2 1/2 cases of soda to split between 5 families

Answer:

Step-by-step explanation:

Hello, "the constant term has been written on the right side", it means that we add 18 to both sides to get.

[tex]x^2+3x-18=0\\\\x^2+3x=18\\\\\text{We can see the beginning of } (x+\dfrac{3}{2})^2 \\\\x^2+3x=(x+\dfrac{3}{2})^2-\dfrac{3^3}{2^2}=18\\\\(x+\dfrac{3}{2})^2=18+\dfrac{9}{4}=\dfrac{18*4+9}{4}=\dfrac{81}{4}[/tex]

Hope this helps.

Thank you.

Answer:

2.25.

Step-by-step explanation:

x^2 + 3x - 18 = 0

First, we need to write the constant on the right of the equation. So, we add 18 to both sides.

x^2 + 3x = 18.

Now, we find the number that will complete the square. It will be [tex](\frac{b}{2} )^2[/tex].

In this case, b = 3.

[tex](\frac{3}{2} )^2[/tex]

= (1.5)^2

= 2.25.

So, the number that will complete the square to solve the equation is 2.25, or 2 and 1/4, or 9/4.

Hope this helps!

━━━━━━━☆☆━━━━━━━

▹ Answer

18x⁴ + 36x³ - 9x²

▹ Step-by-Step Explanation

9x²(4x + 2x² - 1)

36x³ + 18x⁴ - 9x²

18x⁴ + 36x³ - 9x²

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

[tex]Probability = 0.35[/tex]

Step-by-step explanation:

Given

Probability of success free throw = 90%

Number of throw = 10

Required

Determine the probability of 10 consecutive free throws

Let p represents the given probability

[tex]p = 90\%[/tex]

Convert to decimal

[tex]p = 0.9[/tex]

Let n represents the number of throw

[tex]n = 10[/tex]

Provided that each throw is independent;

The probability of n consecutive free throw is

[tex]p^n[/tex]

Substitute 0.9 for p and 10 for n

[tex]Probability = 0.9^{10}[/tex]

[tex]Probability = 0.3486784401[/tex]

[tex]Probability = 0.35[/tex] (Approximated)

Answer:

  B, E

Step-by-step explanation:

You can use these strategies to compare the given graph and the other representations.

  A & B) See if the point (x, y) = (8, 6) marked on the first graph works in the given equation.

A -- 6y = 8x   ⇒   6(6) = 8(8) . . . FALSE

B -- y = (3/4)x   ⇒   6 = (3/4)8 . . . True

__

  C) Compare this graph to the given graph. They don't match.

__

  D & E) Plot a point from the table on the given graph and see where it falls.

D -- The point (x, y) = (3, 4) lies above the line on the given graph.

E -- The point (x, y) = (4, 3) lies on the given graph.

_____

Choices B and E have the same constant of proportionality as shown in the given graph.

Answer:

B and E

Step-by-step explanation:

Answer:

Step-by-step explanation:

(5+(-4))/2 = 1/2 or 0.5

(-7 + 6)/2 = -1/2 or -0.5

the solution is D

(0.5, -0.5)

Answer:

Correct answer is option d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Step-by-step explanation:

Given the equation of regression analysis is given as:

[tex]y= 30,000 + 4x[/tex]

where [tex]x[/tex] is the cost on advertising in Dollars.

and [tex]y[/tex] is the sales in Thousand Dollars.

To find:

The correct increase in sales when there is increase in the advertising cost.

Solution:

Suppose there is an increase of [tex]\$1[/tex] in the advertising cost.

Let the initial cost be [tex]x[/tex] then the cost will be [tex](x+1)[/tex].

Initial sales

[tex]y= 30,000 + 4x[/tex] ....... (1)

After increase of $1 in advertising cost, final cost:

[tex]y'= 30,000 + 4(x+1)\\\Rightarrow y' = 30,000+4x+4\\\Rightarrow y' = 30,004+4x ..... (2)[/tex]

Subtracting (2) from (1) to find the increase in the sales:

[tex]y'-y=30004+4x-30000-4x = 4[/tex]

The units of sales is Thousand Dollars ($1000).

So, increase in sales = [tex]4 \times1000 = \bold{\$4000}[/tex]

So, correct answer is:

d. increase of $1 in advertising is associated with an increase of $4000 in sales.

Answer:

Please see the Step-by-step explanation for the answers

Step-by-step explanation:

1)

∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] 2j

The sum of series from j=1 to j=5 is:

∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)

  =  2 + 4 + 6 + 8 + 10

∑ = 30

2)

This question is not given clearly so i assume the following series that will give you an idea how to solve this:

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²

The sum of series from k=1 to j=4 is:

∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²

  = 2(1) + 2(4) + 2(9) + 2(16)

  =  2 + 8 + 18 + 32

∑ = 60

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²

∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²

  = (2)² + (4)² + (6)² + (8)²

  = 4 + 16 + 36 + 64

∑ = 120

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²- 4

∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4

  = (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4

  = (4-4) + (16-4) + (36-4) + (64-4)

  = 0 + 12 + 32 + 60

∑ = 104

∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²- 4

∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4

  = 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4

  = (2-4) + (8-4) + (18-4) + (32-4)

  = -2 + 4 + 14 + 28

∑ = 44

3)

∑[tex]\left \ {{6} \atop {k=3}} \right.[/tex] (2k-10)

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)  

  = (6-10) + (8-10) + (10-10) + (12-10)

  = -4 + -2 + 0 + 2  

∑ = -4

4)

1+1/2+1/4+1/8+1/16+1/32+1/64

This is a geometric sequence where first term is 1 and the common ratio is 1/2 So

a = 1

This can be derived as

1/2/1 = 1/2 * 1 = 1/2

1/4/1/2 = 1/4 * 2/1 = 1/2

1/8/1/4 = 1/8 * 4/1  = 1/2

1/16/1/8 = 1/16 * 8/1  = 1/2

1/32/1/16 = 1/32 * 16/1  = 1/2

1/64/1/32 = 1/64 * 32/1  = 1/2

Hence the common ratio is r = 1/2

So n-th term is:

[tex]ar^{n-1}[/tex] = [tex]1(\frac{1}{2})^{n-1}[/tex]

So the answer that represents the series in sigma notation is:

∑[tex]\left \ {{7} \atop {j=1}} \right.[/tex] [tex](\frac{1}{2})^{j-1}[/tex]

5)

−3+(−1)+1+3+5

This is an arithmetic sequence where the first term is -3 and the common difference is 2. So  

a = 1

This can be derived as

-1 - (-3) = -1 + 3 = 2

1 - (-1) = 1 + 1 = 2

3 - 1 = 2

5 - 3 = 2

Hence the common difference d = 2

The nth term is:

a + (n - 1) d

= -3 + (n−1)2

= -3 + 2(n−1)

= -3 + 2n - 2

= 2n - 5

So the answer that represents the series in sigma notation is:

∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] (2j−5)

For (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is  [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7, and for (5) the sigma notation is  [tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5.

We have different series in the question.

It is required to find the sum of all series.

In mathematics, a series can be defined as a group of data that followed certain rules of arithmetic.

1) We have:

[tex]\rm \sum j=2j[/tex]   where j = 1 to j = 5

After expanding the series, we get:

= 2(1)+2(2)+2(3)+2(4)+2(5)

=2(1+2+3+4+5)

= 2(15)

=30

2) We have:

[tex]\rm \sum k=(2k^2-4)[/tex]  where k = 1 to k = 4

After expanding the series, we get:

[tex]\rm = (2(1)^2-4)+(2(2)^2-4)+(2(3)^2-4)+(2(4)^2-4)+(2(5)^2-4)\\[/tex]

[tex]\rm = 2[1^2+2^2+3^2+4^2+5^2]-4\times5\\\\\rm=2[55]-20\\\\\rm = 90[/tex]

3) We have:

[tex]\rm \sum k= (2k-10)[/tex]  where k = 3 to k = 6

After expanding the series, we get:

[tex]= (2(3)-10)+(2(4)-10)+(2(5)-10)+(2(6)-10)\\\\=2[3+4+5+6] - 10\times4\\\\=2[18] - 40\\\\= -4[/tex]

4) The series given below:

[tex]1, \frac{1}{2} ,\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}[/tex]

It is a geometric progression:

[tex]\rm n^t^h[/tex] for the geometric progression is given by:

[tex]\rm a_n = ar^{n-1}[/tex]

[tex]\rm a_n = 1(\frac{1}{2})^{n-1}\\\\\rm a_n = (\frac{1}{2})^{n-1}\\[/tex]

In sigma notation we can write:

[tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7

5) The given series:

−3+(−1)+1+3+5, it is arithmetic series.

[tex]\rm n^t^h[/tex] for the arithmetic progression is given by:

[tex]\rm a_n = a+(n-1)d[/tex]

[tex]\rm a_n = -3+(n-1)(2)\\\\\rm a_n = 2n-5[/tex]

In sigma notation we can write:

[tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5

Thus, for (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is  [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex]  where j = 1 to j = 7, and for (5) the sigma notation is  [tex]\rm\sum j = (2j-5)[/tex]  where j = 1 to j = 5.

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The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.

The constant bod proportionality would be 3, which means each pineapple cost $3

Answer:

first of all, brainly better not delete my answer again. (the answer is 3)

Step-by-step explanation:

you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..

The area of the entire shape is 33,562 square units

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

The figure is made up of a square and four 3/4 circles. So the total area will be equal to the sum of the area of the square and the sum of the 3/4 th circles.

Area of Square:-

= 100  x  100   =  10,000

Area of each circle

= π r² = 3.1416  x  50  x  50  =  7854

Area of each 3/4 circle  

= 7854  x  ( 3/4 ) =   5890.5

Area of all four 3/4 circles

= 5890.5  x  4=23562

The TOTAL area will be the sum of all the areas

A  = 23562  +  10,000 = 33,562 square units

Therefore the area of the entire shape is 33,562 square units

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The area of the entire shape is 33,562 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Here, we have,

The figure is made up of a square and four 3/4 circles.

So the total area will be equal to the sum of the area of the square and the sum of the 3/4 the circles.

Area of Square:-

= 100  x  100   =  10,000

Area of each circle

= π r² = 3.1416  x  50  x  50  =  7854

Area of each 3/4 circle  

= 7854  x  ( 3/4 ) =   5890.5

Area of all four 3/4 circles

= 5890.5  x  4=23562

The TOTAL area will be the sum of all the areas

A  = 23562  +  10,000 = 33,562 square units

Therefore the area of the entire shape is 33,562 square units

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Nope, i dont think so

Answer:

no the numbers are infinite

Step-by-step explanation:

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

Explanation:

Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.

So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below

We could also swap the order of either x, y or z, and still have the same result.

Answer:

A

Step-by-step explanation:

r=10 and the angle bln 5√3 and -5 is 330 or 11π/6

Since two of the quantities are squares and the sum of all of three is equal 21, then the possible values of those two quantities are: 1,4,9,16

Let's consider each possibility

1 and 4

21-1-4=16, but 16 is also square and there can be only two square so NO

1 and 9

21-1-9=11, but 11 is prime, so NO

1 and 16

21-1-16=4... 4 is a square ,so NO

4 and 9

21-4-9=8 , 8 is not prime and not a square, so YES

4 and 16

21-4-16=1, but 1 is a square ,so NO

9 and 16

9+16=25>21 so.. NO

Therefore, the amounts in the first three bowls are 4,8,9.

Answer:

x < -2

Step-by-step explanation:

12 − 6x > 24

Subtract 12 from each side

12-12 − 6x > 24-12

-6x > 12

Divide each side by -6, remembering to flip the inequality

-6x/-6 < 12/-6

x < -2

Answer:

x < -2

Step-by-step explanation:

12 − 6x > 24

12 - 12 − 6x > 24 - 12

-6x > 12

-6x/(-6) < 12/(-6)

x < -2

Answer:

100,000

You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.

Answer:

Step-by-step explanation:

Answer:

x+12=78

Step-by-step explanation:

like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.

Answer:

n + 12 = 78

Step-by-step explanation:

Let n = number.

n + 12 = 78

Answer:

vertical angles

Step-by-step explanation:

Angle 1 and 3 are vertical angles.  The angles are made from the same lines and share a vertex.  They are opposite it each other

Answer:

There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.

Answer:

5/100000 tons

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt

ΔS = k/Δt where k is the constant of proportionality

If ΔS = S₂-S₁ and Δt = t₂-t₁

S₂-S₁ = k/ t₂-t₁

If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁  = 162, t₁ = 2 and when   S₂ = 287, t₂ = 4.

On substituting this values into the given functions, we will have;

287 - 162 = k/4-2

125 = k/2

cross multiplying

k = 125* 2

k = 250

Substituting k = 250 into the function ΔS = k/Δt

ΔS = 250/Δt

S = 250/t

Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t

Answer:

217.0588235294118

Step-by-step explanation:

Convert all height to inches.

5' 8" = 68 inches

6' = 72

205/68 = 3.014705882352941

Height/Weight Ratio * Evan's Height = 217.0588235294118

Answer:16

Step-by-step explanation:

Just divide 80 by 5 or skip count by fives.

Answer:

The system is dependent:

x=-3t-7

y=-5t-15

z=t

Step-by-step explanation:

I chose to use a matrix to solve this system of equations. Once put into matrix form, you need to row reduce the system into its simplest form (Row Reduced Echelon form). Doing this, we find that the system is dependent on the z variable. And following usual procedures, we let z equal some other letter; which is t in this case. Then we isolate each variable to get the answer.

Check the attachment for the work.

[The arrows indicate a row swap and the parenthesis indicates addition if a constant multiple of one row to another]

Answer:

B. ⅕

Step-by-step explanation:

Fraction of families having more than 2 pets = families with pets of 3 and above ÷ total number of families in the apartment

From the dot plot above, 3 families have 3 pets, and 1 family has 4 pets.

Number of families with more than 2 pets = 3 + 1 = 4

Fraction of families with more than 3 pets = [tex] \frac{4}{20} = \frac{1}{5} [/tex]

The fraction of families that have more than two pets is B. [tex]\frac{1}{5}[/tex]

Given that:

Fraction of families having more than 2 pets = families with pets of 3 and above/total number of families in the apartment

From the dot plot above:

Number of families with more than 2 pets

= 3 + 1

= 4

Fraction of families with more than 3 pets = [tex]\frac{4}{20} = \frac{1}{5}[/tex]

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Answer:

B. ∠A, ∠B, ∠C

Step-by-step explanation:

1. Draw a model with AB as the shortest line and BC as the longest line.

∠A connects the two shortest lines, making it the largest angle.

∠B connects the shortest and the longest lines, making it the second largest angle.

∠C connects the two longest lines, making it the smallest angle.

Answer:

A > B > C

Step-by-step explanation:

Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.

By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.

Based off of my drawing, it looks like the order is angle A, then B, then, and then C.

Answer:

a) AD is Median

b) AM is Perpendicular Bisector

Step-by-step explanation:

c) Yes because the Median divides the line into two equal parts

Answer:

1. a. tobt = -4.73

2. b. 9

3. a. +- 2.162

4. d. Reject H0; stress affects the menstrual cycle.

Step-by-step explanation:

The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted.

Answer: 0.418 < p < 0.512

Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:

[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]

where:

p is the proportion

z is score in z-table

n is sample size

The proportion for people who said "yes" is

[tex]p=\frac{202}{434}[/tex] = 0.465

For a 95% confidence interval, z = 1.96.

Calculating

[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]

[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]

0.465 ± 1.96*0.024

0.465 ± 0.047

Interval is between:

0.465 - 0.047 = 0.418

0.465 + 0.047 = 0.512

The interval with 95% of confidence is between 0.418 and 0.512.

Answer:

Answer is D.

Step-by-step explanation:

do 4 times every value in the ( )

Answer:

[tex]\boxed{\sf D}[/tex]

Step-by-step explanation:

Answer:

$3870

Step-by-step explanation:

Hello, the initial deposit is $1000.

After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)

= 1000 * 1.07

And we want to compound it so the second year we will get

[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]

And after n years, we will get

[tex]1000 * 1.07^n[/tex]

In that example, we want to know how much we will get after 20 years, so this is:

[tex]1000 * 1.07^{20}=3869.684462...[/tex]

Thank you.

When interest is compounded, it means that both the interest and the amount deposited will earn interest.

We are to determine the future value of $1000 with annual compounding.

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = amount deposited = $1000

R = interest rate = 7%

N = number of years = 20

$1000 x ( 1.07)^20 = $3,869.68

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Answer:

x = -4

Step-by-step explanation:

2 - (7x + 5) = 13 - 3x

add the binomial (7x +5) to both sides

2 = (7x + 5) + 13 - 3x

combine like terms

2 = 4x + 18

subtract 18 from both sides

-16 = 4x

divide by 4

x = -4

Answer:

-4

Step-by-step explanation:

Distribute the negative signs to the values in the parentheses

2 -7x - 5 = 13 - 3x

Add like terms:

-7x - 3 = 13 - 3x

Add 3x to both sides:

-4x - 3 = 13

Add 3 to both sides:

-4x = 16

Divide both sides by -4:

x = -4