Trig Equation from a Graph

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.

For more information,

https://brainly.com/question/24144187

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:

1,188,137,600 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:

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:

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: 1.25 square feet

This converts to the improper fraction 5/4

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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

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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:

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

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:

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:

Not enough data

Step-by-step explanation:

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:

Monday: 7.25

Tuesday: 6.75

Wednesday: 5.2

Thursday: 6.1

Answer:

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

this is the answer

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:

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:

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:

1660

Step-by-step explanation:

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.

1. 3

29-9=19

13+9=22

22-19=3

I don't know number 2, sorry.

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:

Step-by-step explanation:

Use the formula P=MX+B

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).

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:

106

Step-by-step explanation:

5 x 2 = 10

7 + 5 = 12

8 x 12 = 96

96 + 10 = 106 :)

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.