solve ln (5x 7) = 2. round to the nearest thousandth.

Binomial probability distribution for the given set of data is

[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]

What is binomial probability distribution?

"Binomial probability distribution is the representation of  a probability with only two outcomes success and failure under given number of trials."

Binomial probability distribution is given by

[tex]nC_x p^x q^{n-x}[/tex]

n= number of experiments

x = 0, 1, 2, 3,.......

p = probability of success

q = probability of failure

According to the given question

Number of trials  'n' = 100

Probability of success 'p' = (20 / 100)

                                          = 0.20

Probability of failure 'q' = 1 - p

                                       = 1 - (20/100)

                                       =  (80 / 100)

Substitute the value in the formula we get

Required probability = [tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]

Example:

Tossing a coin 6 times getting exactly two heads.

Number of trials 'n' = 6

Number of heads 'x' =2

Only two possible outcomes head or tail

Probability of getting head 'p' = 1 / 2

Probability of not getting head 'q' = 1 /2

Required probability = [tex]6C_2[/tex] (1/2)²(1/2) ⁶⁻²

                                  = [tex]6C_2\\[/tex] (1/2)⁶

Hence, binomial probability distribution for the given set of data is

[tex]100C_x (0.20)^x (0.80)^{100-x}[/tex]

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Dimension of maximize area is, length = 1581 m and breadth = 790.5 m.

Given that a rectangular plot of land adjacent to a river is to be divided into two equal plots. And 3162 ft of fencing to enclose the plot.

Consider the length is L and breadth is B of the plot.

Therefore the perimeter = L + 2B = 3162

⇒ L = 3162 - 2B

We know that area is the product of length into breadth i.e,

Area = L × B

        = (3162 - 2B) × B

Area = 3162B - 2B²

The maximum of the quadratic expression is

ax² + bx + c is at s = [tex]\frac{-b}{2a}[/tex] if a < 0.

Now we will calculate maximum point of the equation,

B = [tex]\frac{-3162}{2(-2)}[/tex]

B = 790.5

Now we will find the value of length,

L = 3162 - 2B

  = 3162 - 2(790.5)

  = 3162 - 1581

L = 1581

Hence the length of the rectangular plot is 1581 m and bredth is 790.5 m.

Therefore the maximize area = 1581 × 790.5 =124978

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32 papers would Ashley have to remain to grade after working for 6 hours.

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Ashley is a teacher and takes home 98 papers to grade over the weekend.

She can grade at a rate of 11 papers per hour.

We have to calculate how many papers would Ashley has remaining to grade after working for 6 hours.

Based on the given conditions, formulate:: 98 - 11 × 6

Calculate the product or quotient: 98 - 66

Calculate the sum or difference: 32

Hence, 32 papers would Ashley have to remain for a grade after working for 6 hours.

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Answer:

3 years

Step-by-step explanation:

L=Lawson. TL=total inches for Lawson's tree

E=Ezra. TE=total inches for Ezra's tree

x=number of years

L ==> TL=3x+14

E ==> TE=5x+8

Now, try to find when the heights are equal by setting both equations equal to each other:

TL = TE

3x+14 = 5x+8

3x-3x+14 = 5x-3x+8  ==> subtract 3x on both sides to isolate x to one side

14 = 2x + 8

14 - 8 = 2x + 8 - 8  ==> subtract 8 on both sides to isolate x

6 = 2x

x = 6/2 ==> simplify

x = 3 years

Value of x shows that the lines parallel is x=60°

What is transversal and parallel line?

From the figure attached we can se that ∠A+ 2x+10= 180°

and ∠B+x-10 =180°

and we know that the is transversal line so ∠A=x-10 & ∠B=2x+10

There fore x-10 +2x+10 =180 °

3x=180°

x=60°

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The residual plot is illogical because it should have a nonlinear curve given that the scatter plot is negative.

A graph where the values of two variables are shown along two axes, showing any correlation via the positioning of the points that results.

A scatter plot is a collection of dots arranged along an axis that runs horizontally and vertically. Scatter plots are essential in statistics because they can show the strength, if any, of the relationship between the values of observed quantities or occurrences (called variables).

It is clear from the scatter plot that it is a nonlinear curve with negative points. Consequently, the Residual plot is illogical because it should have a nonlinear curve given that the scatter plot is negative.

Therefore, the correct answer is option c) The random residusl plot does not make sense because it should have a noninar curve, as the scatter plot is negative.

The complete question is:

The relationship of miles per gallon of SUVs to weight is represented by the following scatter plot:

Beatrice created the following residual plot:

Does her residual plot make sense based on the scatter plot? Explain.

a) The random residual plot makes sense because the scatter plot appears to have a negative relationship.

b) The random residual plot does not make sense because it should have a linear relationship like the scatter plot.

c) The random residusl plot does not make sense because it should have a noninar curve, as the scatter plot is negative.

d) The random residual plot makes sense because the scatter plot appears to have a lines relationship.

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Given that the scatter plot is negative, the random residual plot should have a nonlinear curve, which is why it is illogical.

What is a scatter plot?

From the question, the chart that shows the values of two variables along two axes and shows any correlation via the placement of the points is a scatter plot.

It is a collection of dots that are plotted along a horizontal and vertical axis. Scatter plots are essential in statistics because they can show the level of relationship, if any, between the values of observed quantities or occurrences (called variables).

The scatter plot is a nonlinear curve with negative points, as may be seen.

As a result, the Residual plot is illogical because, given that the scatter plot is negative, it should have a nonlinear curve.

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The solution of the given equation is:

[tex]\frac{log 9}{Log 2} - 1[/tex]  = 2.16992500144

Logarithm:

Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8. Similarly, 2 = log10 100 because 102 = 100. The latter kind of logarithm (that is, the base 10 logarithm) is called the ordinary logarithm or the Briggs logarithm and simply write log n.

Invented in the 17th century to speed up calculations, logarithms greatly reduced the time required to multiply large numbers. These were the basis of numerical computation for over 300 years until the mechanical calculator of the late 19th century and his 20th century computer sophistication made it obsolete for large-scale calculations. However, the natural logarithm (with base e ≅ 2.71828 and written ln n) continues to be one of the most useful functions in mathematics, being applied to mathematical models in the physical and biological sciences.

According to the question:

2ˣ=4.5

Take the logarithm of both sides of the equation

log2ˣ = log9 / 2

x . log2 = log9 − log2

divide both sides of the equation by log 2:

          [tex]\frac{x Log 2}{Log 2} = \frac{Log 9 - Log 2}{Log 2}[/tex]

⇒  x = [tex]\frac{log 9}{Log 2} - 1[/tex]

⇒ x = 2.16992500144.

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The linear equation that models how much Carolina earns depending on the number of hours that she works is:

y = 6*x + 8

Here we know that for every mowing job, Carolina charges $6, plus an initial fee. So if that initial fee is b, we can write the equation as:

y = 6*x + b

We also know that for a 4 hours job she charges $32, then we can replace x by 4 and y by 32 in the equation above.

32 = 6*4 + b

32 = 24 + b

32 - 24 = b

8 = b

Then the linear equation we wanted to find is:

y = 6*x + 8

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The slope of the line which follows is  0.50 and height of the tent 5 feet from the outside pole will be 12.5.

The rise to run ratio is known as the slope. From 10 feet to 25 feet, there is a 15-foot increase. The run is 30 feet from the edge to the center.

slope = rise/run

= 15 /30 = 1/2

= 0.50

25 feet from the center pole is equivalent to 5 feet from the outer pole.

The rise at 25 feet from the central pole is now determined by

rise = m*run

=-12.5

As a result, the height of the pole decreases by 12.5 feet as one moves 25 feet from the central pole to the outside pole.

Consequently, the tent's height at 5 feet from the outside pole would be 25 - 12.5 = 12.5 feet.

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Answer:

8

Step-by-step explanation:

x=-4 perfectly suits x<=-1 since -4<=-1

Hence, when calculating g(-4), you need to apply the expression -x+4

Hence:

g(-4)=

-x+4=

-(-4)+4= ==>   plug in -4 for x

4 + 4 = 8   ==> Negating a negative number is equaled to taking the

                       positive number.

In this experimental design, the y variable is the testosterone levels.

A variable is defined as any symbol or letter that is used to express an unknown quantity. There are two types of variables: the dependent variable (y variable) and the independent variable ( x variable).

An independent variable (x variable) is the variable which causes the change in another variable.

A dependent variable (y variable) is the result or effect of that change in the dependent variable.

If we are interested in what happens to testosterone levels as the men age in adult men ages 18 years and older, then the x variable is the age and the y variable is the testosterone levels.

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Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

An alternative name for a combo is a choice. A combination is a choice made from a predetermined group of options. I won't organize anything here. They will be my choice. The number of distinct r selections or combinations from a set of n objects is indicated by the symbol [tex]^nC_{r}[/tex].

There are eight participants in the focus group, including three software engineers, two nurses, one doctor, and two technicians.

So the 3 software engineers =3! ways, 2 nurses =2! ways,

doctor =1! way , 2 technicians =2! ways.

We must determine how many different configurations are possible so that no two pieces of software may coexist.

In order to prevent two software engineers from being seated next to each other, we first arrange five persons in a row with a space between them.

[tex]We get that in 6 places they can sit in ^6C_{3} ways\\ xi.e ^6C_3 = 20 (by formula of combination)\\ Therefore total ways are,6 X 2 X 1 X2 X 20 = 480.[/tex]

Therefore, there are 480 different ways to arrange individuals in a row so that no two engineers sit together.

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(D) ASA is not a similarity criterion for two triangles.

If two triangles fit one of the following descriptions, they are similar: Angles in two pairs that are corresponding are equal.

The ratio of three sets of corresponding sides is three.

The comparable angles between two pairs of corresponding sides are equal and proportional.

You can use three triangle-specific theorems to quickly distinguish similar triangles.

There are three theorems that can be used to determine whether two triangles are similar: Angle - Angle (AA), Side - Angle - Side (SAS), and Side - Side - Side (SSS).

The triangles' potential similarity criteria are Angle-Angle-Angle (AAA), Side-Angle-Side (SAS), and Side-Side-Side (SSS).

Angle-side-angle (ASA) is thus a choice from the available possibilities to check the congruence of the triangle rather than its similarity.

Therefore, (D) ASA is not a similarity criterion for two triangles.

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Correct question:
Which of the following is not a similarity criterion for two triangles

(A) ASA

(B) SAS

(C) SSS

(D) ASA?

Answer:

It has a radius of 4.9meters so its diameter will be multiplied by two making it 9.8meters

Answer: Diameter of each semicircle is 9.8 m, because there is said that these are semicircles, so 4,9 m means radius.

Step-by-step explanation: Semicircle is half of the circle so that means it's divided in half and pass through center point. Radius is the distance from central point to any point of the circumference, and the diameter is equal 2 times Radius.

Answer:

m-2

Step-by-step explanation:

to start simplify

-3(7/2-2/3m)+17/2-m

-21/2+6/3m+17/2-m

-21/2+17/2+2m-m

-4/2+m

-2+m

m-2

hopes this helps

The polynomial with constant term of 12 that cannot be factored is given as follows:

y = x² - 3x + 12.

It cannot be factored because it has a negative discriminant.

The standard definition of a quadratic equation is given as follows:

y = ax² + bx + c.

The discriminant determines if the function can be factored, and is given as follows:

D = b² - 4ac.

If the discriminant is negative, the function cannot be factored.

In this problem, the function is defined as follows:

y = ax² + bx + 12.

Attributing a = 1, the function is:

y = x² + bx + 12.

Then the coefficients are:

a = 1, c = 12.

It cannot be factored when:

D < 0

Hence:

b² - 4ac < 0.

b² < 48

|b| < 7.

Hence one possible case is when b = -3, giving the equation shown at the answer.

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The probability that out of 52 card the selected 3 cards are not a face card is 0.183.

There are 12 face cards in a deck of 52 cards.

The probability of selecting 3 cards which should not be a face card is ,

=30c3 / 52c3

= 4060 / 22,100

= 0.183

Combination is a means to choose items from a collection without worrying about their order. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen, i.e., nCr .

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Transfer of balance The interest rate for balance transfers to credit cards is expressed as an annual percentage rate, or APR. A starting balance is offered with some cards assume you have got poor credit .

The interest rate you pay on purchases when your credit card balance is still high is known as a purchase annual percentage rate (APR). A credit card's APR, which is applied each month, is an annualized percentage rate.

Transfer of balance The interest rate for balance transfers to credit cards is expressed as an annual percentage rate, or APR. A starting balance is offered with some cards assume you have got poor credit .

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The value of 2 divided by 3 is 0.67

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

2 divided by 3

To start with, we need to represent the expression properly as a quotient

So, we have the following representation

2 divided by 3 = 2/3

Evaluate the quotient expression using a calculator

This gives

2 divided by 3 = 0.67

Hence, the solution to 2 divided by 3 is 0.67

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Answer:

[tex]\textsf{b)} \quad (x-3)^2+(y+1)^2=100[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given:

Substitute the given center and radius into the formula to create the equation of a circle with the given parameters:

[tex]\implies (x-3)^2+(y-(-1))^2=10^2[/tex]

[tex]\implies (x-3)^2+(y+1)^2=100[/tex]

Answer:

4.5x10¹¹ = 450,000,000,000

Step-by-step explanation:

(5x10³)(9x10⁷) = 4.5x10¹¹ = 450,000,000,000

Answer: 1/7

Step-by-step explanation:

There are total of 7 gloves

There is 1 black glove

So take 1 divided by 7

The Fraction is 1/7

if (x+2)² = k , making x the subject is x = √k - 2

The subject of a formula is the variable that is being worked out. It can be recognised as the letter on its own on one side of the equals sign.

For example, if V = πr²h and we want to make r the subject of the formula, we make r in place of V.

Therefore r² = V/πh

r = √ (V/πh)

Similarly

(x+2)² = k

when we square root both sides

x+2 = √k

Collecting like terms

x = √k - 2

therefore making x the subject in the formula (x+2)² = k in terms of k is x = √k - 2

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At [00:16:00] timestamping (every 2 minutes) start in the audio segment of 15-20 minutes

Timestamping is frequently used to highlight a certain section of an audio file and indicate its significance.

In general, timestamps are utilised for the transcription process, in which the audio is used as a reference to convert it to a written form, if there is speech in an audio file other than music. Usually, this occurs in the press and media.

The timestamping software has the following formats: [HH:MM:SS]

HH stands for hours, MM for minutes, and SS for seconds.

For Audio segment of 15-20 minutes ,  [00:16:00] is timestamping every 2 minutes.

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Answer:

67 days

Step-by-step explanation:

40.2/0.6 = 67

Answer: 67 days

The necessary phrase will be s≥150 because the bullet train's cruising speed will be greater than 150 mph.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases. A group of numbers that have been written together using the arithmetic operations addition, subtraction, multiplication, and division is known as a numerical expression in mathematics. The number can be stated in a variety of ways, including verbally and numerically.

Here,

No less than" means "greater than or equal to" (≥).  

So you want s to be greater than or equal to 150 mph.  

s≥150

The required expression will be s≥150 as the cruising speed of the bullet train will be in excess of 150 miles per hour.

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The value of x = 4

The value of y = 3

7x + y = 33    ......eq(1)

3x + y = 17     .....eq(2)

Here subtract eq(2) from eq(1), we get

4x = 16

therefore x = 16/4

x = 4.

Now to get the 'y' value, substitute the 'x' value in eq(2)...

3(4) +y = 17

y = 5

Therefore,

x = 4

y = 3

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Base (cube): [tex]V=s^3[/tex]

   [tex]V=9\cdot9\cdot9=729[/tex]

Top (triangular prism): [tex]V=\frac{1}{2}bhl[/tex]

   [tex]V = \frac{1}{2}(9\cdot7)\cdot9=283.5[/tex]

Together:

   [tex]V = 729+283.5 =1012.5[/tex]

C.

1012.5 cubic units.

The exponential equation may be solved using log base x and log base 10 logarithm bases. The right answer is D.

Finding the base of the logarithm that may be used to determine the value of x is necessary in order to solve an exponential equation with the form log base x (y) = z.

The equation log base x (y) = z applies here. Let's explore each possible logarithm base:

Log base x: The problem may be solved directly using this logarithm base. The value of x that the equation requires may be discovered using the logarithm base x.

Log base 25: The problem cannot be properly solved using this logarithm base. It does not work with the provided equation.

Log base 4: The equation cannot be properly solved using this logarithm base. It does not work with the provided equation.

Log base 10: The problem may be readily solved using this logarithm basis. To determine the value of x that the equation requires, use the logarithm base 10 function.

The logarithm bases that may be utilised to solve the exponential equation based on the provided parameters are log base x and log base 10.

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