2x - 3 y = -1 y = x - 1 Solve each system of equations. Show all your work.

Null hypothesis: H₀ : μ = 55

Alternative hypothesis: H₁: μ [tex]\neq[/tex] 55

Given,

Rating = 55 mpg

For a two-tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis. In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.

the claim is the jeep has a 55 mpg rating and we want to test whether the rating is correct or incorrect. So, it is a two-tailed hypothesis because the rating can be less than or more than 55 mpg.

Therefore, H₀ : μ = 55

H₁: μ [tex]\neq[/tex] 55

These are the required null and alternative hypotheses.

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The quadratic equation 3x² + 2x - 5 = 0 is solved to give x = 1 and -5/3

From the information given, we have the quadratic equation as;

3x² + 2x - 5 = 0

Using the factorization method of solving quadratic equation, we have to take the following steps

Multiply the coefficient of x² by the constant -5

Find the pair factors of the product of their multiplication that sums up to 2

The pair factors are +5 and -3

Substitute the values

3x² + 5x - 3x - 5 = 0

Add parentheses

(3x² + 5x) - (3x - 5) =0

factorize the values

x(3x +5) - 1(3x + 5) = 0

The values of x are;

x= 1 and x = -5/3

Thus, the values are 1 and -5/3

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The complete question:

Solve the quadratic equation 3x2 + 2x - 5 = 0 using factorization method

The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric equation is given below.

sin 2x − √3/2 = 0

Simplify the equation, then we have

sin 2x − √3/2 = 0

sin 2x = √3/2

sin 2x = sin 60°, sin 120°

2x = 60°, 120°, 420°, 480°

x = 30°, 60°, 210°, 240°

The solution of the trigonometric function sin 2x − √3/2 = 0 will be 30°, 60°, 210°, and 240°.

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If Nick spends $4.89 and Riley spends 3 times as much as Nick and Clay spends $12.73 more than Riley , then the total amount spent by Clay is $27.4 .

The amount Nick spends to buy School Supplies is = $4.89 ,

the amount spent by Riley is 3 times of amount spent by Nick ,

that means , Riley spent = 3 × 4.89 = $14.67 ,

the amount spent by Clay is $12.73 more than the amount spent by Riley , which means ;

Clay spent is = $14.67 + $12.73 = $27.4 .

Therefore , Clay spent $27.4 to buy school supplies .

The given question is incomplete , the complete question is

Some friends go to the store to buy school supplies. Nick spends $4.89  Riley spends 3 times as much as Nick. Clay spends $12.73 more than Riley. How much did Clay spend ?

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log(x) = 4 can be restated as an exponential statement: 10^4 = x

x = 10000

Answer:

It is a line that continually approaches a given curve but does not meet it at any finite distance.

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

An asymptote is a line that continually approaches a given curve but does not meet it at any finite distance.

For example, for the rational function [tex]f(x)=\frac{1}{x}[/tex], there's a horizontal asymptote at y=0 because as x approaches infinity, y gets increasingly closer to 0.

Same goes for the vertical asymptote of x=0 where as y approaches infinity, x gets increasingly closer to 0.

The percent of increase from 45 to 72 is 60%.

Using this formula to find the percent of increase

Percent of increase= End value - Start value /Start value  

Where:

End value = 72

Start value = 45

Let plug the formula

Percent of increase =(72 - 45) /45

Percent of increase =27 /45  × 100

Percent of increase = 60%

Therefore we can conclude that the percent of increase is 60%.

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By polar form properties, the product of complex numbers (5 · cos 225° + i 5 · sin 225°) and (2 · cos 135° + i r₂ · sin 135°).

In this question we find the case of the product of two complex numbers in rectangular form but including features of polar form (magnitude, direction). Then, we have the following situation:

(r₁ · cos θ₁ + i r₁ · sin θ₁) · (r₂ · cos θ₂ + i r₂ · sin θ₂)

Result can be found easily by transforming the expression into polar form:

(r₁, θ₁) · (r₂, θ₂) = (r₁ · r₂, θ₁ + θ₂)

[r₁ · r₂ · cos (θ₁ + θ₂) + i r₁ · r₂ · sin (θ₁ + θ₂)]

If we know that r₁ = 5, r₂ = 2, θ₁ = 225° and θ₂ = 135°, then the product of the complex number is:

10 · [cos 360° + i sin 360°]

10 · (1 + i 0)

10

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The domain of the relation is 0 ≤ x ≤ 4 and the range of the relation is all real numbers  (-∞, ∞)

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

We know that Domain : the set of possible x-values (the "input" values)

And also, we know that Range : the set of y-values (the "output" values)

In the given graph we have attached below, the domain of the relation is 0 ≤ x ≤ 4

The range = all real numbers (-∞, ∞)

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Answer: CP = 1418.34

Step-by-step explanation: We've to calculate the cost price (CP)

Selling price (SP) = 1546,  Profit% = 9%

According to the formula,

Profit%= [tex]\frac{SP-CP}{CP} * 100[/tex]

9 = [tex]\frac{1546-CP}{CP} *100[/tex]

9*CP = (1546-CP)*100

109CP = 154600

CP = 154600/109

CP= 1418.34

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If there are multiple coins in a row we call them a streak , the expected number of streaks here are 224

Attempt: I interpreted the number of streaks as the number of switch between either H to T or T to H in the sequence + 1.

The problem has a markov chain structure and so we can  obtain the following equations, given S(n)

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.

number of strike in sequence with n coins:

                 S(n|H) = 0.2s(n-1) + 0.8 (1+s(n-1))

                  S(n|T) = 0.8s(n-1) + 0.2(1+s(n-1))

This implies S(n) = S(n|T)p(T) + S(n|H)p(H)

                           = S(n-1) + 8/25

Therefore,  E[S(700)] = 224.

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It will take 2/3 minutes to run 1 mile.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Amal can run 1/8 mile in 1/12 minutes.

If Amal can maintain that pace,

it will take him to run 1 mile,

= 1/12 ÷ 1/8

= 1/12 x 8/1

= 8/12

= 2/3 minutes.

Therefore, the required time is  2/3 minutes.

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Dan should leave his house at least on 08.33 am.

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

We have,

Dan has to get to work at 10.30 am.

There is a 20 minute walk from the bus stop in Coventry to work.

Dan should arrive at the bus stop in Coventry at 10.10 am.

The latest time of the bus that reaches Coventry closest to the time that Dan should reach at the bus stop in Coventry is 10.06.

The bus which reaches at Coventry at 10.06 depart from Birmingham at 08.38.

There is a 5 minutes to walk from his house to Birmingham bus stop.

Dan should leave the house at 08.33 am.

The latest time that Dan should leave the house is 08.33 am.

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Answer: 26 units

Step-by-step explanation:

Let's label the left side as side a, the bottom as side b, and the hypotenuse (the diagonal side) as side c.

As you can see, side a is 8 units, and side b is 7 units. To calculate side c, you need to plug both a and b in to the Pythagoras' theorem, which states that a² + b² = c².

> 8² + 7² = c²

> 64 + 49 = c²

> 113 = c²

> c = 10.63 which would round up to 11.

Now adding up all the sides together, a + b + c = 7 + 8 + 11 = 26 units

The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.

dV/dt = 4/3π(3r²) dr/dt

We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:

dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min

Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.

We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:

dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min

So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

Note that the negative sign indicates that the volume is decreasing.

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The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.

The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

3/4x +3-2x = -1/4 +1/2x+5

We can simplify by collecting the like terms,

3/4x - 1/2x - 2x = -1/4 + 5 -3

Then we can simplify further as:

-29x/20 = - 9/4

29x = (20*9)/4

29x= 45

x= 45/29

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Violet's money tripled Dylan's money to triple= 23,249.95.

Dylan invested $6,100 in an account paying an interest rate of 2% compound.

Violet invested $6,100 in an account paying an interest rate of 2%

compound.

The formula for compound amounts is A = P(1 + r/n)^(nt),

where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.

Here,

A = ($6100)(1 + 0.02/4)^(12*4)

Evaluating this we get:

A = ($6100)(1.005)^48, or

A  = ($6100)(`1.2704)

A = $7,749.98

Violet's money to triple than for Dylan's money to triple

=3(A)=3*7749.98=23249.95.

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The linear function in slope-intercept form that represents the equation is given as follows:

y = 15 + 25x.

The variables are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which:

He began the year with 15 terms on the list, hence the parameter b is given as follows:

b = 15.

Of the 35 new terms in each chapter, Mr. Snow puts the definitions of 10 terms on the wall and adds the remaining terms to the vocabulary list to be memorized, hence the slope m is obtained as follows:

m = 35 - 10

m = 25.

Then the function is:

y = 25x + 15.

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Based on the conversion of tablespoon to teaspoon, 7 1/3 tablespoons is equal to 22 teaspoons.

In Science, a conversion factor is a number that is used to convert a number in one set of units to another, either by dividing or multiplying.

Generally speaking, there are three (3) teaspoons in one (1) tablespoon. This ultimately implies that, a proportion or ratio for the conversion of tablespoon to teaspoon would be written as follows;

Conversion:

3 teaspoons (tsp) = 1 tablespoon (tbsp)

X teaspoons (tsp) = 7 1/3 tablespoons (tbsp)

Cross-multiplying, we have:

X teaspoons (tsp) = 7 1/3 × 3

X teaspoons (tsp) = 22/3 × 3

X teaspoons (tsp) = 22 teaspoons.

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The probability that the ticket drawn at random has a multiple of four or five is 2/5.

We have to determine the probability that the ticket drawn at random has a multiple of four or five.

Tickets number 1 to 20 are mixed up and then a ticket is drawn at random.

Total number of tickets = 20

The possible numbers of tickets that are multiple of four or five = 4, 5, 8, 10, 12, 15, 16, 20

So total number of outcome that are multiple of four or five = 8

So, the probability that the ticket drawn at random has a multiple of four or five = Total number  of outcome that are multiple of four or five/Total number of tickets

The probability that the ticket drawn at random has a multiple of four or five = 8/20

The probability that the ticket drawn at random has a multiple of four or five = 2/5

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Answer:

x ≤ - 17 or x ≥ 15

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] | x + 1 | ≥ 4 ( multiply both sides by 4 to clear the fraction )

| x + 1 | ≥ 16

Inequalities of the type | ax + b | ≥ c , have solutions of the form

ax + b ≤ - c or ax + b ≥ c , then

x + 1 ≤ - 16 ( subtract 1 from both sides )

x ≤ - 17

or

x + 1 ≥ 16 ( subtract 1 from both sides )

x ≥ 15

solution is x ≤ - 17 or x ≥ 16

a. The probability of exactly two US adults having a mental illness in a sample of six is 0.235904

B. The probability of at least one US adult having a mental illness is >=21

C. The probability of less than three US adults having a mental illness is <=3

a. The probability of exactly two US adults having a mental illness in a sample of six is given by the binomial probability formula:

P(X = 2) = (6 choose 2) * (0.2)^2 * (0.8)^4 = 0.235904

b. To find the probability of at least one US adult having a mental illness, we need to find the probability of zero or one or two or three or four or five or six US adults having a mental illness.

This can be found by summing the probabilities of each event:

P(X >= 1) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

c. To find the probability of less than three US adults having a mental illness, we need to find the probability of zero or one or two US adults having a mental illness.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Note that the binomial probability formula can be used to find the individual probabilities as well.

Therefore, the correct answer is as given above

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The test hypothesis for the 2010 U. S. Census is H0 = Oregon < Latino.

In math the term called hypothesis is defined as an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct.

Here we know that in 2010 U. S. Census, 11. 7% of the people in the state of Oregon were Hispanic or Latino.

And here we have also know that random sample of 853 adults in Oregon and 110 of the people surveyed were Hispanic or Latino.

Then the sample proportion is calculated as,

=> sample proportion=113/853=0.1325

And the value of Test statistic is,

=> z = (0.1325-0.117)/√(0.117*(1-0.117)/853)

=> z = 1.41

So, the hypothesis is written as,

=> H0 = Oregon < Latino.

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Answer:

I think it is just 6

Step-by-step explanation:

I hope it helped!

Step-by-step explanation:

a = 16

b = 3

because only the factor 3 gets repeatedly added every year (x).

the rest (the starting value that gets tripled and then tripled and then tripled ... every year) is constant.

f(x) = 16×3^x

as you know, exponents have the higher priority to multiplications.

if you want to be save you can use brackets like

f(x) = 16×(3^x)

Answer: consecutive interior angles and x=66°

Step-by-step explanation:

The angles are consecutive interior angles. The property is consecutive interior angles are supplementary.

2x+24+24=180          [combine like terms]

2x+48=180                 [subtract both sides by 48]

2x=132                       [divide both sides by 2]

x=66

Therefore, the angle is consecutive interior angles and x=66°.

Papers do you expect to hand in before you receive each possible grade at least once is 14.7.

given,

Total number of grades= 6

Imagine Y to be number of papers till we get all grades once. Hence

Yi= Number of papers till we get i th newer grades

Expected value of Y₆= ?

The difference between getting a new grade maybe represented as

Xi= Yi+1 - Yi

Using above equation for Y₆, we get

[Y₆]= ∑⁵i=o Xi

which means, we need to get 5 different grades from the first grade.

Number of tries to see second new grade maybe represented as

X₁= {(6-1)/6}, which, for generalization is written as Xi=geo{(6-i)/6}

Xi represents the success probability of seeing further new grade.

Expected value of Xi is inverse of parameter of geometric distribution, which is,

[Xi] = 6/(6-i) = 6.{1/(6-i)}

Expected value of Y₆= [∑⁵ i=0 Xi] = ∑⁵ i=0 [Xi]

Substituting value of [Xi] in the above expression

6.∑⁵i=0 {1/(6-i)} = 6. ∑⁶i=1 (1/i)

Now solving for 6 grades

Y₆ = 6[(1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6)]

Y₆ = 6 x 2.45 = 14.7

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If fires occur at points uniformly chosen on (0, A), then [tex]a = \frac{A}{2}[/tex] is the second derivative where should the station be located so as to minimize the expected distance from the fire.

From the question, a fire station is to be located along a road of length A, A < ∞.

If fires occur at points uniformly chosen on (0, A), then we have to find where should the station be located so as to minimize the expected distance from the fire.

E∣X−a∣ = [tex]\int^{A}_{0}|x-a| \frac{1}{A} dx[/tex]

E∣X−a∣ = [tex]\int^{a}_{0}|a-x| \frac{1}{A} dx+\int^{A}_{a}|x-a| \frac{1}{A} dx[/tex]

Now integrating.

E∣X−a∣ = [tex]\frac{1}{A}\left(\frac{a^2}{2}+\frac{A^2}{2}-aA-\left(\frac{a^2}{2}-a^2\right)\right)[/tex]

E∣X−a∣ = [tex]\frac{a^2}{A}-a+\frac{A}{2}[/tex]

If we set the derivative to zero, we get [tex]\frac{2a}{A}-1=0[/tex], where [tex]a = \frac{A}{2}[/tex] is the derivative. One can look at the second derivative, which is always positive, to see if this is the minimizer.

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The complete question is:

A fire station is to be located along a road of length A, A < ∞. If fires occur at points uniformly chosen on (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to minimize E[∣X−a∣] when X is uniformly distributed over (0, A).

The shortest possible height of the vase rounded to the nearest tenth of a centimetres is 45.650.

The concept of rounding the numbers will be used here to find the answer. Concerning this, we must know, that a number will be rounded to next digit, if the subsequent number if 5 or more than 5.

We know 6 preceedes 7 and the number is rounded to nearest tenth. So, the just possible number will be 45.69. However, as mentioned, it will be rounded to 45.7. The same will happen for till 45.65. Proceeding before this, we get 45.64 which will not be rounded to 45.7. Thus, the smallest possible number is 45.65 centimetres.

Similarly, the 1 at hundredths place will be the smallest number. This is because, rounding off 5 will eventually lead to rounding off to 45.7.

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In a recent student government​ election, the number of vote of the winner is 51

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

In a proportion, two ratios are specified to be equal to one another in an equation.

The number of votes of the winner is calculated by writing the ratio

= number of the students who voted / total number of students

let x be the number of students that voted the winner

85 / 100 = x / 60

100x = 60 * 85

x = 5100 / 100

x = 51

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