Find ,H assuming the triangles formed are similar.

Answer:

i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

ii) [tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]

And using the normal standard table or excel we got:

[tex]P(z<-2.25)=0.0122[/tex]

iv) [tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]

Step-by-step explanation:

Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.8,0.8)[/tex]  

Where [tex]\mu=3.8[/tex] and [tex]\sigma=0.8[/tex]

Part i and iii

In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

Part ii

We are interested on this probability:

[tex]P(X<2)[/tex]

We can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we have:

[tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]

And using the normal standard table or excel we got:

[tex]P(z<-2.25)=0.0122[/tex]

Part iv

We want this probability:

[tex]P(2<X<4)[/tex]

Using the z score formula we got:

[tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]

Answer:

70%

Step-by-step explanation:

Divide the two numbers to get a decimal:

112/160 = 0.7

Multiply by 100:

0.7 * 100 = 70

Add a percent sign:

70%

70% percent of the girls in the school study Latin.

Question:

Which represents [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction?

[tex]2+ \frac{3}{6}[/tex]

[tex]3 + \frac{3}{6}[/tex]

[tex]3+ \frac{5}{6}[/tex]

[tex]4+ \frac{1}{6}[/tex]

Answer:

[tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]

Step-by-step explanation:

Given

Mixed Fraction:  [tex]2 \frac{3}{6}[/tex]

Required

Express as the sum of a whole number and fraction.

Given that [tex]2 \frac{3}{6}[/tex]  is a mixed fraction; it can be converted to the sum of a whole number and a fraction by following the steps below.

1. Convert the mixed fraction to improper fraction

[tex]2 \frac{3}{6} = \frac{(6 * 2 + 3)}{6}[/tex]

2. Split the numerator

[tex]2 \frac{3}{6} = \frac{((6 * 2) + (3))}{6}[/tex]

3. Split fraction to 2

[tex]2 \frac{3}{6} = \frac{(6 * 2)}{6} +\frac{(3)}{6}[/tex]

Simplify

[tex]2 \frac{3}{6} = \frac{(12)}{6} +\frac{(3)}{6}[/tex]

[tex]2 \frac{3}{6} = 2 + \frac{3}{6}[/tex]

Hence, [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]

Answer:[tex]236\ in.^2[/tex]

Step-by-step explanation:

Given

Dimension of gift box is

Width [tex]b=8\ in.[/tex]

height [tex]h=6\ in.[/tex]

Length [tex]L=5\ in.[/tex]

So, box is in shape cubiod

and its surface area is given by

[tex]S.A.=2(lb+bh+hl)[/tex]

[tex]S.A.=2(5\times 8+8\times 6+6\times 5)[/tex]

[tex]S.A.=2(40+48+30)[/tex]

[tex]S.A.=2\times 118[/tex]

[tex]S.A.=236\ in.^2[/tex]

So, [tex]236\ in.^2[/tex] of gift paper is required

Answer:x=17 y=10

Step-by-step explanation:

Answer:

19x-19+23y

Step-by-step explanation:

add the like terms

Answer:

36 degrees

Step-by-step explanation:

This problem can be solved with the help  concept of sum of angles of any triangle.

sum of angles of any triangle is 180.

Given angular value of triangle ABC is A=2x B=6x C=2x

Thus sum of A, B , C is 180

A+B+C = 180 plug in th evalue of angle A, B and C

=>2x+6x+2x = 180

=> 10x=180

=> x = 180/10 = 18

Value of angle C in terms of x is 2x

Thus angular value of angle c = 2*18 = 36 degrees.

Answer:

Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.

Step-by-step explanation:

There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.

We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.

The sum of the figures in the third column is 999.

We could also use the formula for rooted trees to calculate the number of games that would be played.

[tex]i=\frac{l - 1}{m - 1}[/tex]

where i is the number of "internal nodes," which represents the number of games played for an "m-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.

The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by

[tex]i=\frac{l - 1}{m - 1} \\\\ i=\frac{1000 - 1}{2 - 1} \\\\= \frac{999}{1} \\\\=999[/tex]

Answer: C. Each internal vertex represents the winner of the game played by its parents, and there are 1000 leaves, one for each contestant.

Step-by-step explanation: A tree is a connected undirected graph with no simple circuits. When its elements has at most 2 children, it is a Binary Tree.

The tree is formed by nodes. The topmost node is called Root and except for it, every node is connected by a direct line from exactly one other node. This type of node is called Parent.

Parent can be direct connect to a number of other nodes, which are Children and can also be internal nodes.

NOdes with no children are Leaves or external nodes.

In the Binary Tree described by the question, the number of participants is 1000, so there will be 1000 leaves. Each internal vertex repsents the winner of a game played by its parents, i.e., each is a Child, a internal node.

The right answer is alternative C.

Answer:

3 gallons is 12 quarts and is less than 15 quarts

Step-by-step explanation:

1 gallon    = 4 quarts

2 gallons = 8 quarts

3 gallons = 12 quarts

Answer

no, 3 gallons is less than 15 quarts

Step-by-step explanation:

1 gallon=3 quarts

3 gallons=12 quarts

Answer:

8n + 46

Step-by-step explanation:

Combine like terms. First, simplify the signs. two negatives directly next to each other equals one positive:

- (-5n) = + 5n

30 + 5n + 16 + 3n = (30 + 16) + (5n + 3n)

(30 + 16) = 46

(5n + 3n) = 8n

8n + 46 is your answer.

Answer:

54000-65000

Step-by-step explanation:

round the numbers first down to 1200 and 45, and multiply, then round up for the larger, like 1300 and 50 to get your answer.

Answer:

20

Step-by-step explanation:

The current area is 120(80)=9600 and he want to expand it by 4400 so that the new area will be 9600+4400=14000 

14000=(120+x)(80+x) 

14000=9600+200x+x^2 

x^2+200x-4400=0 

x^2-20x+220x-4400=0 

x(x-20)+220(x-20)=0 

(x+220)(x-20)=0, since x is an increase it must be greater than zero so 

x=20ft 

(120+20)(80+20)=14000ft^2

Answer:

23 years.

Step-by-step explanation:

It is given that the initial price of painting is $150 and its values increasing by 3% annually.

We need to find how many years will it take until it is doubled in value.

The value of painting after t years is given by

[tex]y=150(1+0.03)^t[/tex]

[tex]y=150(1.03)^t[/tex]

The value of painting after double is 300. Substitute y=300.

[tex]300=150(1.03)^t[/tex]

Divide both sides by 150.

[tex]2=(1.03)^t[/tex]

Taking log both sides.

[tex]\log 2=\log (1.03)^t[/tex]

[tex]\log 2=t\log (1.03)[/tex]

[tex]t=\dfrac{\log 2}{\log (1.03)}[/tex]

[tex]t=23.44977[/tex]

[tex]t\approx 23[/tex]

Therefore, the required number of years is 23.

Answer:

x=8

Step-by-step explanation:

[tex]square \: both \: side \\ \sqrt{ {x}^{2} } = \sqrt{64 } \: \: \: \\ \\x = 8[/tex]

Answer:

15

Step-by-step explanation:

1/6 of 90 is 15

The number of times 3 should be selected is 45/2.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that;

Number of spins= 90

Number of selected= 3

Now,

If the spinner has 4 equal sections and one of them has a 3, then the probability of landing on 3 is 1/4.

To find the expected number of times that the spinner lands on 3 in 90 spins, we need to multiply 1/4 by 90.

=1/4 * 90

=45/2

Therefore, by algebra the answer will be 45/2.

More about the Algebra link is given below.

brainly.com/question/953809

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Answer:

The correct option is B: 94.1%

Step-by-step explanation:

There are 52 weeks in a year so, if we divide 234 by 12 it gives 4.5 accidents per week on average. Given this information, we can say that in any randomly selected week, there will be an 80% probability of at least two accidents occurring on the said intersection. Hence, this means that a traffic light should be very likely will have to get installed in order to ensure safety of the residents.

Hope that answers the question, have a great day!

Answer:

The probability of winning a jackpot is [tex]P = 0.000003[/tex]

The probability of winning the pick 5 game  is  [tex]P_a = 0.00001[/tex]

The earning of the lottery organisation if the game were to be runed for no profit is  [tex]x =[/tex]$10 000

Step-by-step explanation:

From the question

    The sample size is  n= 37

    The number of selection is  [tex]r = 5[/tex]

Now the number of way by which these five selection can be made is mathematically represented as

         [tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]

Now  substituting values

         [tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]

          [tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]

Now the probability of winning  a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as

         [tex]P = \frac{1}{333333.3}[/tex]

        [tex]P = 0.000003[/tex]

Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as

        [tex]k = 10^5[/tex]

Now the probability of winning the game is

      [tex]P_a = \frac{1}{10^5}[/tex]

      [tex]P_a = 0.00001[/tex]

We are told that for a $1 ticket that the pick 5 game returns $50 , 000

  Generally the expected value is mathematically represented as

           [tex]E(X) = x * P(X =x )[/tex]

In this question the expected value is  $1

So

          [tex]1 = x * 0.00001[/tex]

So      [tex]x = \frac{1}{0.00001}[/tex]

        [tex]x =[/tex]$10 000

Answer:

3+2x-x^3is the answer

ANSWER: It is false that All equations are identities, but not all identities are equations, as all identities are equations, but only some equations are identities.

HOPE THIS HELP

Answer:

you need to include a picture of all the graphs

Answer:

1g/h) transportation budget is $6100*0.11=$610+$61= $671

$671 - $150 = $521

So the car payments alone are $521 under the guidelines

1i/j)

$671 - $75 = $596

The car insurance alone is $596 under the guidelines

Note to really compare such things in the real world you would sum up the costs and add gas and repairs to it. That could make such a high budget for transportation plausible.

(would really, reallly appreciate the brainliest)

Answer:

y = 15

Step-by-step explanation:

Given: y varies directly with x, x=4 when y=20

To find:  y when x = 3

Solution:

As y varies directly as x, it means that as x increases, y also increases by the same factor.

As y varies directly with x,

[tex]y=kx[/tex]

Here, k is a constant

As x = 4 when y = 20,

[tex]20=4k\\k=\frac{20}{4}=5\\\Rightarrow y=5x[/tex]

Put x = 3

[tex]y= 5(3) = 15[/tex]

Answer:

  m = 1 + 2log(x)/log(y)

Step-by-step explanation:

Taking logarithms, you have ...

  log(x) +m·log(y) = log(y) +3log(x)

  m·log(y) = log(y) +2·log(x) . . . . subtract log(x)

  m = (log(y) +2·log(x))/log(y) . . . divide by the coefficient of m

  m = 1 +2·log(x)/log(y) . . . . . . . simplify a bit*

_____

* The "simplified" form will depend on your preference. Here, I like the integer 1 brought out because most logs are irrational. The result may be very slightly more accurate if we add 1, rather than log(y)/log(y)--depending on your calculator.

Answer:

5

Step-by-step explanation:

47-5=42

42/6=7

5/6 is the number we have to  subtract from 47/6 to make 7

Two or more expressions with an Equal sign is called as Equation.

We have to find the number when we need to subtract from 47/6 to make 7.

Let the unknown number be x

47/6-x=7

Add x-7 on both the sides

47/6-7=x

Take LCM as 6

(47-42)/6=x

When 42 is subtracted from 47 we get 5.

5/6=x

Hence, 5/6 we have to  subtract from 47/6 to make 7

To learn more on Equation:

https://brainly.com/question/10413253

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Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=5 (over)/6

Decimal Form:

x=0.8¯3

(Hopefully this helped you solve the problem.)

Answer:

(a) 9.18% of people have an intraocular pressure lower than 12 mm Hg.

(b) 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Step-by-step explanation:

We are given that the distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.

Let X = intraocular pressure in the general population

So, X ~ Normal([tex]\mu=16,\sigma^{2} = 3^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                             Z  =  [tex]\frac{ X-\mu}{\sigma } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 16 mm Hg

           [tex]\sigma[/tex] = standard deviation = 3 mm Hg

(a) Percentage of people have an intraocular pressure lower than 12 mm Hg is given by = P(X < 12 mm Hg)

       P(X < 12) = P( [tex]\frac{ X-\mu}{\sigma } }[/tex] < [tex]\frac{ 12-16}{3 } }[/tex] ) = P(Z < -1.33) = 1 - P(Z [tex]\leq[/tex] 1.33)

                                                   = 1 - 0.9082 = 0.0918 or 9.18%

The above probability is calculated by looking at the value of x = 1.33 in the z table which has an area of 0.9082.

(b) We have to find that 80% of adults in the general population have an intraocular pressure that is greater than how many mm Hg, that means;

        P(X > x) = 0.80      {where x is the required intraocular pressure}

        P( [tex]\frac{ X-\mu}{\sigma } }[/tex] > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80

        P(Z > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80

Now, in the z table the critical value of z which represents the top 80% of the area is given as -0.842, that is;

                           [tex]\frac{ x-16}{3 } } = -0.842[/tex]

                           [tex]x -16 = -0.842 \times 3[/tex]

                           x = 16 - 2.53 = 13.47 mm Hg

Therefore, 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Answer:

An angle with a positive measure will have rotated counterclockwise, or doesn't cross over itself at the start of the rotation. As you can see, the only graph that initially turns counterclockwise is the first graph.

Step-by-step explanation: