:

4/12 and 9/12

Step-by-step explanation:

Answer: 4/5 is equal to 8/10

Step-by-step explanation:

First three sum 1/10 + 2/10 + 4/10 Proof: When the numbers in the denominator have the same value, fractions can be compute only with the sum of numerator values and the denominator doesn’t change. 1/10 + 2/10 + 4/10 = 1+2+4 / 10 = 7/10 Second three sum 1/10+1/5 + 2/5, Proof: such kind of fractions can be computed as follows: 1/10 + (1+2 )/5 (same denominators). 1/10 + (1+2 )/5= 1/10 + 3/5= 5x1 +10x3 / 5x10 = 5+30 /50 =35/50, by simplifying by 5, 35/50=7/10 The third three sum is 5/10+ 3/15+8/20,it can be computed by using the same method as given above

Hope it helps

Sorry but I think the question is not completed, can you reupload the question properly? I'll answer it

Answer:

9 = 3 x 3

Explanation:

The doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.

What is the density?

Density is a physical property of matter that measures the amount of mass per unit volume. It is calculated by dividing the mass of an object or substance by its volume. The resulting number represents the amount of matter, or mass, that is present in a given volume.

The formula for density is:

Density = Mass / Volume

First, we need to convert the weight of the patient from kilograms to pounds, as the recommended dosage is in mg/lb:

72.7 kg x 2.205 lbs/kg = 160.305 lbs

The recommended dosage is 5 mg/lb, so for a 160.305 lbs patient, the total dosage per dose would be:

160.305 lbs x 5 mg/lb = 801.525 mg

Now we need to convert this dosage from mg to mL, using the concentration of the solution, which is 0.9 g/mL:

1 g = 1000 mg, so 0.9 g = 0.9 x 1000 = 900 mg

To convert mg to mL, we can use the density formula:

Density = Mass / Volume

Rearranging the formula to solve for volume, we get:

Volume = Mass / Density

So, the volume of solution needed for each dose would be:

Volume = 801.525 mg / 900 mg/mL

Volume = 0.8906 mL

Hence, the doctor should order a prescription of 0.8906 mL of the 0.9 g/mL solution for each dose.

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Answer:

Step-by-step explanation:

Area of a triangle = 1/2 * b * h. 1/2 * 9 * 2; 9 * 1 = 9.

Area of a rectangle is two triangles, so b * h. We use the same base and height from the triangle. b * h; 9 * 2 = 18.

So the correct answer would be C. Hope this helps.

The simplified form of the given expression is 1. Using the trigonometric functions sin b = 7/25.

The Pythagorean identity is a trigonometric identity that relates the values of sine and cosine of an angle in a right triangle.

a)Given cos(b) = 24/25, we can use the Pythagorean identity to find sin(b):

sin(b) = √(1 - cos²(b))

         = √(1 - (24/25)²)

         = √(1 - 576/625)

         = √(49/625)

         = 7/25

Now we can use the definitions of the trigonometric functions to find the remaining values:

cos(b) = 24/25

sin(b) = 7/25

tan(b) = sin(b)/cos(b) = (7/25)/(24/25) = 7/24

csc(b) = 1/sin(b) = 25/7

sec(b) = 1/cos(b) = 25/24

cot(b) = 1/tan(b) = (24/7)

b) By simplifying the given expression using the identity:

[tex]tan x = sin x / cos x[/tex]

[tex]cos x+sinxtanx=cosx+sinx(sinx/cosx)[/tex]

By multiplying through by cos x,

cos² x + sin x sin x = cos² x + sin²x

Using the identity sin² x + cos² x = 1,

cos² x + sin² x = 1

cos x + sin x tan x = 1

The simplified form of the given expression is 1.

c) tan²α(csc²α-1)=1 for all values of α where csc α ≠ 0.

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Answer:

b.40.3 ft2 is the answer hope it helps u u u BRAINLIST

Answer:

D. 41.7 ft.^2

Step-by-step explanation:

rectangle area: 5.2 x 6= 31.2

triangle area: (6 x 3.5)/2=10.5

31.2+10.5= 41.7

Answer:

Step-by-step explanation:

(a) Since the current entering and leaving the intersection of wires must be equal, we have:

x + y = 18 (current entering the top intersection)

z + w = 18 (current leaving the top intersection)

x + z = 9 (current entering the bottom intersection)

y + w = 9 (current leaving the bottom intersection)

We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:

2x + 2y + 2z = 36

2y + 2z - 2x = 0

2z - 2x = 9

Solving for z in terms of x, we get:

z = (x + 9/2)

Substituting this into the first equation, we get:

x + y = 18

Substituting z in terms of x into the second equation, we get:

w = (18 - z) = (18 - x - 9/2) = (27/2 - x)

Therefore, the solution in terms of x, y, z, and w is:

(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)

(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.

The coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

A hyperbola is the location of all the points on a plane whose distances from two fixed points in the plane differ by an amount that is always constant. The centre, represented by O in the above diagram as the centre of an ellipse, is where two foci are connected by a line segment when they are united by a line segment. The transverse axis of the hyperbola is the line segment that passes across both foci.

From the given situation we have,

The length of the transverse axis is 180/2 = 90 miles.

Using the distance formula between the two transmitters we have:

d1 = √((x - 5)² + y²)

d2 = √((x + 5)² + y²)

Now, the equation of d is:

|d1 - d2| = 90

Simplifying and squaring both sides, we get:

(d1 - d2)² = 8100

Substituting the expressions for d1 and d2 and expanding, we get:

[(x - 5)² + y² - (x + 5)² - y²]² = 8100

-40x² + 800x - 400 = 8100

-40x² + 800x - 8500 = 0

Dividing by -40, we get:

x² - 20x + 212.5 = 0

d1 = √((x - 5)² + y²) = √((7.5)² + y²)

d2 = √((x + 5)² + y²) = √((2.5)² + y²)

Substituting d1 - d2 = 90/2 = 45 and simplifying, we get:

y² - 50y + 450 = 0

Solving for y:

We get y = 5 or y = 45.

Since the receiver is in the first quadrant, we take y = 5.

Therefore, the coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

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e. Affirming the Consequent. The argument takes the form of "If P then Q. Q, therefore P."

Consequent is an outcome or result of an event, action, or decision. It is the result of a cause or premise. Consequents are usually expected and predictable, and can be measured or observed. Consequents are important in the study of cause and effect relationships and can be used to determine the success or failure of certain actions. Consequents can also be used to measure the degree of success or failure of certain objectives. Consequents are often used in decision-making, as well as in research and problem-solving, to help determine the best course of action and the best solution.

In other words, the conclusion (Benji's parents buy him a puppy for Christmas) is based on the premise that Benji learns important care-giving skills.

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Answer:

<1 and <2 - Add to 180

<1 and <3 - Equal

<3 and <4 - Add to 180

<2 and <4 - Equal

Step-by-step explanation:

No such step-by-step explanation, but we can reason with theorems.

The Vertical Angle theorem states: the opposing angles of two intersecting lines must be congruent, or identical in value.

The Linear Pair theorem states: If two angles form a linear pair, then the measures of the angles add up to 180°.

<1 and <2

<3 and <4

These angle pairs criteria make them apply to the Linear Pair theorem. Therefore, when a pair of angles are a linear pair, they add up to 180.

<1 and <3

<2 and <4

These angle pairs' criteria make them apply to the Vertical Angle Theorem. Therefore, when a pair of angles are vertical angles, they will be congruent (equal, have the same measure).

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