Find the median of the data set 3 35 23 37 45 5 49 27 48

Answer:  the correct option is (C) (2, 5).

Step-by-step explanation:  We are given to use the substitution method to solve the following system of equations :

[tex]2y+4x=18~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\2y-3x=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Dividing equation equation (i) on both sides by 2, we have

[tex]\dfrac{2y+4x}{2}=\dfrac{18}{2}\\\\\Rightarrow y+2x=9\\\\\Rightarrow y=9-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]

Substituting the value of y from equation (iii) in equation (ii), we get

[tex]2(9-2x)-3x=4\\\\\Rightarrow 18-4x-3x=4\\\\\Rightarrow 18-4=4x+3x\\\\\Rightarrow 14=7x\\\\\Rightarrow x=\dfrac{14}{7}\\\\\Rightarrow x=2.[/tex]

So, from equation (iii), we get

[tex]y=9-2\times2=9-4=5.[/tex]

Thus, the required solution of the given system is (x, y) = (2, 5).

Option (C) is CORRECT.

Answer:

Temperature at 4 am is 66 degrees.

Step-by-step explanation:

First we have to count how many half an hour's are there from 6 pm to 4 am.

Number of hours from 6 pm to 4 am.  =  [tex]10[/tex] hours

Number of half an hours from 6 pm to 4 am.  = [tex]10*2[/tex]

                                                                           =[tex]20[/tex]

It is given that temperature drops [tex]1\frac{1}{4}[/tex] degrees every half an hour.

Therefore,

Temperature drop in 20 half an hours = [tex]1\frac{1}{4}*20[/tex] degrees

                                                                =[tex]\frac{5}{4} *20[/tex] degrees

                                                                =[tex]25[/tex] degrees

Temperature drops 20 degrees from initial 86 degrees.

Therefore, temperature at 4 am = 86 degrees - 20 degrees

                                                      = 66 degrees

yes

assuming the 2 expressions are 36 + 20 and 4(9 + 5)

36 + 20 = 56 and

4(9 + 5 ) = 4(14) = 4 × 14 = 56

Yes, the 2 expressions are 36 + 20 and 4(9 + 5) represent equivalent expressions.

An equation represents the equality of two or more mathematical expressions.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Let assume the 2 expressions are 36 + 20 and 4(9 + 5).

36 + 20 = 56

and

4(9 + 5 )

= 4(14)

= 4 × 14

= 56

Yes, they are equivalent to each other.

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Answer:

[tex]\frac{3}{34}[/tex]

Step-by-step explanation:

In Statistics, the AND function, is simplified, by multiplying the probability of the two events with one another:

[tex]P(AandB)=P(A)*P(B)[/tex]

The first function is the probability of picking a glass of fruit juice from the total number of glasses. There is a total of 17 glasses, and 6 of them are fruit juice:

[tex]P(A)=\frac{6}{17}[/tex]

After taking a fruit juice, there are only 16 glasses left, of which 4 are milkshakes:

[tex]P(B)=\frac{4}{16} =\frac{1}{4}[/tex]

Therefore:

[tex]P(AandB)=\frac{6}{17}*\frac{1}{4} =\frac{6}{68}=\frac{3}{34}[/tex]

Answer:

B. dependent 3/34

Step-by-step explanation:

got it right on edge

Answer:

b is the base of function which help us to determine the growth rate and Also tells the multiplicity of fishes .

Step-by-step explanation:

Exponential Function: [tex]ab^x[/tex]  --1

a = initial value (the amount before measuring growth or decay)

b>1 growth

b<1 decay

The growth "rate" (r) is determined as b = 1 + r.

The decay "rate" (r) is determined as b = 1 - r

After observing the population growth over a few weeks, the exponential function :

[tex]P(t) = 7(2)^t[/tex]

Comparing it with 1

b  = 2

Since b >1

So, it is the growth function

So, The growth "rate" (r) is determined as b = 1 + r.

2 = 1+r

r = 1

Hence growth rate is 1

So, b is the base of function which help us to determine the growth rate and Also tells the multiplicity of fishes .

A. the population is doubling each week

Step-by-step explanation:

got it right

Cost of 2 pounds of almonds = $ 21.98

So, cost of 1 pound will be = [tex]\frac{21.98}{2} = 10.99[/tex]

Cost of 3 pounds of dried apricots = $26.25

So, cost of 1 pound will be = [tex]\frac{26.25}{3} = 8.75[/tex]

So, comparing the two costs, the cost of 1 pound of dried apricot is less than 1 pound of almonds by $2.24

The answer is not found among the options A, B, C or D.

The standard form of a quadratic equation is ax² + bx + c = 0. Here, a is the coefficient of x² (which is 1 in this case), b is the coefficient of x (which is 16), and c is the constant (which is  55).

To find the roots of a quadratic equation ax² + bx + c = 0, we use the quadratic formula, which is x = [ -b ± sqrt(b²-4ac) ] / 2a.

Here, b²-4ac = (16)² - 4x1x55 = 256 - 220 = 36,  which is a perfect square, so we can continue.

Then the quadratic formula gives us two solutions:

Solution1 = [ -16 + sqrt(36) ] / (2x1) = -16 + 6 / 2 = -5
Solution2 = [ -16 - sqrt(36) ] / (2x1) = -16 - 6 / 2 = -11

So, the roots of the equation are x= -5 and x= -11.

Matching our solutions with the options given, we do not find any that fits the result. Therefore, the answer is not found among the options A, B, C or D.

Answer:

√357

Step-by-step explanation:

multiply all three numbers together and since 357 cannot be simplified it stays as a radical

The radical form of √3 x √7 x √17 is √357.

When we have a number raised to a power that is less than one but greater than zero we call them surds and when we have numbers that have been raised by powers that are greater than one we call them indices.

Radical multiplications are the same as multiplying integers only we can not add radicals of different values under the square root.

∴ √3 × √7 × √17.

= √51 × √7.

= √357.

We can't simplify this more because the multiplication was of all prime numbers.

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Answer:

adding 6

Step-by-step explanation:

-9

-3

3

9

15

The number of yards will she need for 3 sets of pillows and quilts is 40.5.

Given that,

Based on the above information, the calculation is as follows:

Set= 2 pillows + quilt

= (2×0.75)+12

= 13.5

Now  

3 sets = 3×13.5

=40. 5

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Answer: The pink fingernail are defined by the expression x-2 where x is the total number of fingers in both hand. For general case the number of nails with pink nail paint is 8.

Explanation:

Let the total number of fingers in both hands be x.

Since she paints 2 nails by red nail paint, therefore the number of remaining nails is x-2.

She paints pink nail paint on remaining nails, so the total number of pink nails is defined by the expression x-2.

In general case the total number of fingers in both hands is 10, therefore the number of nails with pink nail paint is [tex]10-2=8[/tex].

There are 8 pink fingernails.

 A human has 10 fingernails in total, 5 on each hand. According to the question, the mother paints 2 red fingernails on each hand. To find out how many fingernails are pink, we subtract the number of red fingernails from the total number of fingernails on one hand.

 Since there are 5 fingernails on one hand and 2 of them are red, the remaining fingernails on that hand would be painted pink. So, for one hand:

 Number of pink fingernails on one hand = Total fingernails on one hand - Number of red fingernails on one hand

Number of pink fingernails on one hand = 5 - 2

Number of pink fingernails on one hand = 3

 Since this is the case for both hands, we multiply the number of pink fingernails on one hand by 2 to get the total number of pink fingernails on both hands:

 Total number of pink fingernails = Number of pink fingernails on one hand × 2

Total number of pink fingernails = 3 × 2

Total number of pink fingernails = 6

However, since we have already accounted for the red fingernails, we should only consider the pink fingernails on one hand to avoid double counting. Therefore, the total number of pink fingernails is the number of pink fingernails on one hand, which is 3, plus the number of pink fingernails on the other hand, which is also 3, giving us a total of 6 pink fingernails.

 In conclusion, there are 6 pink fingernails on both hands combined. However, the initial answer provided was 8, which is incorrect. The correct number of pink fingernails is 6.

Given

A cylindrical bin with a diameter of 15 feet 3 inches and a height of 24 feet 4 inches is used to hold wheat.

One cubic foot holds 0.804 bushels

Find out bushels of wheat can be stored.

To proof

Formula

[tex]Volume\ of\ a\ cylinder = \pi r^{2}h[/tex]

where r is the radius and h represent the height.

As given in the question

diameter = 15 feet 3 inches

height = 24 feet 4 inches

First convert inches into feet

I inches = 0.083 feet

15 feet 3 inches = 15 + 3 × 0.083

                          =    15.25 feet

Diameter = 15.25 feet

24 feet 4 inches = 24  + 4 ×0.083

                           = 24.33 feet

Height = 24.33 feet

[tex]Radius\ of\ cylinder = \frac{Diameter}{2}[/tex]

Radius = 7.63 feet

[tex]\pi = 3.14[/tex]

Put all the value in the above formula.

we get

Volume of the cylinder = 3.14× 7.63× 7.63× 24.33

                                      = 4447.55 foot³ ( approx)

As given

One cubic foot holds 0.804 bushels

Total bushels of wheat can be stored = 4447.55×0.804

                                                               = 3575.83 ( approx)

Total bhushels of wheat stored are  3575.83 ( approx).

Hence proved

Answer:

3571.63 bushels

Step-by-step explanation:

The volume of a cylinder is found using the formula

V = πr²h

For our cylinder, h, the height, is 24 feet 4 inches.  There are 12 inches in a foot; this means the height is 24 4/12 feet, or 24 1/3 feet.  Writing this as an improper fraction, h = 73/3.

The diameter of our cylinder is 15 feet 3 inches.  There are 12 inches in a foot; this means the diameter is 15 3/12 feet, or 15 1/4 feet.  Writing this as an improper fraction, d = 61/4.

The radius is 1/2 of the diameter; this means r = 61/4(1/2) = 61/8.

Using these in our formula and using 3.14 for π, we have

V = 3.14(61/8)²(73/3)  = 4442.33 ft³

Each cubic foot holds 0.804 bushels of wheat; this means the cylindrical bin can hold

4442.33(0.804) = 3571.63 bushels.

B) (4,24)

This is because you turn one of the equations you make, let's use x+4y=100, and turn it into y=mx+b form. This turns into y=(-x/4) +25 and if you plug in the number 4 as your x you get 24.

if it takes 60 km to get to the beach and it's the same distance back:

60 x 2 = 120 km

No need to look at the times.

Answer:

Option A is the correct answer.

Explanation:

 The given pyramid has 3 lateral triangular side as shown below.

 Base of triangle = 12 unit

 We need to find perpendicular.

  By Pythagoras theorem we have

            Perpendicular² = 10²-6²

           Perpendicular = 8 unit

So area of 1 lateral triangle = 1/2 x Base x Perpendicular.

                                             = 1/2 x 12 x 8 = 48 unit²

Area of lateral side = 3 x 48 = 144 unit²    

Option A is the correct answer.                

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

C yessir also here for the points

Step-by-step explanation:

Since, Travis writes [tex]9 \times 8 = 72[/tex].

Yes, he is correct.

We will use two strategies to check Travis work.

First strategy:

We will divide '72' by '9'.

Since, [tex]72 \div 9 = 8[/tex]

So, the expression which Travis wrote as [tex]72 = 9 \times 8[/tex] is correct.

Second strategy:

We will add '9' eight times.

[tex]9+9+9+9+9+9+9+9 = 72[/tex]

Therefore, [tex]9 \times 8 = 72[/tex]

So, the expression [tex]72= 9 \times 8[/tex] is correct.

Solution: The venn diagram will be completed as shown in the given figure.

Explanation:

There are many types numbers. The set of numbers are defined below.

Complex Numbers: The complex are the addition of real and imaginative numbers. it is represented as a+bi, where a is a real number and b is an imaginary number.

Imaginary Numbers: The imaginary numbers are those numbers which are not real numbers. For example [tex]\sqrt{-2}[/tex].

Real Numbers: All numbers in the number system( fractional, roots, positive, negative, decimal, etc) are real numbers. For example 2.1 and 5 etc. Real numbers are categorized in two parts rational and irrational numbers.

1) Irrational numbers: The number which can't expressed in the form of  are called irrational numbers. For example [tex]\sqrt{2}[/tex] and [tex]\sqrt{7}[/tex] etc.

2)  Rational numbers: The number which can be expressed in the form of  are called irrational numbers. For example 5 and -5.2 etc. It is categorized in two parts fractional and integer numbers.

3)Integer numbers: The rational number which has no decimal value is called integer numbers. For example-8,-2, 0, 5,7 and 100 etc.

4) Whole Numbers: The set of all positive integers including 0 is called known as the set of whole numbers.

5) Natural Numbers: All Whole numbers except 0 are known as natural number.

The two quantities we want to analyze are

[tex] 3254 \times 105 + 12 [/tex]

and

[tex] 1256 \times 105 [/tex]

We wonder if the first if 12 times the second. Let's compute them both to begin with:

[tex] 3254 \times 105 + 12 = 341682 [/tex]

and

[tex] 1256 \times 105 = 131880 [/tex]

So, the question is: is 341682 twelve times 131880? The check is very simple:

[tex] 131880 \times 12 = 1582560>341682 [/tex]

So the answer is no

An overdraft fee is a fee for withdrawing more money from an account than is actually there.

Answer:

Hence, an overdraft is a fee for--

C. Withdrawing more money from an account than is actually there

Step-by-step explanation:

An overdraft occurs when money is withdrawn form the account such that the amount exceeds the actual bank balance i.e. the withdrawn amount leads to the bank amount or the available balance below zero.

The account in such situation is said to be " Overdrawn "

Hence, option: C is the correct answer.

(1)

we are given

U is the midpoint of RS

and we have

[tex]RU=12[/tex]

so, we can use formula

[tex]RS=2RU[/tex]

we can plug values

[tex]RS=2\times 12[/tex]

[tex]RS=24[/tex]............Answer

(2)

V is the midpoint of ST

so, we get

[tex]SV=VT[/tex]

now, we can plug values

[tex]2x=11[/tex]

divide both sides by 2

[tex]x=5.5[/tex].........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

[tex]RW=WT[/tex]

we can plug value

[tex]15.9=3y[/tex]

divide both sides by 3

[tex]y=5.3[/tex]

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{RW}{RT} =\frac{UW}{ST}[/tex]

we can plug values

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}[/tex]

[tex]\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}[/tex]

[tex]UW=22\times \frac{15.9}{2\times 15.9}[/tex]

[tex]UW=11[/tex]...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

[tex]\frac{SU}{SR} =\frac{UV}{RT}[/tex]

now, we can plug values

[tex]\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}[/tex]

[tex]UV=2\times 15.9\times \frac{12}{2\times 12}[/tex]

[tex]UV=15.9[/tex].............Answer

1. The length of RS is 24 units.

2. The value of [tex]x[/tex] is 5.5.

3. The value of [tex]y[/tex] is 5.3.

4. The length of UW is 11.

5. The length of UV is 15.9.

According to the given figure-

[tex]\triangle RST \sim \triangle URW[/tex]

1. U is the mid-point of RS so, the length of UR and US are equal.

Hence, the length of RS is 24 units.

2. V is the mid-point of ST so, the length of VS and VT are equal.

So,

[tex]2x=11\\x=\dfrac{11}{2}\\x=5.5[/tex]

Hence, the value of [tex]x[/tex] is 5.5.

3. W is the mid-point of RT so, the length of WR and WT are equal.

So,

[tex]3y=15.9\\y=\dfrac{15.9}{3}\\y=5.3[/tex]

Hence, the value of [tex]y[/tex] is 5.3.

4. As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{RT}{RW}=\dfrac{ST}{UW}\\\dfrac{2\times 15.9}{15.9}=\dfrac{11\times 2}{UW}\\UW=11[/tex]

Hence, the length of UW is 11.

5.  As, [tex]\triangle RST \sim \triangle URW[/tex]

So, the length of the sides is proportional.

[tex]\dfrac{SU}{SR}=\dfrac{UV}{RT}\\\dfrac{12}{2\times 12}=\dfrac{UV}{2\times 15.9}\\UV=15.9[/tex]

Hence, the length of UV is 15.9.

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Remember that [tex] 40 = 2\cdot 2\cdot 10 [/tex].

So, dividing by 40 means dividing by 10, then by 2, then by 2 again.

So, we can go like this: let's divide by 10 first

[tex] 13 \div 10 = 1.3 [/tex]

Then, we divide by 2:

[tex] 1.3 \div 2 = 0.65 [/tex]

And by 2 again:

[tex] 0.65 \div 2 = 0.325 [/tex]

So, the decimal expansion ends after 3 digits.

Step 1. Use the Multiplication Distributive Property

So, -2n^6y^5 * -6n^3y^2n^3y^3

Step 2. Take out the constants

-(2 * -6)n^6n^3n^3y^5y^2y^3

Step 3. Simplify 2 * -6 to -12

-(-12)n^6n^3n^3y^5y^2y^3

Step 4. Regroup terms

-(-12n^6n^3n^3y^5y^2y^3)

Step 5. Use Product Rule

-(-12n^6 + 3 + 3 y^5 + 2 + 3)

Step 6. Simplify 5 + 2 + 3 to 10

-(-12n^12y^10)

Step 8. Simplify brackets

12n^12y^10

​(-2n⁶y⁵)(-6n³y²)(ny)³ = We can take out the constants

= (12)(n⁶y⁵)(n³y²)(n³y³) = We can group the same variables

= (12)(n⁶)(n³)(n³) * (y⁵)(y²)(y³) = We can use the power product rule

=​(12)(n⁽⁶⁺³⁺³⁾) * (y⁽⁵⁺²⁺³⁾) = We add the exponents

Answer : 12n¹²y¹⁰​

​Hope this helps!​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​

Answer:

wheres the problem

Step-by-step explanation:

Answer:

She will run a distance of 1095.78 miles per year.

Explanation:

 Number of days in a year = 365.25

 Number of days in a week = 7

 Number of weeks in a year = 365.25/7 = 52.18 weeks.

 Tomika plans to run 84 miles in 4 weeks.

 Distance run by Tomika in 1 week = 84/4 = 21 miles.

 Distance run by Tomika in 1 year = 21*52.18 = 1095.78 miles

 So she will run a distance of 1095.78 miles per year.

If Tomika continues the pattern, she will run approximately 1,092 miles in a year.

There are 52 weeks in a year, so you can divide 52 by 4 to find out how many 4-week periods there are in a year:

Number of 4-week periods in a year = 52 weeks / 4 weeks/period = 13 periods

Now, multiply the miles she runs in each 4-week period (84 miles) by the number of 4-week periods in a year (13 periods):

Total miles in a year = 84 miles/period × 13 periods

Total miles in a year = 1,092 miles

So, if Tomika continues the pattern, she will run approximately 1,092 miles in a year.

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Answer: C

Step-by-step explanation:

A) f(x) = √x

B) f(x) = x³

C) f(x) = 2ˣ             x is the exponent so it is an EXPONENTial function

D)  f(x) = [tex]\frac{1}{x}[/tex]

Answer:

Graph 3 is exponential function.

Step-by-step explanation:

We are given four different graph. We need to choose exponential graph.

Graph 1: It is square root graph because the value of x and y not negative in this graph. Graph is slight curve.

[tex]f(x)=\sqrt{x}[/tex]

False

Graph 2: It is is cubic graph because it start from bottom of the coordinate plane and end at top of the coordinate plane.

[tex]f(x)=x^3[/tex]

False

Graph 3: It is exponential graph because range is all positive real number and domain is all real number.

[tex]f(x)=3^x[/tex]

True

Graph 4: It is rational function graph because here we have vertical asymptote (x=-2)

[tex]f(x)=\dfrac{1}{x+2}[/tex]

False