more workers what sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in exercise 36(b)? justify your answer.

The total area of the two triangles is 28 square inches.

Step 1: Calculate the area of the first triangle.

The first triangle is a right triangle with a base of 4 inches and a height of 3 inches.

Area of a triangle = (1/2) * Base * Height

Area of the first triangle = (1/2) * 4 * 3 = 6 square inches.

Step 2: Calculate the area of the second triangle.

The second triangle is an isosceles triangle with a base of 4 inches and a height of 4 inches.

Area of a triangle = (1/2) * Base * Height

Area of the second triangle = (1/2) * 4 * 4 = 8 square inches.

Step 3: Add the areas of the two triangles.

Total area = 6 + 8 = 14 square inches.

Learn more about area here

https://brainly.com/question/13194650

#SPJ4

The volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

Rectangular Prism:

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here.

The Volume of a Rectangular Prism Formula is,

The volume of a Rectangular Prism (V) = l × b × h

Where,

“b” is the base length of the rectangular prism

“l” is the base width of the rectangular prism

“h” is the height of the rectangular prism

The formula for the volume of a rectangular prism is length x width x height. So, the volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.

To learn more about rectangular prism, refer to the link:brainly.com/question/21308574

#SPJ4

The sample correlation coefficient, is represented as  r, measures the strength of correlation  and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the  positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.

The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.

A positive correlation tells us  that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.

So, the value of the sample correlation coefficient between the  rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as  correlated and how strong is this correlation occurs.

To know more about  correlation coefficient,  , click here:

brainly.com/question/15577278

#SPJ4

Grade 7 maths includes integers, shapes, and symmetry etc. that is incorporated with the earlier study of previous grades.

Grade 7 math covers many topics, including: number sense and operations, geometry, data analysis, probability and statistics, expressions and equations, and problem solving. Number sense and operations involves understanding the properties of integers, rational numbers, and real numbers, and how to use them in operations and equations. Geometry focuses on understanding the properties of shapes and angles, and how to measure, construct, and classify them. Data analysis involves collecting, organizing, and interpreting data, as well as understanding the concept of probability. Expressions and equations involves solving equations and manipulating algebraic expressions. Finally, problem solving involves using the knowledge from all of the topics to solve real-world problems. Grade 7 math builds on the fundamentals learned in earlier grades, and is essential for success in math classes in the future.

Learn more about integers here:

https://brainly.com/question/490943

#SPJ4

The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

To know more about probability visit: brainly.com/question/30034780

#SPJ4

The number of cupcakes and brownies Fwam could have purchased is 1.75b + 4.50c ≤50.

The word "inequality" is used in mathematics to refer to expressions that relate variables (for example the prices of different products) using symbols that are different from =, which is used in equations. Due to this, inequalities might have numbers, letters representing variables, and symbols such as ≤, <, >.

1. List the variables

b = cupcakes

c = brownies

4.50 = price of the cupcakes

1.75 = price of the brownies

50 = total money

2. Relate the variables

1.75b + 4.50c ≤50

Each product should be multiplied by its price

The total money can be equal to or less than 50 (≤)

The products should be added

Learn more about inequality in: https://brainly.com/question/20383699

#SPJ1

By using the properties of real numbers the given expression can be written as  -8y.

What is solving an expression?

Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

Given:

The given expression is, [tex]\frac{4}{3}(-6y)[/tex]

According to the distributive property of real numbers, if a, b, c are three real numbers the,

a(bc) = (ab)c

Using the associative property of multiplication, the given expression can be written as,

[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]

Hence, by using the properties of real numbers the given expression can be written as  -8y.

To know more about solving an expression, click on the link

https://brainly.com/question/723406

#SPJ4

Step-by-step explanation:

what is the question ?

solve for x and y ?

multiply the second equation by 3 and add that result to the first equation. then solve for x. then pick any original equation and solve for y.

-2x - 3y = 8

15x + 3y = 18

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

13x 0 = 26

x = 26/13 = 2

5×2 + y = 6

10 + y = 6

y = -4

Answer: [tex]90^{\circ}[/tex]

Step-by-step explanation:

By the converse of the alternate interior angles theorem, we need [tex]\angle CBA \cong \angle BAD[/tex].

The solution to the given initial-value problem is  x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

The given initial-value problem is a second-order differential equation: d2x dt2 + ω2x = f0 sin ωt, x(0) = 0, x '(0) = 0

First, we can solve the homogeneous equation d2x dt2 + ω2x = 0 using the method of characteristic equation. The characteristic equation is r2 + ω2 = 0, which has two solutions r1 = -ω, r2 = ω.

The general solution to the homogeneous equation can be expressed as:

x(t) = c1e-ωt + c2eωt

Next, we can solve the non-homogeneous equation d2x dt2 + ω2x = f0 sin ωt. Since the right-hand side of the non-homogeneous equation has a sinusoidal form, we can use the method of variation of parameters to solve it.

The particular solution can be expressed as:

x(t) = A sin ωt + B cos ωt

By substituting the initial conditions, we can get:

A = 0, B = 0

Therefore, the solution to the given initial-value problem is:

x(t) = c1e-ωt + c2eωt

The constant c1 and c2 can be determined by the initial conditions:

x(0) = c1 + c2 = 0

x'(0) = -ωc1 + ωc2 = 0

Therefore, c1 = -c2 and c1 + c2 = 0.

Hence, the solution to the given initial-value problem is:

x(t) = c1(e-ωt - eωt) = 2c1 sin ωt

Learn more about initial-value problem here:

https://brainly.com/question/8736446

#SPJ4

Answer: Ratios are proportional if they represent the same relationship.

Step-by-step explanation:

One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Equating the total costs of the two rental companies, they would cost the same amount after 625 driving miles.

An equation is a mathematical statement that claims that two or more mathematical expressions are equivalent or equal.

Equations use the equation symbol (=) to depict the equality of the expressions.

                                  Company A    Company B

Fixed rental charge         $75                 $100

Rental charge per mile  $0.07              $0.03

Let the number of miles driven = m

Total cost of Company A's rental = 75 + 0.07m

Total cost of Company B's rental = 100 + 0.03m

For the cost to be the same, 75 + 0.07m = 100 + 0.03m.

Solving for m:

75 + 0.07m = 100 + 0.03m

0.07m - 0.03m = 100 - 75

0.04m = 25

m = 625

Thus, for the two car companies' rental cost to be the same amount, one would rent a car for 625 miles.

Learn more about equations at https://brainly.com/question/2972832

#SPJ1

Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

What is the combination?

In simple words, combination involves the selection of objects or things out of a larger group where order doesn't matter. The formula for combination helps to find the number of possible combinations that can be obtained by taking a subset of items from a larger set.

If none of the numbers can be repeated, Joaquin can choose from a total of 22 numbers (0 through 21), and he needs to select three of them for his locker combination. This is a classic example of a combination problem, as the order in which he chooses the numbers does not matter. The number of ways to choose three numbers from a set of 22 without repetition is given by the formula for combinations:

C(22,3) = 22! / (3!(22-3)!) = 222120/(321) = 2310

So, Joaquin can choose from 2310 different locker combinations if none of the numbers can be repeated.

The name "combination lock" is appropriate because it refers to the process of combining numbers in a specific order to open the lock. In this case, the order of the numbers selected does not matter.

If Joaquin could repeat a number, but not use the same number twice in a row, the number of mathematical combinations are possible is given by the formula for permutations:

A(22,3) = 222120 = 9, 612

Hence, Joaquin would have 9, 612 different locker combinations if he could repeat a number, but not use the same number twice in a row.

To learn more about the combination visit,

brainly.com/question/11732255

#SPJ4

On solving the provided question we can say that so the value of triangle - y + Z = 1+ r = > 1 -r +

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

in triangle

by construction = y0 = r - 1

Pythagoras =  x² + y²

=> (1+r)² = x

=>  x = √(1+r)² - (1-r)²

Pythagoras  = x² + z² = 2²

=> z =√4-4r

so the value of triangle -

=> y + Z = 1+ r

=> 1 -r + 2√1 -r1 =  

=> r = -1 + √5/2

To know more about triangle visit:

brainly.com/question/2773823

#SPJ4

The complete question is "In the diagram, four circles of radius 1 with centres P, Q, R, and S are tangent to one another and to the sides of triangle ABC, as shown."

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal. AB = 8cm ; BC = 6.5 cm.

We should be aware that if a circle encircles a rectangle, its diameter is equal to the diagonal of the rectangle, where 2r is the reciprocal of the diagonal.

The formula for calculating the area of a circle is [pi r 2], which we should keep in mind. With respect to a rectangle, there is only one such circle.The Pythagorean theorem states that the diagonal of a rectangle with sides lengths a and b is equal to a2 + b2.

The radius is simply a2+b22 since the diagonal has a diameter.Keep this response on hand.

BC = x- 1.5

x * (x-1.5) = 52

x^2 - 1.5x - 52 = 0

Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25

We are searching only positive value

(1.5 + 14.5)/2 = 16 / 2 = 8 cm

AB = 8 cm

BC = 8 - 1.5 = 6.5 cm

To learn more about  area  refer

https://brainly.com/question/29301914

#SPJ1

The probability that a randomly selected participant dreams in black and white or color is 0.01

The probability that a randomly selected participant dreams in black and white or color is the sum of the probabilities of the individual events (dreaming in black and white or dreaming in color) and the probability of the intersection of the two events (dreaming in both black and white and color).

The probability of dreaming in black and white is the number of participants who dream in black and white divided by the total number of participants surveyed:

P(b) = 4/200

The probability of dreaming in color is the number of participants who dream in color divided by the total number of participants surveyed:

P(c) = 10/200

The probability of dreaming in both black and white and color is the number of participants who dream in both black and white and color divided by the total number of participants surveyed:

P(b ∩ c) = 12/200

The probability of dreaming in black and white or color is the sum of the individual probabilities and the intersection probability:

P(b ∪ c) = P(b) + P(c) - P(b ∩ c) = 4/200 + 10/200 - 12/200 = 2/200 = 1/100

The probability that a randomly selected participant dreams in black and white or color is 1/100.

To learn more about probability visit: brainly.com/question/30034780

#SPJ4

a) The velocity and position functions are given as follows:

b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...

The acceleration function for this problem is defined as follows:

a(t) = cos(t).

The velocity function is the integral of the acceleration function, hence it is given as follows:

v(t) = sin(t).

(as the integral of cos(t) is sin(t).)

The particle will be at rest when:

v(t) = 0.

Hence:

sin(t) = 0

t = arcsin(0)

t = kπ, k = ± 1, ± 2, ± 3, ...

The position function is the integral of the velocity function, hence it is given as follows:

s(t) = -cos(t) + 3.

As:

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

(a) A system of two equations, x=2 and y=3, is needed to express (2,3) in R2. (b) No, only two equations can express (2,3) in R2. (c) The maximum number of distinct equations that can be added is three. (d) Yes, the general form for the equations is x-2=0, y-3=0, and z=0.

(a) The smallest number of equations you would need is two. The system of linear equations would be:

x + 2y = 6

2x + 4y = 12

(b) Yes, you can add one more equation to the system in (a) so that the new system still has the unique solution (2,3). The equation would be:

3x + 6y = 18

(c) The maximum number of distinct equations you can add to your system in (a) to still maintain the unique solution (2,3) is three. The equations would be:

x + 2y = 6

2x + 4y = 12

3x + 6y = 18

(d) Yes, there is a general form for the equations in (c). The general form is:

ax + by = c, where a, b, and c are constants.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Yes , a right triangle with the given sides 6 cm 10 cm and 8cm can be formed because the sides satisfies the Pythagoras Theorem .

According to Pythagoras Theorem , the square of the hypotnuse of triangle is equal to the square of the other two sides of triangle ;

The sides of the triangle are given as : 6cm ,10cm and 8cm ;

which means that ,

the hypotnuse is = 10 cm ;

According to Pythagoras Theorem ;

⇒ [tex]10^{2} =8^{2} +6^{2}[/tex] ;

⇒ [tex]100 = 64 + 36[/tex] ;

⇒ [tex]100= 100[/tex] ;

the side satisfies the condition to form  the right triangle .

Therefore , the given sides forms a Right Triangle .

Learn more about Right Triangle here

https://brainly.com/question/30238309

#SPJ4

A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need.

One possible solution to the problem of food insecurity is to start a food pantry. A food pantry is a place where people can donate non-perishable food items for those in need. These items can include canned goods, boxed goods, and non-perishable items. People can then come to the pantry and take what they need. This helps to ensure that people in the community have access to the food they need.

A food pantry is a solution to food insecurity, where people can donate non-perishable food items for those in need. People can come to the pantry and take what they need, providing access to food for those in the community.

learn more about solution here

https://brainly.com/question/30109489

#SPJ4

The people who are interviewed constitute a convenience sample.

If the survey company is interviewing anyone who is available in the shopping mall without using any systematic method for selecting the participants, it would be considered a convenience sample.

In a convenience sample, the sample is selected based on ease of access to the participants, and it may not be representative of the entire population. This type of sampling can lead to bias in the sample, as the views of people who happen to be available in the mall at the time may not be representative of the views of the entire population.

To know more on convenience sample

https://brainly.com/question/1413932

#SPJ4

[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]

Answer: X stands for 10

Step-by-step explanation:

If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4

To convert a fraction to a decimal, you simply divide the numerator by the denominator.

To make the polynomial monic, divide even by leading term first.

Then, in order to create an equation even without linear element, replace x = y a12 for the supplied values of x2 + a1x + a0.

A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.

x3=y3 and y2=x2+xy+y2.

Finding a common denominator allows us to determine that x2 + y2 + xy=1 if xy+yx=1.

By multiplying by xy:

x2+y2=−xy

move every term to the left:

x2+xy+y2=0

Consequently, x3y3=(xy)(x2+xy+y2)=(xy)

x/y+y/x+1=0

=>(x²+y²+xy)/xy=0/1

=>x²+xy+ y²=0——(1)

Now, Since,x³-y³=(x-y)(x²+xy+y²)

=>x³ -y³=(x-y)(0). [from equation (1)]

=>x³ -y³=0,Ans.

To know more about  the polynomial monic visit:

https://brainly.com/question/30117170

#SPJ4

A function that depends on another function is referred to as a composite function.

Let's say the price of an item is $1

Scenario #1 - 40% off $1  = 40 cents OFF

The discounted price = 60 cents

Now the 10% off of 60 cents

60-6 = 54 cents.

Scenario #2 - 10% of $1

The discounted price = 10 cents

100(cents) - 10 = 90 cents

Now the 40% off of 90 cents

90-36 = 54 cents

Let's try another value to confirm

Let's say the price of an item is $2

Scenario #1  - 40% off $2 = 80 cents OFF

200-80= 120 = $1.20

Now the 10% off of $1.20

120-12= 108 = $1.08

Scenario #2 - 10% off $2 = 20 cents OFF

200-20 = 180= 1.80

Now the 40% off of $1.80

180-72 = 108 = 1.08

The complete question is,

A store offers a discount of 40 off any one regular-priced item. employees also get 10% off any purchases. in which order should the discounts apply so that the employee pays the least amount?

A. Employee discount then store discount

B. They are both the same

C. Store discount then employee discount

To learn more about composite function refer to:

https://brainly.com/question/10687170

#SPJ1

To create a model to represent (a+b), you could use a mathematical equation such as y = a + b.

Using mathematical concepts and terminology, a mathematical model is an abstract description of a concrete system. To make a forecast or offer insight, mathematical modeling is the act of generating a mathematical representation of a real-world phenomenon.

An equation set and a set of variables that define relationships between the variables make up a mathematical model, which often explains a system. There are numerous types of variables, including texts, boolean values, real or integer numbers, and more.

In this case, the equation y = a + b can be used. This equation represents a linear model where y is the dependent variable and a and b are the independent variables.

Learn more about model on:

https://brainly.com/question/17764105

#SPJ1

For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.

The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.

This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.

For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33

To learn more about keyboard visit:

brainly.com/question/24921064

#SPJ4

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

To learn more about starting lineups visit:

brainly.com/question/28140396

#SPJ4

The true statement is:

The asymptote of g(x) is the asymptote of f(x) shifted three units down.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = [tex](2/5)^x[/tex]

and, g(x) ==  [tex](2/5)^x[/tex] - 3

Now, Using translation the '-3' in g(x) shows the Vertical Translation down by 3 units.

Hence, The asymptote of g(x) is the asymptote of f(x) shifted three units down.

Learn more about Function here:

https://brainly.com/question/12431044

#SPJ1

If Last year, Christine had $20,000 to invest. The amount that she invest in each account is First account $16,000 and Second account: $4,000.

Let x represent the amount Christine invested in an account that paid 8% interest

Let y represent  the amount Christine invested in an account that paid 10% interest

x + y = 20,000    

.8x + .010y = 1920

Multiply each sides of this equation by 100 to  remove  the decimal points.

8x + 10y = 192,000

8(20,000-y) + 10y = 192,000

160,000 - 8y + 10y = 192,000

2y = 32,000

y = 32,000/2

y = $16,000

So,

x = 20,000 - 16,000

x = $4000

Therefore the First account is $16,000 and Second account is $4,000.

Learn more about amount invested here:https://brainly.com/question/25300925

#SPJ1

Answer:

y^2 + 5y - 750 = 0

y(y + 5) = 750

750 - y(y - 5) = 0

Step-by-step explanation: