What is the domain of the exponential function?
[tex]y=2^{x}+6[/tex]

Answer:

No

Step-by-step explanation:

2.20 and 2.2 are the same

but 2.02 is not the same as the others

We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.

A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.

Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.

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The value of the missing angle x is: 38°

We know that the sum of angles in a triangle is 180 degrees and as such:

∠DAE = 180 - (82 + 68)

∠DAE = 30°

Now, we know that alternate angles are congruent. Thus:

∠DAE ≅ ∠ADC = 30°

Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).

Thus:

∠BAE = ∠BDE = 82 + 30

= 112°

Thus:

∠ABC = ∠ACB = 68°

Thus:

∠BAC = 180 - 2(68)

∠BAC = 44°

Thus:

x = 112 - (44 + 30)

x = 112 - 74

x = 38°

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The exact value of sec(θ) is 8√(39)/39.

Given information:

In a right triangle,

Perpendicular side = 5, Hypotenuse side = 8.

Then to find exact secθ:

We can use the definition of secant, which is the reciprocal of cosine:

sec(θ) = 1/cos(θ)

In a right triangle, the cosine of an angle is equal to the adjacent side length divided by the hypotenuse length. Therefore, we first need to find the length of the adjacent side of the angle θ.

Let's label the sides of the right triangle as follows:

the hypotenuse side is H, with a length of 8

the perpendicular side is P, with a length of 5

the base side (adjacent to the angle theta) is B

Using the Pythagorean theorem, we can find the length of the base side B:

B² + P² = H²

B² + 5² = 8²

B² + 25 = 64

B² = 64 - 25

B² = 39

B = √(39)

Now we can use the cosine function to find cos(theta):

cos(θ) = B/H

cos(θ) = √(39)/8

Finally, we can find sec(θ) by taking the reciprocal of cos(θ):

sec(θ) = 1/cos(θ)

sec(θ) = 8/√(39) x √(39)/√(39)

sec(θ) = 8√(39)/39

Therefore, the exact value of sec(θ) is 8√(39)/39. This is the simplified form of the expression and cannot be further reduced because the square root of 39 is not a perfect square.

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Answer:

Marcela used the Associative Property of Addition.

Step-by-step explanation:

The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:

For any three numbers a, b, and c, (a + b) + c = a + (b + c)

For example: (2 + 3) + 4 = 2 + (3 + 4) = 9

So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]

It will take the train 53.33 seconds to pass completely through the tunnel.

We have,

First, let's convert the speed from km/h to m/s:

54 km/h = 54000 m/3600 s = 15 m/s

We need to find the total distance the train travels, which is the sum of its length and the tunnel's length:

So,

distance = 180 m + 620 m = 800 m

Now we can use the formula:

time = distance/speed

time = 800 m / 15 m/s

time = 53.33 seconds

Therefore,

It will take the train 53.33 seconds to pass completely through the tunnel.

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To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.

Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:

- Approximately 68% of the data lies within one standard deviation of the mean.

- Approximately 95% of the data lies within two standard deviations of the mean.

- Approximately 99.7% of the data lies within three standard deviations of the mean.

Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.

Therefore, the interval within which about 95% of the data lies is:

1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles

So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).

d = 5t + 20

your answer is there so i'll be on my way, Have a nice day!!

The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:

Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:

Domain: Not specified

Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:

Range: Not specified

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The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.

(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.

[tex]x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%[/tex]

Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.

(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:

[tex]CI = x \pm z*(S/sqrtn)[/tex]

where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).

From the z-table, the z-score for a 90% confidence level is 1.645.

Plugging in the values, we get:

CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)

Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.

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The most specific correct name for this figure is a trapezoid.

A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.

An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.

A parallelogram has opposite sides parallel. >>>  This figure is not a parallelogram.

A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.

The equation that can be used to calculate the base areas of the rectangular prisms is B = V/6

From the question, we have the following parameters that can be used in our computation:

Volume of rectangular prisms

The volume of rectangular prisms is calculated as

V = Bh

Where

B = Base area

h = height

Given that

h = 6 inches,

We have

V = B * 6

Divide both sides by 6

B = V/6

This means that the the equation to calculate the base areas is B = V/6

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Complete question

Mr. James is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches

Which equation can be used to find B, the area of the base with volume V

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

We have,

We can use the inverse square law to find the distance to the star:

Luminosity / (4π(distance)²) = Apparent brightness

Rearranging this formula to solve for the distance, we get:

distance = √(Luminosity / (4π (Apparent brightness)))

Plugging in the given values, we get:

distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))

Simplifying this expression, we get:

distance = 3.04 × 10^{20} meters

Converting this distance to kilometers, we get:

distance = 3.04 × 10^{17} kilometers

To convert this distance to light-years, we divide by the speed of light in kilometers per year:

distance = (3.04 × 10^{17}) / (9.46 × 10^{12})

Simplifying this expression, we get:

distance = 32.2 light-years

Therefore,

The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.

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Answer:

220 in.²

Step-by-step explanation:

top face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²

bottom face - rectangle: A = LW = 9 in. × 2 in. = 18 in.²

left face - rectangle: A = LW = 12 in. × 2 in. = 24 in.²

right upper face - rectangle: A = LW = 8 in. × 2 in. = 16 in.²

right lower face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²

middle horizontal face - rectangle: A = LW = (9 - 4) in. × 2 in. = 10 in.²

front L-shaped face - 2 rectangles: A = (12 × 4 + 5 × 4) in.² = 68 in.²

back L-shaped face - same as front L-shaped face: A = 68 in.²

total surface area = (8 + 18 + 24 + 16 + 8 + 10 + 68 + 68) in.²

total surface area = 220 in.²

The value of c that makes z = 4 an extraneous solution is c = -1.

We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.

First, we substitute z = 4 into the equation:

√ (3/2 x + 10) = cz + 8

√ (3/2 x + 10) = c(4) + 8

√(16) = 4c + 8

4 = 4c + 8

4c = -4

c = -1

Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.

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The solution for t is t = log(28/3) / 2,  the Logarithm in base-10.

The equation -3 * 10^(2t) = -28 for t,  the exponential term and then take the logarithm of both sides. Let's go through the steps:

Step 1: Divide both sides of the equation by -3:

(10^(2t)) = -28 / -3

Step 2: Simplify the right-hand side:

(10^(2t)) = 28/3

Step 3: Take the logarithm of both sides using base-10 logarithm (log):

log(10^(2t)) = log(28/3)

Step 4: Apply the power rule of logarithms to bring down the exponent:

2t * log(10) = log(28/3)

Step 5: Since log(10) = 1, we have:

2t = log(28/3)

Step 6: Divide both sides of the equation by 2:

t = log(28/3) / 2

Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.

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The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Expression is,

⇒ - 5 (- 6w + 2u - 5)

Now, By using distributive property we get;

⇒ - 5 (- 6w + 2u - 5)

⇒ - 5 × - 6w - 5 × 2u - 5 × - 5

⇒ 30w - 10u + 25

Thus, The value of solution of the expression is,

⇒ - 5 (- 6w + 2u - 5)

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The equation of the circle is (x + 6)² + (y - 1)² = 7² and it's center is (-6, 1)

The standard equation of a circle is given by:

(x - h)² + (y - k)² = r²

Where (h,k) is the coordinates of center of the circle and r is the radius.

In the given problem, the equation is;

x² + y² + 12x - 2y - 12 = 0

This can be rewritten as;

(x + 6)² + (y - 1)² = 7²

The center of the circle is (-6, 1)  from the coordinates (h, k) of the equation of the circle.

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The length of the two tied strings on the number line would be between 96 and 97.

We first need to convert both the lengths of the strings to inches, since the knot's length is given in inches.

The first string is 3 3/4 feet long, which is equivalent to 45 inches (since 1 foot = 12 inches, and 3 3/4 feet = 45 inches).

The second string is 1 1/2 yards long, which is equivalent to 54 inches (since 1 yard = 36 inches, and 1 1/2 yards = 54 inches).

The total length of the two strings before the knot is tied is 45 inches + 54 inches = 99 inches.

Subtracting the length of the knot (2 1/2 inches) from the total length of the two strings gives us:

99 inches - 2 1/2 inches = 96 1/2 inches

Therefore, the length of the two tied strings on the number line would be between 96 and 97.

Since we know that the length is closer to 97 inches than 96 inches, we can mark the length at point 97 on the number line

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The area of the figure is 24.28 cm²

Any figure that we can break and form more than one basic shape from is called a composite figure.

The composite figure can be broken into a right triangle, a rectangle and a semi circle.

area of triangle = 1/2 bh

= 1/2 × 4 × 3

= 2 × 3

= 6 cm²

area of the rectangle = l × w

= 3 × 4

= 12 cm²

area of the semi circle = 1/2 πr²

= 1/2 × 3.14 × 2²

= 3.14 × 2

= 6.28cm²

Therefore the area of the composite figure =

6 + 12 +6.28

= 24.28 cm

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The solution of the equation [tex]\rm 5^{-x/16} = 5[/tex] will be negative 16.

Given that:

Equation, [tex]\rm 5^{-x/16} = 5[/tex]

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Take log on both sides, then we have

(-x / 16) log 5 = log 5

-x / 16 = 1

x = -16

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Answer:

3x+10+5x+18=180

8x+28=180

8x= 152

x=19

The volume of cylinder B include the following: D. 80π cubic units.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Note: Radius of cylinder B = 2r

Height of cylinder B = 2h

By substituting the parameters, we have the following:

Volume of cylinder B = π × (2r)² × 2h

Volume of cylinder B = π × 4r² × 2h

Volume of cylinder B = π × 8r²h

Volume of cylinder B = 8 × πr²h

Volume of cylinder B = 8 × 10π

Volume of cylinder B = 80π cubic units.

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The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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The value of the expression 10 ÷ 40 using the long division method will be 0.25.

The expression is given below.

10 ÷ 40

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The division is given below by the long division method. Then

40 ) 100       ( 0.25

      - 80

         200

      - 200

            0

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The profit earned if 53 mowers are sold is $1104.50.

To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:

Profit = Revenue - Cost

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

P(x) = (-0.5x^2 + 91x) - (38x + 300)

P(x) = -0.5x^2 + 53x - 300

So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.

To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:

P(53) = -0.5(53)^2 + 53(53) - 300

P(53) = -0.5(2809) + 2809 - 300

P(53) = -1404.5 + 2509

P(53) = 1104.5

Therefore, the profit earned if 53 mowers are sold is $1104.50.

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