Graphing Exponential Exponents Practice

Directions: Graph the function. Compare the graph to the graph of the parent function, identify the y-intercepts, asymptotes, domain, and range.

3) f(x)=[tex]\frac{4}{3}[/tex](6)^x

4)f(x)= -([tex]\frac{1}{3}[/tex])^x

This can be modeled as a Poisson distribution. The mean number of patients admitted per day is 2.5, so the Poisson parameter λ = 2.5. The probability that the hospital will not have enough beds on any given day is the probability that more than 1 patients will be admitted, which is given by:

P(X > 1) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - (e^-2.5 * 0 + e^-2.5 / 1!)

= 1 - e^-2.5 * (1 + 2.5)

This is the probability that the hospital will not have enough beds to accommodate its newly admitted patients on any given day.

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Based on the information provided, Derek will have made $480 more in buttered popcorn than in caramel popcorn.

To calculate his earnings with popcorn, let's use the expression given for each type of popcorn:

Buttered popcorn:

8w+9

8 x 12 + 9

96 + 9 =105

105 x 11 = $1155 (Total earnings for buttered popcorn)

Caramel popcorn:

6w-11

6 x 12 - 11

72 - 11 = 61

61 x 11 = $671 (Total earnings for caramel popcorn)

Now, let's calculate the difference:

$1155 - $671 =$480

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The sum of the squares of the solutions of the mentioned equation is 161.38.

The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.

x² - 13x + 4 = 0

Based on Dharacharya formula, stated as -

x = - b ± ✓b² - 4ac/ 2a, we get the roots -

x = 12.7 and 0.3

Now, the next formula to solve will be -

x = 12.7² + 0.3²

Taking the square of each number

x = 161.29 + 0.09

Performing addition on Right Hand Side of the equation

x = 161.38

Thus, the required answer is161.38.

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Step-by-step explanation:

you add all the numbers then you can get the answer

Answer:

5 cm^2

Step-by-step explanation:

I just had this same question and I got it right.

hope this helps

The approximate surface area of this wheel of cheese is 437.6 square inches.

As per the given data, a wheel of cheese has a radius of 7 inches.

Radius r = 7 inches.

Also, a wheel of cheese has a height of 3 inches.

Height h = 3 inches

Also, given to consider the value of pi as 3.14.

π = 3.14

Here we have to determine the total surface area (TSA)of the wheel of cheese.

Since the cheese is a cylinder shaped thing.

The formula for the total surface area (TSA) of the wheel:

TSA = 2πr (r + h)

Substituting the values of the variables into the formula, we have

= 2 (3.14)(7)(7 + 3)

= 2 (21.88)(10)

= 2 (218.8)

= 437.6 square inches.

Therefore the total surface area is 437.6 square inches.

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The length of ED is,  3√10

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In a figure,

⇒ PB = BC = 6

Now, By the figure,

⇒ ΔFPD and ΔEMD are congruent.

Hence, We can formulate;

⇒ FP / EM = PD / MD

Let the length of MD = x

⇒ FP / EM = PD / MD

⇒ 6 / 3 = (9 + x) / x

⇒ 2x = 9 + x

⇒ 2x - x = 9

⇒ x = 9

Hence, The length of MD = 9

Now, In  ΔEMD;

⇒ ED² = EM² + MD²

⇒ ED² = 3² + 9²

⇒ ED² = 9 + 81

⇒ ED² = 90

⇒ ED = √90

⇒ ED = 3√10

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The number of years that it takes to double your money will be 12 years.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account. Then the equation is given as,

$1,000 = $500 x (1 + 0.06)ⁿ

2 = (1.06)ⁿ

ln 2 = n ln 1.06

n = ln 2 / ln 1.06

n = 11.90

n ≈ 12 years

The number of years that it takes to double your money will be 12 years.

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Answer:

C. 6/48

Step-by-step explanation:

mutliply both numerator and denominator

The value of a is given as follows:

a = 12.

We have two parallel lines that are cut by a transversal, and the two angles are between the parallel lines and on the same side of the transversal, meaning that they are consecutive interior angles.

Consecutive interior angles are supplementary, meaning that the sum of their measures is of 180º, hence the value of a can be found as follows:

10a + 2 + 5a - 2 = 180

15a = 180

a = 180/15

a = 12.

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Answer: a = 12.

Step-by-step explanation: did the same question got it right

Answer: Observational

Step-by-step explanation:

If it is a experiment then you can conclude that a variable caused a response

In statistics, correlation refers to the degree to which two variables are related or associated with each other. When the correlation between two variables is close to 1.0, it indicates a strong positive relationship between them. However, it is important to note that this strong correlation does not necessarily imply a cause-and-effect relationship between the two variables, especially in a study where certain conditions may not be met.

A study is a systematic investigation aimed at acquiring knowledge and understanding of a particular phenomenon or subject matter. In order to establish a causal relationship between two variables, certain conditions need to be met, such as the establishment of a temporal sequence, a clear association between the variables, and the elimination of any confounding variables that may influence the outcome. These conditions are essential for any study seeking to establish a cause-and-effect relationship between variables.

In the absence of these conditions, even if the correlation between two variables is close to 1.0, it cannot be concluded that the explanatory variable causes changes in the response variable. This is because correlation does not imply causation. Correlation simply indicates the strength of the association between two variables, but it does not provide information about the direction or the underlying mechanisms of the relationship.

For instance, consider a study examining the relationship between smoking and lung cancer. The study finds a strong positive correlation between smoking and lung cancer, indicating that smokers are more likely to develop lung cancer than non-smokers. However, this correlation alone does not necessarily prove that smoking causes lung cancer. There may be other factors such as air pollution, family history, or genetics that could influence the development of lung cancer.

In summary, the correlation between two variables is a measure of the strength of the association between them. A high correlation does not necessarily imply a cause-and-effect relationship between the variables, especially in a study where certain conditions may not be met. It is important to consider these conditions and rule out other factors that could influence the outcome before drawing any conclusions about the causal relationship between two variables.

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Answer:

The answer is 3.2 x 10-21.

Step-by-step explanation:

To solve this problem, we need to use the rules of exponents. The first step is to calculate the exponents for each number.

For 9 × 104, the exponent is 3 (9 × 104 = 90000).

For 3,000,000, the exponent is 2 (3,000,000 = 3000000).

For 0.00243, the exponent is -3 (0.00243 = 0.00000243).

Now, we can calculate the answer by multiplying the exponents:

3 × 2 × (-3) = -6

Then, we need to multiply the numbers together to get the final answer:

(9 × 104)² × (3,000,000)² × (0.00243) = 9 x 10-6 x 9 x 10-12 x 0.00243 = 3.2 x 10-21.

Answer:

a ) $11.5

b.) 10 million gallons

Step-by-step explanation:

a.) Since it's asking for p if x = 20, we can plug 20 into the original equation

[tex]0.2(20) + 4p = 50[/tex]

0.2 times 20 is 4

4 + 4p = 50. Next we would subtract 4 from each side giving us

4p = 46. Lastly, divide each side by 4

p = 11.5

b.) If the p, also known as p increases by 50 cents, that means it goes from 11.5 to 12.

Now we plug in 12 to p and look for x, the opposite

[tex]0.2x + 4(12) = 50[/tex]

4 times 12 is 48, making it

0.2x + 48 = 50. This is where we subtract 48

0.2x = 2. and lastly, divide by 0.2, making...

x = 10

So demand decreased by 10 million because 20-10=10

Answer: 4a = D; 4b = B

Step-by-step explanation:

The area and the perimeter of the room having rectangular shaped base are respectively,   121 feet² & 44 feet

An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².

Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.

Perimeter = Sum of length of the all the sides

Given that,

2 of the walls are 11 and 11,

The room is into rectangle shape,

Base area of room = length x width

                               =  11 x 11

                               =   121 feet²

Perimeter of base of the room = Sum of lengths and widths

                                                   = 11 + 11 + 11 + 11

                                                   =   44 feet

Hence, the area and perimeter are respectively 121 feet² & 44 feet

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From the given data points representing the number of new homes that built in each neighborhood. The median number of houses is 26.

The median is the middle value of a set of numerical data when the data is arranged in ascending or descending order. In a set of odd number of data points, the median is the middle value. In a set of even number of data points, the median is the average of the two middle values.

To find the median, you arrange the numbers in order from least to greatest and then pick the middle number(s).

5, 12, 13, 20, 26, 29, 30, 31

In this case, there are 8 numbers, so the median is the middle number, which is 26.

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Answer:

Step-by-step explanation:

B. 64^(1/2) is greater than 64^(1/3).

Since the angles in DBC and BDA are equal, we have:

DBC ≅ BDA

What is the Angle-Angle Similarity Theorem?

The Angle-Angle Similarity Theorem, also known as the AA Similarity Theorem, states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Given: AD // BC, AB // CD

To prove: DBC =~ BDA

From the given, we have AD // BC and AB // CD.

This means that AD is parallel to BC and AB is parallel to CD.

Since AB is parallel to CD, corresponding angles are equal.

Let the angle BCD = x.

Then, angle BAD = x.

Since AD // BC, corresponding angles are equal.

Let the angle DCB = y.

Then, angle DAC = y.

Now, we can see that angle BDA + angle DAC = y + x.

And angle DBC + angle DCB = y + x.

Since the sum of the angles in a triangle is 180 degrees,

angle BDA + angle DAC + angle DBC = 180.

So, y + x + y + x = 180.

Therefore, 2y + 2x = 180.

And, y + x = 90.

Since the angles in DBC and BDA are equal, we have:

DBC =~ BDA

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The inches of snow that fall at this rate is 8 inches

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

10 inches of snow fall for 1 1/4 hour

Ths means that the unit rate is

Unit rate = 10 inches/1 1/4 hour

Evaluate the quotint

Unit rate = 8 inches per hour

For one hour, we have

Snow = 8 * 1

Evaluate

Snow = 8

Hence, the amount is 8 inches

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Answer:

1

Step-by-step explanation:

To find slope, m, we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

The top Y on the table is 7 and the bottom one is -1, so we'll plug those into the top.

The top X on the table is 6 and the bottom one is -2, so we'll plug those into the bottom

[tex]m = \frac{7 - ( - 1)}{6 - ( - 2)} [/tex]

[tex]m = \frac{8}{8} = 1[/tex]

There were 75 total number of persons present at the party

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The amount of people who ate lasagna was 12 less than 3/5 of the total number of people.

Let x represent the total number of people at the party.

The number of people that ate lasagna = (3/5)x - 12

The number of people who ate lasagna were 33. Hence:

The number of people that ate lasagna = 33

Therefore the equation is:

33 = (3/5)x - 12

(3/5)x = 45

x = 75

The total number of people is 75

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One example of a polynomial function is given as follows:

p(x) = x^3+4x^2-3x+2

There are two conditions for a polynomial function, and they are listed as follows:

For the example, we have that the exponents are 3, 2, 1 and 0, while it contains only a numerator.

The problem is incomplete, hence the general procedure to identify a polynomial function was given.

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Answer:

25% increase

Step-by-step explanation:

Percentage increase = [tex]\frac{100-80}{80} * 100=\frac{20}{80} * 100 = 25%[/tex]

Answer:

1b

Step-by-step explanation:

Answer:

that means it's a short yam

The length of the yarn is n < 7.5 inches.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

The length of the yarn is less than 7.5 inches.

Let the length of the yarn is n inches.

To show the length of the yarn:

We will establish an inequality.

So,

n < 7.5 inches.

Therefore, n < 7.5 is the inequality.

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The maximum value of the August electric bills of used by customers using the box and whisker plot is equal to $320 .

In box and whisker plot , Data is plotted in as it is divided into :

Five number summary set of data ,

Minimum value ,Maximum value, First Quartile, Third Quartile , Median.

Data of August electric bills ($)  as per given data is:

200  240  160   280  320

Minimum value = $160

Maximum value = $320

First quartile = $200

Third Quartile = $280

Median = $240

Therefore, the maximum value of the August electric bills shown as box and whisker plot is $320.

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_____The above question is incomplete ,the complete question is:

The local utility company released a report showing the August electric bills of their customers. ​ ​This box-and-whisker plot shows the results.

200  240  160 280  320  

August electric bills ($) What is the maximum value?