Which statements are true about exponential functions? Check all that apply.
The domain is all real numbers.
The range always includes negative numbers.
The graph has a horizontal asymptote at x = 0.
The input to an exponential function is the exponent:
The base represents the multiplicative rate of change.

Answer:

Step-by-step explanation:

2cm = 5m, so we know that the length is 5m

4cm = 2cm * 2, so the width is 5m * 2, which is 10m.

Now, we multiply them together.

5*10 = 50

The backyard area is 50 meters

Answer:

50m^2

Step-by-step explanation:

Answer:

37,000

Step-by-step explanation:

10,867 rounds to 11,000 and 26,186 to 26,000. 11,000 + 26,000 = 37,000

The amount Anneliese started with before her deductions is -$235.00.

Total amount spent = $58.00 + $35.00

= $93.00

Amount left in her account = $-142.00

Amount Anneliese started with = -$93.00 - $-142.00

= -$235.00

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Answer:

D

Step-by-step explanation:

to determine the relationship between these two lines you have to find the slope.

=> if they have the same slope ,then they are parallel.

=> if they have negative inverse slope relative to each other ,then they are perpendicular.

=> if the slope for both equations is neither of the above cases ,then the two equations are neither parallel nor perpendicular.

so if we divide the first equation by 3 which is the commen factor for the whole equation and arrange it in the form y=mx +b it would give us y =5x +4. and since the two have the same slope which is 5 ,then we can conclude they are parallel lines.

Using proportions, it is found that the coordinate that is not marked is given by:

c. 3

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

There are 6 congruent segments between -2 and 10, hence the length of each segment is given by:

l = (10 - (-2))/6 = 2.

Then the points are: -2, 0, 2, 4, 6, 8, 10. 3 is not marked, hence option c is correct.

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d=r•t ,  formula show a joint variation ,  Option C is the answer.

The variation when a variable is dependent upon two or more variables and varies directly as either of them are taken constant is called Joint Variation.

According to the question , which among the options shows a Joint Variation.

Option 1  d = 50 t

It shows direct variation , as increase in t will directly increase d 50 times * the increase

Option 2 d = 16t²

It also shows direct square variation .

Option 3 d=r•t

In this variation d is dependent on two variables and so it is a joint variation.

Therefore Option C is the answer.

The complete question is ?

Which distance formula or formulas show a joint variation? d=50t, d=16t^2, d=r•t

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Considering the given data-set, the quartiles are given as follows:

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, the first half is the 12 elements from 1 to 12, and the second half is the 12 elements from 15 to 26.

The first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third quartile is the mean of the 6th and 7th elements of the second half, hence:

Q3 = (91 + 92)/2 = 91.5.

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Answer:

[tex]\huge\boxed{\sf 5.6 \ miles}[/tex]

Step-by-step explanation:

Given that,

Rachel runs 7 miles in 80 minutes.

80 minutes = 7 miles

Using unitary method

Divide 80 to both sides

1 minute = 7/80 miles

1 minute = 0.0875 miles

Multiply 64 to both sides

64 minutes = 0.0875 × 64 miles

64 minutes = 5.6 miles

So, Rachel will run 5.6 miles in 64 minutes.

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

Answer:

We are 90% confident that the true mean lies between 8..6563 and     9.9437  

Step-by-step explanation:

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. Confidence is another word for probability.

mean (x) = 9.3                        

standard deviation (s) = 2                        

sample size (n) = 28                        

T- Distribution:

degree of freedom = n - 1 = 28 - 1 = 27    

90% Confidence Interval ==> α = 0.1

critical value, t =  1.703 ( t-table)

standard error, SE = s/√n = 2 /√28 = 0.3780

margin of error, E = t × SE= 1.703 × 0.3780 = 0.6437

Confidence Interval: x ± E = 9.3 ± 0.6437

lower limit: x - E = 9.3 - 0.6437 = 8.6563    

upper limit: x + E = 9.3 + 0.6437 = 9.9437    

Confidence Interval: 8.6563 < µ < 9.9437

Z - Distribution:

Formula: Confidence Interval = x ± z (s/√n)

Sample Mean = s/√n = 2/√28 = 2/5.29 = 0.3781

z = 1.645 (from z - table)

From formula, z (s/√n): 0.3781 x 1.645 = 0.620 (rounded)

x ± 0.62

lower limit: x - 0.62 = 9.3 - 0.62 = 8.68  

upper limit: x + 0.62 = 9.3 + 0.62 = 9.92

Confidence Interval: 8.68 < µ < 9.92

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The number of orders Michael, Rafael and Amanda served are 16.8, 33.6, and 41.6 servings

respectively.

x + 2x + (2x + 8) = 92

3x + 2x + 8 = 92

5x = 92 - 8

5x = 84

x = 84/5

x = 16.8 servings

Therefore,

Michael = x

= 16.8 servings

Rafael = 2x

= 2(16.8)

= 33.6 servings

Amanda = 2x + 8

= 33.6 + 8

= 41.6 servings

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The function represented by the table is therefore y = -x -2 which is linear in nature

Linear function are functions that have a leading degree of 1. using the coordinate points on the graph

(0, -2) and (1, -3)

Note that the function will be linear since the dependent and independent variables both have the same common difference.

Determine the slope

slope =  -3+2/1-0
slope = -1/1

slope = -1

For the intercept, it is -2 according to the coordinate (0, -2)

The function represented by the table is therefore y = -x -2 which is linear in nature

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The probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121

The distribution of the puppies is given as:

4 ​poodles, 5 ​terriers, and 2 retrievers

The probability of selecting a terrier is;

P(terrier) = 5/11

The probability of selecting a retriever is;

P(retriever) = 2/11

The required probability is

P = 5/11 * 2/11

Evaluate

P = 10/121

Hence, the probability that Rebecka selects a terrier and Aaron selects a retriever is 10/121

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The volume of the pyramid with the given length, width and height is 165in³.

The volume of a right rectangular pyramid is expressed as;

V = ( L × W × H ) / 3

Given that;

We substitute into the equation above.

V = ( L × W × H ) / 3

V = ( 11in × 9in × 5in ) / 3

V = 495in³ / 3

V = 165in³

The volume of the pyramid with the given length, width and height is 165in³.

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Using translation concepts, the graph of [tex]y = 2 - \sqrt{x}[/tex] is described as follows:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function [tex]y = 2 - \sqrt{x}[/tex], in blue in the graph, is the function [tex]y = \sqrt{x}[/tex], in red, reflected over the x-axis and shifted 2 units, as shown in the graph.

Hence the correct statement is:

On a coordinate plane, a curved line approaches the grid line at (3, 0.3), and ends at (0, 2).

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The expanded form of the expression; (-a)^3 is; (-a)(-a)(-a).

It follows from the task content that the expanded form of the expression given is to be written.

On this note, the expression (-a)³ can simply be rewritten in it's expanded form as; (-a)(-a)(-a).

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Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

Given that, in 3 years, Dianna will be 4 times as old as she was 33 years ago.

Let x represent the age of Dianna presently.

Dianna's age in 3 years time will be: x + 3

Dianna's age 33 years ago is: x - 33

Since in 3 years, she will be 4 times as old as she was 33 years ago.

x + 3 = 4( x - 33 )

We solve for x

x + 3 = 4x - 132

3 + 132 = 4x - x

135 = 3x

x = 135/3

x = 45

Given that In 3 years, Dianna will be 4 times as old as she was 33 years ago, her present age is 45.

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Answer:

Scalene Triangle

Step-by-step explanation:

Defn
When all the three sides of the triangle are of different measures, it is a scalene triangle.

Answer:

It is a scalene triangle since all sides have different measurements.

Step-by-step explanation:

The measure of the interior angle at vertex C is D. 144.

Based on the information given, the angle will be calculated thus:

8x + 8x + 8x + 3x + 3x = (5 - 2) × 180

30x = 540

Divide both side by 30

30x/30 = 540/30

x = 18

Therefore, at vertex C, we have 8x. This will be:

= 8x

= 8 × 18

= 144

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The simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

The expression is given as:

[tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex]

Divide 162 and 2 by 2

[tex]\sqrt{\frac{81x^9}{x^{27}}}[/tex]

Take the square root of 81

[tex]9\sqrt{\frac{x^9}{x^{27}}}[/tex]

Apply the quotient rule of indices

[tex]9\sqrt{\frac{1}{x^{27-9}}}[/tex]

Evaluate the difference

[tex]9\sqrt{\frac{1}{x^{18}}}[/tex]

Take the square root of x^18

[tex]\frac{9}{x^9}[/tex]

Hence, the simplified expression of [tex]\sqrt{\frac{162x^9}{2x^{27}}}[/tex] is [tex]\frac{9}{x^9}[/tex]

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Answer:

2MN=RA+TP

13×2=x+18

26=x+18

26-18=x

8=x

The function shows a horizontal shift of the function to the right by 3 units

Transformation is a techniques used to change the position of an object on an xy-plane. Given the parent function f(x) = x

The translated function g(x) = x + 3 shows a horizontal shift of the function to the right by 3 units

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Answer:

156 : 48

Step-by-step explanation:

Solution:

Since

169 : 52 = 156 : X

Then we know

52/169 = X/156

Multiplying both sides by 156 cancels on the right

156 × (52/169) = (X/156) × 156

156 × (52/169) = X

Then solving for X

X = 156 × (52/169)

X = 48

Therefore

169 : 52 = 156 : 48

Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.

It states that, for a normally distributed random variable:

Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.

The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:

P = 0.5 x 99.7% = 49.85%.

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Answer:

25-13=12 kokichi has 12 left

Step-by-step explanation:

hope it helps sorry if I'm wrong

Answer:

Basic math 25 - 13 =   12

Step-by-step explanation:

Any complex number [tex]z[/tex] can be written in trigonometric form as

[tex]z = |z| e^{i\arg(z)} = |z| \left(\cos(\arg(z)) + i \sin(\arg(z))\right)[/tex]

where [tex]|z|[/tex] is the modulus of [tex]z[/tex] and [tex]\arg(z)[/tex] is its argument, i.e. the angle [tex]z[/tex] makes with the positive real axis in the complex plane.

We have

[tex]|z| = \sqrt{3^2 + \left(\sqrt3\right)^2} = \sqrt{12} = 2\sqrt3[/tex]

and

[tex]\arg(z) = \tan^{-1}\left(\dfrac{\sqrt3}3\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) = \dfrac\pi6[/tex]

Then

[tex]3 + \sqrt3 \, i = \boxed{2\sqrt 3 \left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)}[/tex]

Answer:

4.375

Step-by-step explanation:

First add all the numbers together. [tex]3+2+0+1+9+12+3+5=35[/tex] Second, divide the number you just got by how many numbers there are. [tex]35/8=4.375[/tex] Therefore, the mean is 4.375.