when y is directly proportional to x. When x= 2.5, y=20. what is the value of y when x= 22?

Answers

Answer 1
If it’s proportional that means you can put it in a ratio
Y:X
20:2.5
8:1
176:22

Related Questions

on a map, 1 inch equals 8.7 miles. If two cities are 2.5 inches apart on the map, how far are they actually apart?

The distance between the cities is ? miles

Answers

Answer:

the distance between the cities is 21.75 miles.

Step-by-step explanation:

1 inch = 8.7 miles.

2.5 inches x 8.7 miles/inch = 21.75 miles

Let's say you (a 16-year old) open a savings account with an interest rate of 6% per year and you
aren't adding any additional funds in the future. If you make $80,000 within the year you turn 60, what
is the total amount in your account at 60 years old?

Answers

The total amount in the account when turning 60 years is A = $ 11,13,706.08

Given data ,

A savings account with an interest rate of 6% per year and you aren't adding any additional funds in the future

Now , you make $80,000 within the year you turn 60

So , the number of years = 60 - 16 = 44 years

And , from the compound interest , we get

A = P ( 1 + r/n )ⁿᵇ

On simplifying , we get

Where A is the final amount, P is the initial amount (which is 0 in this case), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (let's assume it is compounded monthly, so n=12), t is the time in years (44 years from age 16 to age 60).

A = 80,000 ( 1 + 0.06/12 )¹²ˣ⁴⁴

A = $ 11,13,706.08

Hence , the amount in account is A = $ 11,13,706.08

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Please solve this question

Answers

Answer:

A.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

id

LIGHT The length of the shadow S given by a tower
that is 100 meters high is S = 100/tan θ, where θ
is the angle of inclination of the sun. If the
angle of inclination is 45°, find the length of the shadow.
a. 162 m
b. 62 m
c. 100 m
d. 84 m

Answers

Answer:

  c.  100 m

Step-by-step explanation:

You want the length of the shadow of a 100 m tower if the angle of inclination of the sun is 45°.

Isosceles right triangle

The tower and its shadow are modeled as legs of a right triangle. When the acute angle in such a triangle is 45°, the triangle is isosceles and the legs are the same length.

The shadow is the same length as the height of the tower: 100 m.

__

Additional comment

You can check this by using the formula:

  S = 100/tan(45°) = 100/1 = 100

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Cody works at a vehicle rental company. The vehicles available to rent are listed in the table.



What is the ratio of seats to engine cylinders in the truck?

Answers

The Ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent is approximately 0.625.

The ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent can be calculated by dividing the number of seats by the number of engine cylinders. In this case, the Ford F-150 has a seating capacity of 5 passengers and a V8 engine configuration.

To calculate the ratio, we divide the number of seats (5) by the number of engine cylinders (8):

Ratio of seats to engine cylinders = Number of seats / Number of engine cylinders

Ratio of seats to engine cylinders = 5 / 8

Simplifying the ratio, we get:

Ratio of seats to engine cylinders = 0.625

Therefore, the ratio of seats to engine cylinders in the Ford F-150 truck that Cody wants to rent is approximately 0.625.

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Note the full question may be :

Cody works at a vehicle rental company. The vehicles available to rent are listed in the table below:

Vehicle Type  |  Seats  |  Engine Cylinders

----------------------------------------------

Car           |    5    |         4

SUV           |    7    |         6

Truck         |    3    |         8

What is the ratio of seats to engine cylinders in the truck?

A. 1:3

B. 3:8

C. 8:3

D. 3:1

Choose the correct option that represents the ratio of seats to engine cylinders in the truck.

HELP ASAP PHOTO INCLUDED

Answers

I cannot solve that problem at the moment.

Step-by-step explanation:

But I will help you in the future

[tex]f(x)=\frac{x-3}{x+7}[/tex] find the domain

Answers

The domain of the function f(x) is all real numbers except x = -7. In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

To find the domain of the function f(x) = (x - 3)/(x + 7), we need to determine the values of x for which the function is defined.

The function is defined for all values of x except those that make the denominator, x + 7, equal to zero.

Division by zero is undefined in mathematics.

So, we set the denominator equal to zero and solve for x:

x + 7 = 0

x = -7

Hence, the only value that makes the denominator zero is x = -7. Therefore, the domain of the function f(x) is all real numbers except x = -7.

In interval notation, we can express the domain as (-∞, -7) ∪ (-7, +∞).

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Answer these 3 questions if not able to answer all try question 10 thank you

Answers


9. A function p(x) with x intercepts of (-1,0) and (3,0) can be written as p(x) = a(x+1)(x-3), where 'a' is the leading coefficient.

10. The vertex form of the parabola is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex of the parabola. Since the parabola is translated 5 units down and 2 units right from the parent function f(x), its vertex is at (-2+2, 6-5) = (0,1). We can substitute (-2,6) into the equation and solve for 'a' to get the final equation.

f(x) = a(x-0)^2 + 1

6 = a(-2-0)^2 + 1

5 = 4a

a = 5/4

Therefore, the equation of the parabola in vertex form is f(x) = (5/4)(x-0)^2 + 1.

(If this doesn’t seem right to you comment!)

Need help Which of the following is not an expression?
• A. 3x+4 = 7
O B. x+8
ㅇ G0-품
O D. 2x -

Answers

The answer is A, because it includes an equals sign and a statement of equality.

A. 3x + 4 = 7 is not an expression, but an equation because it includes an equals sign and a statement of equality.

B, C, and D are all expressions. Expression refers to a mathematical phrase that can include numbers, variables, and mathematical operations, but does not contain an equals sign or a statement of equality.

B. x + 8 is a simple expression that includes a variable and a constant.

C. 6 - x/5 is also an expression that involves a constant and a variable, and uses a division operation.

D. 2x-3 is another expression that includes a variable and a constant, and uses a subtraction operation.

Therefore, the answer is A, since it is not an expression.

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Select all of the following that are quadratic equations. 5 x 2+ 15 x = 0 6 x - 1 = 4 x + 7 x 2 - 4 x = 4 x + 7 2 x - 1 = 0 3 x 2 + 5 x - 7 = 0 x 3 - 2 x 2 + 1 = 0

Answers

Answer:

Options A, C and E

-----------------------

Quadratic equation has the form of:

ax² + bx + c = 0

Analyze the given equations and see which has the same form:

A) 5x² + 15 x = 0, Yes, quadratic equation;B) 6 x - 1 = 4, No, it is a linear equation;C) x + 7x² - 4 x = 4, Yes, quadratic equation;D) x + 72x - 1 = 0, No, it is a linear equationE) 3x² + 5x - 7 = 0, Yes, quadratic equation;F) x³ - 2x² + 1 = 0, No, it is cubic equation

Percy's Desserts made a batch of fresh scones with 5/8 of a pound of butter and 1/2 of a
pound of sugar. How much more butter than sugar was used?
Write your answer as a fraction or as a whole or mixed number.
pounds

Answers

Answer:

Step-by-step explanation:

To find the difference between the amount of butter and sugar used, we need to subtract the weight of sugar from the weight of butter.

The weight of butter used is 5/8 pounds, and the weight of sugar used is 1/2 pounds. To subtract these fractions, we need to find a common denominator.

The common denominator for 8 and 2 is 8, so we can rewrite the fractions as follows:

5/8 pounds of butter

4/8 pounds of sugar

Now we can subtract the weight of sugar from the weight of butter:

5/8 - 4/8 = 1/8

Therefore, Percy's Desserts used 1/8 pound more butter than sugar.

Answer: Percy's Desserts used 1/8 pounds more butter than sugar in their batch of fresh scones.

Step-by-step explanation:

1. Identify the quantities of butter and sugar used: Percy's Desserts used 5/8 of a pound of butter and 1/2 of a pound of sugar.

2. Convert the quantities to a common denominator: To compare these quantities, we need to express them with a common denominator. The least common denominator of 8 and 2 is 8. So, we express 1/2 as 4/8.

3. Subtract the quantity of sugar from the quantity of butter: Now that both quantities are expressed in eighths of a pound, we can subtract them: 5/8 - 4/8 = 1/8.

4. Convert the result back to a decimal: 1/8 of a pound is equivalent to 0.125 pounds.

So, Percy's Desserts used 0.125 pounds more butter than sugar in their batch of fresh scones.

100 Points! Geometry question. Photo attached. Determine whether the quadrilateral is a parallelogram. Justify your answer using a theorem. Please show as much work as possible. Thank you!

Answers

The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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Given circle E with diameter CD and radius EA. AB is tangent to E at A. If AB=34 and EB=38, solve for EA. Round to the nearest tenth if necessary

Answers

The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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What can be interpreted from the scatter plot above

Answers

The thing that can be interpreted from the scatter plot above is A. There is a negative association between number of hours of daily TV viewing and math quiz scores.

How to explain the scatterplot

As per given scatter plot, If the number of hour of daily TV viewing increases then the math quiz scores are decreases.

Hence, the number of hour of daily TV viewing and math quiz scores varies inversely.

Therefore, There is a negative ath association between number of hour of daily TV viewing and math quiz scores

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The sin(n/4)equals ?

A. 0.0137
B. 0.7071

Answers

The value of function sin (π/4) is,

⇒ sin π/4 =  0.7071

We have to given that;

The expression is,

⇒ sin π/4

Now, We can simplify the expression as;

⇒ sin π/4

⇒ 1 / √2

⇒ 1 / 1.414

⇒ 0.7071

Thus, The value of function sin (π/4) is,

⇒ sin π/4 =  0.7071

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

The correct answer:

(A) WZ/WX = XW/YW

mathmatically indication example with solution

Answers

A mathematically indication example would be to solve the equation 3x + 2 = 14 for the value of x. The solution would be 4.

How to solve the equation ?

Looking for a mathematically indication example, we can consider a simple mathematical equation with one variable and solve it.

The equation would be 3 x + 2 = 14.

So we can solve for the equation to be :

3x + 2 - 2 = 14 - 2

3x = 12

3 x / 3 = 12 / 3

x = 4

In conclusion, the mathematically indication example would be 3x + 2 = 14 and the value of x would be 4.

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According to the table below, What is the domain of the data

Answers

Answer:

Domain: {15, 17, 19, 21, 23}

Step-by-step explanation:

The domain describes the x-values within a function.

Inputs

In a function, the inputs are the values that are plugged into a function, and the outputs are the resulting values. This means that the inputs represent the x-values and the outputs are the y-values. Since this is a function, each of the inputs has one output. So, each input is unique. We can use the input values to find the domain.

Domain

The domain of a data set is the x-values. Each x-value is one part of the domain. The domain is written as a list of values in numerical order with braces surrounding the values. Since the inputs represent the x-values, we can use the input values as the domain values. This means that the domain of the data is {15, 17, 19, 21, 23}.

The cost of 4 pairs of shorts and 3 sweatshirts is $89. The cost of 9 pairs of shorts and 11 sweatshirts is $247
Enter the cost of one pair of shorts and one sweatshirt

Answers

$11 for one sweatshirt and $14 for a pair of shorts.

Consider the following symbolic logic statement: ¬ (∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))
a) Translate the statement into English using proper syntax and semantics.
b) Identify and explain any potential ambiguities in the translated statement.
c) Rewrite the statement in a way that eliminates any ambiguities and maintains the original meaning.

Answers

(a). The statement can be translated into English as follows "Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)." (b) The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x).  (c). This clarifies that the negation applies to the existence of x such that P(x) and Q(x).

a) Translation into English:

The statement can be translated into English as follows:

"Not exists x such that P(x) and Q(x), and for all y, if R(y) then P(y)."

b) Potential ambiguities in the translated statement:

Ambiguity in the scope of negation: The placement of the negation symbol "¬" might lead to ambiguity. It is not clear whether the negation applies only to the existential quantifier (∃x) or to the entire statement. Specifically, it is unclear if the negation applies to both conjuncts separately or to their conjunction as a whole.

Ambiguity in the scope of quantifiers: The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which variables the quantifiers bind to and how they relate to the predicates P(x), Q(x), R(y), and P(y).

c) Rewritten statement to eliminate ambiguities while maintaining the original meaning:

To eliminate the ambiguities, we can rewrite the statement as follows:

(¬∃x)(P(x) ∧ Q(x)) ∧ (∀y)(R(y) → P(y))

The rewritten statement explicitly places the negation symbol "¬" only in front of the existential quantifier (∃x). This clarifies that the negation applies to the existence of x such that P(x) and Q(x). Additionally, parentheses are used to explicitly define the scope of the quantifiers (∃x) and (∀y), making it clear which variables they bind to.

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Please help answer theses questions

Answers

Answer:

Question 6 :  True

Question 7:  False

Step-by-step explanation:

To find g(f(x)) given f(x) and g(x), substitute the expression for f(x) for every x in g(x)

f(x) = 2x

g(x) = x²

g(f(x) = (2x)² = 4x²

So True

f(x) = x² + x

g(x) = 2x + 1

g(f(x)) = 2(x² + x) + 1 = 2x² + 2x + 1

So False

Consider a sample with six observations of 16, 11, 13, 22, 15, and 19. Compute the z-score for each observation.

Answers

The z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

To compute the z-scores for each observation in the sample, we need to first calculate the mean and standard deviation of the data set.

Given the sample with observations: 16, 11, 13, 22, 15, and 19.

Calculate the mean (μ):

Add up all the observations and divide by the total number of observations.

Mean (μ) = (16 + 11 + 13 + 22 + 15 + 19) / 6 = 96 / 6 = 16.

Calculate the standard deviation (σ):

Subtract the mean from each observation.

Deviation = Observation - Mean

Square each deviation.

Squared Deviation = Deviation²

Calculate the average of the squared deviations.

Average Squared Deviation = (Squared Deviation1 + Squared Deviation2 + ... + Squared Deviation6) / 6

Take the square root of the average squared deviation.

Standard Deviation (σ) = √(Average Squared Deviation)

Let's calculate each step:

Deviation1 = 16 - 16 = 0

Deviation2 = 11 - 16 = -5

Deviation3 = 13 - 16 = -3

Deviation4 = 22 - 16 = 6

Deviation5 = 15 - 16 = -1

Deviation6 = 19 - 16 = 3

Squared Deviation1 = 0² = 0

Squared Deviation2 = (-5)² = 25

Squared Deviation3 = (-3)² = 9

Squared Deviation4 = 6² = 36

Squared Deviation5 = (-1)² = 1

Squared Deviation6 = 3² = 9

Average Squared Deviation = (0 + 25 + 9 + 36 + 1 + 9) / 6 = 80 / 6 = 13.33

Standard Deviation (σ) = √13.33 ≈ 3.65

Now that we have the mean (μ = 16) and standard deviation (σ ≈ 3.65), we can calculate the z-score for each observation.

The z-score (Z) for an observation (X) is calculated using the formula:

Z = (X - μ) / σ

Let's calculate the z-scores for each observation:

Z1 = (16 - 16) / 3.65 = 0 / 3.65 = 0

Z2 = (11 - 16) / 3.65 = -5 / 3.65 ≈ -1.37

Z3 = (13 - 16) / 3.65 = -3 / 3.65 ≈ -0.82

Z4 = (22 - 16) / 3.65 = 6 / 3.65 ≈ 1.64

Z5 = (15 - 16) / 3.65 = -1 / 3.65 ≈ -0.27

Z6 = (19 - 16) / 3.65 = 3 / 3.65 ≈ 0.82

So, the z-scores for the observations 16, 11, 13, 22, 15, and 19 are approximately 0, -1.37, -0.82, 1.64, -0.27, and 0.82, respectively.

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Can someone please answer and provide an explanation for these problems?

Answers

(17) The length of the arc is 39.27 in

(18) The length of the arc is 70.7 cm

(19) The area of the sector is 395.84 in²

(20) The area of the sector is 38.5 cm².

What is the area of the sector?

The area of each of the sector is calculated by using the following formula;

Area = πr² (θ/360)

Where;

r is the radiusθ is the angle subtended by the sector

The formula for length of arc is given as;

length of arc = 2πr (θ/360)

(17) The length of the arc is calculated as;

L = 2π (10 in) (225/360)

L = 39.27 in

(18) The length of the arc is calculated as;

L = 2π (15 cm) (270/360)

L = 70.7 cm

(19) The area of the sector is calculated as;

A = π(12)² (315/360)

A = 395.84 in²

(20) The area of the sector is calculated as;

A = π(7)² (90/360)

A = 38.5 cm²

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9*
Giovanni needs to hire a handyman to paint his house. Charles will charge him
$115 up front and $30 per hour. Peter will charge $40 per hour with an $80 flat fee
for paint. After how many hours will the two men charge the same amount to
complete the job?

Answers

The two men will charge the same amount to complete the job after 3.5 hours.

How to determine After how many hours will the two men charge the same amount to complete the job?

Let's start with Charles' fee, which is a combination of an upfront fee and an hourly fee. We can represent this as:

C(x) = 115 + 30x

where x is the number of hours Charles works.

For Peter, his fee is a combination of an upfront fee for paint and an hourly fee. We can represent this as:

P(x) = 80 + 40x

where x is the number of hours Peter works.

To find out when the two men will charge the same amount to complete the job, we need to set the two equations equal to each other and solve for x:

115 + 30x = 80 + 40x

Subtracting 30x from both sides: 115 = 80 + 10x

Subtracting 80 from both sides: 35 = 10x

Dividing both sides by 10:

x = 3.5

So, the two men will charge the same amount to complete the job after 3.5 hours.

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Find m/ABC.
A. 81°
B. 86°
C. 47°
D. 49.5°
Α.
99°
B
D
94%
C

Answers

m/ABC=86° (because of the cyclic quadrilaterals). Hence, Option (B) is correct.

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

m/ABC +  m/ADC  = 180°

m/ABC + 94° = 180°

m/ABC = 180° - 94°

m/ABC = 86°

Similarly, one can find m/DCB

m/DAB +  m/DCB  = 180°

99° + m/DCB = 180°

m/DCB = 180° - 99°

m/DCB = 81°

Hence, m/ABC = 86°

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PLEASE HELP ASAP 25 POINTS

Answers

Answer:

A) Using Commutative property

Step-by-step explanation:

In step 1, it used distributive property when the number 5 is distributed inside of the equation in the parenthesis.

In Step 4, dividing both sides by 10 to further simplify the equation

In step 2, you combined like terms and it results to the equation in step 3

What is the volume of this figure?

Enter your answer in the box.

ft³
Three-dimensional figure formed by placing two rectangular prisms together to form an L shape where the bottom of the L is on the left and the top of the L extends to the right. The wider part of the L has a width of 3 feet. The other part of the L has a width of 2 feet. The total length of the L is 7 feet, and the length of the narrower part of the L is 6 feet. The height connecting the L shaped bases is 5 feet.

Answers

The volume of the rectangular prism in this problem is given as follows:

99 ft³.

How to obtain the volume of a rectangular prism?

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem can be divided into two prisms, with dimensions given as follows:

3 ft, 5 ft and 7 - 6 = 1 ft.6 ft, 2 ft and 7 ft.

Hence the volume of the prism is given as follows:

V = 3 x 5 x 1 + 6 x 2 x 7

V = 99 ft³.

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Four points are plotted on the number line. Which point best represents 33 1/3% of the distance between zero and one

Answers

The point Y best represents 33 1/3% of the distance between zero and one.

We know that if the mixed fraction a b/c can expressed as improper fraction in below way:

a b/c = (a*c + b)/c

Here the given the mixed fraction is = 33 1/3 = (33*3 + 1)/3 = 100/3

The distance between the point 0 and 1 is given by = 1 - 0 = 1

So the required percentage of the distance = 1*(33 1/3%) = 1*(100/3 %) = 100/(3*100) = 1/3.

From the number line given we can see that the distance between 0 and 1 is divided in to 12 equal parts.

So, 33 1/3% stands at = 12*(1/3) = 4 th parts that is point Y.

Hence the point Y best represents 33 1/3% of the distance between zero and one.

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The question is incomplete. The complete question will be -

Need help with this homework

Answers

Answer:

Step-by-step explanation:

use gauth math it helps with maths

here is my algebra 13 homework screenshot. can someone please help me quick!!

Answers

The slope of the graph f(x) = (1/3)x + 4 is less than the slope of g(x) = 4x-1

f(x) = 1/3 x + 4

g(x) = 4x - 1

The equation of line is given by y = mx +c

On comparing both equation with y = mx + c

m is the slope of the line and c is the intercept of the equation

Let the slope of f(x) is m₁

In f(x) =1/3 x + 4

m₁ = 1/3 = 0.33

Let the slope of g(x) is m₂

In g(x)  = 4x - 1

m₂ = 4

m₁ < m₂

slope of f(x) is less than slope of g(x)

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The weight of a person ABC is 65 kg. About 11. 5kg of his weight is due to the fat deposits in the body. He went for a hunger strike. Can you explainhow long he can survive?i. Without water and food?ii. Without food but with water? increasing crystal field strength of the different ligands is list the shipping city and state for the order that had the longest shipping delay. x His sister drove him to the audition-an obstacle course ofcooking tests to help the owners of the restaurant select anassistant.In this sentence from paragraph 4, the author compares theaudition for the restaurant assistant to an obstacle course toshow thatAthe head chef would be difficult to workwith. what causes a sodium atom to be larger than a lithium atom? Solving for Rates What annual rate of return is implied on a $1,400 loan taken next year when $2,700 must be repaid in year 9? Multiple Choice a. 7.57%b. 11.61% c. 8.56%d. 10.32% the radioactive isotope 237 th 90 has a rate constant of, k = 4.91 x 10^-11 yr^-1. is this nuclide useful for determining the age of bone samples? TRUE OR FALSE recent anthropological evidence support the evolutionary argument that men's tendency to commit violence was biologically transmitted Why is it important to look at the effect size?a. Because p values are not affected by Sphericity corrections but they do alter effect sizes.b. Because p values can be affected by Sphericity errors but they do not alter effect sizes.c. Because p values can be affected by Sphericity corrections and alter effect sizes.d. Because p values can be affected by Sphericity corrections but they do not alter effect sizes. Let vi = [1 0 1 1 ] , v2= [1 6 1 -2] , v3=[1 0 -1 0] , v4=[-1 1 -1 2]. Let W1 Span {V1, V2} and W2 = Span {V3, V4}. (a) Show that the subspaces W1 and W2 are orthogonal to each other. (b) Write the vector y = [1 2 3 4] as the sum of a vector in W1 and a vector in W2. create a cisco access control list entries to allow the outside world to get access to your web server. your web server has the ip address of 6.45.31.42 Which of the following is a FALSE statement about a chi-square test? (Select all that apply) The chi squared distributions assuming the null is true are symmetric distributions It is can be used for data summarized into one or two categorical variables The Chi Squared Test statistic is computed as: (Obs Count-Exp Count)^2 summed over each categorical level Degrees of freedom does not depend on sample size A chi-square test-statistic will always be nonnegative (zero or positive).Previous question In order to study the effect of an antibiotic on a bacterial growth, you design an experiment in which you add varying concentrations of antibiotic to several groups of bacteria. you keep the exposure to light and the temperature constant among the various groups. what is an appropriate control? Nynet, inc., paid a dividend of 4.18 last year. The company management does not expect to increase its dividend in the foreseeable future. If the required rate of return is 18.5 percent. What is the current value of the stock? a man walks 18m east then 9.5 north. what is the direction of his displacement? 62o 28o 242o 208o Consider the vector field F(x,y)=zk and the volume enclosed by the portion of the sphere x2+y2+z2=a2 in the first octant and the planes x=0, y=0, and z=0.(a) Without using the Divergence Theorem, calculate the flux of the vector field across the ENTIRE surface of the volume in the direction away from the origin.(b) Using the Divergence Theorem, calculate the same flux as in the previous part. (Answer should be the same) Compare the Maastricht Treaty convergence criteria with the OCA criteria. How are these convergence criteria related to the potential benefits and costs associated with joining a currency union? If you were a policymaker in a country seeking to join the EMU, which criteria would you eliminate and why? If sin(x) = 1/4 and x is in quadrant I, find the exact values of the expressions without solving for x. (a) sin(2x) (b) cos(2x) (c) tan(2x) A small telescope has a concave mirror with a 2.4 m radius of curvature for its objective. Its eyepiece is a 4.4 cm focal length lens.a. What is the telescopes angular magnification?b. What angle (in degrees) is subtended by a 25,000 km diameter sunspot? Assume the sun is 1.50 108 km away.c. What is the image angular size (in degrees) in this telescope? consider the following initial-value problem. y' 6y = f(t), y(0) = 0,