5a + 4b = 31
5a + 6b = 39
What is a and what is b

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:

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:

Step-by-step explanation:

Use the formula P=MX+B

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:

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

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:

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:

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:

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:

I thimk it is B

Step-by-step explanation:

Answer:

I think the answer is the sequence is arithmetic because the term have a common difference

The correct option is The sequence is not arithmetic because the terms do not have a common difference.

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k.

This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k called the common difference.

Given is graph, we need to conclude the true about the graph,

Finding the common difference,

4-1 = 3    

9-4 = 5

16-9 = 7

25-16 = 9

Clearly from the set of values that are given in the graph we could observe that the function that is formed using these set of values is:

y=f(n)=n² where n=1,2,3,4,5,.....

That mean, the following sequence is not an arithmetic sequence as the common difference is different.

Hence, the correct option is The sequence is not arithmetic because the terms do not have a common difference.

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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:

1660

Step-by-step explanation:

Answer:

106

Step-by-step explanation:

5 x 2 = 10

7 + 5 = 12

8 x 12 = 96

96 + 10 = 106 :)

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:

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:

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: 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:

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

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:

[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:

B

Step-by-step explanation:

SOH CAH TOA

sin theta = opp/hyp

csc theta = hyp/opp

csc theta = 10/8 = 5/4

cos theta = adj/hyp

sec theta = hyp/adj

sec theta = 10/6 = 5/3

Answer: B