A population of insects increases at a rate of 290+8t+0.6t2 insects per day.
Find the insect population after 5 days, assuming that there are 70 insects at t=0. Round your answer to the nearest whole number.

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 probability that both are red is 0.0791.

Given,

Total marbles: 37 + 15 = 52

According to the number of red cards out of all the cards, there is a 15/52 possibility that a red card will be pulled during our initial pull.

Depending on how many red/total marbles are still in there, there is a 14/51 probability that the second marble pulled will also be red.

Our two fractions are multiplied together from here,

15/52 * 14/51

We can start by simplifying a little bit; the numbers 14 and 52 share a 2;

15/26 * 7/51

Our result is 35/442

Depending on whether you choose to maintain it in fractional, ratio, or percentage form, the result of dividing is around 0.0791, which rounds to 7.91%.

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Answer: D. y = 2 x + 1

Step-by-step explanation:

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

Some other names for the unit rate are:

A general proportional relation is written as:

y = k*x

You can see that it goes through the origin because when we evaluate in x = 0, we get:

y = k*0 = 0

So it passes through (0, 0).

The value "k" has several names, unit rate is the one given here, but it is generally called the "constant of proportionality"

It is also called the slope (like in a linear equation with an y-intercept equal to 0).

Or the rate of change or gradient, which are equivalent terms that particularly in the case of linear equations are equal to the slope (but not for other functions).

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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 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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An equilateral right angled triangle is not possible because a triangle can only consist of 180°. Since a right angle is 90°, there is no way that a triangle can be have three right angles. 180° ≠ 270°

An isosceles acute triangle is possible because two angles can be acute and have the same degree values and the last angle can have a different value of another acute angle. The two angles that are acute would have the same value for their corresponding sides.

A scalene obtuse triangle is possible because one angle can be obtuse and the other ones can be acute. All the sides can be different.

I hope this helps you! Have an amazing rest of your day!

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

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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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 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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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 value of expected time ex(b)=1 day approximately if b is the number of days a busy student delays Laundry.

The basic anticipated value formula is (P(x) * n): the probability of an occurrence multiplied by the number of times the event occurs.

The expected value (also known as the expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average in probability theory. The anticipated value is the arithmetic mean of a large number of independently chosen random variable outcomes.

Let b be the number of days a busy student puts off doing laundry.

The given information is tabulated as below:

Days(b)                      1              2

Probability, p(b)       2/3          1/3

The expected time is given as,

E(b)=∑i=1ᵇp(b)

=(1×(2/3))+(2×(1/3))

=4/3

=1.3333

Therefore, the value of ex(b):

1.3333 day ≈ 1 day

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The given number 8 is not a prime number.

Given that,
To justify whether the number 8 is a prime number or not.

A prime number is a whole number bigger than one with just the number one and itself as factors.

Here,
A prime number is given as 1,2, 3,5, 7, 11, 13, and so on,
From the above series, it is determined that 8 is not a prime number.

Thus, the given number 8 is not a prime number.

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

Answer:

6,942 steps left!

Step-by-step explanation:

OK so this is easy so we know that if 1 / 19 = 0.052 we minus that by - 3 because - 3 is our exponent that gives us 3.052 so now we just take 3.052 - 10,000 which gives us exactly 6942 you two steps so he needs 6942 steps left

Answer:

3,141 steps

Step-by-step explanation:

Let x be equal to the number of steps he needs to reach his goal

10,000 = [tex](\frac{1}{19} )^{-3}[/tex]+ x

10,000 = 6,859 + x

3,141 = x

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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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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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 recommended statistic is statistic II because this statistic is unbiased and has the smallest standard deviation of three.

Unbiased statistic is more accurate than biased statistic because which on sampling distribution mean equal to population parameter.

Standard deviation is value of dispersed of observed value sampling around population parameter. Smaller standard deviation can be equated with a smaller deviation of data. Which in unbiased statistic means lots of value closer to population parameter.

If even statistic is unbiased but standard deviation high (statistic III) it not recommended because lots of value is not close enough to population parameter.

Thus, the recommended statistic is unbiased statistic and have smallest standard deviation which is statistic II.

Your question is incomplete, but most probably your full question was (image attached)

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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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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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If the theater club fulfills its sales target, 40 student tickets can be sold in total when the drama club members need to sell 100 tickets.

Given that,

The drama club members need to sell 100 tickets. If the drama club fulfils its sales target, will tickets cost $5 each and be sold to students. Tickets cost $10 for non-students. The total amount of ticket sales that the drama club must get is at least $800. The number of student tickets, s, and the number of non-student tickets, n, that the members must sell are represented by the system of inequalities.

s+n≤100

5s+10n≥800

We have to find if the theater club fulfills its sales target, how many student tickets can be sold in total.

We know that,

Take the system of inequality

s+n≤100

5s+10n≥800

By solving the inequality we get s=40 and n=60

Therefore, if the theater club fulfills its sales target, 40 student tickets can be sold in total.

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Answer:

A.

Step-by-step explanation:

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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