Really need help on question 10.

Answer:

We conclude that the population means checkout times of the two new systems differ.

Step-by-step explanation:

We are given the result in the following summary of the data;

System          System B

n1=120             n2=100

x1=4.1 min       x2=3.4 min

σ1=2.2 min     σ2= 1.5 min

Let [tex]\mu_1[/tex] = population mean checkout time of the first new system

[tex]\mu_2[/tex] = population mean checkout time of the second new system

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1=\mu_2[/tex]      {means that the population mean checkout times of the two new systems are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1\neq \mu_2[/tex]      {means that the population mean checkout times of the two new systems differ}

The test statistics that will be used here is Two-sample z-test statistics because we know about population standard deviations;

                          T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }[/tex]  ~ N(0,1)

where, [tex]\bar X_1[/tex] = sample mean checkout time of the first new systems = 4.1 min

[tex]\bar X_2[/tex] = sample mean checkout time of the second new systems = 3.4 min

[tex]\sigma_1[/tex] = population standard deviation of the first new systems = 2.2 min

[tex]\sigma_2[/tex] = population standard deviation of the second new systems = 1.5 min

[tex]n_1[/tex] = sample of the first new systems = 120

[tex]n_2[/tex] = sample of the second new systems = 100

So, the test statistics =  [tex]\frac{(4.1-3.4)-(0)}{\sqrt{\frac{2.2^{2} }{120} + \frac{1.5^{2} }{100}} }[/tex]  

                                    =  2.792

The value of z-test statistics is 2.792.

Now, at 0.05 level of significance, the z table gives a critical value of -1.96 and 1.96 for the two-tailed test.

Since the value of our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the population mean checkout times of the two new systems differ.

Answer:

(3, 1)

Step-by-step explanation:

Plug-in points and see which one works. (x, y). <=  means less than or equal to.

Answer:

D. (3,1) is the correct answer

Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution

Answer:

x = 40

Step-by-step explanation:

4/x = 50/500

Simplify the right side

4/x = 1/10

Using cross products

4*10 = 1*x

40 = x

Step-by-step explanation:

4/x = 50/500

4/x = 0.1

x = 4/0.1

x = 40

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

Answer:

[tex]x= \frac{5^{14}+3}{2}[/tex]

Step-by-step explanation:

The correct steps to solve the equation are:

[tex]14=log_5(2x-5)[/tex]

[tex]5^{14}=5^{log_5(2x-3)}[/tex]

Because [tex]a^{log_am}=m[/tex]

So, solving we get:

[tex]5^{14}=2x-3[/tex]

Sum 3 on every side:

[tex]5^{14}+3=2x-3+3\\5^{14}+3=2x[/tex]

Dividing by 2 into both sides:

[tex]\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x[/tex]

So, the answer is  [tex]x= \frac{5^{14}+3}{2}[/tex]

Answer: Step 2

Step-by-step explanation:

This is correct according to Edge 2021

Answer:

A real root of fifth-grade multiplicity/No complex roots.

Step-by-step explanation:

The Fundamental Theorem of Algebra states that every polynomial with real coefficients and a grade greater than zero has at least a real root. Let be [tex]f(x) = (x+7)^{5}[/tex], if such expression is equalized to zero and handled algebraically:

1) [tex](x+7)^{5} = 0[/tex] Given.

2) [tex](x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7)\cdot (x+7) = 0[/tex] Definition of power.

3) [tex]x+7=0[/tex] Given.

4) [tex]x = -7[/tex] Compatibility with the addition/Existence of the additive inverse/Modulative property/Result.

This expression has a real root of fifth-grade multiplicity. No complex roots.

Answer:

(0,0), (-4,0), (0,-5).

Step-by-step explanation:

Note: Matrices are not in proper format.

Consider the given matrix is

[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

It means vertices are (0,0), (4,0) and (0,5).

Transformation matrix is

[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]

To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.

[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]

[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]

It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).

Answer:

A

Step-by-step explanation:

E2020

Answer:

X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]

Step-by-step explanation:

4B = -2X - 2A

Dividing both sides by -2

=> -2B = X + A

Subtracting A to both sides

=> X = -2B-A

Now, Let's Solve:

=> X = [tex]-2\left[\begin{array}{ccc}0&2&-2\\5&0&3\end{array}\right] -\left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}-2*0&-2*2&-2*-2\\-2*5&-2*0&-2*3\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}0&-4&4\\10&0&6\end{array}\right] - \left[\begin{array}{ccc}-2&3&1\\-3&0&4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}0-(-2)&-4-3&4-1\\10-(-3)&0-0&6-4\end{array}\right][/tex]

=> X = [tex]\left[\begin{array}{ccc}2&-7&3\\13&0&2\end{array}\right][/tex]

Answer:  3/(28) ≈ 10.7%

Step-by-step explanation:

3 blue + 2 red + 3 green = 8 total pens

   First pick    and           Second pick

 [tex]\dfrac{3\ blue\ pens}{8\ total\ pens}\quad \times \quad \dfrac{2\ remaining\ blue\ pens}{7\ remaining\ total\ pens}\quad =\large\boxed{\dfrac{3}{28}}[/tex]  

Answer:

a:b:c

1a) 14:16:7

b) 2:1:5

c) 2:1:48

d) 15:24:32

2) 56:12:3

Step-by-step explanation:

Untuk membentuk nisbah tiga kuantiti, pertama-tama kita menukar masing-masing menjadi unit yang sama.

a) 2 minggu hingga 16 hari hingga 1 minggu

Menukar semuanya menjadi bilangan hari, kerana ia sangat setanding.

2 minggu = 14 hari

16 hari = 16 hari

1 minggu = 7 hari

2 minggu hingga 16 hari hingga 1 minggu = 14 hari hingga 16 hari hingga 7 hari

14: 16: 7

b) 0.1 kg hingga 50 g hingga 0.25 kg

Menukar semua menjadi gram

= 100 g hingga 50 g hingga 250 g

= 100: 50: 250

Bahagikan dengan 50

= 2 : 1 : 5

c) 4 minit hingga 120 saat hingga 1.6 jam

Menukar semua menjadi beberapa saat

= 240 saat hingga 120 saat hingga (1.6 × 60 × 60) saat

= 240 saat hingga 120 saat hingga 5,760 saat

= 2: 1: 48

d) 3 m hingga 480 cm hingga 6 400 mm

Menukar semua ini menjadi mm

= 3000 mm hingga 4800 mm hingga 6400 mm

Membahagi hingga 200 mm

= 15:24:32

2) RM5.60 hingga RM1.20 hingga 30 sen

Menukar semuanya kepada sen

= 560 sen hingga 120 sen hingga 30 sen

Membahagi hingga 10

= 56: 12: 3

Semoga ini Membantu !!!

English Translation

Solution

0.02 m: 3 cm: 4.6 cm = 2 cm: 3 cm: 4.6 cm = 2: 3: 4.6

20:30:46

10:15:23

Self Training 4.1a

1. Represent the relationship between the following three quantities in the form a: b: c.

(a) 2 weeks to 16 days to 1 week

(b) 0.1 kg to 50 g to 0.25 kg

(c) 4 minutes to 120 seconds to 1.6 hours

(d) 3 m to 480 cm to 6 400 mm

2. Tahir pays RM5.60 for a plate of beriani rice, RM1.20 for a glass of tea and 30 cents for a piece of cake.

Represent the price relationship for beriani rice, tea and cake in the form of a: b: c.

Solution

To form a ratio of three quantities, we first convert each of them to the same units.

a) 2 weeks to 16 days to 1 week

Converting all of it to number of days, as itnis very comparable.

2 weeks = 14 days

16 days = 16 days

1 week = 7 days

2 weeks to 16 days to 1 week

= 14 days to 16 days to 7 days

14 : 16 : 7

b) 0.1 kg to 50 g to 0.25 kg

Converting all into grams

= 100 g to 50 g to 250 g

= 100 : 50 : 250

Divide through by 50

= 2 : 1 : 5

(c) 4 minutes to 120 seconds to 1.6 hours

Converting all into seconds

= 240 seconds to 120 seconds to (1.6×60×60) seconds

= 240 seconds to 120 seconds to 5,760 seconds

= 2:1:48

(d) 3 m to 480 cm to 6 400 mm

Converting all of this to mm

= 3000 mm to 4800 mm to 6400 mm

Dividing through by 200 mm

= 15:24:32

2) RM5.60 to RM1.20 to 30 cents

Converting it all to cents

= 560 cents to 120 cents to 30 cents

Dividing through by 10

= 56:12:3

Hope this Helps!!!

Answer:

[tex]x=-3[/tex]

Step-by-step explanation:

So, we are given:

[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]

First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.

[tex]x\neq 0[/tex]

Now, cross multiply.

[tex]3(x^2)=x(4x+3)[/tex]

[tex]3x^2=4x^2+3x[/tex]

Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).

[tex]3x=4x+3[/tex]

[tex]-x=3[/tex]

[tex]x=-3[/tex]

We didn't run into any possibilities for extraneous solutions.

Answer:

156.75 tons

Step-by-step explanation:

627/4 = 156.75

Answer:

156(3/4)

Step-by-step explanation:

with this your divide.

627/4=156.75

as a mixed numer it would 156(3/4). It is 3/4 because the number ends in .75

Answer:

25

Step-by-step explanation:

150/6

The Unit rate of calories per ounce will be 25 calories per ounce.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Weight of the Greek yogurt container = 6 ounce

Calories per container = 150 calories

The Unit rate of calories per ounce = 150 / 6 = 25

Therefore, the unit rate of calories per ounce will be 25 calories per ounce.

Learn more about the unitary method;

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Answer:

Sample size 'n' = 384

Step-by-step explanation:

Explanation:-

Given margin of error = 0.04

The sample proportion 'p'= 0.80

The margin of error is determined by

                               [tex]M.E = \frac{Z_{\alpha } \sqrt{p(1-p)} }{\sqrt{n} }[/tex]

                             [tex]0.04 = \frac{1.96 \sqrt{0.80(1-0.80)} }{\sqrt{n} }[/tex]

Cross multiplication, we get

                             [tex]\sqrt{n} = \frac{1.96 \sqrt{0.80(1-0.80)} }{0.04 }[/tex]

                             √n = 19.6

Squaring on both sides , we get

                            n = 384.16≅384

Answer:

B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

The term "correlation does not imply causation", simply means that because we can deduce a link between two factors or sets of data, it does not necessarily prove that there is a cause-and-effect relationship between the two variables. In some cases, there could indeed be a cause-and-effect relationship but it cannot be said for certain that this would always be the case.

While correlation shows the linear relationship between two things, causation implies that an event occurs because of another event. So the phrase is actually saying that because two factors are related, it does not mean that it is as a result of a causal factor. It could simply be a coincidence. This occurs because of our effort to seek an explanation for the occurrence of certain events.

Answer: B. The fact that two variables are strongly correlated does not in itself imply a​ cause-and-effect relationship between the variables.

Step-by-step explanation:

Answer:

54 units^2

Step-by-step explanation:

The formula to find the area of a right triangle is bh/2.

Plug the values in.

9*12/2

Multiply.

108/2

Divide.

52

The area is 54 units squared.

Answer: 54u²

Step-by-step explanation:

The area of a triangle is 1/2bh

1/2bh

1/2(12)(9)

(6)(9)

54

Hope it helps <3

approximately 36.633 cm if you use pi = 3.14

approximately 36.6519 cm if you use the calculator's stored value of pi

Work Shown:

L = arc length, r = radius, x = central angle in degrees

L = (x/360)*2*pi*r

L = (300/360)*2*pi*7

L = (35/3)pi .... exact arc length in terms of pi

L = (35/3)*3.14

L = 36.633 .... approximate arc length

Keep in mind that I used pi = 3.14 which isn't that great an approximation for pi. If you want to use more digits of pi, then use your calculator's built in version of it to get (35/3)*pi = 36.6519; of course it will depend on which option your teacher prefers.

Answer:

center : (-2, -2.5)

Step-by-step explanation:

Midpoint point formula says that if there are two points (x1,y1) and (x2,y2) then

coordinate of midpoint is given by

midpoint (x1+x2)/2 , (y1+y2)/2

_______________________________________________

In the problem, we have to find the center of circle of by using the midpoint formula.

Since the circle is circumscribed in square. Its center will be midpoint of either of the diagonal.

To find the center we can take coordinate of any of two diagonal points of square and find midpoint for this and that will be center of circle.

_________________________________________________

1st diagonal pair(4,8) and (-8,-3)

Then midpoint is (4 + -8)/2 , (8+ -3)/2  

midpoint (-2, -2.5)

Thus, center of circle is (-2,-2.5)

we can verify this by using other diagonal pair (-8,8) and (4,-3)

Midpoint in this case can be calculated as

midpoint (-8+4)/2 , (8 + -3)/2

midpoint (-2,-2.5)

Thus, we see that in both cases Midpoint is same and hence center is (-2, -2.5)

Answer:

work is shown and pictured

Answer:

It's Just 1.

Step-by-step explanation:

Check The Guys Work Above.

Answer:

5 : 7 i guess

Step-by-step explanation:

Answer:

26 and 11

Step-by-step explanation:

When your add them you get 37, and when you multiply 26 by two you get 52. 52-11 is 41.

Answer:

Its B and D

Step-by-step explanation:

Because thats where the points intersects/meet.

Answer: 6 / √26

Step-by-step explanation:

Given that f(x, y, z) = xe^y + ye^z + ze^x

so first we compute the gradient vector at (0, 0, 0)

Δf ( x, y, z ) = [ e^y + ze^x,  xe^y + e^z,  ye^z + e^x ]

Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]

Now we were also given that  V = < 4, 3, -1 >

so ║v║ = √ ( 4² + 3² + (-1)² )

║v║ = √ ( 16 + 9 + 1 )

║v║ = √ 26

It must be noted that "v"  is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)

so

⊆ =  ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]

therefore by equation   D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆

D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]

= ( 1×4 + 1×3 -1×1 ) / √26

= (4 + 3 - 1) / √26

= 6 / √26

Answer:

the dimensions of the poster with the smallest area is 36cm by 54cm

Step-by-step explanation:

✓Let us represent the WIDTH of the printed material on the poster as "x"

✓Let us represent the HEIGHT of the printed material on the poster as "y"

✓ The given AREA is given as 864 cm2

Then we have

864 cm2= xy ...................eqn(1)

We can make "y" subject of the formula.

y= 864/x .......................eqn(2)

✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is

(y+18)

✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is

(x+12)

✓Then AREA OF THE TOTAL poster

A= (y+18)(x+12) ...................eqn(3)

Substitute eqn (2) into eqn(3)

A= ( 18+ 864/x)(x+12)

We can now simplify by opening the bracket, as

A=18x +1080 +10368/x

A= 18x +10368/x +1080

Let us find the first derivative of A which is A'

A'= 18-(10368/x²)

If we set A' =0

Then

0= 18- (10368/x²)

18= (10368/x²)

x²= 10368/18

x²= 576

x=√576

x=24

The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum

The value of "y" when x=24 can now be be calculated using eqn(2)

y= 864/x

y= 864/24

y=36cm

✓The total width of the poster= (x+12)

= 24+12=36cm

✓The total height big the poster= (y+18)=36+18=54cm

the dimensions of the poster with the smallest area is 36cm by 54cm

Answer:

The total width of the paper [tex]=36 cm.[/tex]

The total height of the paper [tex]=54cm[/tex]

Step-by-step explanation:

Given information:

Top margin of the paper = 9 [tex]cm\\[/tex]

Bottom margin of the paper = 6 [tex]cm\\[/tex]

Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]

Let, the width of the printed material = [tex]x[/tex]

And the height of the printed material = [tex]y[/tex]

So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]

After including margins;

Width of the paper [tex]= (x+12)[/tex]

Height of the paper [tex]= (y+18)[/tex]

Area [tex](A) = (y+18) (x+12)[/tex]

[tex]A=18x+(10368/x)+1080\\[/tex]

Take first derivative:

[tex]A'= 18- (10368/x^2)[/tex]

When [tex]A'=0[/tex]

Then,

[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]

Now ,when we take second derivative and check if it is positive or not ,

We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.

Hence ,

[tex]x \times y=864\\y=864/24\\y=36\\[/tex]

Now ,

The total width of the paper

[tex]= 24+12\\=36 cm.[/tex]

And , total height of the paper

[tex]=36+18\\=54 cm.[/tex]

For more information visit:

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Answer:

$1387.4

Step-by-step explanation:

Total cost for the computer will be sum of down payments and monthly installments.

____________________________________

Given

down payment = $200

monthly installment value = $98.85

no. of installments = 12

total value of monthly installments = 12*98.95 = $1187.4

Total cost of computer system = $200+  $1187.4 = $1387.4

Answer:

0

Step-by-step explanation:

x ^2/2 + y^2/2 = 0

Then x and y can be 0

0^2/2 + 0^2/2

0/2 +0/2 = 0

0 + 0 = 0

0 = 0

Answer:

Starcraft

a) Probability of losing at most 2 games = 33%

b) Probability of winning at least 4 games = 67%

Step-by-step explanation:

a) To lose 2 out of 6 games, the probability is 2/6 x 100 = 33.333%

b) To win at least 4 games out of 6, the probability is 4/6 x 100 = 66.667%

c) Since Serral is playing 6 games, for her to lose at most 2 of the games is described as a probability in this form 2/6 x 100.  This shows the chance that 2 of the games out of 6 could be lost by Serral.  On the other hand, the probability of Serral winning at least 4 of the 6 games is given as 4/6 x 100.  It implies that there is a chance, 4 out of 6, that Serral would win the game.

Answer:

Increase

Step-by-step explanation:

Precision describes the closeness of estimates from different samples, it refers to the width of the confidence interval and can aso be described as the margin of error. While the confidence level describes the accuracy.

Going for a higher confidence level will bring about a wider confidence interval, and thus lead to a less precise estimate.

Parameterize the square (call it S) by

[tex]\mathbf s(u,v)=2u\,\mathbf x+2v\,\mathbf z[/tex]

with both [tex]u\in[0,1][/tex] and [tex]v\in[0,1][/tex].

Take the normal vector pointing in the positive y direction to be

[tex]\dfrac{\partial\mathbf s}{\partial v}\times\dfrac{\partial\mathbf s}{\partial u}=4\,\mathbf y[/tex]

Then the current is

[tex]\displaystyle\iint_S(y^2+5)\,\mathbf y\cdot4\,\mathbf y\,\mathrm dA=20\int_0^1\int_0^1\mathrm dA=\boxed{20\,\mathrm A}[/tex]

where [tex]y^2+5[/tex] reduces to just 5 because [tex]y=0[/tex] for all points in S.