Erin makes the following statements. The scale factor from ∆ABC to ∆XYZ is 31. The area of ∆XYZ is 13 the area of ∆ABC.

The linear regression equation that represents this set of data is given as follows:

y = -27.3x + 843.2.

The estimate of the calendar year in which the number of new cases would reach 604 is of:

2019.

The linear regression equation is obtained inserting the points of the data-set into a linear regression calculator.

From the table given at the end of the answer, the points of the function are given as follows:

(0, 832), (1, 827), (2,800), (3,750).

Inserting these points into the calculator, the equation is given as follows:

y = -27.3x + 843.2.

The number would reach 604 when:

y = 604

-27.3x + 843.2 = 604

x = (843.2 - 604)/27.3

x = 8.7

2011 + 8.7 -> during the year of 2019.

The table is given by the image shown at the end of the answer.

More can be learned about linear regression at https://brainly.com/question/29613968

#SPJ1

If they keep running at the same pace, they will eventually meet at the same end of the course after 30 minutes.

The rate at which distance and time change is what is meant by speed. It has the aspect of temporal and spatial distance. The basic unit of distance with the basic unit of time are combined to form the SI unit of speed. This means that the SI unit of speed is the metre per second.

The way that the issue is described is vague.

I believe what is being said here is that they continue to jog at the same speed.

Half a mile per ten minutes is Diane's speed.

2/3 miles per 10 minutes is Jack's speed.

The numerator and denominator (top and bottom of the ratio) must be multiplied by the factor between 10 minutes and an hour (60 minutes) in order to convert this to a standard miles per hour format.

60/10 = 6.

In order to convert the above speeds to miles per hour, we must multiply both speeds by 6.

Diane: (1/3 divided by 6)/hour equals 2 miles/hour

Jack: (4 miles per hour) = (2/3 x 6) / hour

Diane will complete one length in the time it takes Jack to complete a round trip (back) because he runs twice as fast as she does.

Running a mile at a speed of two miles per hour takes Diane 30 minutes.

Running 2 miles (back and forth) at a speed of 4 miles per hour will take Jack 30 minutes.

So after 30 minutes they will meet again at his starting point.

To know more about speed visit:-

https://brainly.com/question/2004627

#SPJ1

Therefore the percentage of increase in yearly sales is 35% by last year.

Percentage refers to a number that is "out of one hundred." As with fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When utilizing percentages, the total is regarded as being composed of 100 equally sized components. In addition to the abbreviation "pct," which is used less frequently, the symbol "%" is used to denote percentages in numbers.

Here,

the company sold a total of 720,460 pictures  Last year.

This year, they sold 972,621 pictures

therefore first we have to find the difference between the last year and this year pictures sold

it comes out to be,

=>972,621-720,460=252,161

Therefore the increase in percentage this year=

=> 252,161/720460 * 100

=>0.35*100

=> 35%

Therefore the percentage of increase in yearly sales is 35% by last year.

To know more about percentage , visit

https://brainly.com/question/28269290

#SPJ1

To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.

Given,

A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.

We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

Here,

To obtain the sample size,

n = z² pq / ME²

Where,

P is the proportion of voters

M. E is the margin of error.

q is the proportion of non-voters

z is the corresponding z score

The z score for the 95% confidence interval is 1.96.

n = 1.96² pq / 0.05²

n = 1536.64 pq

If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.

n = 1536.64 pq = 61.42

≈ 62 voters

Therefore,

62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%

Learn more about number of voters to be surveyed here;

https://brainly.com/question/29387914

#SPJ4

The value of x in the given ratio is 2.

The relationship in quantity, amount, or size between two or more things.

Given is a ratio, x:5/2 = 8:10

x/5/2= 8/10

2x/5 = 8/10

2x = 40/10

2x = 4

x = 2

Hence, The value of x in the given ratio is 2.

For more references on ratios, click;

https://brainly.com/question/13419413

#SPJ1

The coefficient of x²  in simplified form is 5

What is coefficient ?

A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.

a symbol or number that multiplies another symbol or number (used as a mathematical variable). The coefficient of x in the phrase 3x is 3, and it is a number that represents a quality (such as the metal's coefficient of expansion) of a substance or device.

(4y + 5y² - 6) - (5y + 27 - 2²)

4y + 5y² - 6 - 5y - 27 + 4

5y² - 1y - 29

To learn more about coefficient from the given link  

https://brainly.com/question/1038771

#SPJ1

Mean = 54.52

V(X) = 3.2712

S.D = 1.8086

To calculate the mean (expected value) of a binomial distribution B(n, p) you need to multiply the number of trials n by the probability of successes p , that is: mean = n × p

Where, n= 58

p = 0.94

Therefore, mean = 54.52

To find the Variance of the given binomial distribution

Variance = np(1-p)

=58 X 0.94 ( 1- 0.94)

= 54.52 X 0.06

V(X) = 3.2712, when we know the variance and the mean then we can calculate the standard deviation easily

To find the standard deviation of the given binomial experiment = [tex]\sqrt{np(1-p)}[/tex]

= [tex]\sqrt{3.2712}[/tex]

S.D = 1.8086

To know more about binomial distribution

https://brainly.com/question/29732172

#SPJ4

Answer: 20°

Step-by-step explanation:

The sum of all the interior angles of a triangle is 180°

So to find the missing angle you just need to subtract 25° and 135° from 180°, which equals 20°

Answer:

I belive it would be 102

Step-by-step explanation:

Answer:

306 cm

Step-by-step explanation:

the opposite side is the same as the shaded side

18 x 17 = 306 cm

The probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

Given that,

Poisson (2.)

Let x = The number of pairs of twins

That will be born in the Country in 2015

To find : Calculate the probability that exactly 18 pairs of twins will be born in the country in 2015.

We know that

Here,

The probability mass function (pmt of x) is given by

P ( X = x ) = e⁻²¹ x 21ˣ / x!

where x = 0,1,2 , . . .

Substitute x = 18 in above equation,

Then we get,

P ( x = 18 ) =  e⁻²¹ x 21¹⁸ / 18!

P( x = 18 ) = 0.07472

P ( x = 18 ) = 0.07472

Therefore, the probability that exactly 18 pairs of twins will be born in the county in 2015 is 0.07472.

To learn more about probability click here:

brainly.com/question/29538993

#SPJ4

Answer:

[tex](x+2)(x+3)[/tex]

Step-by-step explanation:

⭐What does factorisation mean?

⭐What are factors?

Thus, we have to write [tex]x^2+5x+6[/tex] in terms of its factors.

I have a picture attached to this response to show you how factorisation works, but I will also explain it here.

How to factorise:

The picture of factorisation is attached to this response.

⭐ if this response helped you, please mark it the "brainliest"!⭐

Step-by-step explanation:

you just need to put the value for t into the equation and then solve for s.

t = 3s + 2

t = 11

11 = 3s + 2

3s = 11 - 2 = 9

s = 3

t = 17

17 = 3s + 2

3s = 17 - 2 = 15

s = 5

t = 23

23 = 3s + 2

3s = 23 - 2 = 21

s = 7

t = 29

29 = 3s + 2

3s = 29 - 2 = 27

s = 9

The probability of getting a full house is 0.001441 or 0.14%.

When you dealt five cards from a thoroughly shuffled standard check of cards then for the probability of getting a full house we need to know the total number of full house combinations and possible cards hands.

This is calculated by taking the number of possible full house combinations (3,744) and dividing it by the total number of possible 5-card hands (2,598,960). This can be written as :

Mathematically, this can be expressed as:

P(Full House) = 3,744 / 2,598,960 = 0.001441 or 0.14%

Therefore the probability of getting a full house is 0.001441 or 0.14%

For more questions like Probability click the link below:

https://brainly.com/question/13815890

#SPJ4

The graph of the linear function y = 36 - 4x that represents this situation is given by the image shown at the end of the answer.

To graph the linear function, these three steps are taken:

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are detailed as follows:

Initially, he has 36 overdue activities, hence the intercept is of:

b = 36.

And thus the coordinates of the y-intercept are given as follows:

(0,36).

Each day, he can do 4 activities, meaning that the number of remaining activities decays by 4, and thus the slope is of:

m = -4.

Thus the definition of the function is presented as follows:

y = -4x + 36.

The x-intercept of the function is the value of x when the output variable assumes a value of 0, hence it is obtained as follows:

-4x + 36 = 0

4x = 36

x = 9.

Thus the coordinates of the x-intercept are given as follows:

(9,0).

Finally, a line is traced connecting the y-intercept (0,36) and the x-intercept (36,0).

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

#SPJ1

504 ways are there to line up all of the tas such that each tas with recitation partner(s) is standing next to them

Given :

cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation.

Number of ways = 9P6 * 9C3 * 1 / 5!

= 9! / ( 9 - 6 ) ! * 9! / ( 9 - 3 ) ! * 1 / 5!

= 9! / 3! * 9! / 6! * 1/5!

= 9 * 8 * 7 * 6 / 3 * 2 * 9 * 8 * 7

= 9 * 8 * 7

= 504 ways

Learn more about the line here:

https://brainly.com/question/2696693

#SPJ4

The perimeter of the quadrilateral is 10 + 6√2 units.

What is a quadrilateral?

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.

The coordinate of the vertices of the quadrilateral are A(-5,1), B(-1,4), C(2,1), D(-2,-2).

The length of AB arm is √[(-5-(-1))² + (1 - 4)²] = √25 = 5 units

The length of BC arm is √[(-1-2)² + (4 - 1)²] = √18 = 3√2 units

The length of CD arm is √[(2-(-2))² + (1 - (-2))²] = √25 = 5 units

The length of AD arm is √[(-5- (-2))² + (1 - (-2))²] = √18 = 3√2 units

The perimeter of a quadrilateral is the sum of length of all arms.

The perimeter of the quadrilateral is

AB + BC + CD + AD

= 5 + 3√2 + 5 + 3√2

= 10 + 6√2

To learn more about perimeter of a quadrilateral, click on below link:

https://brainly.com/question/21893103

#SPJ1

The solution of the equation is -2.

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

What is distributive property?

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Given equation is 2(4x+3)+4=3x-(2x+4).

Apply distributive property in 2(4x+3):

8x + 6 + 4 = 3x - (2x+4)

8x + 10 = 3x - (2x+4)

Open parenthesis on the right side:

8x + 10 = 3x - 2x - 4

Combine like terms:

8x - 3x + 2x = -4 -10

7x = -14

Divide both sides by 7:

x = -14/7

x = -2

To learn more about solution of linear equation, click on below link:

https://brainly.com/question/19786981

#SPJ1

Answer:

$215.50

Step-by-step explanation:

To calculate the amount of interest that Albert will earn on his account over the course of 4 years, we can use the formula for compound interest:

Interest = principal * (1 + rate/n)^(n*t) - principal

Where:

principal is the initial amount of money in the account ($1,000 in this case)

rate is the annual interest rate (5% in this case)

n is the number of times that interest is compounded per year (annually in this case, so n=1)

t is the number of years the money is invested (4 years in this case)

Plugging these values into the formula, we get:

Interest = $1,000 * (1 + 0.05/1)^(1*4) - $1,000

= $1,000 * (1.05)^4 - $1,000

= $1,000 * 1.2155 - $1,000

= $215.50

To the nearest cent, the interest Albert will earn in 4 years is $215.50.

Answer: 13,900

Step-by-step explanation:

To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.

The options for 856 to round to is either 800 or 900.

The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.

Therefore, the answer would be 13,900.

According to the Central Limit Theorem, the mean of the sampling distribution of means will be equal to The mean of the Original Population.

Central Limit theorem:

The central limit theorem (CLT) is a statistical concept that states that the sample mean distribution of a random variable assumes an approximately normal or normal distribution when the sample size is large enough. Simply put, the theorem states that the mean sampling distribution approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

For example:

An investor wants to estimate the return on the ABC stock market index, which consists of 100,000 shares. Due to the large size of the index, the investor cannot analyze each stock individually and instead chooses to use a random his sample to obtain an estimate of the index's total his return. Investors select a sample of stocks. Each sample contains at least 30 strains. Samples should be random and previously selected samples should be replaced by subsequent samples to avoid bias.

If the average return of the first sample was 7.5%, the average return of the next sample could be 7.8%. Due to the nature of random sampling, each sample will produce different results. As you increase the sample size for each selected sample, the sample means begin to form their own distribution.

The distribution of the sample mean approaches a normal distribution as the value of n increases. The average return of the index example stocks estimates the return of the entire index of 100,000 shares, and the average returns follow a normal distribution.

According to the central limit theorem, if a large sample is chosen from an unknown population with mean μ and standard deviation σ, the sampling distribution of the sample mean follows a normal distribution.

The mean and standard deviation of this sampling distribution are:

                        μₐ = μ

                      σₐ = σ/√n

This standard deviation of the sampling distribution of the mean is called the standard error.

Learn more about Central Limit Theorem:

https://brainly.com/question/898534

#SPJ4

The total price of 4 pounds of apples this week at the grocery store is $5.76

Total price of apples this week = Last week price of apples per pound × Quantity of apples

= $1.60 × 4

= $6.4

Actual price paid = Total price of apples this week - (Discount × Total price of apples this week)

= $6.4 - (10% × $6.4)

= 6.4 - (0.1 × 6.4)

= 6.4 - 0.64

= $5.76

In conclusion, 4 pounds of apples cost $5.76 this week at the grocery store.

Read more on discount:

https://brainly.com/question/843074

#SPJ1

There are 60 grams of protein in 9 ounces of sauteed fish.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that there are 20 grams of protein in 3 ounces of sauteed fish.

Let's assume that 9 ounces of sauteed fish contain x grams of protein.

As per the given information, we can write the ratio would be as:

20 grams of protein : 3 ounces = x grams of protein : 9 ounces

20/3 = x/9

x = (20 × 9)/3

x = 180/3

x = 60

Hence, there are 60 grams of protein in 9 ounces of sauteed fish.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ1

The question seems to be incomplete the correct question would be:

There are 20 grams of protein in 3 ounces of sauteed fish. If 3 ounces of sautéed then, what are the grams of protein fish has?

y = mx + b
y = -4

m = 0
b = -4

Since the slope (m) is 0, the line is horizontal. The y-intercept (b) is -4, meaning that the graph is a horizontal line at y = -4.

See the attached file for the graph.

Answer:

[tex]$\frac{5}{8}$[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

J Square Roots and Cube Roots To find the square root of a number, you want to find some number that when multiplied by itself gives you the original number. In other words, to find the square root of 25, you want to find the number that when multiplied by itself gives you 25. The square root of 25, then, is 5. The symbol for square root is equation.

groceries has a higher population mean annual credit card charge

What is population mean?

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

The population mean can be calculated by the sum of all values in the given data/population divided by a total number of values in the given data/population.

Given that Bank of America’s Consumer Spending Survey collected data on annual credit card  charges in seven different categories of expenditures: transportation, groceries, dining out,  household expenses, home furnishings, apparel, and entertainment (US Airways Attache,  December 2003).

Sample size n =42

Mean difference d = 850

Std dev s = 1125

Point estimate of the difference is 0

95% confidence level would be

= 0A ± tcritical * stderrror

=  A ± 2.021*173.59

= (-350.83 , 350.83)

Learn more about Population mean at :

https://brainly.com/question/28103278

#SPJ4

The mass of a proton is 0.18 x 10⁴ times the mass of an electron.

Given is that mass of an electron is approximately 9.7 x 10⁻³¹ kilograms and the mass of a proton is approximately 1.7 x 10⁻²⁷ kilograms.

It is given that -

mass of electron = m{e} = 9.7 x 10⁻³¹ kilograms.

mass of proton = m{p} = 1.7 x 10⁻²⁷ kilograms.

Assume that the mass of a proton is [K] times the mass of an electron. So, we can write -

m{p} = K m{e}

K = m{p}/m{e}

K =  (1.7 x 10⁻²⁷/9.7 x 10⁻³¹)

K = (1.7/9.7) x (10⁴)

K = 0.18 x 10⁴

Therefore, the mass of a proton is 0.18 x 10⁴ times the mass of an electron.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ1

{Question in english language -

The mass of an electron is approximately 9.7 x 10^-31 kilograms. ​The mass of a proton is approximately 1.7 x 10^-27 kilograms. About ,how many times greater is the mass of a proton than the mass of an electron?}

Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

Equations are logical statements in mathematics with two algebraic expressions on either side of the equals (=) symbol. The expressions on the left and right are demonstrated to be equal in relation to one another. All mathematical equations start with LHS = RHS (left hand side = right hand side). To find the value of an unknown variable, or unknown quantity, you can solve equations. If the statement does not contain an "equal to" sign, it is not an equation. As an expression, it will be considered. An explanation of the differences between an expression and an equation will be provided later in this essay.

Here,

P=850+5x

so the band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.

So new equation formed is

50x-P=5000

50x-(850+5x)=5000

50x-5x-850=5000

45x=5850

x=5850/45

x=130

Therefore they have to sell 130 concert tickets to equal $5,000 per concert.

To know more about equation ,visit

https://brainly.com/question/10413253

#SPJ1

The dilutions in one step, or have to do serial dilutions.

There is a limit to how much can dilute a sample in one step.

Dilute by more than a factor of 100 in a single step, because that a large volume of dilute solution.

Rather, use the serial dilution technique.

Remember the formula for dilution factor (DF):

DF =Vf /Vi

, where

Vi = aliquot  volume

and Vf = final volume = aliquot volume + diluent volume

a) DF = 50

For a single dilution.

This time  add 0.2 mL of sample to 9.8 mL of saline.

Vf = 0.2 mL + 9.8 mL= 10.0 mL

DF = Vf/Vi = 10.0mL 0.2mL= 50

b) DF = 100

For a single dilution.

This time  add 0.1 mL of sample to 9.9 mL of saline.

Vf = 0.1 mL + 9.9 mL=10.0 mL

DF =Vf/Vi = 10.0mL/0.1mL = 100

c) For a serial dilution.

The formula for serial dilutions is

DF =DF1×DF2×DF3×…

about a 1:100 dilution followed by a 1:2 dilution

(1) Add 0.1 mL of sample to 9.9 mL of diluent.

DF1 = 100 Call this "Solution 1".

(2) Add 5 mL of Solution 1 to 5 mL of saline. Call this "Solution 2".

Vi = 5 mL

Vf = 5 mL + 5 mL= 10 mL

DF2 = Vf/Vi = 10mL/5mL=2

DF = DF1×DF2 = 100 ×2= 200

DF = 50

DF = 100

DF = 200

The dilutions in one step, or  have to do serial dilutions.

To learn more about Serial dilution visit:

brainly.com/question/28997625

#SPJ4

The pencil was reduced by 1/6 of its original length. Hence, the correct option is Option C.

To calculate the fraction, you must divide the remaining length (15 cm) by the original length (18 cm). In order to get a fraction, you have to divide it by their highest common factor, which in this case is 3.

= \frac{15}{18}

= \frac{5}{6}

This is the length of the pencil left at the end of the day. To find the fraction used, you have to subtract this fraction from its whole.

= 1 - \frac{5}{6}

= \frac{5}{6} - \frac{5}{6}

= \frac{6-5}{6}

= \frac{1}{6}

For more information on fractions, please refer to the question given below:

https://brainly.com/question/10354322