A researcher wants to know whether the acidity of rain (pH) near Houston, Texas, is significantly different from that near SC Chicago, Illinois. He randomly selects 12 rain dates in Texas and 14 rain dates in Illinois and obtains the following data: Texas 4.69 5.10 5.22 4.46 4.93 4.65 5.22 4.76 4.25 5.14 4.11 4.71 Illinois 4.40 4.22 4.64 4.54 4.35 4.69 4.69 4.75 4.40 4.63 4.45 4.49 4.36 4.52 Source: National Atmospheric Deposition Program (a) Is the sampling method dependent or independent? Why? (b) Because the sample sizes are small, what must be true regarding the populations from which the samples were drawn? (c) Draw side-by-side boxplots of the data. What does the visual evidence imply about the pH of rain in the two states? () Does the evidence suggest that there is a difference in the pH of rain in Chicago and Houston? Use the x = 0.05 level of significance.
Previous question

The dimensions of the rectangle are:

Length = 10 m

Width = 6.5 m

Recall that the area of aa rectangle is given as, length × width.

Given the following:

Area of the rectangle = 65 m²

Let the width of the rectangle be represented as w.

Length of the rectangle = 2w - 3 m

Therefore:

(2w - 3)(w) = 65

Expand:]

2w² - 3w = 65

2w² - 3w - 65 = 0

Factorize:

w = 6.5 or w = -5

The width cannot be negative, therefore, the width = 6.5 m.

Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m

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Answer:

26.74

Step-by-step explanation:

add the money John spends on the week days(13.75) to 12.99 and you get your answer

Answer:

70

Step-by-step explanation:

1 million = 10 hundred thousands because 100,000 x 10 = 1,000,000

The propagated error in computing the area of the square is 6.01 cm

According to the question,

It is given that Length of side of square was found = 30cm

The possible error in measurement = 0.1cm

So, the length will be 30 + 0.1cm or 30 - 0.1cm

As we know that

Area of the square : A = x²

Where x is side of square

The differential of this equation =

=> dA/dx = 2x --------(1)

If dx is the error of the side length of the square

dA = 2(30)(0.1)

=> dA = 6

Therefore , The propagated Error = ΔA = (x + Δx)² - x²

=> (30 + 0.1)² - (30)²

=> 906.01 - 900

=>  6.01

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Both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

We have the following integers -

- 3, 1 and 3.

The given inequality are -

- 3 > 1 - 3 = 3

1 < 3 - 3 < 1

- 3 > 1 - 3 = 3

- 3 > - 2 = 3

Which is false.

1 < 3 - 3 < 1

1 < 0 < 1

Which is false.

Therefore, both the inequalities (- 3 > 1 - 3 = 3)  and  (1 < 3 - 3 < 1) are false.

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If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.

Average score = (x+y)/2

he scored 10 points less on the second test than he did on the first.

y = x - 10

Replace y with x-10

(x + x - 10) / 2

(2x-10)/2

Average score on both tests is 75

(2x-10)/2 = 75

Multiply both sides of this equation by 2

2x-10 = 150

Add 10 to both sides

2x = 160

Divide both sides  by 2x

x = 160/2

x = 80 (She got 80 on the first test)

He got 80 - 10 = 70 (She got 70 on the second test)

(80+ 70) / 2 = 150/2 = 75 (She got average  of 75 on both tests)

Therefore she scored 70 on the second test is your solution.

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The descending order of the polynomial is (x³ + 8y³)

The term polynomial in algebra is defined as  an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Here we have given that (x+2y)(x²−2xy+4y²)

And we have to multiply the polynomial and write your answer in descending order.

Here we have the polynomial (x+2y)(x²−2xy+4y²).

Now, we have to use the identity

=> a³ + b³ = ( a² − ab + b² ) ( a + b ) ,

Now, we have to apply these identity one the given polynomial, then we get,

=> ( x + 2y ) ( x² − 2xy + 4y² )

=> (x³ + ( 2 y )³) = (x³ + 8 y³) .

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there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

answer is D. None of the above.

To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:

X2 = (n-1)*(s2/σ2)

where n is the sample size, s2 is the sample variance and σ2 is the population variance.

In this case, n = 16, s2 = 3.25 and σ2 = 4

X2 = (16-1)*(3.25/4) = 12.1875

The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.

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Answer: [tex]y=-\frac{1}{2} x-3[/tex]

Step-by-step explanation:

[tex]3x+6y=-18[/tex]

[tex]-3x[/tex]             [tex]-3x[/tex]

[tex]6y=-3x-18[/tex]

[tex]\frac{6y}{6} =\frac{-3x}{6} -\frac{18}{6}[/tex]

[tex]y=-\frac{1}{2 } x-3[/tex]

The statement If B ⊂ A, then A U B = A is true.

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

If BCA, then AUB=A.

When the above statement is represented properly, we have the following representation

If B ⊂ A, then A U B = A

The statement If B ⊂ A means that

The set B is a subset of the set A

In other words, the whole of set B is in set A

If this is true, then the union of both sets represented by A U B is set A

Hence, it is true that If B ⊂ A, then A U B = A

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You will pay a price of $72.31 if you wait to purchase tickets at the door

Discount is defined as a deduction from the usual cost of something. You will save 22% off the door price by prepay $56.40 per ticket now.

Let P represent the original price. We can write that:

P - 22% of P = $56.40. It should be noted that this can be rewritten as:

P - (22% × P) = 56.40

P - 0.22P = 56.40

Subtract

0.78P = 56.40

Divide through by 0.78

P = 56.40/0.78

P = $72.31

Therefore the price is $72.31.

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The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

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

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Let the missing number be 'x'. Then the equation is given as,

25 - x = 13

Simplify the equation, then the value of the variable 'x' will be given as,

25 - x = 13

x = 25 - 13

x = 13

The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.

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Answer:

[tex]y=2^x-5[/tex]

Step-by-step explanation:

The y-intercept occurs when x = 0.

Therefore, substitute x = 0 into each equation to find its y-intercept.

[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]

[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]

Therefore, the exponential function that has a y-intercept of (0, -4) is:

[tex]\large\boxed{y=2^x-5}[/tex]

Answer:

Step-by-step explanation:16x^2+9=25

                                             16x^2=16

                                               x^2=1

                                                 x=1 or -1

                                                   D

The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)

The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.

The slope of a line is given as ( y1-y2)/(x1-x2)

for AB and CD to be perpendicular

( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1

therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)

1/-3 ×(y4-4)/(x4-3) = -1

(y4-4)/(x4-3) = 3/1

therefore 3= y4-4 and 1 = x4-3

therefore y4 = 3+4= 7

and x4 = 1+3= 4

therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)

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95% confidence interval for the true mean breaking strength of the white wood is (71.66 MPA, 78.74 MPA)

The result above means that the lower limit of the true mean breaking strength of the white wood is 69.89 MPA and the upper limit is 81.51 MPA.

The definition says, "A confidence interval is a range of values ​​derived from a sample statistic that likely includes the value of an unknown population parameter."

To calculate the confidence interval, we need to know three parameters of the sample: the mean (average value) μ, the standard deviation σ, and the sample size n (number of measurements). Then you can calculate standard error and tolerance using the following formulas:

                      standard error = σ/√n

Given in the question:

Confidence interval = mean + or - Error margin (E)

Mean = 75.2 MPA

Standard deviation = 8.6 MPA

Sample size, n = 25

Now,

Degree of freedom = n - 1 = 25 - 1 = 24

Confidence level (C) = 95% = 0.95

Significance level = 1 - C

                              = 1 - 0.95

                              = 0.05 = 5%

Therefore, t-value corresponding to 24 degrees of freedom and 5% significance level is 2.06

Again,

E = t × sd/√n

  = 2.06 × 8.6/√25

  = 2.06 × 1.72

  = 3.54 MPA

Lower limit = Mean - E

                  = 75.7 - 5.81

                  = 69.89 MPA

Upper limit = Mean + E

                   = 75.7 + 5.8

                   = 81.51 MPA

95% confidence interval is (69.89 MPA, 81.51 MPA)

The result means that the true mean breaking strength of the white wood is between 69.89 and 81.51 MPA.

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The area under the given curve is 77/60. SO the option B is correct.

In the given question we have to estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.

The given function is

F(x) = 1/x; [1,5]; n=4

The given options are:

A≈77/240

A≈77/60

A≈77/15

A≈25/3

A≈25/12

Since, f(x) =1/x

∆x = (b-a)/n

∆x = (5-1)/4

∆x =4/4

∆x = 1

Now the table is

x               1            2            3            4            5

f(x)            1            1/2          1/3         1/4          1/5

R(4) = [f(2)+f(3)+f(4)+f(5)]∆x

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

R(4) = (30+20+15+12)/60

R(4) = 77/60

Hence, the area under the given curve is 77/60. SO the option B is correct.

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The right question is given below:

Answer:

y = [tex]\frac{7}{5}[/tex] x + 4

Step-by-step explanation:

Perpendicular slopes are opposite reciprocals.  

So the slope is 7/5  

Us the slope and the point to find the y intercept

m = 7/5

x = -5

y = -3

y= mx + b

-3 = (7/5)(-5) + b

-3 = -7 + b  Add 7 to both sides

4 = b

y = mx + b

y = 7/5 x + 4

Answer:

x = 13

x = 1

Step-by-step explanation:

The (x – 7)2 = 36 gives the value of x as 25.

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. LHS = RHS is a common mathematical formula.

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:

(x – 7)2 = 36

Now, dividing both side by 2

(x – 7)2/2 = 36 /2

(x – 7) = 18

Now, add 7 both side

x- 7+ 7= 18 + 7

x = 25

Hence, the value of x is 25.

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Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

If 60% of the population supports massive federal budget cuts.

We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.

So, the probability is, 155 / 250 = 0.62

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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The dimensions of the rectangular package with the condition of maximum volume is equal to  x = 19inches and y = 38inches.

As given in the question,

Let us consider length of the cross section which is square be x

Perimeter of the cross section is 4x

And y be the length of the rectangular package

Maximum combined ( length + perimeter of the cross section ) = 114

y + 4x = 114

⇒ y = 114 -4x

Volume of the package 'V' = x²y

⇒V = x²(114 -4x)

⇒V = 114x² -4x³

Differentiate both the side of the equation with respect to x,

dV/dx = 228x - 12x²

For maximum Volume

dV/dx =0

228x -12x² = 0

⇒12x( 19 -x ) =0

⇒12x = 0 or 19 - x =0

⇒x =0 or x =19

x =0 is not possible

⇒x =19inches

y = 114 - 4(19)

  = 38inches

Therefore, the dimensions of the rectangular package with the given condition of volume is equal to x = 19inches and y = 38inches.

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Answer: No mistake

It seems that there are not any problems with these steps.

The amount Sally’s share would be;

⇒ $30,000

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio.

And, The profits are $70,000.

Now,

Since, The profits are $70,000.

Hence, We get;

⇒ 2x  + 3x + 2x = $70,000

⇒ 7x = $70,000

⇒ x = $10,000

So, The amount of Sally’s share would be;

⇒ 3x = 3 × 10,000

         = $30,000

Thus, The amount Sally’s share would be;

⇒ $30,000

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The non-zero orthogonal vector to the plane is 486i + 243j + 162j and the area of the triangle is 4374 unit squares.

The vertices of the triangle are P(9, 0, 0), Q(0, 18, 0), and R(0, 0, 27).

So, firstly we should find the vector PQ and PR,

Now,

PR = (0)i + (-18)j + (27)k

PR = -18j + 27j

And PQ,

PQ = (-9)i + (18)j + (0)k

PQ = -9i + 18j

Now, the normal vector which is also a non-zero orthogonal vector,

n = PQ x PR

n = 486i + 243j + 162j

Now, the area of the ΔPQR will be,

Ar(PQR) = [tex]\left[\begin{array}{ccc}9&0&0\\0&18&0\\0&0&27\end{array}\right][/tex]

Solving further,

Ar(PQR) = 4374 unit square.

So, the area of the triangle is 4374 unit square.

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The nonprofit company charges $100 each ticket for the opportunity to win a $50,000 vintage Mustang. With four prizes and 1500 tickets sold, he expects to lose $54.53 on each one.

The chance of winning is multiplied by the bet multiplier to determine the mathematical anticipated value. Typically, expected value is estimated for a bet of one unit. To determine the predicted profit, multiply the win chance by the stake amount.

Chances of getting first prize = 1/1500

Chances of getting second prize = 1/1500

Chances of getting third prize = 1/1500

Chances of getting Fourth prize = 1/1500

Cost of one ticket = $100

Expected winning = -100 +1/1500 (56000 + 6600 + 4300 + 1300)

= -100 + 68200/1500

= - 54.53 dollars

There is an expected loss of $54.53.

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the interval, the function returns zero (-6,-2)  –6 < x < –2

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The given f(x) = (x + 2)(x + 6)

In this function, a quadratic equation is represented (vertical parabola open upward)

The vertex stands for a minimum.

the use of a graphing tool

view the attached image

x=-6 and x=-2 are the x-intercepts.

Point: the y-intercept

The point is called the vertex.

The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)

The range is in the range [-4,].

x -6 or x > -2 make the function positive.

For the interval, the function returns zero (-6,-2)  –6 < x < –2

Hence, the interval, the function returns zero (-6,-2)  –6 < x < –2

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Answer:

I think Numerical and univariate

Step-by-step explanation:

Answer:

Step-by-step explanation:

This would be numerical and univariate because the information shown represents a stem and leaf plot.

Hope this helps! :)

Answer:

the observed value of 9 is 13 units lower than the predicted value of 22.

Step-by-step explanation:

A residual is the difference between the observed value of a data point and the predicted value of that data point based on a given model. In a regression analysis, the residual is calculated using the formula e = y - y', where y is the observed value, y' is the predicted value, and e is the residual.

In this case, we are given the point (4,9) and the regression equation y = 5x + 2. Plugging in the value x = 4 into the regression equation, we get:

y' = 5(4) + 2 = 22

Since we are also given that the observed value of the point (4,9) is 9, we can plug these values into the formula for the residual to calculate the residual:

e = 9 - 22 = -13

Therefore, the residual e when x = 4 is -13. This means that the observed value of 9 is 13 units lower than the predicted value of 22.

Tamia will need 166 feet of fabric

Given that:

Tamia wants each curtain to be 24 inches long

At the fabric store, fabric is sold by the foot

Tamia's curtain company wants to make 83 curtains

1 curtain = 24 inches

83 curtains = 24×83 = 1992 inches

To convert inches to feet multiply by 1/12:

1992 inches =  1992 × 1/12 feet = 166 feet

Thus, she will need 166 feet

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