what is the correct postulate to prove these two triangles congruent?

A. SAS
B. ASA
C. SSS
D. AAS
E. HL

Answer: Nice

Step-by-step explanation:

Answer:

3*3*3 or 3^3

Step-by-step explanation:

27/3=9/3=3

so 3*3*3 or 3^3

Using the concepts of probability, we got that 0.4286 is the probability  that the battery life for an iPad Mini will be 10 hours or less  which is about 42.86%.

From the given information;

Let  X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B

where A and B  are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12

[tex]f_X(x)=[/tex](1/3.5)8.5<x<12

The  probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

F(10)=[tex](x-A)/(B-A)[/tex]

F(10)=(10-8.5)/(12-8.5)

F(10)=1.5/3.5

F(10)=0.4286

Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286

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(Complete question)

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

If LR equals 12 and PR equals 4, then: LP = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.

The Segment Addition Postulate states that when there are two endpoints on a line segment (L) and (C), a third point (P) would lie on the line segment (LR), if and only if the magnitude of the distances between the endpoints satisfy the requirements of this equation LP + PR = LR.

This ultimately implies that, the Segment Addition Postulate is only applicable on a line segment that contains three collinear points.

By applying the Segment Addition Postulate to the given endpoints, the value of LP is given by:

LP + PR = LR

LP = LR - PR

Substituting the given parameters into the formula, we have;

LP = 12 - 4

LP = 8.

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Complete Question:

Larissa is standing at point L. Pj is standing at point P and Raelynn is standing at points are on segment LR as shown in the figure If LR equals 12 and PR equals 4, find LP. explain

LP = 16 because 12 + 4 = 16 according to the addition property of equality.

LP = 8 because 12 - 4 = 8 according to the subtraction property of equality.

PR = 16 because LR + LP = PR according to the Segment Addition Postulate, and 12 + 4 = 16 using substitution.

PR = 8 because LP + PR = LR according to the Segment Addition Postulate, and 8 + 4 = 12 using substitution.

Answer: Lp = 8

Step-by-step explanation:

Got it right

The length (in cm) of the hypotenuse is 17 cm.

According to Pythagoras' theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

H² = P² + B²

Let the hypotenuse = H

Shortest side = B

Third side = P

So, according to the question

H = 2B +1    ..... (1)

P = 2B -1     ..... (2)

Use Pythagoras' theorem,

H² = P² + B²

(2B+1)² = (2B-1)² + B²

4B² + 1 + 4B = 4B² + 1 - 4B + B²

4B = - 4B +B²

B² =-8B

B = - 8

But the length cannot be negative, so B = 8 cm

The length of the shortest side = 8 cm

So the hypotenuse will be

H = 2B + 1

= 2(8) + 1

= 17 cm

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This relationship is not a function because more than one amount of plant food remains each day.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that, Ryan did an experiment by observing the effects of plant food and the growth of the sprouting bean plant. He made a note of the height of the bean plant and the amount of food remaining in the container for the plant after feeding each day.

Thus, he observed that the plant food in the container decreases by an equal amount every day as the bean plant grew. Thus, this states that it is not a  function between the two, as there are more than one plant food remaining each day for the plant.

Hence, This relationship is not a function because more than one amount of plant food remains each day.

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Answer:

16.97

Step-by-step explanation:

The complement of set A is { 3, 6, 13, 14, 17, 19}

The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).

U = {2,3,6,9,10,13,14,17,19}, A =  {2,9,10}

set A complement are all the elements in the Universal set U not contained in set A. Those elements are in set A' =  { 3, 6, 13, 14, 17, 19}

In conclusion the complement of set A is  { 3, 6, 13, 14, 17, 19}

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The rule that represents the transformation is g(x) = -6x⁵ + 3x³ + 3x² + 11

The equation of the function is given as

f(x) = 2x⁵ - x³ + x² + 4

The sequence of transformations is given as follows:

When the above transformations are combined, we have:

g(x) = 3f(-x) - 1

So, we have

3f(-x) - 1 = 3[2(-x)⁵ - (-x)³ + (-x)² + 4] - 1

This gives

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 12 - 1

Expand

3f(-x) - 1 = -6x⁵ + 3x³ + 3x² + 11

So, we have

g(x) = -6x⁵ + 3x³ + 3x² + 11

Hence, the function is g(x) = -6x⁵ + 3x³ + 3x² + 11

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a. Timothy is correct regarding the dilation, considering the vertices of each triangle.

b. The two triangles are similar, as they have congruent angle measures.

A dilation occurs when each of the vertices of a polygon is multiplied by a constant, which is called scale factor.

The effects of a dilation are given as follows:

The vertices of each triangle in this problem are given as follows:

The scale factor is obtained by the division of any of the equivalent factors, hence:

k = 4.5/3 = 1.5.

Confirming that Timothy's statement regarding the scale factor of the dilation is correct.

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The absolute maximum value is f(0,±2) = 4 and the absolute minimum value is f(1,0) = -1.

The given function is  F(x,y) = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]   → 1

D is the closed triangular region with the vertices (0,0), (0,2) and (0,-2).

Differentiate 1 partially with respect to x:

df/dx =  [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]

[tex]f^{'}[/tex](x) = 2x - 2

Differentiate 1 partially with respect to y:

df/dy = [tex]x^{2}[/tex] + [tex]y^{2}[/tex] - [tex]2x[/tex]

[tex]f^{'}[/tex](y)  = 2y

Consider [tex]f^{'}[/tex](x) = 0 and [tex]f^{'}[/tex](y) = 0 to find the critical points.

[tex]f^{'}[/tex](x) ⇒ 2x -2 =0

x = 1

[tex]f^{'}[/tex](y) ⇒ 2y

y = 0

Thus, the critical point is (x,y) = (1,0).

Calculate the values of f(x,y) at (0,0), (0,2), (0,-2) and (1,0).

At (x,y) = (0,0)

f(0,0) ⇒ 0 + 0 - 0 = 0

At (x,y) = (0,2)

f(0,2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (0,-2)

f(0,-2) ⇒ 0 + 4 - 0 = 4

At (x,y) = (1,0)

f(1,0) ⇒ 1 + 0 - 2 = -1

Therefore, the absolute maximum is f(0,±2) = 4 and the absolute minimum is f(1,0) = -1.

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The first five terms of the arithmetic sequence with the formula a(n) = a(n - 1) - 5 is; -5, -10, -15. -20, -25

The general formula for an arithmetic sequence is;

aₙ = a + (n - 1)d

where;

a is first term

d is common difference

aₙ is the nth term of the sequence

Now we are given the formula for the nth term of a sequence as;

a(n) = a(n - 1) - 5

Thus;

1) First term is when n = 1;

a(1) = a(1 - 1) - 5

a(1) = -5

2) Second term is when n = 2;

a(2) = -5(2 - 1) - 5

a(2) = -5 - 5

a(2) = -10

3) Third term is when n = 3;

a(3) = -5(3 - 1) - 5

a(3) = -15

4) Fourth term is when n = 4;

a(4) = -5(4 - 1) - 5

a(4) = -20

5) Fifth term is when n = 5;

a(5) = -5(5 - 1) - 5

a(5) = -25

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Complete question is;

Write the first five terms sequence defined by a(n) = a(n - 1) - 5

If 700% of a number is 1540, then the number is 220

The given percentage = 700%

The percentage of a number is defined as the ratio that can be expressed as the fraction of 100.

Consider the number as x

Here the 700% of the number is 1540

Then the equation will become

x × 700% = 1540

Solve the equation and find the value of x

x × (700/100) = 1540

Divide the terms first

x × 7 = 1540

Move the 7 to the right hand side of the equation

x = 1540/7

Divide the terms

x = 220

Hence, if 700% of a number is 1540, then the number is 220

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With a net change of +0.72 yesterday's closing price was 19.81 and stock dividend yield for yesterday's closing price is 7.2%.

How to calculate the Dividend Yield?

To calculate dividend yield, all you have to do is divide the annual dividends paid per share by the price per share.

Dividend Yield = Annual Dividends Paid Per Share / Price Per Share

According to the given question:

Net change = today's price - yesterday's price

0.72 = 19.09 - yesterday's price

∴ Yesterday's price = 19.81

Stock dividend yield

= (1.43/19.81) x 100

= 7.2%

Therefore the stock yield of yesterday's closing price is 7.2%

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The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The points are given below.

(1, −4) and (5, −1)

The equation of the line that passes through (1, −4) and (5, −1) will be given as,

(y + 4) = [(−1 + 4) / (5 − 1)](x − 1)

y + 4 = (3/4)x − 3/4

y = (3/4)x + 13/4

The equation of the line in the slope-intercept form will be y = (3/4)x + 13/4.

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The probability that b will occur given that a has occurred is 2/5 as the probability of a is 0.45 and the probability of the intersection of a and b is 0.15.

It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 12. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

P(A)=0.45

P(A∩B)=0.15

P(A∪B)=1

P(B)=1-(0.45+0.15)

=1-0.60

=0.4

=2/5

With a probability of 0.45 and a and b's intersection having a 0.15 probability each, the likelihood that b will happen given that a has happened is 2/5.

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Answer:

6.4

Step-by-step explanation:

I guessed and got it right.

The values of y respective to x values are when x = -2 then y = 12 when x = 0 then y = 2 when x = 2 then y = -8, & when x = 4 then y = -18.

What is a function rule?

The equation-based relationship between the dependent and independent variables is known as a function rule. In simple words, a function is an association between inputs in which each input is connected to precisely one output.

Given,  y = -5x + 2

when x= -2, y = (-5)* (-2) + 2 = 10 + 2 = 12, y = 12

when x= 0, y = (-5)* (0) + 2 = 0 + 2 = 2, y = 2

when x= 2, y = (-5)* (2) + 2 = -10 + 2 = -8, y = -8

when x= 4, y = (-5)* (4) + 2 = -20 + 2 = -18, y = -18

Hence, these are the required values of y to the respective input value of x.

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Answer:

(y + 6)(y + 13) = y² + 19y + 78

Step-by-step explanation:

[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]

In linear equation, 27/2 pancakes are in the box .

What in mathematics is a linear equation?

Number of b pancake mix  to be need  =  1½ cups

Number of box has pancake mix   = 9 cups

Therefore, in order to get the total number of  batches of pancakes  needed for the batches will be calculated thus

             =  1½  * 9

             = 3/2 * 9

             = 27/2

therefore 27/2 pancakes are in the box .

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Answer: always, always

Step-by-step explanation:

Every circle is similar to every other circle.

The solution of  | x | +5 ≤ 1 is  option C, All values are solutions

We need to find the solution of  | x | +5 ≤ 1

Upon removing the modulus function, the term presnet within it can be either negative or positive

considering it as postive

| x | +5 ≤ 1

x + 5 ≤ 1

x ≤ 1 - 5

x ≤ -4

considering it as negative

| x | +5 ≤ 1

-x + 5 ≤ 1

-x ≤ 1 - 5

-x ≤ -4

x ≥ -4

Therefore, the solution of  | x | +5 ≤ 1 is  All values are solutions

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He should invest $86.29 in the account now, which has a 7% interest compounded monthly.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:

B = P(1 + r/n)^t

where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months

Based on the given information, P is the unknown and

B = $5000

t = 5 years = 60 months

r = 7% = 0.07

n = 1

Plug in the values and solve for P or the amount that should be invested today.

B = P(1 + r/n)^t

$5000 = P(1 + 0.07/1)^60

$5000 = P(1.07)^60

P = $5000/(1.07)^60

P = $86.29

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Answer:

-40

Step-by-step explanation:

The Concept here is Complex Numbers

where [tex]\sqrt{-1}=i \ and \ i^{2} = -1[/tex]

Then [tex]\sqrt{-4}=\sqrt{4i^{2} } =\sqrt{(2i)^{2} } =2i[/tex]

Also [tex]\sqrt{-25}=\sqrt{25i^{2} } =\sqrt{(5i)^{2} } =5i[/tex]

Then [tex](\sqrt{-4} )(4\sqrt{-25} )=(2i)(4*5i)=40i^{2} =40*-1=-40[/tex]

Glad to Help:)

Answer:h

Step-by-step explanation:

ihlug

The equation that can be used to find the amount of electricity Jeremy used per day during the month of December is 3.8KWH per day and Jeremy used 3.8KWH per day electricity in the month of December.

Electricity Jeremy used in November = 6 kilowatt hours (KWH)

Total electricity used in the holiday season = 120KWH

He took the decorations down on December 30

Amount of electricity Jeremy used per day during the month of December =

(Total electricity used in the holiday season - Electricity Jeremy used in November) / 30 days

= (120KWH - 6KWH) / 30

= 114KWH / 30

= 3.8KWH per day

In conclusion, the amount of electricity Jeremy used per day in December is 3.8KWH per day.

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The percentage of men who didn't expect to meet the height requirements be 96.29%

Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.

Find the percentage of men who meet the height requirements.

z(64) = (64-69)/2.8 = 1.7857

z(78) = (78-69)/2.8 = 3.2143

P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%

So, the percentage of men who meet the height requirements be 3.71%

Now, the percentage men who didn't expect to meet the height requirements be

100 - 3.71 = 96.29%

Hence, the percentage of men who didn't expect to meet the height requirements be

96.29%

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Answer: 66.66.....% (6 recurring) / 66.67%

Step-by-step explanation: To get the percent form of this, you'll need to turn this into a fraction, which would be 18/27, then you can simplify it to 2/3 and convert it to a percent which would be 66.66..... .

The confidence interval for the population mean with 99% confidence interval is (6.90;8.50).

A confidence interval is a set of values that, with a particular level of certainty, includes a population value. When a population mean is between an upper and lower interval, it is frequently stated as a percentage.

The population mean is mean [tex]\bar{x}[/tex]=7.3.

The sample's standard deviation is 2. 9

Number of samples: 42

The range of possibilities for the mean, [tex]\bar{x}[/tex]

The confidence interval for the mean is

[tex]\bar{x}[/tex] ± (σ/√n)

To calculate the critical value, we must first determine the degrees of freedom, which are given by:

df=n-1

df=42-1

df=41.

Since the confidence level is 0.99 or 99%, the values of and can be used to calculate the critical value using Excel, a calculator, or a table is 2.701

7.3-2.701(2.9/√42)=6.9013

7.3+2.701(2.9/√42)=8.5086

The 99% confidence interval in this instance would therefore be provided by (6.90;8.50).

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Answer:

The least coomon denominator is 12, so

9/12 and 10/12