solve the following system of equations

1/2x+1/4y=-2
-2/3x+1/2y=6

x=

y=​

Answer:

[tex]\dfrac{-14}{9}[/tex].

Step-by-step explanation:

The given number is [tex]-1.\overline{5}[/tex].

We need to find a rational number in fraction form that is equivalent to given number.

Let [tex]x=-1.\overline{5}[/tex]

[tex]x=-1.555...[/tex]     ...(1)

Multiply both sides by 10.

[tex]10x=-15.555...[/tex]  ...(2)

Subtracting (1) from (2), we get

[tex]10x-x=-15.555...-(-1.555...)[/tex]

[tex]9x=-14[/tex]

Divide both sides by 9.

[tex]x=\dfrac{-14}{9}[/tex]

Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].

Answer:

Explained below.

Step-by-step explanation:

In this case we need to test whether the extra carbonation of cola results in a higher average compression strength.

(a)

The hypothesis for the test can be defined as follows:

H₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. μ₁ - μ₂ = 0.

Hₐ: The extra carbonation of cola results in a higher average compression strength, i.e. μ₁ - μ₂ < 0.

(c)

Since the population standard deviations are not provided, we would use the t-test for difference between means.

The test statistic is:

[tex]t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]

  [tex]=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502[/tex]

The test statistic value is -2.502.

(c)

Compute the p-value as follows:

[tex]p-value=P(t_{16}<-2.052)=0.012[/tex]

*Use a t-table.

The p-value of the test is 0.012.

(d)

The significance level of the test is, c

p-value = 0.012 < α = 0.05.

The null hypothesis will be rejected.

Conclusion:

The data suggest that the extra carbonation of cola results in a higher average compression strength.

(e)

The assumption necessary for the analysis is:

The distributions of compression strengths are approximately normal.

The correct option is (A).

Answer:

2 ( x+4) ( x+1)

Step-by-step explanation:

2x^2+10x+8

Factor out 2

2 ( x^2 +5x+4)

What two numbers  multiply to 4 and add to 5

4*1 = 4

4+1 = 5

2 ( x+4) ( x+1)

[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]

By middle term factorisation,

⇛ 2x² + 2x + 8x + 8

⇛ 2x(x + 1) + 8(x + 1)

⇛ (2x + 8)(x + 1)

⇛ 2(x + 4)(x + 1)

☃️ Now you can break it down and check which are the factors of the polynomial according to options.

━━━━━━━━━━━━━━━━━━━━

Answer:

I'm gonna say C

Answer:

19 purses

Step-by-step explanation:

Set up an inequality where x represents the number of purses:

127 [tex]\geq[/tex] 7x

Solve for x by dividing each side by 7:

18.14 [tex]\geq[/tex] x

Round up to 19 because purses have to be whole

So, 19 purses have to be sold.

Answer:

-8, -6, -4, -2, ...

Step-by-step explanation:

-8, -6, -4, -2, ...  is an arithmetic sequence:  each new term is obtained by adding 2 to the previous term.

Answer:

-8, -6, -4, -2

Step-by-step explanation:

"An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence."

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

Answer:

486

Step-by-step explanation:

Hello!

To find the surface area of a cube we use the equation

[tex]S = 6a^{2}[/tex]

S is the surface area

a is the side length

Put what we know into the equation

[tex]S = 6*9^{2}[/tex]

Solve

S = 6 * 81

S = 486

Hope this Helps!

Answer:486[tex]ft^{2}[/tex]

Step-by-step explanation:

surface area= 6[tex]l^{2}[/tex]

l=9

sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]

Hector outperformed the challenge rate as he exercised 2.88 hours a week.

It is best to convert the mixed fraction to decimals for easier calculation.

The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:

= 2 + ¹/₂

= 2 + 0.5

= 2.5 hours per week

In the 4 week period, Hector exercised 11¹/₂ hours which is:

= 11 + ¹/₂

= 11 + 0.5

= 11.5 hours

The number of hours he exercised per week is:

= Number of hours in total / Number of weeks

= 11.5 / 4

= 2.88 hours per week

When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate

Find out more at https://brainly.com/question/17951676.

Answer:

The answer is 2 7/8

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan x = 8/10

taking the inverse tan of each side

x = tan ^-1 (8/10)

x=38.65980825

To the nearest tenth

x = 38.7

Answer: 72576m7

Step-by-step explanation:

2m x 8m x 6m x 9m x 7m x 6m x 2m

All together equals my answer 72576m7

Hope this helps!

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Answer: Hi!

The distance between the coordinates (4,2) and (0,2) is 4 units.

The coordinates have the same location on the y axis, but the coordinates have different locations on the x axis. (4,2) is 4 units to the right of the x axis and 2 up on the y axis, while (0,2) goes just straight up to 2 on the y axis. If we graphed these, the two points would be aligned with each other, but a distance of 4 units would separate them horizontally.

Hope this helps!

Answer:

(A) The probability that a male spent less than $210 online before deciding to visit a store is 0.0668.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is 0.0655.

(C) Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Step-by-step explanation:

We are given that the reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.

Let X = the spending limit

The z-score probability distribution for the normal distribution is given by;

                           Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean spending limit = $240

           [tex]\sigma[/tex] = standard deviation = $20

So, X ~ Normal([tex]\mu=\$240,\sigma^{2} =\$20^{2}[/tex])

(A) The probability that a male spent less than $210 online before deciding to visit a store is given by = P(X < $210)

     P(X < $210) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$210-\$240}{\$20}[/tex] ) = P(Z < -1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                                            = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is given by = P($270 < X < $300)

     P($270 < X < $300) = P(X < $300) - P(X [tex]\leq[/tex] $270)

     P(X < $300) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$300-\$240}{\$20}[/tex] ) = P(Z < 3) = 0.9987

     P(X [tex]\leq[/tex] $270) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$270-\$240}{\$20}[/tex] ) = P(Z [tex]\leq[/tex] 1.50) = 0.9332

The above probability is calculated by looking at the value of x = 3 and x = 1.50 in the z table which has an area of 0.9987 and 0.9332 respectively.

Therefore, P($270 < X < $300) = 0.9987 - 0.9332 = 0.0655.

(C) Now, we have to find ninety percent of the amounts spent online by a male before deciding to visit a store is less than what value, that is;

         P(X < x) = 0.90     {where x is the required value}

         P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

         P(Z < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

In the z table, the critical value of z that represents the bottom 90% of the area is given as 1.2816, i.e;

                     [tex]\frac{x-\$240}{\$20}=1.2816[/tex]

                     [tex]x-240=1.2816\times 20[/tex]

                     [tex]x=240 + 25.632[/tex]

                     x = 265.632

Hence, Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Answer:

x>125

Step-by-step explanation:

Answer:

x > 125

Step-by-step explanation:

I hope this helps!

Answer:

If a number is an integer, then it is irrational.  ⇒ false statement

Step-by-step explanation:

Let's check:

If a number is an integer, then it is irrational.

- incorrect, as all integers are rational

If a number is a natural number, then it is rational.

- correct, natural numbers are subset of rational numbers

If a number is a fraction, then it is rational.

- correct, they can be shown as p/q

If a number is a whole number, then it is rational.

- correct, whole numbers are subset of rational numbers

The statement "If a number is an integer, then it is irrational" is false.

The statement "If a number is an integer, then it is irrational" is false. This is because not all integers are irrational.

The other statements are all true:

"If a number is a natural number, then it is rational." This is true because all natural numbers are integers, and all integers are rational.

"If a number is a fraction, then it is rational." This is true because a fraction is a number of the form p/q, where p and q are integers and q is not equal to 0. Any number of this form is rational.

"If a number is a whole number, then it is rational." This is true because all whole numbers are integers, and all integers are rational.

Therefore, the false statement is the first one: "If a number is an integer, then it is irrational."

Below is a table summarizing the statements:

Statement                                                                  Truth value    

If a number is an integer, then it is irrational               False

If a number is a natural number, then it is rational     True

If a number is a fraction, then it is rational                  True

If a number is a whole number, then it is rational      True

Learn more about rational numbers on:

brainly.com/question/22221295

#SPJ6

Answer:

The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Step-by-step explanation:

Let the random variable X represent the amount of gas in Sarah's car.

It is provided that [tex]X\sim Unif(1, 16)[/tex].

The amount of gas in a car is a continuous variable.

So, the random variable X follows a continuous uniform distribution.

Then the probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]

For a continuous probability distribution the probability at an exact point is 0.

So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:

P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)

              = P (6.5 < X < 7.5)

              [tex]=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067[/tex]

Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Answer:

box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35

Step-by-step explanation:

The scores of the students represented on the dot plot are:

1 dot => 24

3 dots => 26, 26, 26

3 dots => 27, 27, 27

5 dots => 28, 28, 28, 28, 28

3 dots => 30, 30, 30

3 dots => 32, 32, 32

1 dot => 35

Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.

The minimum score = 24

The maximum score = 35

The median score is the 10th value, which is the middle value of the data point = 28

Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".

Answer:

2/3×3/5=2/3. 3/4×1/6=1/8

2/3-1/8=11/40

Answer:

Step-by-step explanation:

[tex]( \frac{2}{3} \times \frac{3}{5} ) - ( \frac{3}{4} \times \frac{1}{6} )[/tex]

Reduce the numbers with Greatest common factor 3

⇒[tex] \mathsf{(2 \times \frac{1}{5} ) - ( \frac{1}{4} \times \frac{1}{2} )}[/tex]

Calculate the product

⇒[tex] \mathsf{( \frac{2}{5} )- ( \frac{1}{4} \times \frac{1}{2}) }[/tex]

Subtract the fractions

⇒[tex] \mathsf{ \frac{2 \times 8 - 1 \times 5}{40} }[/tex]

⇒[tex] \mathsf{ \frac{16 - 5}{40} }[/tex]

⇒[tex] \mathsf{ \frac{11}{40} }[/tex]

Hope I helped!

Best regards!

Answer:

34

Step-by-step explanation:

= 26 + 8

= 34

Answer: 139/7

Step-by-step explanation:

Answer:

139/7

Step-by-step explanation:

182/10 = 18.2 < 18 7/11

219/12 = 18 + 3/12 = 18 1/4  < 18 7/11

139/7 = 19 + 4/7 > 18 7/11

179/10 = 17.9 < 18 7/11

Answer:

7

Step-by-step explanation:

First plug in the variable amounts so the expression now looks like this:

(3 × 4 - 12) + 1/2(4 × 6 - 10)

Now, start by solving the multiplication parts first, so it now looks like this:

(12 - 12) + 1/2(24 - 10)

Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)

Next, solve the multiplication part, so it now looks like this: 0 + 7

Solve that and the answer is 7.

Answer:

Step-by-step explanation:

(1-CotA)² + (tanA-1)² = 4csc2A(csc2A-1)

To prove this equation we will take the expression given in left hand side and will convert it into the expression given in right hand side of the equation.

L.H.S. = (1-CotA)² + (tanA-1)²

          = 1 + Cot²A - 2CotA + 1 + tan²A - 2tanA

          = cosec²A - 2CotA + Sec²A - 2tanA

[Since, (1 + Cot²A = cosec²A) and (1 + tan²A = Sec²A)]

          = (cosec²A + Sec²A) - 2(CotA + tanA)

          = [tex](\frac{1}{\text{SinA}})^{2}+(\frac{1}{CosA} )^{2}-2\text{(tanA}+\frac{1}{\text{tanA}})}[/tex]

          = [tex]\frac{1}{(\text{SinA.CosA})^2}-2(\frac{tan^2A+1}{tanA} )[/tex]

          = [tex]\frac{4}{\text{(Sin2A})^{2}}-4(\frac{1}{\text{Sin2A}} )[/tex]

[Since 2SinA.CosA = Sin2A and [tex]\frac{2(\text{tanA})}{1+\text{tan}^{2}A}=\text{Sin2A}[/tex]]

          = 4Cosec²2A - 4Cosec2A

          = 4Cosec2A(Cosec2A - 1)

          = R.H.S. (Right hand side)

Hence the equation is proved.

Answer:

Y=2(1)+4

Y=2+4

Y=6

Step-by-step explanation:

Please follow me

Answer:

C. 360/900 = 0.40

Step-by-step explanation:

The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.

Answer: There is an moderate relationship between  the aptitude test scores with the chronological ages of the subjects.

Step-by-step explanation:

Here , variables →  aptitude test scores and chronological ages of the subjects.

Since correlation coefficient (-0.42) lies between  -0.5 and -0.3 .

[-0.5< -0.42< -0.3]

That means there is an moderate relationship between  the aptitude test scores with the chronological ages of the subjects.

Answer:

Surface Area = 4(3.14)((m/2)^2)

Step-by-step explanation:

The formula of surface area is 4(3.14)(r^2)

where r is the radius

We are given the diameter M which is just the radius times 2. So to find the radius we divide m by 2. So our radius is m/2.

Answer:

m<A = 133 degrees

m<B = 17 degrees

m<C = 30 degrees

Step-by-step explanation:

In a triangle, all the angles add up to 180 degrees.

So, adding all the angles gets us,

39x + 24

This equals 180 degrees so,

39x + 24 = 180

Subtract 24 from both sides,

39x + 24 - 24 = 180 - 24

39x = 156

Divide both sides by 39

x = 4

Now we have x = 4, we use this to plug in each equation of the angles.

m<A = 40(4) - 27 = 160 - 27 = 133

m<B = 25 - 2(4) = 25 - 8 = 17

m<C = 26 + 4 = 30

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x   this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.