Statement about the function f(x)=5(0.9)^x

The expression is equivalent to \(5^2\).

Given

Expression; \(\rm \dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}\)

The definition of exponential form is a way of writing a number that is multiplied by itself more than once.

To solve the exponential equation follow all the steps given below.

Therefore,

The expression is equivalent to;

\(\rm =\dfrac{(5^2)^{-3}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6}\times 5^4}{5^{-4}}\\\\=\rm \dfrac{(5)^{-6+4}}{5^{-4}}\\\\=\rm \dfrac{5^{-2}}{5^{-4}}\\\\=5^{-2+4}\\\\=5^2\)

Hence, the expression is equivalent to \(5^2\).

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Answer:

a) y=0.50x+15  

b) The graph of this equation form on a coordinate plane is a line.

c) Slope  =0.50 and y-intercept = 15

Step-by-step explanation:

Let x = Number of miles driven by car

Given: The cost of renting a car for a day is $0.50 per mile plus a $15 flat fee.

a) Total cost = 0.50x+15

If y =total cost of renting the car, then y=0.50x+15   (i)

b) Above equation is similar to y= mx+c  (ii) [m = slope , xc=y-intercept] which a linear equation .

So the graph of this equation form on a coordinate plane is a line.

c) Comparing (i) and (ii)

m=0.50 , c=15

Hope this helps :)

Answer:

\(w = 10 \sqrt{2} \)

\(y = 20\)

Step-by-step explanation:

Use the Sine Rule to solve for the unknown sides.

Triangle with sides AB = 8cm , CA = 5cm , BC = 7cm and AB = 7cm , BC = 10cm , CA = 8cm can construct a Triangle.

Condition : For forming the triangle, the sum of two sides must be greater than the third side.

a.  AB = 4cm, CA = 3cm, BC = 10cm

   CA+BC=AB

   3+1=4

   4=4

Therefore, it cannot form a triangle because it is not satisfying the condition.

b.  AB = 8cm , CA = 5cm , BC = 7cm

    AB+CA>BC

    AB+BC>CA

    CA+BC>AB

    Therefore, it can form a triangle because it satisfies the condition.

c.  AB = 7cm, BC = 10cm, CA = 8cm

   AB+BC>CA

   AB+CA>BC

   BC+BC>AB

  Therefore, it can form triangle because it satisfies the condition.

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Answer:

0.3232323232... is an irrational number

Step-by-step explanation:

An irrational number is any number that cannot be written as a fraction of whole numbers.

The equations should be matched with the correct transformation rule as follows;

In Mathematics and Geometry, the translation of a graph to the left means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

y = |x + 1|

In Mathematics and Geometry, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

y = x² - 1

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y);

y = -|x|

In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y);

y = (-x)²

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Answer:

ans: option D

Step-by-step explanation:

exterior angle of triangle is equal to sum of opposite interior angle I.e

angle ACD= angle CAB + angle ABC

Answer:

d

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ACD is an exterior angle of the triangle, then

∠ ACD = 80° + 60° = 140° → d

Answer:

x = 3

y = 9

Step-by-step explanation:

It is an equilateral triangle so all sides are equal and all angles are 60°.

This means that 20x = 60 and y=AB=AC=BC=9

Maria can also utilize other descriptive statistics measures such as measures of dispersion (e.g., range, standard deviation) to capture the variability in tuition costs and provide a more comprehensive understanding of the data set.

To report the average cost of college tuition from the 1950s until the present time, Maria, the researcher, would use descriptive statistics. Descriptive statistics involves organizing, summarizing, and presenting data to describe and understand a particular phenomenon or variable.

In this case, Maria wants to calculate the average cost of college tuition, which is a measure of central tendency that provides a representative value of the entire data set. The average, also known as the mean, is obtained by summing up all the tuition costs and dividing it by the total number of observations.

Descriptive statistics will allow Maria to analyze the historical trends and variations in college tuition costs over time. She can calculate the mean tuition costs for each decade or specific time periods, presenting the average values to provide insights into the overall cost trends.

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By following below steps, you will be able to determine which triangle represents the image of triangle XYZ after the given transformations.

To determine which triangle represents the image of triangle XYZ after it was reflected across line M and then dilated to form a similar triangle, you should follow these steps:

1. Identify the reflection: Find the image of triangle XYZ after reflecting it across line M. The reflected triangle will have the same shape and size, but its orientation and position will be changed.

2. Identify the dilation: From the reflected triangle, find the image that represents a similar triangle by checking if all corresponding angles are equal and the side lengths are proportional. This triangle will have the same shape as the reflected triangle, but its size may be different due to dilation.

By following these steps, you will be able to determine which triangle represents the image of triangle XYZ after the given transformations.

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Answer: B

Step-by-step explanation:

Remember that if f and g are inverses of one another, then

f(g(x)) = g(f(x)) = x

1/2. Take a = 0 and b = 1 (or any non-zero number) so that

f(x) = x + 0/1   ⇒   f(x) = x

If g is to be an inverse of f, we need

g(f(x)) = g(x) = x

so that c = 1 and d = 0.

3. With f(x) = x + a/b and g(x) = cx - d, we have

g(f(x)) = g(x + a/b) = c (x + a/b) - d = cx + ac/b - d

and of course, with a,b,c,d as before, we get g(f(x)) = x.

4. This would be a very uninteresting graph for the example I've cooked up here, just containing the line y = x...

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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Answer:

80+60+3x+4=180

140+3x+4=180

144+3x=180

3x=180-144

3x=36

x=12

Answer:

x = 12

Step-by-step explanation:

All triangles equal to 180 degrees so, we can set up this expression:

180 = (3x + 4) + 80 + 60

All we have to do is solve:

180 = (3x + 4) + 80 + 60

180 = 3x + 4 + 140

180 = 3x + 144

-144        -144

36 = 3x

/3     /3

12 = x

The Solution set for the inequality x - \(6\frac{1}{3}\) ≤ \(1\frac{1}{2}\)  is {x | x ∈ R, x ≤ \(7\frac{5}{6}\)}  , the correct option is (a) .

In the question ,

the inequality is given as

x - \(6\frac{1}{3}\) ≤ \(1\frac{1}{2}\)

we first convert the complex fractions into normal fractions ,

\(6\frac{1}{3}\) = (6 * 3 + 1)/3 = 19/3

and  \(1\frac{1}{2}\) = (1 * 2 + 1)/2 = 3/2

rewriting the given inequality , we get

x - 19/3 ≤ 3/2

adding 19/3 to both sides of the equation ,

we get ,

x ≤ 19/3 + 3/2

Taking LCM of 3 and 2 as 6 and

Simplifying further ,

we get ,

x ≤ 38/6 + 9/6

x ≤ 47/6

x ≤ \(7\frac{5}{6}\)

Therefore , the solution set is {x | x ∈ R, x ≤ \(7\frac{5}{6}\)}  .

The given question is incomplete , the complete question is

Given: x - \(6\frac{1}{3}\) ≤ \(1\frac{1}{2}\) . Choose the solution set.

(a) {x | x ∈ R, x ≤ \(7\frac{5}{6}\)}

(b) {x | x ∈ R, x ≤ \(7\frac{2}{5}\)}

(c) {x | x ∈ R, x ≤ \(5\frac{1}{6}\)}

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Answer:

-55/4

Step-by-step explanation:

The measures of the corresponding inscribed angles, and then add those angles together to find the measure of angle L. Therefore, the measure of angle L is 64 degrees.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. In other words, if we have an angle whose vertex is on the circumference of a circle, and whose sides intersect two points on the circumference, then the measure of the angle is half the measure of the arc between those two points.

In this problem, we are given the measures of two arcs, DR and SV, and we want to find the measure of angle L. We can start by using the Inscribed Angle Theorem to find the measures of the corresponding inscribed angles. Let's call these angles A and B, where A is the inscribed angle that intercepts arc DR, and B is the inscribed angle that intercepts arc SV.

Using the Inscribed Angle Theorem, we can find that m∠A=12m⌢DR=12(34∘)=17∘m∠B=12m⌢SV=12(94∘)=47∘

To find the measure of angle L, we simply add angles A and B together: m∠L=m∠A+m∠B=17∘+47∘=64∘

Therefore, the measure of angle L is 64 degrees.

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Answer:

-8

Step-by-step explanation:

Answer:

y = ax^2 + bx + c

Answer:

uihuvbuh ufsghiusgu 8y39 8y3yy894y87y48jhfjhjbvhjjavjlh ailhli

Step-by-step explanation:

The standard deviation is 7.35.

Standard deviation is used to determine how the values in a group differs from the mean of the values in the group

In order to determine the standard deviation, take the following steps:

Determine the mean of the observation: (87 + 91 + 74 + 73 + 80 + 84 + 68 + 75) / 8 =79

Determine the difference between each value and the mean and then square the result:

(87 - 79)² + ( 91 - 79) ² + (74 - 79)² + (73 - 79)² + (80 - 79)²  + (84- 79)²  + (68 - 79)²  +( 75- 79) ²

64 + 144 + 25 + 36 + 1 + 25 + 121 + 16 = 432

Determine the mean of the sum of the squared differences and then find the square root of the mean:

√432 / 8 = 7.35

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Answer:

kinder

Step-by-step explanation:

1. 8

2. 2

9514 1404 393

Answer:

  see attached (black dot)

Step-by-step explanation:

We assume you want to plot (r, θ) = (-3, -π/3), where the angle is in radians.

The basic idea is to locate the ray that is in the direction -π/3 radians, then go 3 units in the opposite direction. The point (3, -π/3) is identified in the attached graph by a red circle. Its reflection across the origin is how you plot the point for a negative radius. That reflected point is the black dot.

The equivalent coordinates are ...

  (r, θ) = (-(-3), -π/3+π) = (3, 2π/3)

Answer:

C

Step-by-step explanation:

The greatest common factor of 8 and 10 is 2

The greatest common factor of a^4 and a^3 is a^3

The binomial whose greatest common factor is 2a³ is 8a⁴ + 10a³.

The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.

Given the a³ is not common in  A and B they are wrong

C. 8a⁴ + 10a³

common factors of 8 and 10 is 2

so 8a⁴ + 10a³  has factors 2a³

Hence option C is correct.

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Answer:

Step-by-step explanation: 40 see attachment

A. subtract the bottom equation from the top equation

Step-by-step explanation:

The elimination method for solving systems of linear equations uses the addition property of equality. You can add the same value to each side of an equation. So if you have a system: x – 6 = −6 and x + y = 8, you can add x + y to the left side of the first equation and add 8 to the right side of the equation.

// have a great day //

Referring to Table 3.1, if the government imposes a price of $3, a shortage will result.

To determine the outcome when the government imposes a price of $3, we need to compare the quantity demanded and quantity supplied at this price level.
According to Table 3.1, at a price of $3, the quantity demanded is 30 units, while the quantity supplied is 40 units. The quantity demanded (30 units) is less than the quantity supplied (40 units), resulting in a situation known as a shortage.
A shortage occurs when the quantity demanded exceeds the quantity supplied at a given price. In this case, a shortage of 10 units occurs because consumers are willing to buy more than what producers are offering at the price of $3.
To summarize, if the government imposes a price of $3 based on Table 3.1, a shortage will result. This means that the quantity demanded exceeds the quantity supplied at the given price, indicating that consumers are unable to purchase all the units they desire.

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 the complete question is:

Table 3.1
Quantity Demanded.
Price per Unit
Quantity supplied
10
$5
50
20
30
$4
$3
40
30
40
50
$2
$1
20
10
Refer to Table 3.1. If the government imposes a price of $3.
a shortage will result.
Market is in equilibrium.
the price will fall to $1 because producers will be forced to incur losses.
a surplus will result.

Answer:

The radius of the sphere is approximately 62.71 cm

Step-by-step explanation:

The question relates to the definition of a sphere

The given parameters are;

The distance between the sharp parallel blades through which the sphere is rolled = 77 centimeters

The radii of the circular faces left by cutting the sphere with the blade = 39 cm  and 60 cm

From the triangles formed by the cross-section of the sphere, we have;

AB ║ DE Given

∠A ≅ ∠E, ∠D ≅ ∠B Alternate angles

∠C ≅ ∠C by reflective  property

∴ ΔABC ~ ΔDCE by Angle-Angle similarity theorem

CF/CG = AB/DE = 78/120 = 13/20

CF = CG × 13/20

CF + CG = 77

∴ CG × 13/20 + CG = 77

33·CG/20 = 77

∴ CG = 140/3

CF = 13/20 × CG = 13/20 × 140/3 = 91/3

CF = 91/3

The diameter of the sphere AE = AC + EC

By Pythagoras's theorem

AC = √(FA² + CF²) = √(39² + (91/3)²) = 13·√(130)/3

EC = √(CG² + GD²) = √((140/3)² + 60²) = 20·√(130)/3

∴ AE = AC + EC = 13·√(130)/3 + 20·√(130)/3 = 11·√(130)

The diameter, 'D', of the sphere, AE = 11·√(130)

The radius of the sphere = D/2 = 11·√(130)/2 ≈ 62.71 cm

Answer:

  -20, -18, -16

Step-by-step explanation:

For consecutive integer problems, it often works well to let a variable represent the middle one (or their average value).

__

Here, we can let x represent the second integer. Then the first is (x-2), and the third is (x+2). The given relation can be written as ...

  (5 +x)(-7) = 11 +5(-(x+2))

  -35 -7x = 11 -5x -10 . . . . . . eliminate parentheses

  -36 = 2x . . . . . . . . . add 7x -1

  -18 = x . . . . . . . . divide by 2

The three integers are -20, -18, -16.

Answer: 200 m²

Step-by-step explanation:

The perimeter is calculated by the formula:

= (2 * length) + (2 * width)

We have the perimeter so we can find the width:

60 = (2 * 10) + (2 * w)

60 = 20 + 2w

2w = 60 - 20

w = 40 / 2

w = 20 meters

Area of a rectangle can be used because this fits the characteristics of a rectangle:

= Length * Width

= 10 * 20

= 200 m²