determine if a-1 c = c a–1 given

The required linear function y = -x + 2.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The equation for the slope, m, of a line is:

m = y₁- y₀ / x₁ - x₀                         {equation 1}

The equation f(0) = 2 tells us that x₀ = 2and y₀ = 0,

substitute this into equation [1].

m = y₁- (0) / x₁ - 2                         {equation 2}

The equation f(3) = -1 tells us that x₁ = -1 and y₁= 3,

substitute this into equation [2].

m = 3/-3

m = -1

Substitute m to the equation y = mx + b,

y = -x + b

Now, substitute the value of x = 2 and y = 0

b = 2.

Now the linear function,

y = -x + 2

Therefore the linear function y = -x + 2.

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The missing statements and reasons in the proof are:

R3: Alternate Interior ∠s theorem

S4: Reflexive property

R5: ASA

A proof involves statements that are stated on one column, then followed by reasons that justify the statements stated, on another column.

The missing statements and reasons in the given proof above are explained below:

Statement                                                    Reason                                            

1. Parallelogram ABCD with diagonal AC  1. Given

2. AB║CD and AD║BC                               2. Def. of parallelogram

3. ∠1 ≅ ∠2 and ∠3 ≅ ∠4                             3. Alternate Interior ∠s theorem

4. AC ≅ AC                                                  4. Reflexive property

5. ΔABC ≅ ΔCDA                                       5. ASA

6. AB ≅ CD and AD ≅ BC                          6. CPCTC

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Answer:

1/4 as a percent is 25%

25% as a decimal is .25

Step-by-step explanation:

1/4 is one quarter, .25

25%, move the decimal to the left twice

25----> 2.5------> .25

Answer:

a. w = -18 x = -10 y = -2 z = 10

b. x and z are opposites because they are the opposite value of each other.

c. the integers w, x, y are less than zero because they are negative integers.

Step-by-step explanation:

a. because they are counting by twos it has to be the even numbers for both sides of the number line

b. because they are the same number just one is negative while the other isn't making them opposites.

c. because every number besides ten are negative making them below the value of zero.

The total time ran by Katie on Tuesday and Wednesday together is given by the equation A = 16.23 minutes

where A is the total time

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total time ran by Katie on Tuesday and Wednesday be = A

Now , the equation will be

The time required by Katie to run a mile on Tuesday = 8.34 minutes

The time required by Katie to run a mile on Wednesday = 7.89 minutes

So ,

Total time ran by Katie on Tuesday and Wednesday A = time required by Katie to run a mile on Tuesday + time required by Katie to run a mile on Wednesday

Substituting the values in the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 8.34 minutes + 7.89 minutes

On simplifying the equation , we get

Total time ran by Katie on Tuesday and Wednesday A = 16.23 minutes

Therefore , the value of A is 16.23 minutes

Hence , The total time ran by Katie on Tuesday and Wednesday together is A = 16.23 minutes

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Answer:

y = - 8x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 8 and c = 5 , then

y = - 8x + 5 ← equation of line

The indicated critical value of Z for given significance level, α = 0.04 is 1.75..

The critical Z-value is the point at which the area below the standard normal distribution is cut off. A critical value of z can indicate the probability that a particular variable has. If the absolute value of the test statistic is greater than the critical value, statistical significance is declared and the null hypothesis is rejected. The critical values of Z and t are approximately the same. The critical value test is:

Steps to determine the critical value:

We have given that,

α = 0.04 then α/2 = 0.02

then 1 - 0.02 = 0.98

Using the Z-table,

p-value = 1.7911 4444 ~ 1.75

Hence the critical values z, 0.04, is 1.75

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Answer:

x= -2

y= 0

Step-by-step explanation:

isolate y in second equation

-3x=6-y

 +y.   +y

-3x+y=6

+3x.    +3x

y=3x+6

now we know y is the same as 3x+6 we can put it into the first equation where y is

-4x+2(3x+6)=8

-4x+6x+12=8

2x+12=8

   -12.  -12

2x= -4

/2.  /2

x= -2

now fill in x to find y

-3(-2)=6-y

6=6-y

-6. -6

0= -y

/-1. /-1

0 =y

hopes this helps please mark brainliest

The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

Given that,

a to b is translated by the vector (4/-3)

We have to find what is the vector converting b to a.

We know that,

Quantities with both magnitude and direction are referred to as vectors. Additionally, it refers to the type of the quantity.

Here,

We have a vector,

ab=(4/-3)

Its direction will be reversed to translate the vector in the other way,

For

ba=-(4/-3)

ba=4/3

Therefore, The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).

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Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

Equations are logical statements in mathematics with two algebraic expressions on either side of the equals (=) symbol. The expressions on the left and right are demonstrated to be equal in relation to one another. All mathematical equations start with LHS = RHS (left hand side = right hand side). To find the value of an unknown variable, or unknown quantity, you can solve equations. If the statement does not contain an "equal to" sign, it is not an equation. As an expression, it will be considered. An explanation of the differences between an expression and an equation will be provided later in this essay.

Here,

P=850+5x

so the band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.

So new equation formed is

50x-P=5000

50x-(850+5x)=5000

50x-5x-850=5000

45x=5850

x=5850/45

x=130

Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

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The computed t-value of -1.708 for a two-tailed hypothesis test of the difference of two means with sample size of 26 would yield a p-value of 0.10.

This statement is a false statement.

To make inferences about a population parameter or population probability distribution, a statistical process known as hypothesis testing analyzes data from a sample. First, a hazy assumption about the parameter or distribution is made.

The null hypothesis is that 50% is true, while the alternative hypothesis is that 50% is not accurate, for instance, if someone wants to test whether a penny has an exact 50% chance of landing on heads.

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If Sebastian has x nickels and y pennies. He has at least 20 coins worth at most $0.65 combined then he has 27 nickels.

Two or more expressions with an Equal sign is called as Equation.

Given,

x represents nickels and y represents dimes.

x+y=20...(1)

0.05x+0.10y=0.65...(2)

From equation 1,

y=20-x

0.05x+0.10y=0.65

0.05x+0.10(20-x)=0.65

0.05x+2-0.10x=0.65

2-0.05x=0.65

Subtract 2 from both sides

-0.05x=0.65-2

-0.05x=-1.35

Divide both sides by -0.05

x=27

x+y=20

27+y=20

y=20-27

y=-7

Hence the number of nickels are 27 and dimes are minus seven.

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Answer: x can equal 9 or -1

Step-by-step explanation:

Total Total revenues will exceed = 8782.01

What is Total Revenue?

Total revenue is the overall sum of money received by a business through the sale of its products and services. Based on demand and price, it measures how successfully a company is generating revenue from its main operations.

Let x - normal (101.15 ,12.15)

where µ = 101.15

σ = 12.15

Mean for 85 customers

µ = 85 * 101.15 =8597.75

standard deviation for 85 customers

σ = [tex]\sqrt{85}[/tex] * 12.15 = 112.017

P ( x >x₁ ) = 0.05

P ( x-µ/ σ > x₁-8597.75/112.017) = 0.05

P (Z >Z₁) = 0.05

Where

Z₁ = x- 8597.75/112.017

Z₁ = 1.645

Then x = 112.017 *1.645 +8597.75

x = 8782.01

Total total revenues will exceed = 8782.01

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The simplification of [tex](16)^{1/2}[/tex] is 4.

To simplify [tex](16)^{1/2}[/tex] , you can use the property of exponents that says that [tex]{(a^b)}^c = a^{(b*c)[/tex]. Therefore, [tex](16)^{1/2}[/tex] can be rewritten as [tex]16^{(1/2)}[/tex].

The square root of 16 is 4, so [tex]16^{(1/2)}[/tex] = 4. Therefore, [tex](16)^{1/2}[/tex] = 4.

You can also simplify [tex](16)^{1/2}[/tex]  by writing 16 as a product of its prime factors: 16 = [tex]2^4[/tex]. The square root of 16 is the same as the square root of 2^4[tex]2^4[/tex], which is [tex]2^{(4/2) = 2^2} = 4[/tex]. Therefore, [tex](16)^{1/2}[/tex] = 4.

Simplification is a process of making something simpler or easier to understand. This can be done by reducing the complexity of a system, removing unnecessary components, or making the language more concise.

Simplification complexity is the process of reducing the complexity of a problem, system, or process. This can involve breaking down a complex problem into smaller, more manageable parts, or reorganizing the system or process to make it simpler and easier to understand and use. Simplifying complexity can make a system or process more efficient and easier to maintain.

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The answer is true.

When a child presents with commonly occurring phonological patterns such as fronting, cluster reduction, stopping, and final consonant deletion, the minimal pairs approach readily comes to mind as an option. Not only are there a lot of meaningful minimal pair contrasts that you can use as part of therapy, but these developmental patterns were the ones that the majority of researchers targeted in their studies. We’ve established what developmental phonological error patterns are, but some children present with unusual or non-developmental patterns. Studies have used this approach with patterns such as backing and medial consonant deletion. Dodd et al., (2003) actually recommend prioritising those non-developmental error patterns over developmental ones.

It's true due to one of the reasons why it is important to learn the minimal pair's approach is that it can be used with a large range of severity, from mild-severe phonological impairments. If the child has a severe-profound phonological impairment, Williams (2000a) suggests that students are best suited to another approach.

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Answer: Linear

Step-by-step explanation:

The value of a in the equation is 32/81

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

log2 ab = 5 and log3 b = 4

Rewrite the above equations properly

So, we have the following representations

log₂ ab = 5 and log₃ b = 4

Apply the exponent law of logarithm

This gives

ab = 2⁵ and b = 3⁴

Divide both equations

So, we have the following representation

ab/b = 2⁵/3⁴

Evaluate the quotient

a = 32/81

Hence, the value of a is 32/81

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Therefore, the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on process.

Probability theory examines numerical illustrations of the probability that an event will happen or that a statement is true. An event's probability is expressed as a number between 0 and 1, with 1 generally denoting certainty and 0 generally denoting impossibility.

Here,

f(x,y) =[tex]xe^{-x(1+y)}[/tex]

Took the double integral of the equation above, first the integral with respect to y (from 0 to infinity) and then with respect to x (from 5 to infinity).

therefore the integration,

[tex]\int\limits^ {infinity}_0{xe^{-x(1+y)} } \, dx[/tex]

[tex]\left \{ {{y=infinity} \atop {x=0}} \right. \frac{-x}{y+1} e^{-x(y+1)} + \frac{1}{y+1} \int\limits^{infinity} _0{ e^{-x(y+1)} \, dx[/tex]

[tex]=\frac{1}{(y+1)^2}[/tex]

[tex]fX(x)[/tex] is easier with:fX(x) =[tex]\int\limits^{infinity}_0 {x}e^{-(x(y+1))} \, dy[/tex]=[tex]xe^{-x} \int\limits^{infinity}_0 x {e^{-xy} } \, dy=e^{-x}[/tex]

We get

We used u substitution to end up with    [tex]e^{-x(1+y)}[/tex] which is needed to evaluate from 0 to infinity, which left me with [tex]e^{-x}[/tex]

Then the integral with respect to x from 5 to infinity which left with an answer of [tex]e^{-5}[/tex]

So the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on my process.

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Answer:

21

Step-by-step explanation:

If it is in the center than DC is 21 and CM is 21

42÷ 2

Answer:

Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

Step-by-step explanation:

To determine at which point Plan A is a better deal than Plan B, we need to compare the total cost of each plan for a given amount of data usage.

The total cost of Plan A for 3GB of data is $52 per month. For every additional GB of data, the cost is $3, so if we use x GB of data beyond the included 3GB, the total cost of Plan A would be $52 + $3x.

The total cost of Plan B for 5GB of data is $65 per month. For every additional GB of data, the cost is $1.75, so if we use x GB of data beyond the included 5GB, the total cost of Plan B would be $65 + $1.75x.

To determine at which point the total cost of Plan A is less than the total cost of Plan B, we can set the two equations equal to each other and solve for x:

$52 + $3x = $65 + $1.75x

$1.25x = $13

x = $13 / $1.25

x = 10.4

Therefore, Plan A is a better deal than Plan B when you use more than 10.4 GB of data in a month. For any usage lower than that, Plan B would be the cheaper option.

The simplest form in fraction will be 20666667/1000000 that can be find out using decimal and fraction relation.

How to convert decimal to fraction?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value.

For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.

Steps :
1. Write down the decimal divided by 1, like this: decimal/1

2. Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

3. Reduce the fraction.

In given que 2.0666667 ,

7 decimal points are here.

so, equation will be 20666667/10^7

i.e. 20666667/10000000.

As both no. is indivisible to each other

So this is the simplest from.

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The value of the test statistic = 2.06

What is Statistic ?

The science of statistics focuses on creating and researching strategies for gathering, analyzing, interpreting, and presenting empirical data.

What is normally distribution?

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme.

Given,

weights of sugar bags are normally distributed.

Sample mean=5.2

sample standard deviation = 0.2366

Test statistic

t = x(bar) -µ/σ [tex]\sqrt{n}[/tex]

= 5.2-5/0.2366/[tex]\sqrt{6}[/tex]

= 2.0705

The test statistic's value is 2.06

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We need to select different combinations of friends for a week and include every friend at least once. The possible number of ways is 72.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The formula for combination is as follows:

[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]

Number of for first 5 days = C(7,3)+C(6,3)+C(5,3)+C(4,3)+C(3,3)

=70

2 friends are remaining for last two days and we can assign them in any group of 3.

Total number of ways = 70 +2

=72

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Using Percentage concept, Kareem had $7939 at the end of last year

Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

In this problem, we could attempt to use reverse of simple interest formula, however, we can directly find 6.6% of 8500 and subtract it from the principal.

This is calculated as;

6.6/100 = x / 8500

0.066 = x / 8500

x = 8500 * 0.06

x = 561

The investment decreased by $561

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Answer:

Angle = 71.08°

Step-by-step explanation:

Since we're given all of the sides, we're able to use any one of the trigonometric proportions.  I can go through all three to show how they all yield the same answer.

The sine proportion is [tex]\frac{opposite}{hypotenuse}[/tex]

Using the ? angle as our reference angle (which we can refer to as "a" for the sake of the math), the side measuring 70 units is the opposite side and the side measuring 74 units is the hypotenuse:

[tex]sin (a)=\frac{70}{74}\\ sin^{-1}=\frac{70}{74}=a = 71.07535558=71.08[/tex]

The cosine proportion is [tex]\frac{adjacent}{hypotenuse}[/tex]

Using a as our reference angle still, the side measuring 24 units is the adjacent side and the side measuring 74 units is the hypotenuse:

[tex]cos (a)=\frac{24}{74}\\ cos^-^1=\frac{24}{74}=71.07535558=71.08[/tex]

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex]

Using a as our reference angle still, the side measuring 70 units is the opposite side and the side measuring 24 units is the adjacent side:

[tex]tan(a)=\frac{70}{24}\\ tan^-^1=\frac{70}{24}=a=71.07535558=71.08[/tex]

Again, just use the steps for either one of the three trigonometric proportions

After 1 week Luca and his friend  will have passed the same number of scales and the number of scales = 11

In this question, we have been given a situation.

we need to write a system of equations to describe the situation.

Let x be the number of weeks and y be the number scales.

luca has passed 9 scales, whereas his friend warren has passed 8 of them. going forward, luca has committed to passing 2 scales per week, and warren has committed to passing 3 per week.

So, we get a system of equations as:

y = 2x + 9

y =  3x + 8

We need to find the amount of time(weeks) it would take that the two friends will have passed the same number of scales.

Also, we need to find the number of scales.

When the two friends will have passed the same number of scales,

2x + 9 =  3x + 8

3x - 2x = 9 - 8

x = 1

After 1 week the two friends will have passed the same number of scales.

And  the number of scales would be,

y = 11

Therefore, after 1 week the two friends will have passed the same number of scales.

And  the number of scales would be 11

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The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

A box of cookies contains 12 chocolate-chip cookies, 6 peanut-butter cookies, and 6 sugar cookies.

Total number of cookies = 12 + 6 + 6 = 12 + 12 = 24

Now,

The probability of randomly selecting a chocolate-chip cookie.

= 12/24

= 1/2

The remaining chocolate.

= 24 - 1

= 23

Now,

The probability of randomly selecting a sugar cookie.

= 6/23

Now,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie

= 1/2 X 6/23

= 3/23

Thus,

The probability of randomly selecting a chocolate-chip cookie, eating it, and then randomly selecting a sugar cookie is 3/23.

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The probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

Given that,

Poisson (2.)

Let x = The number of pairs of twins

That will be born in the Country in 2015

To find : Calculate the probability that exactly 18 pairs of twins will be born in the country in 2015.

We know that

Here,

The probability mass function (pmt of x) is given by

P ( X = x ) = e⁻²¹ x 21ˣ / x!

where x = 0,1,2 , . . .

Substitute x = 18 in above equation,

Then we get,

P ( x = 18 ) =  e⁻²¹ x 21¹⁸ / 18!

P( x = 18 ) = 0.07472

P ( x = 18 ) = 0.07472

Therefore, the probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

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Answer: p = 3

Step-by-step explanation:

7−4p−(−5)

7-4p + 5

Because negative one times negative five equal positive 5

12 - 4p

To solve further

-4p = -12

p = 3