Evaluating an exponential function

Answer:

$3820 total, $32 per alumnus.

Step-by-step explanation:

The total cost will be [tex]12\times120+650+730+1000=3820[/tex]

Each alumnus pays [tex]\frac{3820}{120} =31\frac{5}{6}[/tex]

Rounding to nearest whole number = $32 per alumnus.

Answer:

The value of g(-2) and g(4) cannot be compared because they are two different functions with two completely different values.

Step-by-step explanation:

So, you plug in -2 in the function of the x in g(x) = 8x - 2

Then, you multiply 8 by -2 in g(-2) = 8x - 2

8 × -2 would be -16

Afterwards you subtract -16 by 2 in g(-2) = -16 - 2

The function of g(-2) is -14 in g (x) = -14

You plug in 4 in the function of x in g(4) = 8x - 2

g(4) = 8 (4) - 2

Then, You multiply 8 by 4 which will give you 32 in

g(4) = 32 - 2

Lastly, you subtract the 32 by 2 and the function of the answer would be 30 in g(x) = 30

Answer:

3x + y = 9.5

Step-by-step explanation:

1) The equation of a line is in the form of y = mx + c, where m is the gradient and c is the y-intercept. Write the given values in that form.

y = -3x + c

2) Find the value of k by using the following formula: m = y2 - y1 / x2 - x1. We already know m.

-3 = 8 - k / k - 3

-3(k - 3) = 8 - k

-3k + 9 = 8 - k

-3k + k = 8 - 9

-2k = -1

k = -1/-2

k = 1/2

3) Therefore, a line with gradient of - 3 passes through the points (3, 1/2) and (1/2, 8). We can find the y-intercept (c). To do so, choose one of the coordinates and substitute.

y = -3x + c

1/2 = -3(3) + c

1/2 = -9 + c

1/2 + 9 = c

9.5 = c

Completed equation of the line: y = -3x + 9.5

4) Write it in the form of ax + by = c.

3x + y = 9.5

A is zero

B) D

C) x= - 1 & x= 4

Hope this helps!

Answer:

down there

Step-by-step explanation:

we can see that angel rso and esk are congruent because they are verticle angels.

we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra

The additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

The six basic properties of parallelograms are primarily;

Now, looking at the parallelogram properties above and comparing with the given image of the quadrilateral attached, we can say that the additional information that would allow us to prove that the image is a parallelogram is that; Line EJ ≅ Line GJ

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Based on the given parameters about old cone, the height of the new cone is 12 inches

Old cone:

New cone:

equate ratio of radius to height in old and new cone

2 : 6 = 4 : h

2/6 = 4/h

cross product

2 × h = 6 × 4

2h = 24

h = 24/2

h = 12 inches

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Answer:

the distance between both points is 10

Step-by-step explanation:

Distance (d) = √(-14 - -8)2 + (-16 - -8)2

= √(-6)2 + (-8)2

= √100

= 10

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

We have,

To find the distance between two points in a coordinate plane, you can use the distance formula:

Distance = [tex]\sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

In this case, the two points are (-8, -8) and (-14, -16).

Let's plug the values into the distance formula:

Distance = √[(-14 - (-8))² + (-16 - (-8))²]

Distance = √[(-14 + 8)² + (-16 + 8)²]

Distance = √[(-6)² + (-8)²]

Distance = √[36 + 64]

Distance = √100

Distance = 10

Thus,

The distance between the two points (-8, -8) and (-14, -16) is 10 units.

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The correct statement regarding when the events will be independent is given as follows:

B. The probability of getting a red convertible is 0.06.

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

In this problem, the probabilities are given as follows:

The events will be independent if:

[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]

The intersection of events A and B is a red convertible car, hence the correct option is:

B. The probability of getting a red convertible is 0.06.

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[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

The lines shown below are perpendicular. Is this statement true or false?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

In order for a pair of lines to be perpendicular, they must intersect at a [tex]\bf{90^\circ}[/tex] angle. (a right angle)

[tex]\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]

The radius of the base is 8.245 cm

Given, a vase with a circular base exerts

Pressure = 700 N/m²

Force = 15 N

Area = ?

∴ area = πr²

By finding out the area of the vase we can calculate the radius.

We know that Pressure = Force/Area

According to the equation, pressure is inversely related to area but directly related to force. Pressure rises at a constant area as the force exerted increases in strength.

therefore apply the above the formula to find out the area and radius.

700 = 15/πr²

 πr² = 15/700

 πr² = 3/140

  r² = 3/140 × 3.14

since π value is 3.14

  r² = 0.0068

   r = √0.0068

   r = 0.0824 m

   r = 0.0824 × 100

   r = 8.245 cm

we get radius as 8.245 .

Hence we get the radius of the base of the vase as 8.245 cm.

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Answer:

5

Step-by-step explanation:

2x + 15 = 3x + 10

3x + 10 = 2x + 15

3x - 2x = 15 - 10

x = 5

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

[tex]2x + 15 = 3x + 10[/tex]

• Group like terms together:

  • Subtract 5 from both sides:

     [tex]2x = 3x - 5[/tex]

  • Subtract 3x from both sides:

      [tex]-x = -5[/tex]

• Multiply both sides by -1:

[tex]x = 5[/tex]  

Answer:

significa que 1 barra de chocolate dividida entre 4 amigos es igual a 1 4. Por lo tanto, cada persona recibe 1 4 de la barra”. 6.

Step-by-step explanation:

Answer:

3/4 divided by 3 is 0.25

Step-by-step explanation:

We know that he has 3/4 of a candy bar and he wants to share it with himself plus 2 people.

The expression 3/4 divided by 3 represents this.

To change division to multiplication we use the reciprocal.

3/4 times 1/3 is 0.25.

Hope this helps. (:

The amount of stockholders’ equity as of August 31 of the current year is $26400.

The owner's equity will be:

= Cash + Supplies + Equipment - Account payable

= 27900 + 900 + 8500 - 7300

= 26400

Therefore, the amount of stockholders’ equity as of August 31 of the current year is

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By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:

[tex]\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}[/tex]

[tex]\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}[/tex]

tan θ ≈ 77.173°

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

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The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.

Exponents are the base raised to a power, It is written in the superscript of a number.

The expression given in the statement can be written as

[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]

By the Exponent rule,

[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]

So the expression can be written as

=[tex]\rm 2^{5/8}[/tex]

=[tex]\rm \sqrt[8]{2^5}[/tex]

Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.

The complete question is

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 7 over 8 power, all over 2 to the 1 over 4 power

the eighth root of 2 to the fifth power

the fifth root of 2 to the eighth power

the square root of 2 to the 5 over 8 power

the fourth root of 2 to the sixth power

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Answer: 18 feet

Step-by-step explanation:

The area of a rectangle is given by [tex]A=lw[/tex], which means that the length of the unknown side is [tex]\frac{216}{12}=18[/tex] feet.

The given expression is equivalent to the number 147.

We have given that,

[tex](3\times4)^2+\frac{6}{2}[/tex]

We have to determine the value of the given expression.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

[tex]=(12)^2+\frac{6}{2} \\=144+3\\=147[/tex]

Therefore the given expression is equivalent to the number 147.

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Answer:

29 ft

Step-by-step explanation:

The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.

a² + b² = c²

(21 ft)² + (20 ft)² = c²

c² = 841 ft²

c = √(841 ft²)

c = 29 ft

Answer: 29 ft

Answer:

-100/3,0

Step-by-step explanation:

substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

if that makes sense Hope this helps pls brainliest have a nice day :>

Answer:

100- 3X

Step-by-step explanation:

SLAY

Answer: 10

Step-by-step explanation:

The first term is 3 and the common ratio is 1/2.

Using the sum of a geometric series formula,

[tex]\frac{3069}{512}=\frac{3(1-(1/2)^{n}}{1-(1/2)}\\\\\frac{3069}{1024}=3(1-(1/2)^{n})\\\\\frac{1023}{1024}=1-(1/2)^{n}\\\\-(1/2)^{n}=-\frac{1}{1024}\\\\(1/2)^n=\frac{1}[1024}\\\\2^{-n}=2^{-10}\\\\n=10[/tex]

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:

x + y = 28500    (1)

Also:

(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310

0.1x - 0.04y = 1310   (2)

From equation 1 and 2:

x = 17500, y = 11000

$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.

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By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

Herein we must simplify an expression that uses logarithms by applying any of the following three laws:

[tex]\log_{a} (b \cdot c) = \log_{a} b + \log_{a} c[/tex]      (1)

[tex]\log_{a} \left(\frac{b}{c} \right) = \log_{a} b - \log_{a} c[/tex]     (2)

[tex]\log_{a}{b^{c}} = c \cdot \log_{a} b[/tex]     (3)

Now we proceed to simplify the expression:

[tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 8\cdot x^{3} - \log_{2} \frac{8\cdot x^{3}}{2}[/tex]

[tex]\log_{2} 2 \cdot y = \log_{2} \frac{\frac{8\cdot x^{3}}{1} }{\frac{8\cdot x^{3}}{2} }[/tex]

[tex]\log_{2} 2\cdot y = \log_{2} 2[/tex]

By the relationship between logarithms and powers of same base:

2 · y = 2

y = 1

By applying logarithm laws and the relationship between logarithms and powers of same base, the expression [tex]\log_{2} \frac{8\cdot x^{3}}{2} = \log_{2} 8\cdot x^{3} - \log_{2} 2\cdot y[/tex] is equal to y = 1.

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Answer:

y = -19x + 14

Step-by-step explanation:

For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14

Answer: {-3, -2, 1, 5}

Step-by-step explanation:

The domain is the set of x-values.

Answer:

1.25 is the median for the first 12 days in January

By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

In this question we must apply algebraic rules to find the roots of a quadratic equation, the roots are the values of the equation such that is equal to zero. Now we present the complete procedure:

6 · x² + 18 · x = 0

6 · x · (x + 3) = 0

x = 0 ∨ x = - 3

By applying algebraic handling and the concept of polynomials, we conclude that the quadratic equation 6 · x² + 18 · x = 0 has two roots: 0, - 3.

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Answer:

9 miles

Step-by-step explanation:

If 3 miles is equal to 15 mins

Then you do 3 miles and times by 3 cause if you times 15 by 3, you'll get 45 mins

So the answer= 9 miles

Answer:

First Question: 1. 60 hours 2. Wednesday 6:00 PM

Step-by-step explanation:

Sorry but I couldn't figure out the answer to the second question :(

Hope this helped :D

Answer:

Shirt: $45 , Tie: $12

Step-by-step explanation:

Let s be the price of the shirt

Let t be the price of the tie

Given the information from the question,

s + t = 57 - Equation 1

s - t = 33 - Equation 2

We will use substitution method to find the prices.

We will rearranging equation 1.

s = 57 - t

We will substitute s into equation 2.

57 - t - t = 33

57 - 2t = 33

-2t = 33 - 57

-2t = -24

t = -24 / -2

= 12

We now substitute t into Equation 1.

s + 12 = 57

s = 57 - 12

= 45

From here we know, the shirt costs $45 and the tie costs $12