5. Use the properties of logarithms to expand log₂
constant multiple of variables. (Assume all variables are positive.)
as a sum, difference, and/or

The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

What is the Central Limit Theorem?

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.

Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.

Let's call X = mean thickness,

if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15

if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15

Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

To learn more about the Central Limit Theorem visit,

https://brainly.com/question/18403552

#SPJ4

11 students could sell 1870 cookies.

A statement, at least two variables or integers, and one or more arithmetic operations make up a mathematical expression. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers.

Combining numbers, variables, and operators to represent something's value is known as a mathematical expression. Setting two expressions equal to one another creates an equation, a mathematical statement.

An expression is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in certain ways. Language phrases can comprise actions on their own, but they do not make up complete sentences.

=  10 X 17

=  170 X 11

= 1870

To learn more about expressions refer to:

https://brainly.com/question/1859113

#SPJ4

Answer:

perimeter= 9+9π cm

area= 40.5-10.125π cm²

Step-by-step explanation:

area of the square =9x9=81cm²

area of the two semicircles which have the same diameter =area of one circle

= (9÷2)²π =(81÷4)π

area of the whole shaded part = 81- (81÷4)π cm²

the area of each shaded part= (81-(81÷4)π)÷2

= 40.5-10.125π cm²

circumference of 2 semicircles= circumference of 1 circle = 2πr = 2x9xπ= 18π cm

then are perimeter of the whole shaded part = 18π+9+9= 18+18π cm

perimeter of each shaded part = (18+18π)÷2=

9+9π cm

Answer:22 days

Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,

Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)

so, 2000/90 = we will get number of days

therefore 22.22 days

Which emplies 22 days.

Answer: B

Step-by-step explanation:

B) 180−m180-m180−m

Answer:

-4 and 12 are the zeros of the quadratic.

Step-by-step explanation:

What value does X need to be so (x+4) is 0? -4

What value does X need to be so (x-12) is 0? 12

The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.

The waterfall model of the software development life cycle is the greatest technique for creating systems.

This includes the following elements:

1. The requirements phase, which takes into account the needs needed to build the product

2. The product's design is created

3. The programmers who wrote the code to put the product into action built the product.

4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.

5. The systems are periodically maintained to ensure continued operation and proper output

To know more about the waterfall model, refer to this link:

https://brainly.com/question/13439438

#SPJ4

An equation that shows what the cost of renting a car will be: C=R+mc.

Let the rental cost = R

consider m to be the number of miles driven= m

let c be the cost per mile

And C is the total cost of renting;

Then C = R+mc

the given equation $40 + $0. 10 per mile

Now, in the above equation consider:

R =$40 ( the rental cost)

c = $0.10 ( the cost per mile)

The total cost is C = $40+$0.10m

Ex:

if m is known assume m=1000 miles

Then the total cost C = $40+($0.10/mile)(1000miles)

then  C = $40+$100=$140

To know more about the equation of cost of renting:

https://brainly.com/question/16404189

#SPJ4

The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.

Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.

Remaining candies = total number of candies - 1/5×total candies

Keep the values in formula

Remaining candies = 20 - 1/5×20

Remaining candies = 20 - 4

Remaining candies = 16

Total candies for Kyla = remaining candies - 3/8×remaining candies

Candies for Kyla = 16 - 3/8×16

Candies for Kyla = 16 - 3×2

Candies for Kyla = 16 - 6

Candies for Kyla = 10

Thus, Kyla received 10 candies.

Learn more about fraction -

https://brainly.com/question/1622425

#SPJ4

Answer:

1. y-2=2/3(x-1) slope: y=2/3x+4/3 standard: 2x-3y=-4

Step-by-step explanation:

The three sides of a triangle are referred to as the base, the height, and the hypotenuse.

The base and height of a triangle can be used to calculate the area of the triangle using the formula:

Area = (Base x Height) / 2

To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.

The formula for the Pythagorean Theorem is:

a2 + b2 = c2

where a and b are the two sides of the triangle and c is the hypotenuse.

To calculate the hypotenuse of a triangle, the following steps are taken:

1. Measure the length of each side of the triangle.

2. Square the length of each side (multiply the length by itself).

3. Add the two values together.

4. Find the square root of the sum. This is the length of the hypotenuse.

Learn more about Pythagorean Theorem here:

https://brainly.com/question/28361847

#SPJ4

share of rimmy and simmi is rs15000 and rs25000.

this question is of ratio and proportion, and the solution is as follows,

total amount = rs 40000

Rimmy and Simmi in the ratio = 3:5

sum of shares= 3+ 5 = 8.

so,

share of Rimmy is = 3/8 X 40000

= 120000/8

= 15000

share of simmi is = 5/8 X 40000

= 200000/8

= 25000

so the share of rimmy and simmi is rs15000 and rs25000.

Learn more about ratios here :-

https://brainly.com/question/13419413

#SPJ4

The resultant output of  the given question is 7 by 2 is 14.

This is because 7 multiplied by 2 is equal to 14

When you multiply two numbers, the result is the product of the two numbers. In this case, 7 multiplied by 2 is equal to 14.

Mathematicians use the process of multiplication to calculate the product of two or more given numbers. It is a fundamental mathematical operation in maths that is frequently utilised in everyday life. When we need to combine groups of similar sizes or values , we utilise multiplication.

Hence the correct answer to the given question is 14 .

To know more about multiplication here

https://brainly.com/question/27646651

#SPJ4

Answer:

Step-by-step explanation:

ASA requires that both triangles have two angles and the included side to be congruent.

We have one side and an adjacent angle and need the second angle adjacent to the marked side to be congruent as well

It is the ∠BAC of ΔABC and ∠DPF of ΔPDF or simply ∠A and ∠P.

The x- coordinate of the vertex P is  -4  and the y coordinate is -3. The coordinates of the image of vertex P is thus,  (-4, -3).

Coordinates are numbers describing the position of a point or shape in a line or particular space. We can represent a line or shape in the space between number lines with both positive and negative coordinates.

The vertical axis in the number line is called y-axis and the horizontal axis is called the x- axis. The coordinate of a point is written as (x, y). The x, y represents the numbers on x-axis and y -axis touched at which the point lies in the graph.

For the given vertex P, the vertex lies on the point -4 on x-axis and on -3 in y axis. Hence, the coordinate of P is (-4, -3).

Find more on coordinates:

https://brainly.com/question/27749090

#SPJ1

Following are three steps 1. Isolate the variable: First, identify the variable you are trying to solve for and use the other terms in the equation to isolate that variable. This means using inverse operations to move any terms containing the variable to one side of the equation and any terms without the variable to the other side of the equation.

2. Simplify the equation: Once the variable is isolated, use the properties of equality and inverse operations to simplify the equation, if needed.

3. Solve the equation: Finally, use the inverse operations to solve the equation and find the value of the variable.

To know more about equation here

https://brainly.com/question/30187464

#SPJ4

On solving the provided question, we can say that so, we apply permutation P(12,4) = 12!/ 8! = 11880

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.

so, we apply permutation

P(12,4) = 12!/ 8! = 11880

To know more about permutation visit:

https://brainly.com/question/1216161

#SPJ4

The expected time until the tourist arrives in the city is 4.75 hours.

The expected time until the tourist arrives at the city can be calculated by using the formula for the expected value:

Expected value = (probability of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...

In this case, there are two possible outcomes: the tourist takes road A or road B.

If the tourist takes road A, the expected time until he arrives in the city is the average of the two possible travel times (4 hours and 8 hours). The probability of this outcome is 0.5 (the tourist has an equal chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.

If the tourist takes road B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this outcome is (0.5) x 7 = 3.5 hours.

To find the overall expected time until the tourist arrives in the city, we add up the expected values for each outcome:

Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours

So the expected time until the tourist arrives in the city is 4.75 hours.

To learn more about the probability, visit:

brainly.com/question/30034780

#SPJ4

The ratio of days in May and days in a year is 31 to 365 or 31:365

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We need to find the days in May and days in a year as a ratio

Therefore, Days in may = 31

Days in a year = 365

Thus, the expected ratio = 31/365

Or

31:365

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ1

Answer:

(n - 6)(n -4)

Step-by-step explanation:

Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.

Rotation of PQRS by 90 degree.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location. What are the four mathematical transformations?

Translation, rotation, reflection, and enlargement. You must be able to carry out each transformation and recognize which ones have already been done.

To know more about geometric figure visit:-

brainly.com/question/11266123

#SPJ1

Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

The slope of the line is 3 and the y-intercept is -5.

The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.

The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.

Learn more about slope here

https://brainly.com/question/3605446

#SPJ4

Answer: The width of the room is 36 feet and the length of the room is 48 feet.

Step-by-step explanation:

To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.

Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:

l = w + 12

We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:

144 = 2 * (w + 12 + w)

Combining like terms and solving for w, we get:

w = 36

Substituting this value back into the equation for the length of the room, we get:

l = 36 + 12 = 48

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.

For example, we could solve the equation l = w + 12 for w to get:

w = l - 12

Substituting this expression for w into the equation for the perimeter, we get:

144 = 2 * (l - 12 + l)

Combining like terms and solving for l, we get:

l = 48

Substituting this value back into the equation for the width of the room, we get:

w = 48 - 12 = 36

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

It will take 13 weeks to gather funds that sum up to $4500.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: I have $2485 and I save $155 weekly

Thus amount left to be gathered is $4500-$2485=2015

If I save $155 weekly then we get = $2015/$155

                                                        =13 weeks

Hence, It will take 13 weeks to gather funds that sum up to $4500.

Learn more about the unitary method here:

https://brainly.com/question/22056199

#SPJ1

The average monthly salary of all the staff is going to be 19,333.34 ₹.

Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,

So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that

No. of males=10

No. of females=5

So, the total no. of figures = 15

Sum total of  set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be

=(20,000 × 10 + 18,000 × 5) ₹/15

=(200,000+90,000)/15₹

=290,000/15 ₹

=19,333.34 ₹

Learn more about Averages on

https://brainly.com/question/24057012?referrer=searchResults

#SPJ4

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

--The question is incomplete, answering to the question below--

" Can 1, 2 and 3 make the sides of a triangle?"

To know more on  triangle inequality theorem

https://brainly.com/question/30195794

#SPJ4

Answer:

7:15 ,2 weeks=14 days and 30 days divide by 2 = 7 and 15 put them to a ratio and you'll get 7:15.

Step-by-step explanation:

I have to assume the equations are

4x + y = 13

(1/2)y = -2x + 5

let's bring both of them into a "y = ..." form :

y = -4x + 13

y = -4x + 10

now we see that both equations are lines with the same slope but different y-intersect.

so, they are parallel but not identical.

therefore, there are 0 solutions. the lines will never intersect and have no point in common.