The data set represents the total number of pencils each student in a class needs to sharpen. 0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9 which box plot correctly represents the data?

Option (a) Sample

Sample is the research that analyzes a portion of an entire population.

A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.

By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.

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Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.

Answer:

25 / 4

Step-by-step explanation:

To find the left sum, you need to....
1.) Find Δx

2.) Find [tex]x_{k-1}[/tex]

3.) Find ∑[tex]^n_{k=1}f(x_{k-1})[/tex]Δx

4.) Solve for the left sum

The linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

A linear function is modeled by:

y = mx + b

In which:

In this problem, we have that:

Hence the linear functions with their slopes ranked from least to greatest are given as follows:

E. I, K, J.

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The volume of the cylinder is [tex]3.14 inch^3[/tex]

Given that

radius = 1 inch

height = inch

we know that volume =[tex]V = \pi \times r^2 \times h[/tex]

now put the value in the above equation we get

[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]

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Answer:

[tex] \frac{1 \\ }{3125} [/tex]

Answer:

x = 9

Step-by-step explanation:

        [tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]

[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]

Base are same. Compare the exponents.

 x - 14 = -5

        x = -5 + 14    {Addition property of equality}

        x = 9

Answer:

  See attached

Step-by-step explanation:

Each point on the line segment moves to 2 times its previous distance from the origin.

The center of dilation, the origin, is an invariant point. It doesn't move for any dilation factor. One end of the line segment is there, so it will not move.

The coordinates of each point are multiplied by the dilation factor. The other end of the line segment is (5, 5), so it moves to 2×(5, 5) = (10, 10).

The dilated line segment extends from (0, 0) to (10, 10). It is shown in red in the attached graph.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:g(f( - 5)) = 5[/tex]

[tex]\textsf{\underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:f(x) = |2x + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = |2( - 5) + 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 10+ 9| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = | - 1| [/tex]

[tex]\qquad❖ \: \sf \:f( - 5) = 1[/tex]

next,

g(f(-5)) represents value of y at x = f(-5) = 1

hence,

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

B

Step-by-step explanation:

It's B

Answer:

Option B

Step-by-step explanation:

The equation is:

[tex]y=10-2x[/tex]

when x=2

[tex]y=10-2(2)010-4=6[/tex]

When x = 3

[tex]y=10-2(3)=10-6=4[/tex]

When x=4

[tex]y=10-2(4)=10-8=2[/tex]

Hope this helps

Answer: Look at stwp by step

Step-by-step explanation:

Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2

P/10 = 7.2/3

P = 7.2x10/3

P=72/3

P= 24

Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

The probability that exactly 12 of them are strikes is 0.09.

In this question,

Number of pitches, n = 22

Probability of throwing a strike for each pitch, p = 0.431

Then, q = 1 - p

⇒ q = 1 - 0.431

⇒ q = 0.569

Number of strikes, x = 12

The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,

[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]

⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]

⇒ P(X=12) = (646646)(0.000041)(0.00355)

⇒ P(X=12) = 0.09431 ≈ 0.09

Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.

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¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

Pascal's triangle is a triangle written in such a way that it forms the coefficients of a binomial expansion. The coefficients of the terms are gotten through combination.

Combination is the number of ways r in which n objects can be selected. It is given by ⁿCₓ = n!/x!(n - x)!

Since we have ¹³C₈ + ¹³C₉ and we want to write it as a single term, we have that

So,  ¹³C₈ + ¹³C₉ =  13!/8!5! +  13!/9!4!

= 13!/(8! × 5 × 4!) +  13!/(9 × 8! × 4!)

= 13!/8!4![1/5 + 1/9]

= 13!/8!4! × [(9 + 5)/45]

= 13!/8!4! × 14/45]

= 13!/8!4! × 14/(9 × 5)]

= 14 × 13!/8! × 9 × 4! × 5)]

= 14!/9!5!

= 14!/9!(14 - 9)!

= ¹⁴C₉

So,  ¹³C₈ + ¹³C₉ as a single term from Pascal's Triangle is ¹⁴C₉

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Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]

To find the distance between the two complex numbers using the formula

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

where,

[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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answers :

a.

coordinates of A are (2,4)

b.

coordinates of B are (6,0)

i.

(4,2) is the midpoint

ii.

y = -3x + 18 is the parallel line

Step-by-step explanation:

a.

if two things are equal to the same thing then they are equal to each other

y = 4

2x + y = 8 is y = -2x +8 so

-2x +8 = 4

-2x = -4

x = 2

coordinates of A are (2,4)

b.

if two things are equal to the same thing then they are equal to each other

y=0

3x+y=18 is y = -3x+18 so

-3x+18=0

x = 6

coordinates of B are (6,0)

midpoint formula is

(X1+X2)/2 , (Y1+Y2)/2

(2,4) (6,0)

(X1+X2)/2 , (Y1+Y2)/2

(2+6)/2 , (4+0)/2

(4,2) is the midpoint

parallel line has the same x value

so for a line parallel to 3x+y=18 or y = -3x+18

the parallel line would be

y = -3x

point slope formula

point slope formulay - y1 = m (x - x1)

3x+y=18 or y = -3x+18 was 6,0 at y = 0

y - y1 = m (x - x1)

y - 0 = m (x - x1)

since it's a parallel line the m has to be the same

(6,0)

y - 0 = -3 (x - 6)

y = -3x + 18 is the parallel line

y=5(14-x)(x) quadratic equation best models the volume of the box .

What is volume of cuboid?

Perimeter = 2(width + length) =28

Let x=width of base, then length of base = (28/2)-x = 14-x

Volume of box = length*width*height

=x(14-x)*5  ⇒ 5x(14-x)(x)

Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .

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the parallel linear equation is:

y = (2/5)*x - 3

Two lines are parallel if the lines have the same slope but different y-intercept.

Here we know the line equation:

y = (2/5)*x + 4

Then a parallel line is of the form:

y = (2/5)*x + c

Where c is different than 4.

We want this line to pass through (5, -1), then:

-1 = (2/5)*5 + c

-1 = 2 + c

-1 - 2 = -3 = c

Then the parallel linear equation is:

y = (2/5)*x - 3

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120=!3÷!6

!2-!5=!3

to 120 modes

The exponential function illustrated as f(x)=50(1.02)^x has a growth rate of 2%.

The exponential function is a mathematical function that is represented by e^x. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

In this case, the function is given as:

f(x)=50(1.02)^x

It should be noted 1 + 2% = 1.02 which us the value in the parentheses.

In conclusion, the growth rate is 2%.

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Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.

Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".

Given the equation:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

where L is the length in feet and T is the time in seconds.

Given that T = 1.9sec,

Hence:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

L = 2.93 feet

A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.

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Answer:

The second option:

[tex]2\sqrt{x}[/tex]

Step-by-step explanation:

If you need work please ask!

Have a nice day!

Examples of population parameter are mentioned below .

According to the question

Population parameter :

A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.  

The examples of population parameter is

1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.

2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.  

Hence, examples of population parameter will depend on the population .

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Correct answer is C. the number of times blue ball appears is 56

Given,

probability of picking a green ball is 0.5,

the probability of picking a blue ball is 0.4,

the probability of picking a red ball is 0.1.

a ball is picked and replaced = 140

Probability = (the number of ways of achieving success) / (the total number of possible outcomes)

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

For this item, the number of times that we should expect that a blue ball is picked should be the product of the number of times  and the probability of picking a blue ball (which is equal to 0.4)

                            = (140)(0.4) = 56

Therefore, we should expect that the blue ball will be picked 56 times.

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The area of the shape is 35 square units

The given shape is a trapezoid, and it has the following side lengths

Parallel bases = 6 and 8

Height = 5

The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height

Substitute the known values in the above equation

A = 0.5 * (6 + 8) * 5

Evaluate the product

A = 35

Hence, the area of the shape is 35 square units

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The area of the given trapezoid is given as 35 square units

The given shape is quadrilateral known s a trapezoid. The formula for calculating the are of the trapezoid is expressed as;

A = 1/2(a+b)*h

where

a and b are parallel sides

h is the height of the trapezoid.

Given the following parameters

a =6units

b = 8 units

h - 5 units

Substitute to have:

A = 1/2(6 + 8) * 5

A = 1/2(14) *5

A = 7 * 5

A = 35 square units

Hence the area of the given trapezoid is given as 35 square units

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The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Length of Charles garden = 12.5 m * 12 = 150 m

Length of Stephen chain = 150 m /18 = 25/3 m

Breadth of Charles garden - 25/3 * 10 = 250/3 m

Area of Charles garden = 150 m * 250/3 m = 12500 m =

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Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:

Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

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Answer:

Points ABC and points OBC form two separate triangles. Triangle ABC is made up of angles BAC, ABC, ACB, while triangle OBC is made up of angles BOC, OBC, OCB. Since interior angles of triangles add up to 180 degrees, m<BAC + m<ABC + m<ACB = 180 and m<BOC + m<OBC + m<OCB = 180. 180 is equal to 180, so m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB.

Since OB bisects <ABC and OC bisects <ACB, m<ABO = m<OBC and m<ACO = m<OCB. We can also say that m<ABC = 2m<ABO and m<ACB = 2m<ACO. Substitute and simplify the equation.

m<BAC + m<ABC + m<ACB = m<BOC + m<OBC + m<OCB

m<BAC + 2m<ABO + 2m<ACO = m<BOC + m<ABO + m<ACO

m<ABO + m<ACO = m<BOC - m<BAC