For the binomial distribution, which formula finds the standard deviation? Choose the correct answer below: a)np b)npq c)Vnp d)Vnpa

The pair of transformations that is equivalent to the transformation described by (x,y) -> (x,-y+1) is (x, -y) and (x, y + 1)

From the question, we have the following parameters that can be used in our computation:

(x,y) ⇒ (x,-y+1)

The above represents the transformation from a point to the image of the point

The first transformation is from

(x,y) ⇒ (x,-y)

This represents a reflection across the x-axis

The second transformation is from

(x,-y) ⇒ (x,-y + 1)

This represents a translation up by 1 unit

Hence, the pair of transformations is (x,y) ⇒ (x,-y) and (x,-y) ⇒ (x,-y + 1)

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The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.

The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,

y = abˣ

Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.

Given that, a car is sold for $18,000.

So, the initial value a = 18000.

After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as

11700 = 18000(b)¹

⇒ b = 11700/18000 = 0.65

Since b < 1, the function is exponentially decaying.

Then, the value of the car after 'x' years is given by the exponential decay function as

y = 18000(0.65)ˣ

(It is given that, the rate of decrease is the same each year).

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This indicates that the probability is 0.4402% without replacement.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

n = 5

x = 1

p = 5/20 = 0.25

15C4 = 15! / 4! * 11! = 1365

P = (5C1 * 15C4) / 20C5

Replacing:

P = 5 * 1365/15504

P = 0.4402

Hence, This indicates that the probability is 0.4402% without replacement.

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This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

The probability of getting a specific number of heads in a given number of flips follows a binomial distribution, which describes the probability of getting a certain number of successes in a given number of independent trials. The probability of getting a specific number of heads in ten flips can be calculated using the formula:

P(x heads in n flips) = (n choose x) * p^x * (1-p)^(n-x)

where p is the probability of getting a head on each flip and x is the number of heads.

For example, the probability of getting exactly 3 heads in ten flips is:

P(3 heads in 10 flips) = (10 choose 3) * 0.35^3 * (1-0.35)^(10-3) = 0.241

This means that the probability of getting exactly 3 heads in ten flips is about 24.1%.

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Answer:

i just had this lol its a and d

Step-by-step explanation:

The new length is 35+10=45 and the new width is 18+10=28.

To Find the Area of a rectangle is length times the width.

Given that enclosure at the zoo is 35 feet long by 18 feet wide. It means the length is 35 feet and the width is 18 feet.

Area of Rectangle=Length × Width

=35×18

=630

The zoo wants to double the area of the enclosure by adding the same distance x to the length and width.

(35+x)×(18+x)=1260

630+35x+18x+x2=1260

x2+53x+630-1260=0

x2+53x-630

Now we will apply the quadratic formula we get

x=10.

The new length is 35+10=45

The new width is 18+10=28.

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discount= 27.5

S.P= 522.5

Step-by-step explanation:

Marked price of dress(m.p)= 550

Discount % = 5%

Discount amount = 5% of MP

=5÷100×550

=27.5

S.P of the dress = ?

we know,

S.P = MP- discount

= 550-27.5

=522.5

This city's data had the higher median monthly apartment cost of the two cities by $155.

The city of austin's data had the higher interquartile range of the two cities by $87.

The city of austin had the greater variability among monthly apartment costs because the standard deviation was $49.13 more than that of the other set of data.

The given data for the cost of renting a one-bedroom apartment in Dallas in ascending order is as follows;

$994, $1,322, $1,075, $1,189, $1,172, $1,465, $1,215, $930, $1,090, $1,288

$930, $994, $1,075, $1,090, $1,172, $1,189, $1,215, $1,288, $1,322, and $ 1,465

Analyzing the above using Microsoft Excel, we see that;

Dallas Mean = $1180.5

Dallas Interquartile range = $213

Standard Deviation = $159.9597

The given data for the cost of renting a one-bedroom apartment in Austin in ascending order using is;

$900, $950, $1,100, $1,250, $1,296, $1,375, $1,389, $1,400, $1,450, $1,495

Analyzing the above using Microsoft Excel, we see that;

The mean = $1335.5

The interquartile range = $300

The standard deviation of the sample = $209.0945

The difference in the median cost of the two cities is $1,335.5 - $1,180.5 = $155

Therefore, the Austin's city data has the higher median monthly apartment cost of the two cities by $155

The difference in the sample standard deviation of the two cities is $209.0945 - $159.9597 = $49.13476

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The center of the circle shifted 6 units to the right when it's center is on line x=6.

A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry. Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle. A circle can be compared to a hula hoop. The circle is only present at the border's points.

Here,

Centre of circle=(-4,3)

-4+6=2

New centre is (2,3).

When the circle's center is on line x=6, its center has moved 6 units to the right.

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The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0  

When two lines cross at a straight angle or 90° then the pair of lines said to a pair of perpendicular lines.  If the slopes of the two perpendicular lines are m₁, m₂, then the connection between the slopes of perpendicular lines will be represented by the following formula

Here we have

Given line y = −23x+5 ------ (1)

A line perpendicular to the line (1) passes through the point (0, –2).

Here given line is y = −23x+5 which is in the form of y = mx + c

On comparing both equations

=> Slope of line m = −23

Let (y - y₁) = m(x - x₁) be the required equation

=>  (y - y₁) = m(x - x₁) ----- (2)

As we know product of slopes of line(1) and (2) is - 1

=>  mm₁ = - 1

=>  −23m₁ = -1

=>  m₁ = 1/23

Substitute m₁ = 1/23 in line (2)

=>  (y - y₁) = [1/23](x - x₁)

=>  23(y - y₁) = (x - x₁)

Given the line passes through the point (0, –2).  

=>  23(y - (-2)) = (x - 0)  

=>  23(y + 4) = x

=> 23y + 4 = x

=> x - 23y - 4 = 0

Therefore,

The equation of the Line that is perpendicular to the given number is
x - 23y - 4 = 0  

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f(t) =  [tex]0.01 ( 2 )^{t}[/tex] is  which investment will eventually have the greater value.

What investment means?

An asset or object purchased with the intention of generating income or appreciation is referred to as an investment. An asset's value increasing over time is referred to as appreciation.

                               When a person buys a product as an investment, they don't intend to utilize it right away; instead, they plan to use it to make money later on.

F(t) = [tex]a(b)^{t}[/tex]

option a -                      a = 5

                                b = 1.5

                        f(t) = 5(1.5)

option b -                    a  = 0.01

                                  b = 2

               f(t) =  [tex]0.01 ( 2 )^{t}[/tex]

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By using some exponent properties, we will find the equivalent expression:

(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²

Here are some exponent properties that we need to use:

(aⁿ)ˣ = aⁿ*ˣ

(a⁻ⁿ) = (1/a)ⁿ

Here we have the expression:

(m⁻²*n⁻³)⁻⁴

The exponents can be distributed under multiplication, then:

(m⁻²)⁻⁴*(n⁻³)⁻⁴

Now we can use the first property so we get:

(m⁻²)⁻⁴*(n⁻³)⁻⁴ = m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾

m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾ = m⁸*n¹²

That is the equivalent expression.

(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²

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Answer:

there were 91,487.414 gallons of water in the tank before the leak.

Step-by-step explanation:

To find out the number of gallons of water that was in the tank before the leak, you can use the following equation:

Number of gallons before the leak = Number of gallons after the leak + Number of gallons leaked

Plugging in the values given in the problem, we get:

Number of gallons before the leak = 91,468 gallons + 19.414 gallons

Solving this equation gives us:

Number of gallons before the leak = 91,487.414 gallons

So there were 91,487.414 gallons of water in the tank before the leak.

56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

Given that,

Amira will put $580 into an account and let it sit there for 17 years.

We have to find what interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

We know that,

We have a formula

A=P(1+r/n[tex])^{nt}[/tex]

Here,

A=$840

P=$580

n=12

t=17

We get

840=580(1+r/12[tex])^{12\times17}[/tex]

840=580(1+r/12)²⁰⁴

42/29=(1+r/12)²⁰⁴

r=0.56

Therefore, 56% interest rate, to the nearest hundredth of a percent, would be necessary for Amira to end up with $840 assuming the interest is compounded continuously.

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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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The height of the pyramid can be represented ,as per the given details as 3x.

The volume is 3/2 times 3 x 3, and the hexagon base's area is six times greater than the equilateral triangle's.

A pyramid's base edge's length is equal to x units.

In other words, the pyramid's height is three times as long as its base edge.

The pyramid's height is equal to 3x

A three-dimensional structure with a polygon at its base is referred to as a pyramid. You must be familiar with The Great Pyramid of Giza, which was built using a similar framework. This structure has a distinct shape because each corner is connected to a single apex.

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Therefore, the probability that the mean number of lightning strikes per square kilometer is less than 5 is P([tex]X^{'}[/tex]<5)=0.0016

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Here,

mu =6

α=2.4

n=50

Σxi=250

Formula used:

z=[tex]\frac{x-u}{\alpha }[/tex]

Step 2: Calculation

[tex]x^{'}[/tex] = Σ[tex]\frac{xi}{n}[/tex] = 250/50 = 5

z = [tex]\frac{x^{'} - u_{x} }{\alpha x^{'} }[/tex] = [tex]\frac{x^{'} - u_{x} }{ \frac{\alpha }{\sqrt{n} } }[/tex] = [tex]\frac{5- 6}{ \frac{2.4}{\sqrt{50} } }[/tex] ≈ -2.95

P([tex]X^{'}[/tex]<5)=P(Z<-2.95)

=0.0016

or 0.16%

Therefore, the probability  probability that the mean number of lightning strikes per square kilometer is less than 5 is P([tex]X^{'}[/tex]<5)=0.0016

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Answer:

-6y + 13.3 = 0

y = 13.3/6

Step-by-step explanation:

This equation don't need any step-by-step explanation :). Hope it helps!

The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:

y - 4 = -4/7(x - 2).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The function in this problem is defined as follows:

y = square root(3x² + 2x).

Then the derivative of the function, applying the chain rule, is given as follows:

y' = (6x + 2)/(2 x square root(3x² + 2x))

y' = (3x + 1)/square root(3x² + 2x)

At x = 2, the numeric value of the derivative is of:

y' = 7/square root(16) = 7/4.

The slope of the normal line is calculated as follows:

m x 7/4 = -1

m = -4/7.

(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).

The coordinates of the point at (2,4), hence:

x' = 2, y' = 4.

Then the definition of the normal line is given as follows:

y - 4 = -4/7(x - 2).

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Answer:

x = -2, y = (1/9)

x = -1, y = (1/3)

x = 0, y = 1

x = 1, y = 3

x = 2, y = 9

Graph B

Step-by-step explanation:

f(x) = 3ˣ

y = 3ˣ

                  1

y = 3⁽⁻²⁾ = ------

                 9

                  1

y = 3⁽⁻¹⁾ = -------

                  3

y = 3⁽⁰⁾ = 1

y = 3⁽¹⁾ = 3

y = 3⁽²⁾ = 9

I hope this helps!

The measurement of side DF is 4cm.

Here in the figure attached below,

Given two triangles ΔABC and ΔDEF

Also given that,

ΔABC and ΔDEF are congruent to each other.

Given AC = 4cm

Since both triangles are congruent ,

Side AC is congruent to DF

Therefore DF = 4cm (based on SSS theorem).

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The measure of DF is 4cm.

What is congruent triangle?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

Here in the figure attached below,

There are two triangles ΔABC and ΔDEF and it is given that ΔABC and ΔDEF are congruent to each other.

From the figure, side AC = 4cm

The side DF = AC = 4cm, because the triangles  ΔABC and ΔDEF are congruent to each other and based on Side-Side-Side Theroem, we can confirm that.

Hence, DF = 4cm.

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In the regression line y = a+ bx+ e, a is the slope of the regression line.

The above statement is False.

The correct Statement is :

The linear regression line has an equation of the form Y =a + bX

where, Y is called the dependent variable or response.

X means independent or predictor or explanatory variable.

a is the y-intercept and b is the slope of the line.

Regression Line:

A regression line is a statistical tool that shows the correlation between two variables. Specifically, it is used when the variation of one (the dependent variable) depends on changes in the value of the other (the independent variable).

Simple linear regression has two cases:

The formula for the least squares regression line (LSRL) from Y to X is:

                           Y=a + bX + ɛ

where,

Y is the dependent variable.

a is the Y intersection.

b is the slope of the regression line.

X is the independent variable.

ɛ is the residual (error).

and

b = (N∑XY-(∑X)(∑Y) / (N∑X2– (∑X)2) ;

and

a = (∑Y – b ∑X) / N

where, N is the total number of observations.

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Answer: 60%

Step-by-step explanation:

6/10 = 60/100 = 60%

Answer: 60%

Step-by-step explanation:

6/10=60/100

10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

percentage, a relative value indicating hundredth parts of any quantity.

The formula for quarterly compound interest formula:

[tex]A=P(1+\frac{r}{4} )^{4t}[/tex]

P is the principle amount

t is time

r is rate of interest

A is final amount

[tex]1750=1000(1+\frac{0.0575}{4} )^{4t}[/tex]

[tex]1750=1000(1+0.0144)^{4t}[/tex]

[tex]1750=1000(1.0144)^{4t}[/tex]

Divide both sides by 1000

[tex]1.75=1.0144^{4t}[/tex]

Take log on both sides

log1.75=4tlog1.0144

0.243=4t(0.006)

0.243=0.024t

Divide both sides by 0.024

t=10.12

t=10 years

Hence, 10 years it takes for 1000 to grow to 1750 if invested at 5.75% compounded quarterly.

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A bar graph is the most popular visual representation of quantitative data.

Another name for them is bar charts. One tool used in statistics for data processing is the bar graph. Using a bar diagram, it is simple and quick to compare sets of data among several groupings. On one axis of the graph are discrete numbers, while on the other are categories. The purpose is to illustrate how the two axes are related. Bar charts can also show significant alterations in data over time.

Given,

A bar graph is the most popular visual representation of quantitative data.

b) Bar graph

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Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

In mathematics, an equation is a logical statement with two algebraic expressions on either side of the equals (=) sign. In relation to one another, the expressions on the left and right are equal. Every mathematical equation begins with the expression LHS = RHS (left hand side = right hand side). The value of a variable or quantity can be found by solving an equation. Unless the statement contains the "equal to" sign, it is not an equation.

Here,

The company charges a monthly fee of $31 to deliver a box of pet supplies each month

x be the number of subscribers and y be the price.

equation used is

Since , company currently has 290,000 subscribers. For each $1 increase in price ,the company loses 10,000 subscribers

Therefore to  to maximize monthly revenue

he has to increase the price by $2

Therefore he will loose 20,000 subscribers

and the maximum revenue he will generate is

=> 270,000 * 33

=>8,910000

Therefore the maximum revenue company will generate is $8,910,000 and thus price should be increased by $2

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Sides and angles are congruent then ΔBAE ≅ ΔCAD

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

AD≅AE and ΔCFE≅ ΔBFD

we need to prove ΔBAE≅ΔCAD

n the given figure it has similar triangles

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

AD=AE because both are congruent sides

ΔCFE≅ ΔBFD the angles are congruent in the similar triangles

As both sides and angles are congruent then ΔBAE is similar or congruent to ΔCAD

Hence,  sides and angles are congruent then ΔBAE ≅ ΔCAD

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After using the arithmetic: They sold 40 small bowl of ice cream and 23 large bowl of ice cream.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the standard operations on numbers—addition, subtraction, multiplication, division, operation, and extraction of roots.

Main body:

Cost of small bowl of ice cream = $2.25

Cost of large bowl of ice cream  = $3

Total number of bowls sold = 63

total value  = $159

let number of small bowls be x and  large bowl be y.

Hence ,

x +y = 63                       ---(1)

2.25 x +3 y = 159          ---(2)

from equation 1 substitute the value of x in equation 2 .

2.25 x + 3 (63- x) = 159

2.25 x + 189 - 3x = 159

taking like terms to one side ,

3x - 2.25x = 189-159

0.75x = 30

x = 40

so x = 40 then y = 23.

Hence they sold 40 small bowl of ice cream and 23 large bowl of ice cream.

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