During each summer, many families spend part of their vacation time at a beach along the East or West Coast. Due to the popularity of movies like Jaws and The Shallows, and publicity about recent shark attacks on surfers, swimmers, snorkelers, and spearfishermen, Americans have become increasingly concerned about water activities. Research suggests that 58% of all shark attacks involve surfers. One thousand records of shark attacks are selected, and each is categorized by the victim group. Identify the population, sample, and variable for the study.
Population Sample Variable
a. all families who spend part of their vacation at a beach along the East or West coast
b. Americans who are concerned about water activities
c. the percentage of shark attacks that involve surfers
d. the set of groups to which the victims of shark attacks belong
e. all shark attacks
f. the 1000 records of shark attacks that were examined

There are  [tex]55[/tex] ways of these integers be selected to give a sum.

Given that:

It has [tex]12[/tex] consecutive integers .

Now,

Definition of consecutive integers :

" Consecutive integers are the integers that follow in the fixed sequence .

Consecutive integers is represented by  [tex]n,n+1,n+2,n+3,....[/tex] where [tex]n[/tex] is an integer."

By given :

we have [tex]12[/tex] consecutive integers .

Thus,[tex]n=1[/tex] and substitute the equation is,

[tex]1,(n+1),(1+2),(1+3),(1+4),(1+5),(1+6),(1+7),(1+8),(1+9),(1+10),(1+11)\\\\\implies 1,2,3,4,5,6,7,8,9,10,11,12[/tex]

Now,

Split all the integers into 4 equal parts,

Part 1:  Those integers are divisible by [tex]4[/tex] and the remainder be 0.

Then,  

   [tex]a=0(mod 4)[/tex]

Part 2:  Those integer producing the remainder [tex]1[/tex] when it is divisible by [tex]4[/tex].

Then,

   [tex]a=1(mod 4)[/tex]

Part 3:  Those integer producing the remainder [tex]2[/tex]  when it is divisible by[tex]4[/tex].

Then,

    [tex]a=2(mod 4)[/tex]

Part 4: Those integer producing the remainder [tex]3[/tex]  when it is divisible by[tex]4[/tex].

Then,

   [tex]a=3(mod4)[/tex]

Since, three of these integers be selected to give a sum which divides by [tex]4[/tex] is,

In any 12 consecutive integers there are [tex]12\div4[/tex]

i.e. exactly 3 numbers of each category of mod4 namely ,

[tex]0(mod4), 1(mod4), 2(mod4), 3(mod4)[/tex]

Thus, the  total combinations of above [tex]5[/tex] categories of sets of [tex]3[/tex] integers are

                 [tex]3C_1=3(1)=3[/tex]

            [tex]3C_1*3C_2=3(1)*3=9[/tex]

           [tex]3C_1*3C_1*3C_1=3*3*3=27[/tex]

           [tex]3C2 * 3C1 = 3*3 = 9[/tex]

           [tex]3C1 * 3C2 = 3*3 = 9[/tex]

Thus, sum of the total ways be [tex]12[/tex] consecutive integers of three integers is divisible by 4 is,

       [tex]3+9+27+9+9=55[/tex]

Hence, it has [tex]55[/tex] ways.

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Answer:

Step-by-step explanation:

y = mx + b is the slope-intercept form of a line where m is the number value of the slope and b is the number value of the y-intercept. Our slope is given as 7, therefore, m = 7 in our equation. Our y-intercept is given as -10; thus, b = -10. Filling that in gives us y = 7x - 10

Answer:

ABC is congruent to EDC because m<3 = m<4 and m<1 = m<5

Step-by-step explanation:

m<3 and m<4 are vertical angles so they are congruent. m<1 and m<5 are alternate interior angles so they are also congruent.

Answer:

B,C,D

Step-by-step explanation:

Square both sides of the equation to get rid of the square root surrounding x.

sqrtX^2 = x and 7^2 = 7*7 = 49

x<49

And since we have a radical, we have to have non-negative solutions (the radical used in the equation actually only means the positive square root) meaning x>0

So which one of the choices is less than 49 and greater than 0?

B,C, and D are all less than 49, and greater than 0

Answer:

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 2.7 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.7, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 2.5 feet.

This is the p-value of Z when X = 2.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.5 - 2.7}{0.4}[/tex]

[tex]Z = -0.5[/tex]

[tex]Z = -0.5[/tex] has a p-value of 0.3085

0.3085 = 30.85% probability that an individual man’s step length is less than 2.5 feet.

Answer:

remember how the absolute value works:

|x| = x   if x ≥ 0

|x| = -x  if x < 0

Then we can rewrite:

|x| ≤ a

as:

-a ≤ x ≤ a

Now let's apply this to our case:

|3x + 5| ≤ 1

we can rewrite this as:

-1 ≤ 3x + 5 ≤ 1

We could solve this for x now, first subtracting 5 in the 3 sides:

-1 - 5 ≤ 3x + 5 - 5 ≤ 1 - 5

-6 ≤ 3x ≤ -4

now dividing by 3 in the 3 sides:

-6/3 ≤ 3x/3 ≤ -4/3

-2 ≤ x ≤ -(4/3)

So we rewrote the inequality without the absolute value part.

Answer:

A is the correct answer

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Remember X intercept is when y is equal to zero

So basically f(x-4) is literally equal to y=radical (x-4)

When graphing them you will notice that the x intercept is 4 units lower

Step-by-step explanation:

V should be written as (1/3) pi r^2 h

V = (1/3) pi r^2 h multiply by 3

3V = pi r^2 h Divide by pi

3V/ pi = r^2 h Divide by r^2

3V / (pi *r^2 ) = h

Answer:

1,188,137,600 possible combinations

Step-by-step explanation:

The first three and last two digits can be any letter while the middle two digits can be any number.

26*26*26*10*10*26*26=1,188,137,600

Answer:

1) x = -17 +6y + 2z/3

2) x= -13 - 4y - 5z/6

3) x= -22 +4y + 3z/3

Step-by-step explanation:

1) 3x-6y-2z=-17

3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )

3x=-17+6y+2z

3x/3= -17/3 +6y/3 + 2z/3

x = -17 +6y + 2z/3

2) −6x+4y+5z=13

-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )

-6x=13-4y-5z

-6x/-6= 13/-6 - 4y/-6 - 5z/-6

x= -13 - 4y - 5z/6

3) −3x−4y−3z=22

-3x=22+4y+3z

-3x/-3 = 22/-3 + 4y/-3 +3z/-3

x= -22 +4y + 3z/3

Answer:

C. -2x +3y-6=0

this is the answer

Answer:

106

Step-by-step explanation:

5 x 2 = 10

7 + 5 = 12

8 x 12 = 96

96 + 10 = 106 :)

Answer:

Step-by-step explanation:

Use the formula P=MX+B

Answer:

1/6

Step-by-step explanation:

Rhianna has 3/6 or 1/2 of a box of pencils

When she divides 3/6 among three people, you get 1/6

Each friend gets 1/6 of a box

Answer:

For that you should prove Ac²=Ab²+Bc²

Step-by-step explanation:

Use distance formula for finding each distance Ac,Ab and BC and prove "Ac²=Ab²+Bc²" as true

Answer: 1.25 square feet

This converts to the improper fraction 5/4

===========================================================

Explanation:

The area of the triangle on the left is base*height/2 = 0.5*2/2 = 0.5 square feet. Note that 1/2 = 0.5

The area of the triangle on the right side is base*height/2 = 0.2*3/2 = 0.75 square feet. This converts to the fraction 3/4

Add up the two results: 0.5+0.75 = 1.25 square feet

-----------

If you need the answer as an improper fraction, then,

1.25 = 1 + 0.25

1.25 = 1 + 1/4

1.25 = 4/4 + 1/4

1.25 = (4+1)/4

1.25 = 5/4

Answer:

1660

Step-by-step explanation:

Answer:

9:125

Step-by-step explanation:

To write a ratio correctly, you need the same units for both numbers.

Let's convert liters into milliliters.

1 L = 1000 mL

Ratio of 72 mL to 1000 mL =

= 72:1000

Divide both numbers by their GCF, 8.

= 9:125

Answer:

81.85.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Suppose the mean height for men is 70 inches with a standard deviation of 2 inches.

This means that [tex]\mu = 70, \sigma = 2[/tex]

What percentage of men are between 68 and 74 inches tall?

The proportion is the p-value of Z when X = 74 subtracted by the p-value of Z when X = 68.

X = 74

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74 - 70}{2}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

X = 68

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{68 - 70}{2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

0.9772 - 0.1587 = 0.8185

0.8185*100% = 81.85%.

Thus the percentage is 81.85%, and the answer is 81.85.

Answer:

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Step-by-step explanation:

Given

[tex]Pennies = 22[/tex]

[tex]Dimes = 27[/tex]

[tex]Nickels = 9[/tex]

[tex]Quarters = 30[/tex]

Required

[tex]P(Penny\ and\ Dime)[/tex]

This is calculated as:

[tex]P(Penny\ and\ Dime) = P(Penny) * P(Dime)[/tex]

Since it is a selection without replacement, the computation is:

[tex]P(Penny\ and\ Dime) = \frac{Penny}{Total} * \frac{Dime}{Total-1}[/tex]

So, we have:

[tex]P(Penny\ and\ Dime) = \frac{22}{22+27+9+30} * \frac{Dime}{22+27+9+30-1}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{22}{88} * \frac{27}{87}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{1}{4} * \frac{9}{29}[/tex]

[tex]P(Penny\ and\ Dime) = \frac{9}{116}[/tex]

Answer: Robert and Chris can skate 10 miles in 45 minutes.

Step-by-step explanation:

Let's start by finding the unit rate.

[tex]\frac{4}{18} =\frac{2}{9} \\\frac{18}{18} =1[/tex]

Robert and Chris can skate [tex]\frac{2}{9}[/tex] of a mile in 1 minute. Now we can multiply both by 45 to see how far the can go in 45 minutes.

[tex](\frac{2}{9}) (\frac{45}{1} )\\\frac{(2)(45)}{(9)(1)} \\\frac{90}{9} \\10[/tex]

45x1=45

The can skate 10 miles in 45 minutes.

Answer:

8

Step-by-step explanation:

When multiplying numbers with the same base

the exponents are added

1/4 + 1/4 + 1/4 + 1/4  = 1

8¹ = 8

Answer:

1850 cents or $18.50

Step-by-step explanation:

50*8=400

3*35=105

5*269=1345 ($2.69 can be converted to 269 cents)

400+105+1345=1850

Answer:

Hence the correct option is option d.

Explanation:

We can 95% confident that between 28.1% and 39.2% of all rental property owners own a property by the water.  

Here correct option for interpretation of the 95% confidence interval. The remaining options are about probabilities and sample proportions.

Answer:

36%

Step-by-step explanation:

Step-by-step explanation:

Loss percentage= loss/cost× 100%

250-180=70

70/180=0.3888

0.3888×100%=39%

Answer:

I thimk it is B

Step-by-step explanation:

The last equation says z = 3, so that in the second equation we get

y + 2z = y + 6 = 5   ==>   y = -1

and in turn, the first equation tells us

x - 2y + 2z = x + 2 + 6 = x + 8 = 9   ==>   x = 1

So the solution to the system is (x, y, z) = (1, -1, 3).