20. Every day Isabel swims 10 to 20 laps in a 50-meter pool. She tracks the numbers of laps she swims and how long it takes her to complete the lap, in
minutes.

There is a probability of 66.5 % chance of it landing on a 5 at least once in 6 dice.

Because there are six faces on a die, you have an even chance of the dice landing on one of these faces each time you roll:

This means that each time that you roll, there is a 5/6 chance that you will not roll a 5.

The probability of not rolling a 6 twice is 5/6 or 69.4%.

Roll the die six times, and the probability of not rolling a 5 is

(5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6)

= (5/6)⁶

= 33.5%

Therefore, the probability of rolling a 5 at least once in 6 dice

= 100%  - 33.5%

= 66.5%

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The cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

Two or more expressions with an Equal sign is called as Equation.

The cost of each pounds of Caramels = $ 9.28,

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of caramels =  [tex]1\frac{3}{4}[/tex]×9.28

=7/4×9.28=$16.24

The cost of each pounds of milk chocolate = $ 12.80

So, the cost of [tex]1\frac{3}{4}[/tex]  pounds of milk chocolate = [tex]1\frac{3}{4}[/tex]  ×12.8

=$22.24

∵ 22.4 > 16.24,

the cost of  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate  > The cost of   [tex]1\frac{3}{4}[/tex]pounds of caramels

22.4-16.24=6.16

Hence, the cost for  [tex]1\frac{3}{4}[/tex] pounds of milk chocolate is $ 6.16 more than the cost for  [tex]1\frac{3}{4}[/tex] pounds of caramels.

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Answer:

C

Step-by-step explanation:

The problem states:

"The second anthill has one and one-third the amount of ants of the first hill."

Answer: C

The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

Given,

In the question:

Your grandmother is 87 years old and she has remarked to you that nearly all of her friends are women. She told you that it is rare to see a man older than age 85. She is correct because, after age 85, for every 100 men, there are __________.

Now, According to the question:

Your grandmother is 87 years old and she told you that all of her friends are women. There is no single man in her circle of friends. She also told that it is rare to see a man over the age of 85. It is because of the fact that women are more in number than man above the age of 85 and this ratio is like 100 men per 200 women, which means the chances of getting a male friend is almost half after the age of 85. So women are more in number than men.

Hence, The correct answer is Yes, past age 85 years of age, for every 100 men, there are 200 women.

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Answer:

B. 60

Step-by-step explanation:

Side VU must be equal to side WX

15 = (1/4)y

divide both sides by 1/4

15 / (1/4) = y

60 = y

According to the histogram, the percentage of the tournament participants are under the age of 20 is 50%.

A histogram approximately represents a distribution of grouped data with numerical values.

It uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.

Age Group (year)  Number of People

0 to 19                            30

20 to 39                         20

40 to 59                         10

60 to 79                         0

Total                             60

Percentage of ages 0-19  =  30/60 x 100 = 50%

Thus, using the histogram, we can assure the percentage of the tournament participants are under the age of 20 is 50%.

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The amount compounded at a rate of 8% over a period of 6 years is  $8,551.56

The compound interest is the interest-based on the initial principal amount and the interest collected over the period of time. The formula for compound interest can be derived from the formula for simple interest. The formula for simple interest is the product of the principal, time period, and rate of interest (SI = ptr/100). Before looking into to derivation of the formula for compound interest, let us understand the basic difference between simple interest, compound interest computation. The principal remains constant over a period of time, for simple internet computation, but for compound interest computation the interest is added to the principal, for compound interest computation.  The compound interest formula is given below:

A = P(1 + r/n)^nt

Applying the formula of compound interest here;

A = 5300(1 + 0.08/12)^12 * 6

A =  $8,551.56

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The value of a in this question is 1.

Here, we've been given the matrix A=[2 0 1; 0 2 0; a 0 2]

For eigenvalues, the characteristic polynomial of A -

= det(A-  λI) = 0

= Let [(2 0 1; 0 2 0; a 0 2) - (λ 0 0; 0 λ 0; 0 0 λ)] = 0

= [2-λ 0 1; 0 2-λ 0; a 0 2-λ] = 0

= (2-λ)(2-λ)² - a[+(2-λ)] = 0

= 8+2λ² -8λ-4λ-λ³ +4λ²-2a+aλ = 0

= -λ³ +6λ² +(a-12)λ+8-2a = 0

For the given eigenvalues 1,2, and 3, the characteristic polynomial must have the roots at λ=1,2,3

= -(λ-1)(λ-2)(λ-3)

=-λ³+6λ²-11λ+6

Hence, -λ³+6λ²-11λ+6 = -λ³ +6λ² +(a-12)λ+8-2a

From equating these, we get-

a = 1

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The goal of a hypothesis test is to determine if the data can refuse an assumption a parameter or a population.

Statistical hypothesis test: A statistical hypothesis test is a technique for determining whether the available data are sufficient to support a specific hypothesis. We can make probabilistic claims about population parameters through hypothesis testing.

The purpose of a hypothesis test is to ascertain whether the data can refute a parameter or population assumption.

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If the coefficient of determination is a positive value, then the correlation coefficient can be negative or positive, which means the value of the correlation coefficient is between -1 and +1. If the variable x increases, the variable y also increases, and if the variable x decreases, then the variable y also decreases.

The coefficient of determination is a statistical measurement which examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event. The coefficient of determination is a number between 0 and 1 that measures how well a statistical model predicts an outcome. This provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.

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The radical expression as an expression with a rational exponent is A- seven to the five fourths power.

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

Given, the fourth root of 7 to the fifth power, we have to write the radical as a rational exponent.

The formula to change a radical to a rational exponent is given by:

= a ^(m/n)

Now, cube root of the seventh power can be written as:

4✓7^5

Therefore, the rational exponent is A.

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The equation of the line that shown in the graph is;

y = x + 3

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

We know that Point-Slope Form:

y - y₁ = m(x - x₁)  

Where x₁ - x coordinate and y₁ - y coordinate

m - slope

Point are (3, 6) and (4,5)

Then Slope m = 1

Now Write the equation as;

y - 6 = 1(x- 3)

y = x - 3 + 6

y = x + 3

Hence, the equation of the line that shown in the graph is;

y = x + 3

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There exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

Here, we are given an equation as follows-

12x + 1 = 3( 4x + 1 ) – 2

Let us solve the equation to get the value of the variable x.

12x + 1 = 12x + 3 – 2

12x + 1 = 12x + 1

Thus, here, we see that the Left hand side is exactly equal to the right hand side. This means that the given equation has infinitely many solutions.

Therefore, there exists infinitely many solutions for the given equation 12x + 1 = 3(4x + 1) – 2  

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The following are the two lines: y = 4x - 1. y = -1.25x + 10.5.

Their point of intersection is: (2.19, 7.76).

The two vertices through which the line y = 4x - 1 pass are as follows:

(2.19, 7.76) and (3,11).

The slope is:

m = (7 - 3)/(2 - 1) = 4.

Hence:

y = 4x + b.

When x = 1, y = 3, the intercept b is calculated as follows:

3 = 4 + b

b = -1.

The first line is then: y = 4x - 1.

The points for the second line are (2,7) and (6,2).

As a result, the slope is m = (2 - 7)/(6 - 2) = -5/4 = -1.25.

The solution is y = -1.25x + b.

When x = 2, y = 7, therefore the intercept b is as follows:

7 = -1.25(2) + b

b = 10.5.

As a result, the second line is:

y = -1.25x + 10.5.

The intersection's x-coordinate is as follows:

4x - 1 = -1.25x + 10.5

5.25x = 11.5

x = 11.5/5.25

x = 2.19.

The intersection's y-coordinate is:

y = -1.25(2.19) + 10.5 = 7.76.

Another position where the line y = 4x - 1 intersects is:

y = 4(3) - 1 = 11.

As a result, point (3,11).

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The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.

The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.

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A normal distribution is continuous, but a binomial distribution is not, and this difference is taken into account by the continuity correction factor. It is necessary to add a continuity correction factor when using a normal distribution to approach a binomial distribution. Just add or subtract, and you're done.

When a discrete probability distribution is approximated by a continuous probability distribution, the continuity correction factor is utilized. The continuum correction factor serves as a link between the discrete binomial and the continuous normal distribution.

By allowing us to evaluate the variability of occurrence or provide estimates of the likelihood that a specific event will occur, probability distributions aid in the modeling of our environment. They are a typical technique to explain and maybe anticipate the likelihood of an event.

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The linear system of equation y =-6x+2 and 12x+  2y =- 4 has only one solution.

The linear equation is y = -6x+2 .

Now for any value of x we find the value of y ,

at x=0 ,y = 2

at x=1 , y = -4

at x=-2 , y = 14

Hence there are infinitely many solutions on the line . All points on the straight line are solutions.

The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.

The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.

Disclaimer: the complete question is :

How many solutions does this linear system have Y =- 6x + 2 and 12x + 2y =- 4?.

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The blue tiles on the floor is an illustration of proportions. The blue tiles will cover 25% of the floor

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.

From the complete question, the dimension of the floor is 4 ft by 4 ft.

So, the area of the floor

Area = 4 x 4

Area = 16

The blue tiles cover 4 square feet.

So, the percent of floor is:

= 4/16 x 100

= 1/4 x 100

= 25%

Hence, the blue tiles will cover 25% of the floor. Also, he doesn't need to buy another set of blue tiles.

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Interpreting the graph, it is found that the function has two real solutions

The number of different real solutions that a function has is given by the number of times it crosses the x-axis(also known as the horizontal axis) on the graph. If the graphs of the equations intersect, then there is one solution that is true for both equations.

In this problem, the function crosses the x-axis, at 0 and -4

Using the above we find that the given graph has solution at the x intercepts.

X intercepts are 0 and -4

Hence the solutions are two real and they are x=0 and x =-4

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Number expressed in the form a+ bi is complex number.

A number system is defined as a system of writing to express numbers.

The number is expressed in the form a + bi

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i² = −1.

The number a+bi, in which a is real number and b is imaginary number.

Hence, number expressed in the form a+ bi is complex number.

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The simplified equation is 2x y²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.

Given that,

The equation is

√x² y³ +2√x³y⁴ +x y√y

We have to simplify the equation.

We know that,

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Take the equation

√x²y³ +2√x³y⁴ +x y√y

x y√y +2√x³y⁴ +x y√y

2√x³y⁴ + 2x y√y

2x y²√y + 2x y√y

Therefore, The simplified equation is 2xy²√y + 2x y√y when the actual equation is √x²y³ +2√x³y⁴ +x y√y. Option -B is correct.

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Answer:

B on edge

Step-by-step explanation:

The inequality representing the problem is 5x+32y≤400

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, A solar panel can generate power at a maximum rate of 400 kilowatts per day. When it is cloudy, it can only generate 5 kilowatts per hour and when the sky is clear, 32 kilowatts per hour.

According to question,

5x+32y≤400

Hence, The inequality representing the problem is 5x+32y≤400

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Properties used in the given equation is Commutative property, Associative property, Additive inverse, Identity property.

In a commutative property multiplication and addition which posses commutative property takes place without considering the order of arrangement of data.

12.2 + 18.6 + -4.3 + (-18.6)

12.2 + -4.3 _ 18.6 + (-18.6)

The second step results into the presence of a commutative property.

12.2 + -4.3 + [18.6 + (-18.6)] is an associative property because here, regrouping of numbers which gives the same result.

[18.6 + (-18.6)] is an additive inverse since the result is zero. Additive inverse occurs when the addition of a number to another number results into zero.

12.2 + -4.3 + (0) is an identity property.

This property occurs when the addition of any number with zero eventually resulted into that number.

So here we used 4 properties which are

Commutative property,

Associative property,

Additive inverse,

Identity property.

Given question is written in wrong language.

Here is the given question 12.2 + 18.6 + -4.3 + (-18.6)12.2 + -4.3 + 18.6 + (-18.6)12.2 + -4.3 + [18.6 + (-18.6)]12.2 + (-4.3) + (0)12.2 + -4.3 7.9

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The number of different possible orders that are there for the group is  15504 .

In the question ,

it is given that ,

total number of friends = 5 ,

the number of dishes that restaurant offers for dinner = 20 dishes .

It is given that, group collectively orders 5 different dishes to share and waiter just needs to place all 5 dishes in the center of the table.

So , the 5 dishes from the 20 dishes can be selected in ²⁰C₅ ways .

²⁰C₅ = 20!/(15! * 5!)

= 20*19*18*17*16*15! / (15! * 5!)

= (20*19*18*17*16)/(5*4*3*2*1)

Simplifying Further , we get

= 1860480/120

= 15504 ways

Therefore , There are 15504 possible orders for the group .

The given question is incomplete , the complete question is

A group of five friends go to a restaurant for dinner. the restaurant offers 20 different main dishes. Suppose that the group collectively orders five different dishes to share. the waiter just needs to place all five dishes in the center of the table. how many different possible orders are there for the group ?

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Answer: D. y = 2 x + 1

Step-by-step explanation:

No they are not the same . AAS stands for Angle Side Angle and SAA stands for Side Angle Angle .

The margin of error for the confidence interval for the population proportion with a 95% confidence level is 0.000207

finding the percentage of 65 of 330 individuals

65 / 330 * 100 = 19.697% = 0.19697

number of samples, n = 330

standard deviation, σ   is calculated from

= √{(p(1 - p)) / n}

= √{(0.197 * (1 - 19.7)) / 330}

= √{(0.197 * (0.803)) / 330}

= 0.022

Margin of error, E

= Z(0.95) * σ/√(n)

= 0.171 * 0.022/√(330)

= 0.171 * √(0.022²/330)

= 0.000207

= 0.021%

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If Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, how many books they can buy,

Rs 30 = 45 book

Rs 30 = 45

Rs 1 = 45 / 30

Rs 24 = 3/2 × 24

Rs 24 = 34 books

Thus, if Sabia and Arlan bought 45 books for rs 30, then at the rate of rs 24, they can buy 34 books.

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