test is used to conduct an anova for any design comparing three or more means that contains a within-subjects variable

Answer:

X = 3, Y = -6

Step-by-step explanation:

y = -2x

y = -9x + 21

Bring Y and X on the same side (alone).

0 = -2x – y

-21 = -9x – y

Multiply the top equation by -1 so we can cancel out y later on (to make it easier to solve for x).

0 = 2x + y

-21 = -9x – y

Add the equations.

-21 = -7x

Divide by -7.

X = 3

Solve for Y and check.

Y = -2(3)

Y = -6

Use the other equation to make sure.

(-6) = -9(3) + 21

-6 = -27 + 21

Have a nice day :D

Answer:

Angle ABC = 82°

Step-by-step explanation:

Given triangle ABC is an isosceles triangle so we can write

angle BAC = angle BCA = 49°

Then,

angle BAC + angle BCA + angle ABC = 180° (Sum of all angles of a triangle is 180°)

or, 49° + 49° + angle ABC = 180°

or, angle ABC = 180° - 98°

or, angle ABC = 82°

The patient consumed 1547.1098 milliliters of fluids in total. By converting the given units into milliliters, we get the required value.

The required conversions are:

1 ounce (oz) = 29.5735 ml

1 cup  = 236.588 ml

1 tbsp = 14.7868 ml

Given that, a patient consumed the following fluids:

1) 1000 ml of IV

2) 4 oz of juice ⇒ 4 × 29.5735 ml = 118.294 ml

3) 8 oz of milk ⇒ 8 × 29.5735 ml = 236.588 ml

4) 1/2 cup of chicken broth = 236.588/2 = 118.294 ml

5) 5 tbsp of jello = 5 × 14.7868 ml = 73.9338 ml

So, the total milliliters of liquid taken by the patient is

= 1000 + 118.294 + 236.588 + 118.294 + 73.9338 = 1547.1098 ml

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Answer: 7 47/63

Step-by-step explanation: First, find the common denominator of 6/7 and 8/9. You can do this by writing out the multiples of each denominator:

7 14 21 28 35 42 49 56 63

9 18 27 36 45 54 63

The first number at which they match is the common denominator. Next, find the sum of the numerators relative to this new denominator:

6/7 * 63 = 54

8/9 * 63 = 56

Finally, add the numerators, simplify the improper fraction, and add that to the sum of the original whole numbers:

(54 + 56)/63 = 110/63 = 1 47/63

(4 + 2) + 1 47/63 = 7 47/63

Answer:

-16

Step-by-step explanation:

In order to solve this equation, we want to plug in -2 anywhere we see x.

This would turn f(x)=x(2-6) into f(-2)=-2(2-6)

Next we just need to simplify. First, distribute the -2.

-2(2-6) ----> -2(2) and -2(6)

-2(2)= -4 and -2(6)=-12

So now our equation looks like this: f(-2)=-4-12.

Now we just need to subtract 12 from -4.

This gives us our answer, -16.

Hope this helps!!

Answer:

• a=0

• a=2

• a=2

Step-by-step explanation:

factorise a³-4a²+4a=0

thus,a(a-2)²=0

Answer:

Step-by-step explanation:

Answer: 1.57 meters

Step-by-step explanation:

takes 2 places to get from cm to meters

157 / 100

1.57 m

h(x) is decreasing on (0, 2π/3) ∪ (4π/3, 2π).

Given the interval:

h(x) = cos(3x/2)

To find critical points:

To find the critical points of a function y = f(x), first, we have to find x-values where the derivative f'(x) = 0 and also the x-values where f'(x) is not defined.

h'(x) = -(3/2)sin(3x/2) = 0 when 3x/2 = kπ, k = 0, ±1, ±2, ...

If k = 0, then x = 0

If k = 1, then 3x/2 = π. So, x = 2π/3.

If k = 2, then 3x/2 = 2π. So, x = 4π/3.

If k = 3, then 3x/2 = 3π. So, x = 2π.

When 0 < x < 2π/3, h'(x) < 0. So, h(x) is decreasing.

When 2π/3 < x < 4π/3, h'(x) > 0, So, h(x) is increasing.

When 4π/3 < x< 2π, h'(x) < 0. So, h(x) is decreasing.

h(x) is increasing on (2π/3, 4π/3).

h(x) is decreasing on (0, 2π/3) ∪ (4π/3, 2π)

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A total of 3 cups of vinegar goes into 27 total cups

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

1/4 cups of vinegar

2 cups of water

So, we have

Water : Vinegar = 2 : 1/4

Rewrite as

Water : Vinegar = 8 : 1

Multiply by 3

Water : Vinegar = 24 : 3

The sum of 24 and 3 is 27

So, we have

Vinegar = 3

Hence, the number of cups of vinegar is 3

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Measures of   median  are the values located  at the middle of the  data set

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The middle number is obtained by sorting all the data points and choosing the center one, or the middle two numbers, if there are two of them.

We use graph to interpret  dot plots

A line graph shows ordered pair plotted on the coordinate plane. The ordered pairs are connected with  line      segment

A bar graph uses  to central tendency  represent data

A     graph  divided into wedges called sectors

A sample of population is a subset of the     histogram  

A population is a complete set of all possible observation.

The mode i the most often repeated item in a data set.

The number of population in each interval is called frequency.

A mean uses ranges instead of individual  numbers to represent data.

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A reaction that acts to amplify or reinforce an initial change is termed a positive feedback.

The positive-feedback mechanism is used in climatic change, any effect that acts to reinforce the initial change.

In Asian philosophy, yin and yang are viewed as forces that interact and are connected to one another and are crucial parts of a dynamic system. Positive and negative feedbacks function something like yin and yang in the Earth system; they are integral parts of the total system that eventually help to maintain a more or less stable state. While negative feedback mechanisms stabilize a system and keep it from reaching extreme states, positive feedback mechanisms increase or magnify an original change. The evolution of Earth's climate system can be viewed in many ways as a kind of conflict between these two feedback mechanisms.

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Note that the dimensions that the rug should have given the above factors is:  25 by 19 This problem is solved using the concept of Quadratic Equations.

To compute the dimensions that the rug should have, let x = the width of the uniform strip around the rug then the dimensions of the rug will be (35-2x) by (29-2x)

The equation thus is represented as:

(35-2x) * (29-2x) =  475 sq/ft expanding the brackets we have

⇒ 4x² - 128x + 1015 = 475 ; which is a quadratic equation.

Subtract 475 from both sides to get

⇒ 4x² −128x + 1015 − 475  = 475 − 475

⇒ 4x² −128x +540 = 0;

Factor left side of the equation.

4(x−5)(x−27)=0

Set factors equal to 0.

x−5=0 or x−27=0

x=5 or x=27

Note that only 1 solution makes sense

x = 5 ft is the width of the uniform strip around the rug

Find the dimensions of the rug

35 - 2(5) = 25 ft

29 - 2(5) = 19 ft

Thus, the rug should be 25 by 19 which has an area: 25 * 19 = 475.

She can afford 475ft², and the resolution of the quadratic expression for this problem indicates that using x=5 arrives at two dimensions 25ft, and 19ft, thus, hence we can conclude that the right dimensions which result in the area of carpet that Cynthia can afford (457ft²) is: 25ft by 19ft.

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z = -1.34 <  (a - 70)/9

And if we solve for we got

a = 70 - 1.34 * 9 = 57.95 = 98

So, the value of height that separates the bottom 9% of data from the top 91% is 58.

And the answer for this case would be:

a) 58

What is the Normal distribution and Z-score?

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The solution to the problem

Let X be the random variable that represents the scores of a population, and for this case we know the distribution for X is given by:

X ~ N (70, 9)

Where μ = 70, and σ = 9

For this case, the figure attached illustrates the situation for this case.

We know from the figure that the lower limit for D accumulates 9% or 0.09 of the area below and 0.91 or 91% of the area above.

we want to find a value a, such that we satisfy this condition:

 P(X > a) = 0.91  (a)

 P(X < a) = 0.09 (b)

Both conditions are equivalent in this case. We can use the z score again in order to find the value a.  

As we can see in the figure attached the z value that satisfies the condition with 0.09 of the area on the left and 0.91 of the area on the right it's z=-1.34. On this case P(Z<-1.34)=0.09 and P(z>-1.34)=0.91

If we use condition (b) from the previous we have this:

P(X < a) = P(X - μ)/σ < (a - μ)/σ) = 0.09

P(z < (a - μ)/σ) = 0.09

But we know which value of z satisfies the previous equation so then we can do this:

z = -1.34 <  (a - 70)/9

And if we solve for we got

a = 70 - 1.34 * 9 = 57.95 = 98

Hence, the value of height that separates the bottom 9% of data from the top 91% is 58.

And the answer for this case would be:

a) 58

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Answer: To solve this problem, we need to set the two equations equal to each other and solve for the number of text messages that were sent by each person. We know that the cost of Jack's plan is c = 0.30t + 9 and the cost of Jill's plan is c = 0.60t. To find the number of text messages they each sent, we can set these two equations equal to each other and solve for t:

0.30t + 9 = 0.60t

0.30t = 0.60t - 9

0.30t = 0.60t - 9

-0.30t = -9

t = 30

Therefore, if Jack and Jill paid the same amount for their text plans, they each sent 30 text messages.

[tex]V=4\pi b^{2}(5b+3)[/tex].

[tex]V=\pi r^{2} h[/tex]

[tex]V=\pi r^{2} h\\ \\V=\pi (2b)^{2} (5b+3)[/tex]

[tex]V=\pi (2^{2} b^{2} ) (5b+3)\\ \\V=\pi (4 b^{2} ) (5b+3)[/tex]

Use the distributive property of multiplication in order to operate.

[tex]V=\pi (4 b^{2} ) (5b+3)\\ \\V=\pi ((4 b^{2})(5b)+(4 b^{2})(3))\\ \\V=\pi ((20b^{3} )+(12 b^{2}))\\ \\V=4\pi (\frac{20b^{3}}4} +\frac{12 b^{2}}{4} )\\ \\V=4\pi (5b^{3} +3b^{2})\\ \\V=4\pi b^{2}(\frac{5b^{3}}{b^{2}} +\frac{3b^{2}}{b^{2}} )\\ \\V=4\pi b^{2}(5b+3)[/tex]

[tex]V=4\pi b^{2}(5b+3)[/tex].

The mass of the rectangular box B where B is the box determined by 0≤x≤1, 0≤y≤4, and 0≤z≤4 is 736.77

According to the question,

A rectangular box B is given with density ρ(x , y , z) = ze^(x+y)

We will find the mass of rectangular box B by using Triple integration method

In the question, The boundary limit for the density is given

0≤x≤1, 0≤y≤4, and 0≤z≤4

Mass formula = [tex]\int\int\int\limits_B {\rho (x,y,z)} \, dV[/tex]

Where , dV is dz dy dx

So, [tex]\int\limits^1_0 \int\limits^4_0 \int\limits^4_0 {\rho(x,y,z)} \, dz dy dx[/tex]

Putting  ρ(x , y , z) = ze^(x+y)

=> Mass = [tex]\int\limits^{1}_{0} \int\limits^{4}_{0} \int\limits^{4}_{0} ze^{(x+y)} \, dz dy dx[/tex]

=> [tex]\int\limits^{1}_{0} \int\limits^{4}_{0}e^{(x+y)} [\frac{z^{2}}{2}]^{4}_{0} \, dy dx[/tex]

=> [tex]\int\limits^{1}_{0} \int\limits^{4}_{0} 8e^{(x+y)} \, dy dx[/tex]

=> [tex]\int\limits^{1}_{0} \int\limits^{4}_{0} 8e^{x}e^{y} \, dy dx[/tex]

=> [tex]\int\limits^{1}_{0} 8e^{x} [e^{y}]^{4}_{0} \, dx[/tex]

=> [tex]\int\limits^{1}_{0} 8e^{x} (e^{4}-1) \, dx[/tex]

=> [tex]8 (e^{4}-1) [e^{x}]^{1}_{0}[/tex]

=> [tex]8 (e^{4}-1) (e^{1}-1)[/tex]

=> 8(e⁴⁺¹ - e⁴ - e¹ + 1)

=> 8(e⁵- e⁴ - e¹ + 1)

Writing value of exponential function,

Mass of rectangular box B = 736.77

Hence, The mass of the rectangular box B where B is the box determined by 0≤x≤1, 0≤y≤4, and 0≤z≤4 is 736.77

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Answer:

12.6

Step-by-step explanation:

Use pythag

8 / 2 = 4

a² + b² = c²

4² + 12² = c²

16 + 144 = c²

c² = 160

c = 12.6

The lowest common multiple (LCM) of the numbers 22 and 38 is 418.

The L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers, while H.C.F. defines the highest common factor present in between given two or more numbers,

Given the numbers 22 and 38, we can express them as products of their prime factors and thus derive their LCM as follows;

22 = 2 × 11

38 = 2 × 19

LCM = 2 × 11 × 19

LCM = 418

Therefore, the LCM of 22 and 38 is 418 using prime factor method.

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Step-by-step explanation:

To find Δy and Δx (change in y and change in x), you need to do y2-y1 and x2-x1.

Example on how to solve problem 1:

change in y: Pick 2 numbers from the y side of the table that are next to each other (it doesn't matter which 2 ). You're going to subtract the first one one the list that you picked from the second one from the list that you picked. example: 4-1= 3

change in x: repeat the same process with the x side of the table (make sure that you pick x points that go with the y, otherwise it won't work). If you picked 4-1 on the y table, the you have to pick 0- -3, which equals 3 (due to two negatives making a positive).

now, you divide your change in y by your change in x. example: 3÷3 = 1. This means that your m (slope) = 1 (on the first problem)

This kinda sounds confusing but hope this helps a bit. If not, you can look up lots of tutorials online with better explanations :)

By comparing the credit card and debit card we noticed that the uses of debit card are most preferable.

The card that allows a card holder to pay electronically while purchasing.

The debit card is directly connected to card holder's bank account.

The card that allows a card holder to borrow funds within a pre-approved credit limit.  It also helps a card holder to purchase by borrowing money.

The one of the most advantages of debit card compared to a credit card is a debit card has automatic overdraft protection.

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The 95% confidence interval for the mean reduction in cholesterol level is given as follows:

(51.3, 96.7).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 7 df, is t = 2.3646.

From the image given at the end of the answer, the sample of the differences is given as follows:

37, 72, 86, 78, 60, 47, 124, 88.

Hence the parameters are given as follows:

[tex]\overline{x} = 74, s = 27.1, n = 8[/tex]

Then the lower bound of the interval is of:

74 - 2.3646 x 27.1/square root of 8 = 51.3.

The upper bound of the interval is of:

74 + 2.3646 x 27.1/square root of 8 = 96.7.

The table is given by the image shown at the end of the answer.

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The data form a 2x4 frequency matrix and the ratio of each cell represents the result. Each participant's rating is a birth order category (1, 2, 3, 4). The Mann-Whitney test can assess the significance of differences between groups.

The chi-square test of independence determines whether the proportions are significantly different for each birth order group. Effect sizes are measured in Cramer's V. Alternatively, the data form two sets of ratings, one for each personality group. Each participant's rating is a birth order category (1, 2, 3, 4). The Mann-Whitney test can assess the significance of differences between groups.

The chi-square test (also called chi-square or chi-square test) is a statistical hypothesis test used in contingency table analysis when the sample size is large. Simply put, the main purpose of this test is to test whether two categorical variables (the two dimensions of the contingency table) independently affect the test statistic (the values ​​in the table) . The test is valid when the test statistic is a chi-square distribution based on the null hypothesis, specifically Pearson's chi-square test and variants thereof. Use Pearson's chi-square test to determine whether there is a statistically significant difference between the expected and observed frequencies for one or more categories in the contingency table. For contingency tables with small sample sizes, Fisher's exact test is used instead.

In statistics, the Mann-Whitney U test (also known as the Mann-Whitney-Wilcoxon (MWW/MWU), Wilcoxon rank sum test, or Wilcoxon-Mann-Whitney test) is a test of the null hypothesis used at random. It is a non-parametric test. Values ​​X and Y selected from two populations where the probability of X being greater than Y is equal to the probability of Y being greater than X.

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The correct option that describes the vertical asymptote is; A: At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

f(x) = 8(x - 1)/(x² + 2x - 3)

Simplifying the denominator gives;

(x² + 2x - 3) = (x + 3)(x - 1)

Thus, our function is;

f(x) = 8(x - 1)/[(x + 3)(x - 1)]

(x - 1) will cancel out to give;

f(x) = 8/(x + 3)

Vertical asymptote:

Point in which the denominator is 0, so:

(x + 3) = 0

x = -3

Thus, we conclude that x = -3 is the vertical asymptote

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Answer:

x<2

Step-by-step explanation:

Cancel terms that are in both the numerator and denominator

And, Divide the numbers

I hope this answers your question :)

The expression Salina created using the greatest common factor in addition and distributing the property is

9(4 + 6)

9x4 + 9x6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

36 + 54

Taking out the greatest common factor.

9(4 + 6)

Using the distributive property over addition

9 x 4 + 9 x 6

Thus,

9 x 4 + 9 x 6 is the expression Salina created.

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They should sell at least 40 items to make a profit of at least $65.

Inequality is a relationship between two expressions which are not equal and connected by the signs, ≤, ≥, <, and >

Given that, the students of a class want to make a profit of at least $65 by selling items they spent $55 for the materials to make the items they will sell each item for $3

Since, they want $65 at least profit,

Therefore, selling price for the profit = 55+65 = $120

Profit = Selling price - cost price

Since, selling price of each item = $3

Let they are selling x items, Therefore, selling price for x items = 3×x = $3x

Now, establishing the inequality,

3x ≥ 120

x  ≥ 120/3

x  ≥ 40

Hence, there should be 40 or more items to be sold.

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Label a ray with endpoint Y. An appropriate name for a ray whose endpoint is XY displays a ray with the endpoint Y.

A line with a single defined endpoint that continuously moves away from another is known as a ray (endpoint B in this case).

A segment of a line that lacks an endpoint but has a specified starting point. It can go on forever in a single direction. A ray cannot be measured since it has no end point.

In mathematics, a ray is a segment of a line with a definite starting point but no ending. It can go on forever in a single direction. A ray cannot be measured since it has no end point. Two rays with the same terminal are united to form an angle. The vertex of the angle is referred to as the common endpoint of the rays, while the sides of the angle are referred to as the rays themselves.

The ray in the hypothetical situation has one endpoint B and an endlessly extending endpoint A. (as shown by the arrowhead).

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The pounds of the jellyfish's weight in water is 418

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.

Three categories of expressions exist:

There can only be one possible mathematical value from a mathematical expression.

A character expression results in a single character value when evaluated.

A logical or relational expression yields only one logical value upon evaluation.

Given ,

pound = 440

jelly fish weight = 440*95/100

= 418

Therefore The pounds of the jellyfish's weight in  water is 418

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