Write the converse, inverse, and contrapositive of the following conditional statement.
"If I eat too much candy, I will get sick."

Answer:

decimal form> -4.87577494

Exact form> -In(212)/In(3)

The number of communication channels, 10 channels would five people require.

To find number of communication channels, we use;

On the other hand, it might be a sign of the scope and intensity of the project communication management needed in huge projects and so-called megaprojects. This could, for example, entail allocating specific resources to project communication responsibilities in accordance to the number of available channels for communication. These factors may be especially important for teams working on sensitive projects and projects where information flow may be unclear or even fraudulent.

Number of potential communication channels = n x (n-1)/2

Given n = 5;

→ x = 5*(5 - 1)/2

     = 5*2

     = 10

The number of communication channels, 10 channels would five people require.

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Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

So, the distance of the building from John and Fred is:

Now, we get the formula:

Calculate as follows:

John's distance:

Fred's distance:

Therefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.

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Plot these points on a graph and draw a line connecting them beginning at (0, 4) and ending at (18, 31). The graph is plotted below.

Given:

Starting cart denotes that the number of nested carts is zero.

So, let the x axis represent the number of nested carts and the y axis represent the height of the nested carts.

As per question,

When x = 0 , the height is y = 4 ft

When x = 13, the height is  y = 2.5 ft

When x = 18, the height is  y = 31 ft

So, the points on the graph are (0,4), (13, 23.5) and (18, 31).

Plot these points on a graph and draw a line passing through all these points starting at (0, 4) and ending at (18, 31).

The graph is shown below.

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31 Americans should be surveyed  by Z mean.

What does critical value of Z mean?

If the prior population proportion is unavailable then the formula to find the sample size is given by

           n = 0.25[tex](\frac{z^{*} }{E} )^{2}[/tex]

where z* = Critical z-value

E = margin of error

Given,  Confidence level = 98%

The critical z-value for 98% confidence interval is 2.326  ( BY z-table)

Margin of error : E= 0.21

             n = 0.25 [tex](\frac{2.326}{0.21})^{2}[/tex]

             n = 0.25 * ( 11 .07)²

             n = 0.25 * 122.5449

             n =  30.363225  ≈ 31

Hence,  31 Americans should be surveyed.

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Answer:

58

Step-by-step explanation:

PEMDAS!

1) 20/2 = 10

2) 10*5+8

3) 10*5 = 50
4) 50 + 8 = 58

Answer is 58, hope this helps ;)

Answer:

L

Step-by-step explanation:

(7) 55 is 181.81% of 100

(8) 22% of 110 is 24.2

(9) 19 is 50% of 38

(10) 25 is 32% of 78.125

(11)  40% of 70 is 28.

(12) 30 is 200% of 60.

What is percent?

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.", "pct.", and occasionally "pc" are also used to indicate it, while the percent symbol, "%," is most frequently employed. A % has no dimensions and no standard measurement.

(7) Suppose 55 is x%  of 100.

So,

55x/100 = 100

x/100 = 100/55

x = 1.8181 x 100

x = 181.81%

Therefore, 55 is 181.81% of 100.

(8) Suppose 22% of x is 24.2

So,

x(22)/100 = 24.2

x = 24.2 x 100/22

x = 110

Therefore, 22% of 110 is 24.2

(9) Suppose 19 is 50% of x.

So,

19 = 50(x)/100

x = 19 x 100/50

x = 38

Therefore, 19 is 50% of 38.

(10) Suppose 25 is 32% of x.

So,

25 = 32(x)/100

x = 25 x 100/32

x = 78.125

Therefore, 25 is 32% of 78.125

(11) Suppose 40% of x is 28

So,

40(x)/100 = 28

x = 28 x 100/40

x = 70

Therefore, 40% of 70 is 28.

(12) Suppose 30 is x% of 60

So,

30(x)/100 = 60

x = 60 x 100/30

x = 200

Therefore, 30 is 200% of 60.

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Using the section formula, point F lie on 3/5 in the number line.

In the given question,

On a number line, point D is at -3, and point E is at 6.

The point F lies on segment DE .

The ratio of DF to FE is 2 : 3.

We have to find where point F lie on the number line.

Since point D lies is at -3 at x axis so the point should be ( -3,0).

Point E lies is at 6 at x axis so the point should be ( 6,0).

F lies on segment DE. So let the point of F is (X, Y)

The ratio is 2:3.

Now firstly finding the value of X using section formula

X = [tex]\frac{mx_{2}+nx_{1}}{m+n}[/tex]

where [tex]x_{1}[/tex]= -3, [tex]x_{2}[/tex]= 6, m= 2 and n=3

Now putting the value

X = {2×6+(-3)3}/(2+3)

Simplifying

X = (12-9)/5

X = 3/5

Now firstly finding the value of Y using section formula

Y = [tex]\frac{my_{2}+ny_{1}}{m+n}[/tex]

where [tex]y_{1}[/tex]= 0, [tex]y_{2}[/tex]= 0, m= 2 and n=3

Now putting the value

Y = (2×0+3×0}/(2+3)

Y = 0/5

Y = 0

Hence, point F lie on 3/5 in the number line.

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The length of the rectangular area is 800 yards and width is 800 yards

The perimeter of the rectangular area = 3200 yards

The perimeter of the rectangle = 2 (l + w)

Then the equation will be

2(l + w) = 3200

l + w = 3200 / 2

l + w = 1600 yards

w = 1600 - l

The area of the rectangular area = l × w

= l(1600 - l)

Since the area is maximizing the the rate of change of area will be zero

l × w = 0

1600 - 2l = 0

2l = 1600

l = 1600/2

l = 800 yards

Then

w = 1600 - l

Substitute the value of l in the equation

w = 1600 - 800

w = 800 yards

Hence, the length of the rectangular area is 800 yards and width is 800 yards

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The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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Answer:

  AD = 32

Step-by-step explanation:

You want the length of side AD of square ABCD, when CD = (x+15) and angle ABC is (6x-12)°.

The value of x can be found by recognizing that the measure of any angle in a square is 90°.

  (6x -12)° = 90°

  6x = 102 . . . . . . . . divide by °, add 12

  x = 17

The sides of a square are congruent, so ...

  AD = CD = (x +15) = 17 +15 = 32

The length of AD is 32 units.

Answer:

39.94

Step-by-step explanation:

Ask? :)

Answer:40,000        porque dice que redondees a la centecima mas cercana              

The area of the figure is 1875 sq.in.

In this question, we need to find the area of the given figure.

the area of the figure = area of rectangle + area of two triangles.

For rectangle,

length =  50 inch and width = 30 in.

Using the formula for the area of rectangle,

A1 = length * width

A1 = 50 * 30

A1 = 1500 sq.in.

For triangle,

base = 1/2 * length of rectangle

so, base = 25 in and height = 15 inch

Using the formula for the area of triangle,

A2 = 1/2 * base * height

A2 = 1/2 * 25 * 15

A2 = 187.5 sq.in.

so, the area of the figure would be,

A = A1 + (2 * A2)

A = 1500 + (2 * 187.5)

A = 1875  sq.in.

Therefore, the area of the figure is 1875 sq.in.

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The possible number of license plates is 6084000 .

We have to make a 6 word license plate in which first two are letters and remaining four are digits.

conditions are :

1. letters and digits can repeat themselves

2. 1st digit can't be 0.

taking into account these conditions

we know total letters are 26 and total digits are 10 ( 0,1,2,3,4,5,6,7,8,9)

Now if we divide number plate in 6 columns where first two are filler by letters and rest four by digits so

1st column can be filled in ways = 26

2nd column can be filled in ways = 26

3rd column can be filled in ways = 9 ( as zero is not allowed )

4th column can be filled in ways = 10

5th column can be filled in ways = 10

6th column can be filled in ways = 10

therefore, total number of ways = 26x26x9x10x10x10

                                                      = 6084000 ways

The possible number of license plates is 6084000 .              

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The length of backyard in drawing is 37 inch when 74 feet long in real life and scale of drawing is 1 inch: 2 feet.

A proportion is a form of ratio in which the denominator also contains the numerator. For example, the fraction of male deaths would be deaths to men divided by deaths to males + deaths to females (i.e. the total population). A population proportion is a percentage of the population that possesses a specific feature. Assume you have 1,000 persons in your population, with 237 of them having blue eyes. Blue eyes account for 237 of every 1,000 persons, or 237/1000.

Here,

as the given scale is 1 inch: 2 feet.

actual length of backyard=74 feet

length of backyard in drawing is x inch,

1/2=x/74

2x=74

x=37 inch

The length of the backyard in the drawing is 37 inches, although it is 74 feet long in real life, and the scale of the drawing is 1 inch: 2 feet.

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The equation which has infinitely many solutions from the given answer choices is; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

It follows from the task content the the equation with infinitely many solutions among the given answer choices is to be determined.

An equation of the type; a(1)x + b(1) = a(2)x + b(2) is said to have infinitely many solutions if; a(1) = a(2) and b(1) = b(2).

Hence, the equations which have infinitely many solutions among the given answer choices are; Choice A: -76x+76=-76x+76 and Choice B: 76x + 76 = 76x + 76.

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The probability that shooting stars are there in the fall is 0.5904.

The probability of not seeing any falling star in that time period of 15 minutes is 1 - 0.2 = 0.8.

In this way, the combined probability of not seeing any of the falling stars in the four-time period is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096

= 1 - 0.4096 = 0.5904

=P(X = x) = μˣ * e^-μ / x!

Here, the span is of 15 minutes. In this way, the typical number of events in the span is 15λ. The probability of witnessing 0 occasions (i.e X = 0) is:

P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)

(1) is equal to 80% as the probability of at least one event happening is 20%.

So, 1 / e^(15λ) = 0.8

or, e^(15λ) = 1.25

or, 15λ = ln(1.25) = 0.2231

= λ = 0.0149 / min

In this way, the typical number of occasions (falling stars) is 0.0149 per minute.

Presently, the typical number of occasions in an hour is:

0.0149 * 60 = 0.8926 / hour

So, the Poisson distribution expression becomes:

P(X = x) = 0.8926ˣ * e^-0.8926 / x! — — (2)

Here, the time span is 60 minutes.

Presently, we should find the probability of not having even a solitary occasion in 60 minutes:

P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096

So, the probability of having at least one event is the complement of the above probability.

So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904

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Answer:

x=6

Step-by-step explanation:

x-8=-2

x=-2+8

x=6

Answer:

x = 6

Step-by-step explanation:

x - 8 = -2

x - 8 + 8 = -2 + 8

x + 0 = 6

x = 6

Check:

6 - 8 = -2

Step-by-step explanation:

length(l)=x+4

breadth(b)=x-3

Area of rectangle(A)=l×b

60=(x+4)×(x-3)

60=x^2-3x+4x-12

60=x^2+x-12

x^2+x-12-60=0

x^2+x-72=0

x^2+9x-8x-72=0

x(x+9)-8(x+9)=0

(x+9)(x-8)=0

equating equation

x+9=0.....eq(i)

x=-9 it is not possible

x-8=0.....eq(ii)

x=8

Then,length(l)=x+4

=8+4=12

breadth(b)=x-3

=8-3=5

The lessons can a student take if they pay no more than $175 is 25x + 50 < 175.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

In the 12U Softball division, Olivia gets chosen. What is Olivia's age? Olivia's age is unknown to you because the word "equals" is missing. However, since you are aware that she should be under or equal to 12, you can write Olivia's Age 12. This is a real-world example of an inequality.

given:

Per lesson charges= $25

Recital f= $50

Total money can be spend= $175

let the number of lessons taken be x.

So, the inequality is

25x + 50 < 175

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Answer:

y=3x-2

Step-by-step explanation:

y is for how many miles she wants to walk which is 6. she walks 3 miles per hour which is 3x (x is for hours) and -2 because she already walked 2 miles

Answer:

  17 cm

Step-by-step explanation:

You want the hypotenuse (c) in a right triangle that has c=2a+1, b=2a-1.

The relation between the side lengths in the right triangle is ...

  a² +b² = c²

Substituting the given relations, we have ...

  a² +(2a-1)² = (2a+1)²

  a² +4a² -4a +1 = 4a² +4a +1

  a² -8a = 0 . . . . . . write in standard form

  a(a -8) = 0 . . . . . . factor

  a = 0 or a = 8

We are almost never concerned with triangles that have 0 area, so the solution of interest is a=8. Then the hypotenuse is ...

  c = 2(8) +1 = 17

The hypotenuse is 17 cm.

__

Additional comment

You may recognize these side lengths as the (8, 15, 17) Pythagorean triple.

The probability that in any given period of 400 days there will be an accident on one day is 0.2707

Given that;

In a certain industrial facility, accidents occur infrequently. it is known that the probability of an accident on any given day is 0.005 and accidents are independent of each other.

n = 400, p = 0.005

Poisson distribution is given by;

e P(x) = (λˣe^λ ) / x!

Here, Mean(λ) = np

                        = 400*0.005

                        =2

The probability that there will be an accident on one day;

(P(x = 1)) = (λxe-λ)/x!

             = 2*e-2

             = 0.2707

The probability that in any given period of 400 days there will be an accident on one day is 0.2707

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The finance charge for Julie's installment loan of $4,600 at 13% for 36 months is D. $979.64.

The finance charge represents the interest and other administrative charges for granting a loan to an individual or organization.

The finance charge is always described in terms of the APR (annual percentage rate) that accrues on the loan, depending on the amount and the period.

N (# of periods) = 36 months (3 years x 12)

I/Y (Interest per year) = 13%

PV (Present Value) = $4,600

FV (Future Value) = $0

Results:

PMT = $154.99

Sum of all periodic payments = $5,579.64

Total Interest = $979.64

Thus, Julie will pay a finance charge of $979.64.

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Option D. $979.64

The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]

What are mixed numbers?

A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.

Given,     [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]

             [tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]

             [tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]

              [tex]= \frac{26}{9} +\frac{50}{9}[/tex]

               [tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]

Hence, the required answer for the given term is  [tex]8\frac{4}{9}[/tex] .

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Directly proportional to x.

Acc to our question-

Hence,Directly proportional to x.

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The mason should order 250 cubic yards of grit to use all the cement.

It is given that the mixture has 20 cubic yards of grit for 4 cubic yards of cement.

So the unit rate for the number of cubic yards of grit for per unit of cement is given by : 20 ÷ 4 = 5 cubic yards.

Now amount of grit required for 50 cubic yards of cement

= 50 × 5 = 250 cubic yards.

By utilising 1 as the denominator, a unit rate compares two quantities while using the second quantity as the unit of measurement. If someone runs three kilometers in 30 minutes, they have ran one mile.

Miles per minute is a unit of measurement for how far something is moving in a certain amount of time. For unit rate, the quantity value 1 is always used.

Hence he should order about 250 cubic yards in order to use all the cement.

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We can conclude that the table in option (D) represents a linear function.

So, the linear function will be:

Then,

So, option (D) is correct.

Therefore, we can conclude that the table in option (D) represents a linear function.

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