I need help with these questions

Answer:

Metro and Medec

METRO

Post-merger Financial Position, using the pooling of interest method:

Pre-merger Financial Positions:

                           Metro (RM ‘000)

Assets  

Current assets                          120

Fixed assets                             830

Total assets                             950

Liabilities and Equities  

Current liabilities                      40

Long term debt                      200

Common stock (RM1 par)      480

Capital surplus                       120

Retained earnings                  110

Total liabilities and equity    950

Earnings available to

common stockholders            230

Common Dividends                  150

Addition to Retained Earnings  80

Step-by-step explanation:

Pre-merger Financial Positions:

                           Metro (RM ‘000)    Medec(RM ‘000)

Assets  

Current assets                          50                     70

Fixed assets                           650                    180

Total assets                            700                   250

Liabilities and Equities  

Current liabilities                      30                     10

Long term debt                       140                    60

Common stock (RM1 par)      400                    80

Capital surplus                         50                    70

Retained earnings                   80                    30

Total liabilities and equity     700                 250

Earnings available to

common stockholders            100                  130

Common Dividends                  50                  100

Addition to Retained Earnings 50                   30

Exchange ratio = 1:2

Explanation:

It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.

We can have the responses along the rows and the party affiliation along the columns, or vice versa.

See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).

As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.

A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.

As per the given information in the question,

A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.

To know more about Pie charts:

https://brainly.com/question/24207368

#SPJ5

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

Answer:

x > 2, x < -8

Interval notation:

( -infinity, -8) U (2, infinity)

Step-by-step explanation:

x(x+6) > 16

distribute x into x+6, multiply

x^2 + 6x > 16

bring 16 to left side, subtract

x^2 + 6x - 16 > 0

factors of -16 that add to +6 is -2 and +8

(x - 2)(x + 8) > 0

solve for x:

x < -8,  x > 2

Interval notation:

( -infinity, -8) U (2, infinity)

The line in the middle is half the length of the line on the outside. Multiply the middle line by 2 and set it equal to the outside line.

2(x-3) = x + 6

Simplify:

2x -6 p x + 6

Add 6 to both sides

2x = x + 12

Subtract x from both sides:

X = 12

The answer is B) 12

Answer:

Answer = √(0.301 × 0.699 / 83) ≈ 0.050

A 68 percent confidence interval for the proportion of persons who work less than 40 hours per week is (0.251, 0.351), or equivalently (25.1%, 35.1%)

Step-by-step explanation:

√(0.301 × 0.699 / 83) ≈ 0.050

We have a large sample size of n = 83 respondents. Let p be the true proportion of persons who work less than 40 hours per week. A point estimate of p is  because about 30.1 percent of the sample work less than 40 hours per week. We can estimate the standard deviation of  as . A  confidence interval is given by , then, a 68% confidence interval is , i.e., , i.e., (0.251, 0.351).  is the value that satisfies that there is an area of 0.16 above this and under the standard normal curve.The standard error for a proportion is √(pq/n), where q=1−p.

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

[tex]a = 2i + j -3k[/tex]

[tex]b = 3i - 2j -k[/tex]

Required

The angle between them

The cosine of the angle between them is:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

First, calculate a.b

[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]

Multiply the coefficients of like terms

[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]

[tex]a \cdot b =7[/tex]

Next, calculate |a| and |b|

[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]

[tex]|a| = \sqrt{14[/tex]

[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]

[tex]|b| = \sqrt{14}[/tex]

Recall that:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

This gives:

[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]

[tex]\cos(\theta) = \frac{7}{14}[/tex]

[tex]\cos(\theta) = 0.5[/tex]

Take arccos of both sides

[tex]\theta =\cos^{-1}(0.5)[/tex]

[tex]\theta =60^o[/tex]

Pentagon has sum of 540°

Answer:

A. (1, -5), (2, -1), (-1, 7)

Step-by-step explanation:

Reflecting a function over the x-axis:

When a function is reflected over the x-axis, the x-value stays the same, while y changes the signal, so the transformation rule is:

[tex](x,y) \rightarrow (x,-y)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,5) \rightarrow (1,-5)[/tex]

[tex](2,1) \rightarrow (2,-1)[/tex]

[tex](-1,-7) \rightarrow (-1,-(-7)) = (-1, 7)[/tex]

Thus the correct answer is given by option a.

Answer:

It is letter A and please give me brainliest

Step-by-step explanation:

Answer:

p and q are two numbers.whrite down an expression of

9514 1404 393

Answer:

  no

Step-by-step explanation:

We assume you are concerned with the cubic

  x³ -9x² -14x +24

Its factors are all irrational, as shown in the attached graph. x-3 is not a factor.

__

x-3 is a factor if the expression evaluates to zero when x=3. Here, it does not.

  ((x -9)x -14)x +24 for x=3 is ...

  ((3 -9)(3) -14)(3) +24 = (-18 -14)(3) +24 = -96 +24 = -72

The remainder from division by x-3 is not zero, so x-3 is not a factor.

Answer:

The responses to these question can be defined as follows:

Step-by-step explanation:

For point a:

[tex]\to P(1) = 0.73[/tex]

For point b:

[tex]\to P(2\ or\ 3) = P(2) + P(3)[/tex]

                    [tex]= 0.27 \times 0.73 + 0.27\times 0.27\times0.73\\\\=0.1971+0.1971\times 0.27\\\\=0.1971+0.053217\\\\=0.250317[/tex]

Answer:

0.001831055

Step-by-step explanation:

Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 14)

P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2

               = 120 * 0.5^14 *(1-0.5)^2

= 0.001831055

Answer:

[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]

The graph is shown below.

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

Explanation:

Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.

This is close to 5x-7, except we're off by 2 units.

In other words,

5x-7 = (5x-5)-2

since -7 = -5-2

Based on that, we can then say,

[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]

This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).

-------------------------

Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]

We can see that

The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.

The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.

The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.

The graph is shown below. Some points of interest on the hyperbola are

Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.

Answer:

[tex]Var = 1.9[/tex]

Step-by-step explanation:

Given

[tex]p = \frac{1}{20}[/tex]  i.e. 1 per 20cc of water

[tex]n = 40[/tex] -- sample size

Required

The variance

This is calculated using:

[tex]Var = np(1 - p)[/tex]

So, we have:

[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]

[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]

[tex]Var = 2 * \frac{19}{20}[/tex]

[tex]Var = \frac{38}{20}[/tex]

[tex]Var = 1.9[/tex]

Answer:

Step-by-step explanation:

If the triangles given in the picture are similar,

ΔVUT ~ ΔVLM

By the property of similarity of two triangles, their corresponding sides will be proportional.

[tex]\frac{TV}{VM}= \frac{VL}{VU}[/tex]

[tex]\frac{49}{14}=\frac{28}{8}[/tex]

[tex]\frac{7}{2}=\frac{7}{2}[/tex]

True.

Therefore, ΔVUT and ΔVLM will be similar.

Answer:

The answer is 40 chocolates in the box in total

Step-by-step explanation:

let y = x+5/4

Interchanging x and y , we get ;

x = y+5/4

or, 4x = y+5

or, 4x-5 = y

or, g(x) -1 = 4x-5

Answer:

In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:

4x-5

Answer:

Solution given:

B.g(x)=[tex]\frac{x+5}{4}[/tex]

let

g(x)=y

y=[tex]\frac{x+5}{4}[/tex]

Interchanging role of x and y

we get:

x=[tex]\frac{y+5}{4}[/tex]

doing crisscrossed multiplication

4x=y+5

y=4x-5

So

g-¹(x)=4x-5

Answer:

SAS=side angle side

there is two side and one angle

Answer:

SAS theorem

explanation:

Answer:

0.25

Step-by-step explanation:

Given that :

Charity raffle price = $1000

Amount of ticket sold = 4000

Only one winner is to be selected ;

Point ticket buyer is expected to break even :

Probability of winning = 1 / number of ticket sold = 1 / 4000 = 0.00025

P(winning) * raffle price = 0.00025 * 1000 = 0.25

Answer:

A FORMULA is an expression that uses variables to state a rule.

Answer:

we conclude that population mean is not 11.5

Step-by-step explanation:

The hypothesis :

H0 : μ = 11.5

H1 : μ ≠ 11.5

The test statistic :

(xbar - μ) ÷ (s/√(n))

Test statistic = (12 - 11.5) ÷ (2/√(16))

Test statistic = (0.5) ÷ (2 ÷ 4)

Test statistic = 0.5 / 0.5

Test statistic = 1

The Pvalue from test statistic value, df = n - 1 = 16 - 1 = 15

Pvalue = 0.333

Pvalue > α ; we fail to reject the null ; Hence, we conclude that population mean is not 11.5

↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]

[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Step-by-step explanation:

hope it is h helpful to you

Answer:

C

Step-by-step explanation: just C-

Answer: Its not c

Step-by-step explanation: It is A

Answer:

Bunny Hill Ski Resort:

y = 10x + 35

Diamond Ski Resort:

y = 5x + 40

Point where the cost is the same:

(1, 45)

Step-by-step explanation:

The question tells us that:

$35 and $40 are initial fees

$10 and $5 are hourly fees

This means that x and y will equal:

x = number of hours

y = total cost of ski rental after a number of hours

So we can form these 2 equations:

y = 10x + 35

y = 5x + 40

Now we are going to use System of Equations to find what point the cost of both ski slopes is the same.

Because they both equal y, we can set the equations equal to each other:

10x + 35 = 5x + 40

And we use basic algebra to solve for x:

10x + 35 = 5x + 40

(subtract 5x from both sides)

5x + 35 = 40

(subtract 35 from both sides)

5x = 5

(divide both sides by 5)

x = 1

Remember, x equals the number of hours.

That means when your rent out the skis for 1 hour, you will get the same price of $45 (you find the price by plugging in 1 into both of the equations)

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

Given:

Substitute x= -3:

Answer: 10

Step-by-step explanation:

4 x 2 x 5 = 40

9 + 2 + 7 + 8 + 4 = 30

40 - 30 = 10

= 10

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Step-by-step explanation:

6/10 > _ > 1/3

3/5 > _ > 1/3

½(⅗+⅓)

½(9+5/15)

½(14/5)

=7/15

Answer:

7/15

Step-by-step explanation: 10 and 3 LCM is 30

6/10 x 3 =18/30 and 1/3x 10= 10/30

10/30 and 18/30 average is 14/30 which simplified is 7/15

The answer is 7/15

Hope it helps