Question 12 of 40 Given right triangle ABC, which of the following statements must be true? Check all that apply. A C A. sin C = cos(90° - C) B. ZA and ZC are complementary C. sinC = cos(A-90°) D. sinC = cos(90° - A)​

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:

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:

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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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]

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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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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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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Answer:

2347 elevated in the cube

Step-by-step explanation:

nashe

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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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:

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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Answer:

  (a)  none

Step-by-step explanation:

A "hole" in the graph of f(x) is located at an x-value where the left limit of the function and the right limit are the same finite value, but the function is undefined at that value of x.

The function f(x) = (x -2)/(x -2) can be reduced to the function f(x) = 1, which is defined everywhere. That reduction occurs when the numerator factor (x-2) cancels the same binomial denominator factor. A graph of the original function will be a straight horizontal line with a "hole" at (2, 1).

The attachment shows a graph.

The given function can be reduced, but the reduced function remains undefined at x=1/2. Not all of the denominator factors are cancelled there. The function is graphed in the second attachment. At x=1/2, there is a vertical asymptote, not a hole.

  [tex]g(x)=\dfrac{(2x-1)(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^3}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}\\\\g(x)=\dfrac{(x+4)^2(x-1)(3x+2)}{3x(x-4)(2x-1)^2}\qquad x\notin \left\{0,\dfrac{1}{2},4\right\}[/tex]

There are no holes in the function's graph.

__

Additional comment

A hole can occur for a variety of reasons. In the graph of a rational function, it will generally be found where numerator and denominator zeros cancel each other completely, and the function can be "reduced" to one that is define at the location of those zeros.

It can also occur in piecewise defined functions, where the pieces are defined on adjoining (half) open intervals. For example:

  [tex]f(x)=\begin{cases}-x&\text{for }x < 0\\x&\text{for }x > 0\end{cases}[/tex]

has a hole at (0, 0).

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 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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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:

The original price of a laptop that is 65% of the sales price is R3 1076923.07692

The sale price of a laptop is R3 700,00,which is only 65% of the original price.

Therefore,

let

x = original price

Hence,

700, 000 = 65% of x

700,000 = 65 / 100 of x

cross multiply

70000000 = 65x

divide both sides by 65

x = 70000000 / 65

x = 1076923.07692

Therefore, the original price of the laptop is R3 1076923.07692

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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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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:

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.

The inverse of the function are respectively; f⁻¹(3) = 2 and f⁻¹(8) = 8.5

The formula to find the equation of this function using two coordinates is;

(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Using the first 2 coordinates, we have;

(y - 1)/(x + 1) = (3 - 1)/(2 + 1)

(y - 1)/(x + 1) = 2/3

3y - 3 = 2x + 2

3y = 2x + 5

y = ¹/₃(2x + 5)

Thus, the inverse is;

f⁻¹(x) = (3x - 5)/2

Thus;

f⁻¹(3) = (3*3 - 5)/2

f⁻¹(3) = 2

Similarly;

f⁻¹(x) = (3x - 5)/2

Thus;

f⁻¹(8) = (3*8 - 5)/2

f⁻¹(8) = 8.5

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Answer:

2MN=RA+TP

13×2=x+18

26=x+18

26-18=x

8=x

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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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:

37,000

Step-by-step explanation:

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

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:

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 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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