The mean potassium content of a popular sports drink is listed as 149 mg in a 32-oz bottle. Analysis of 28 bottles indicates a sample mean of 148 mg.
(a) State the hypotheses for a two-tailed test of the claimed potassium content.
a. H0: μ = 149 mg vs. H1: μ ≠ 149 mg
b. H0: μ ≤ 149 mg vs. H1: μ > 149 mg
c. H0: μ ≥ 149 mg vs. H1: μ < 149 mg

Answer:

\( - 2x + 4x = 2 \\ 2x = 2 \\ x = 1 \\ \\ 1 + y = 2 \\ y = 1\)

Answer:

\(x=1\\y=1\)

Step-by-step explanation:

Solve by substitution:

\(x+y=2\\-2x+4x=2\)

\(2x=2;x+y=2\)

Solve \(2x+2\) for x:

\(2x=2\)

\(x=2/2\)

\(x=1\)

Substitute 1 for x in \(x+y=2\)

\(x+y=2\)

\(1+y=2\)

\(y=2-1\)

\(y=1\)

\(x=1\) & \(y=1\)

hope this helps...

Answer:

\(\frac{x}{2} *\sqrt{x^{2} +4}\) +\(\frac{1}{2}\)*LN(|\(\frac{x+\sqrt{x^{2} +4} }{2}\)|) +C

Step-by-step explanation:

we will have to do a trig sub for this

use x=a*tanθ for sqrt(x^2 +a^2) where a=2

x=2tanθ, dx= 2 sec^2 (θ) dθ

this turns \(\int\limits {\sqrt{x^{2}+4 } } \, dx\) into integral(sqrt( [2tanθ]^2 +4) * 2sec^2 (θ) )dθ

the sqrt( [2tanθ]^2 +4) will condense into 2sec^2 (θ) after converting tan^2(θ) into sec^2(θ) -1

then it simplifies into integral(4*sec^3 (θ)) dθ

you will need to do integration by parts to work out the integral of sec^3(θ) but it will turn into (1/2)sec(θ)tan(θ) + (1/2) LN(|sec(θ)+tan(θ)|) +C

then you will need to rework your functions of θ back into functions of x

tanθ will resolve back into \(\frac{x}{2}\) (see substitutions) while secθ will resolve into \(\frac{\sqrt{x^{2} +4} }{2}\)

sec(θ)=\(\frac{\sqrt{x^{2} +4} }{2}\)  is from its ratio identity of hyp/adj where the hyp. is \(\sqrt{x^{2} +4}\)  and adj is 2 (see tan(θ) ratio)

after resolving back into functions of x, substitute ratios for trig functions:

= \(\frac{x}{2} *\sqrt{x^{2} +4}\) + \(\frac{1}{2}\)*LN(|\(\frac{x+\sqrt{x^{2} +4} }{2}\)|) +C

The point where marginal cost equals $15 is at the production of the 7th pizza. Therefore, the firm should produce 7 pizzas.

The firm's shut-down price is the price at which the firm is indifferent between producing and shutting down.

Using the table provided, we can calculate the missing values:

Variable Cost:

For 0 pizzas, the variable cost is $0.

For 1 pizza, the variable cost is $10.

For 2 pizzas, the variable cost is $12.

For 3 pizzas, the variable cost is $2.

For 4 pizzas, the variable cost is $1.

For 5 pizzas, the variable cost is $2.

For 6 pizzas, the variable cost is $3.

For 7 pizzas, the variable cost is $13.

For 8 pizzas, the variable cost is $16.

For 9 pizzas, the variable cost is $3.

For 10 pizzas, the variable cost is $6.

For 11 pizzas, the variable cost is $4.

Total Cost: To calculate the total cost, we simply add the variable cost and the fixed cost for each level of output. The fixed cost is not given in the table, so we cannot calculate the total cost.

Average Variable Cost:

To calculate the average variable cost, we divide the variable cost by the level of output. For example, the average variable cost for 1 pizza is $10/1 = $10.

Average Fixed Cost:To calculate the average fixed cost, we divide the fixed cost by the level of output.

Average Total Cost: To calculate the average total cost, we add the average variable cost and the average fixed cost. The firm should produce pizzas up to the point where marginal cost equals marginal revenue.

This is the point where the firm maximizes its profit. From the table, we can see that the marginal cost is increasing as output increases, while the marginal revenue remains constant at $15.

Learn more about variable cost at:

brainly.com/question/26373444

#SPJ1

The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

Learn more chi-square test of independence about at https://brainly.com/question/28348441

#SPJ11

In give word problem June 25, 1987 fell on Thursday.

What is word problem?

  Math word problems are math problems consisting of one or more sentences that require children to apply their math knowledge to "real world" scenarios. This means that in order to understand word problems, children must be familiar with the vocabulary associated with familiar mathematical symbols. Students must develop models.

One year = 365 days except for leap years = 366 days

52 weeks in a year 7 days per week = 364 days

1982 25th a Friday, if we move 365 days in the next year we end up on the 25th, but the weekday will be Saturday since we have moved 52 weeks + 1 day into the future.

Hence,

1982 25th Friday

1983 25th Saturday (+1 day)

1984 25th Monday (+1 day and +1 extra day for leap year)

1985 25th Tuesday (+1 day)

1986 25th Wednesday (+1 day)

1987 25th = Thursday

If the system had been 364 days per year, every year we would have end up on the same day every year.

Therefore June 25 , 1987 fell on Thursday.

To learn more about word problem refer the below link

https://brainly.com/question/21405634

#SPJ4

Answer:

i cant see that

Step-by-step explanation:

Answer:

\(y = -x + 115\)

Step-by-step explanation:

Given

See attachment for graph

Required

The equation of best fit

First, we pick two corresponding points on the graph,

We have:

\((x_1,y_1) =(55,60)\)

\((x_2,y_2) =(45,70)\)

Calculate slope (m)

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

This gives:

\(m = \frac{70 - 60}{45 - 55}\)

\(m = \frac{10}{-10}\)

\(m = -1\)

The equation is the calculated using:

\(y = m(x - x_1) + y_1\)

This gives

\(y = -1(x - 55) + 60\)

Open bracket

\(y = -x + 55 + 60\)

\(y = -x + 115\)

Answer:

c

Step-by-step explanation:

edg 20/21

If a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, A retailer marks up the price of a coffee mug from $6.25 to $8.77.

We have to find the percentage by which the price increase,

% increment = New rate - old rate / old rate × 100

% increment =(8.77 - 6.25)× 100

% increment =40.32%

Thus, if a store raises a coffee mug's price from $6.25 to $8.77. The price increase was 40.32%. Option C is correct.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ6

Answer: 4(−a+1)(a−1)

Step-by-step explanation:

Answer:

-4(a-1)^2

Step-by-step explanation:

just did the assignment

The corrosion rate is approximately 0.267 mpy. To calculate the corrosion rate in mils per year (mpy), we can use the following formula:

Corrosion Rate (mpy) = (Weight Loss (g) / (Density (g/cm³) * Area (cm²))) * 0.254

Given:

Weight Loss = 5 Kg = 5000 g

Density of steel = 7.9 g/cm³

Area = 6000 cm²

Substituting these values into the formula:

Corrosion Rate (mpy) = (5000 g / (7.9 g/cm³ * 6000 cm²)) * 0.254

Corrosion Rate (mpy) = (5000 / (7.9 * 6000)) * 0.254

Corrosion Rate (mpy) = (5000 / 47400) * 0.254

Corrosion Rate (mpy) ≈ 0.267 mpy

Therefore, the corrosion rate is approximately 0.267 mpy.

To know more about corrosion visit :

https://brainly.com/question/33225181

#SPJ11

Answer:

A. two table cloths

B. 24$

Step-by-step explanation:

First, develop your functions:

\(f(x)=3x+18\\g(x)=2x+20\)

f(x) is the first company, g(x) is the second company.

A.

Set the two equations to be equal to each other and solve for x:

\(f(x)=g(x)\\3x+18=2x+20\\3x-2x=20-18\\x=2\\\)

B.

Just plug in the value you got from A into either function:

\(f(2)=3(2)+18\\f(2)=24\)

The direction of vector D is perpendicular to vector A, and it makes an angle of 90 degrees with vector A.

We are given that:

vector A + vector B = vector C

vector A - vector B = vector D

To find the direction of vector C,

we can use the fact that the tangent of the angle between vector A and vector C is equal to the ratio of their magnitudes.

That is:

tan(theta) = |vector C| / |vector A|

where theta is the angle between vector A and vector C.

Similarly, to find the direction of vector D,

we can use the fact that the tangent of the angle between vector A and vector D is equal to the ratio of their magnitudes.

That is:

tan(phi) = |vector D| / |vector A|

where phi is the angle between vector A and vector D.

We want to find the angle between vector A and vector D, which is equal to the supplement of the angle between vector A and vector C.

That is:

theta + phi = 180 degrees

Rearranging, we get:

phi = 180 degrees - theta

Substituting the equations for theta and phi, we get:

tan(180 degrees - phi) = |vector D| / |vector A| = tan(phi)

Simplifying, we get:

tan(180 degrees - phi) = tan(phi)

Using the identity tan(180 degrees - theta) = -tan(theta), we can rewrite this as:

-tan(phi) = tan(phi)

Solving for phi, we get:

2*phi = 180 degrees

phi = 90 degrees

For more questions on Addition of vectors

https://brainly.com/question/2927458

#SPJ4

Complete question may be:

If, vector A + vector B = vector Cvector A - vector B = vector D, then find the direction of vector D is perpendicular to vector A?

Answer

1.5; log8 22.627

Step-by-step explanation:

To find dz/dt using the chain rule, we need to calculate the derivatives of z with respect to x and y separately, and then multiply them by the derivatives of x and y with respect to t.

Given:

z =  \(cosh^{2} (xy)\)

x = (1/2)t

y = \(e^{t}\)

Let's start by finding the partial derivatives of z with respect to x and y:

∂z/∂x = \(2cosh(xy) * sinh(xy) * y\)  (using the chain rule)

∂z/∂y = \(2cosh(xy) *sinh(xy)*x\)    (using the chain rule)

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 1/2

dy/dt = \(e^{t}\)

Finally, we can use the chain rule to find dz/dt:

dz/dt = (∂z/∂x)(dx/dt) + (∂z/∂y)(dy/dt)

      = \(2cosh(xy) *sinh(xy)*y*(1/2) + 2cosh(xy)*sinh(xy)*x*e^{t}\)

Now, substitute the given expressions for x and y:

\(dz/dt = 2cosh((1/2)t*e^{t} * sinh((1/2)t*e^{t} *(1/2)* + 2cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t} *((1/2)t)\)

Simplifying further, we have:

\(dz/dt = cosh((1/2)t*e^{t} *sinh((1/2)t*e^{t})* e^{t} + cosh((1/2)t* e^{t}*sinh((1/2)t*e^{t}* ((1/2)t)\)

This is the expression for dz/dt using the chain rule with the given values of x and y.

To know more about chain rule refer here:

https://brainly.com/question/31585086?#

#SPJ11

The approximate percent increase in consumption from 1986 to 1997 is:

B. 20%

The initial consumption level for the year, 1986 is 62 million barrels per day and by 1997, the percent increase in consumption shot up to 74 million barrels per day.

When we subtract the latter consumption levels from the former, we will have a total of 12 million barrels per day. So, the percentage increase will be:

12 million barrels per day/ 62 million barrels per day × 100

= 19.35 %

Thus, we can arrive at the conclusion that the total consumption levels per day increased by 19.35%, which is approximately 20%.

Learn more about percentage increments here:

https://brainly.com/question/28398580

#SPJ1

Answer:

\(x=-\frac{15}{2}\)

Step-by-step explanation:

Start by distributing the 6 to each of the terms in the parentheses:

6(x)+6(9)=9

6x+54=9

Subtract 54 from both sides

6x+54-54=9-54

6x=-45

Divide both sides by 6

x=-45/6

Divide the fraction by 3/3 since it is the greatest common factor of 45 and 6. Note we can only do this since 3/3 is equivalent to 1, so we are essentially dividing the fraction by 1.

x=-15/2

\(\huge \boxed{\tt x= - 7.5}\)

Step-by-step explanation:

\( \to \sf6(x+9)=9\)

\( \\ \\ \)

\( \to \sf(x+9)= \dfrac{9}{6} \)

\( \\ \\ \)

\( \to \sf(x+9)= \dfrac{3}{2} \)

\( \\ \\ \)

\( \to \sf x= \dfrac{3}{2} - 9\)

\( \\ \\ \)

\( \to \sf x= \dfrac{3 - 18}{2} \)

\( \\ \\ \)

\( \to \sf x= \dfrac{ - 15}{2} \)

\( \\ \\ \)

Round of -15 / 2 to get product as - 7.5

\( \to \sf x= - 7.5\)

Verification:

6(x+9)=9

6(- 7.5 +9) = 9

6 × 1.5 = 9

9 = 9

Hence verified ~☆

Answer: y > -4

Step-by-step explanation: i believe this is your answer because i think you are asking for the range more or less. when you do this, you have to just ask yourself what points would be acceptable (any y point above -4) so the answer would be any y value more than -4, y > -4

The inequality for all the points of y above 4 is y > -4.

An inequality is comparison between two non-equal quantitates.

Inequalities are of four types.Less than,less than or equal to,greater than and greater than or equal to.If a is greater than be it is written as a>b.

For a is greater than or equal o b it is written as a ≥ b and for the other two types in equality will switch it's direction.

According to the given question we have to describe an inequality that describes all the points on the co-ordinate plane above y = -4.

This can be represented as y > -4 the range of the points can be defined as (-4,∞).

learn more about inequality here :

https://brainly.com/question/20383699

#SPJ2

Answer:

I would say like terms and addition.

Step-by-step explanation:

The probability of a student doing well on an exam given that they spend time reading is approximately 0.983 or 98.3%.

To calculate the probability of a student doing well on an exam given that the student spends time reading, we need to use conditional probability.

Let's denote:

P(R) as the probability of a student spending time reading (P(R) = 0.59),

P(E) as the probability of a student doing well on an exam (P(E)),

P(E|R) as the probability of a student doing well on an exam given that they spend time reading (P(E|R) = 0.58).

The formula for conditional probability is:

P(E|R) = P(E and R) / P(R).

Given that P(E and R) = 0.58 (the probability of a student doing well on an exam and spending time reading) and P(R) = 0.59 (the probability of a student spending time reading), we can substitute these values into the formula:

P(E|R) = 0.58 / 0.59 = 0.983.

Therefore, the probability of a student doing well on an exam given that the student spends time reading is approximately 0.983 or 98.3%.

To know more about probability, visit:

https://brainly.com/question/29120105

#SPJ11

The principal value of (1−i)4i is (1−i)4i = -4.

To show that u(x,y) = 2x−x^3+3xy^2 is harmonic, we need to demonstrate that it satisfies Laplace's equation, which states that the sum of the second partial derivatives of a function is zero. Let's calculate the Laplacian of u(x,y):

∇^2u(x,y) = (∂^2u/∂x^2) + (∂^2u/∂y^2)

= (2 - 6x^2) + 6y

Since both terms are independent of each other and the sum is zero, we can conclude that u(x,y) is indeed harmonic.

To find the harmonic conjugate v(x,y), we can use the fact that it satisfies the Cauchy-Riemann equations: (∂u/∂x) = (∂v/∂y) and (∂u/∂y) = - (∂v/∂x).

From the given function u(x,y), we can see that (∂u/∂x) = 2 - 3x^2 + 3y^2 and (∂u/∂y) = 6xy. By equating these expressions to (∂v/∂y) and - (∂v/∂x), respectively, we can solve for v(x,y).

(∂v/∂y) = 2 - 3x^2 + 3y^2

(∂v/∂x) = -6xy

Integrating the first equation with respect to y, we get v(x,y) = 2y - x^2y + y^3 + h(x), where h(x) is an arbitrary function of x.

Next, we differentiate this expression with respect to x and equate it to the second equation:

-6xy = (∂v/∂x) = -6xy + h'(x)

We can see that h'(x) = 0, which implies that h(x) is a constant. We can set this constant to zero without loss of generality.

Therefore, the harmonic conjugate of u(x,y) is v(x,y) = 2y - x^2y + y^3.

Hence, the function u(x,y) = 2x−x^3+3xy^2 is harmonic, and its harmonic conjugate is v(x,y) = 2y - x^2y + y^3.

Learn more about partial derivatives here:

https://brainly.com/question/28751547

#SPJ11

We have the data set:

This shows the moves a player made forward or backward in a board game. Then, graphically, this is:

In this situation, 0 means that the player stayed at his position.

If the data of the research subjects are presented in a frequency distribution graph, a histogram-type graph should be used.

If the data are presented in a frequency distribution graph, then the type of graph that should be used is a histogram. A histogram is a type of bar graph that displays the distribution of a continuous variable by dividing the range of values into intervals, and bins, and counting the number of observations that fall within each bin.

If the academic majors were nominal a bar graph could also be used to display the frequency of each major. In a bar graph, each category would be plotted on the horizontal axis, and the frequency of students in each category would be plotted on the vertical axis.

To learn more about the histogram

https://brainly.com/question/30701461

#SPJ4

Given:

There are between 24 and 40 students in a class.

The ratio of boys to girls is 4:7

To find:

The number of students in the class.

Solution:

Let the number of boys are girls are 4x and 7x respectively, where, x must be a positive integer because number of boys and girls is always a positive integer. Then, the total number of students is

\(\text{Total students}=4x+7x\)

\(\text{Total students}=11x\)

It means total number of students is multiply of 11.

Multiples of 11 are 11, 22, 33, 44, ... . So, multiples of 11 between 24 and 40 is 33.

Therefore, the total number of students in the class is 33.

Answer:

72+ 18x

Step-by-step explanation:

9x+72+5x+4x

72+ 18x

Answer:

NL= 7.81cm.

∡LNP= 39.8°

Area of shape =60 cm².

Step-by-step explanation:

Given:

To find:

Solution:

First find NP:

NP=NO-LM

Here, LM=PO opposite side of the rectangle is equal.

NP=15 cm - 9 cm=6 cm

Now

LP=MO=5 cm opposite side of the rectangle is equal.

By Using Pythagoras law, we can find NL

Since ΔLPN is right angled triangle.

NL is a hypotenuse(h):

Base(b) is LP and Perpendicular(p)is NP.

Using Pythagoras law:

\(\boxed{\tt h^2=p^2+b^2}\)

substituting value:

\(\tt h^2=6^2+5^2\)

\(\tt h^2=61\)

Doing square root on both side:

\(\tt \sqrt{h^2}=\sqrt{61}\)

\(\tt h=7.81 cm\)

Therefore, NL is 7.81cm.

\(\hrulefill\)

To find ∡LNP, we can use sin law:

\(\tt Sin \: N= \frac{Opposite \:side\: of \:N }{Hypotenuse}\)

\(\tt Sin\: N=\frac{LP}{LN}\)

\(\tt Sin\: N=\frac{5}{7.81}\)

We can find ∡LNP, since ∡LNP is inverse of SIn N.

∡LNP=\(\tt sin^{-1}(\frac{5}{7.81})=39.8^0\)

Therefore, ∡LNP=39.8°

\(\hrulefill\)

Area of the shape : Area of rectangle MOPL+ Area of triangle LPN

\(\tt =length*breadth+\frac{1}{2}Base*Height\)

\(\tt =LM*MO+\frac{1}{2}LP*NP\)

\(\tt =9*5+\frac{1}{2}*5*6\)

=60 cm²

Therefore, Area of Shape is 60 cm².

The value of x in the domain of f(x) is x = 10.option (A)

To find the domain of the function f(x) = √(x - 8), we need to consider the values of x for which the expression under the square root is non-negative.

That is, x - 8 ≥ 0

Simplifying, we get x ≥ 8

Therefore, any value of x that is greater than or equal to 8 is in the domain of the function.

Out of the given options, only option A. x = 10 satisfies this condition.

So, the value of x in the domain of f(x) is x = 10.

Learn more about  square root

https://brainly.com/question/3120622

#SPJ4