Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
[tex]m = mo e^{kt}[/tex]
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]
1) Prepare a post merger financial position for METRO using the pooling of interest method.
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
Lolz please help me I would gladly appreciate it
Pentagon has sum of 540°
Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00
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
Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
Question 5 Multiple Choice Worth 1 points)
(01.03 MC)
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point
the cost of both ski slopes is the same.
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 (●'◡'●)
One number is 1/4 of another number. The sum of the two numbers is 5. Find the two numbers. Use a comma to separate your answer
Answer: 1, 4
Step-by-step explanation:
Number #1 = xNumber #2 = [tex]\frac{1}{4} x[/tex][tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]
Number #1 = x = 4Number #2 = [tex]\frac{1}{4} x[/tex] = [tex]\frac{1}{4} *4=\frac{4}{4} =1[/tex]If the angles (4x + 4)° and (6x – 4)° are the supplementary angles, find the value of x.
Answer:
18
Step-by-step explanation:
Supplementary angles means sum of angles is 180.
4x + 4 + 6x - 4 = 180
4x + 6x + 4 - 4 = 180
10x = 180
x = 180 / 10
x = 18
Answer:
x=18 degree
Step-by-step explanation:
If they are supplementary angles, then their sum = 180 degree
4x+4 + 6x-4 =180
4x+6x + 4-4 = 180
10x = 180
x=180/10
x=18
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answer:
A FORMULA is an expression that uses variables to state a rule.
Coliform bacteria are randomly distributed in a river at an average concentration of 1 per 20cc of water. What is the variance of the number of Coliform bacteria in a sample of 40cc of water
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]
A box contains 5 white balls, 3 black balls, and 2 red balls.A-What is the probability of drawing a white ball?B- How many white balls must be added to the box so that the probability of drawing a white ball is 3/4?C-How many black balls must be added to the original assortment so that the probability of drawing a white ball is 1/4?
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
The distribution of the number of apples trees a farmer can plant each day is bell-shaped and has a mean of 62 and a standard deviation of 8. Use the empirical rule to help you answer the following. What is the approximate percentage of trees planted between 38 and 68
Answer:
The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 62, standard deviation of 8.
What is the approximate percentage of trees planted between 38 and 86?
38 = 62 - 3*8
86 = 62 + 3*8
So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Plz help I’ll mark u
Answer:
SAS=side angle side
there is two side and one angle
Answer:
SAS theorem
explanation:
please help i am stuck on this assignment
Answer:
answer
x = -13/ 15, 0
Step-by-step explanation:
15x^2 + 13 x = 0
or, x(15x + 13) = 0
either, x = 0
or, 15x + 13 = 0
x = -13/15
Answer:
The answer should be C...............
imma sorry if I'm wrong
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Answer:
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 46% of politicians are lawyers.
This means that [tex]p = 0.46[/tex]
Sample of size 662
This means that [tex]n = 662[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.46[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]
What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?
p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So
X = 0.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a p-value of 0.9803
X = 0.42
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]
[tex]Z = -2.06[/tex]
[tex]Z = -2.06[/tex] has a p-value of 0.0197
0.9803 - 0.0197 = 0.9606
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Please help!! How do I solve for x?
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
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
Can you help me answer this question? Screenshot is added.
9514 1404 393
Answer:
(c)
Step-by-step explanation:
[tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answer:
[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]
Substitute for x in equation (a) :
[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]
Substitute for y in equation (b) :
[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]
2x+4y =8
x=3y-6 ——> x–3y=–6
x–3y = – 6 ] ×(–2) ——> –2x +6y=12
2x+4y=8
–2x+6y =12
__o_o____
0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2
2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0
(x,y) —> (0,2)
Allie rode her bike up a hill at an average speed of 12 feet/second. She then rode back down the hill at an average speed of 60 feet/second. The entire trip took her 2 minutes. What is the total distance she traveled. [Hint: use t = time traveling down the hill]
Answer:
The total distance Allie traveled was 0.81 miles.
Step-by-step explanation:
Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:
12 + 60 = 72
72 x 60 = 4320
1000 feet = 0.189394 miles
4320 feet = 0.8181818 miles
Therefore, the total distance Allie traveled was 0.81 miles.
what is the difference between the products of the digits in 425 and the sum of the digits in the numeral 92784
Answer: 10
Step-by-step explanation:
4 x 2 x 5 = 40
9 + 2 + 7 + 8 + 4 = 30
40 - 30 = 10
= 10
which of the following is a geometric sequence -3,3,-3,3... 11,16,21,26, ... 6, 13, 19, 24, ... -2,6,14,22, ...
Answer:
p and q are two numbers.whrite down an expression of
On dividing 12x³ by 4x the quotient is …..
Answer:
12x^3 is equivalent to
12x*12x*12x which if we multiply is
1728x
we divide by 4x
1728x divided by 4x=432x
Hope This Helps!!!
Answer:
3x^2
Step-by-step explanation:
when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2
Can someone please help me, with part B
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
solve the inequality x(x+6) >16
please show steps and interval notation!
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)
Which of the following equations describes this graph?
A. y=(x-1)^2-
B. y=(x-3)^2+2
C. y=(x+1)^2-2
D. y=(x-2)^2+3
Answer:
The choose (A)
y=(x-1)²-2
SOMEONE PLS HELP ME I WILL MAKE U BRAINLIST ! In a survey sample of 83 respondents, about 30.1 percent of the samplework less than 40 hours per week. What is the estimated standard error for the group of respondents who work 40 hours or more per week?
(*round to two decimal places)
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
What do you know to be true about the values of p and ?
p"
q
601
454
45
A. p> 9
B. p<9
C. p= 9
D. Can't be determined
A random sample of 16 values is drawn from a mound-shaped and symmetric distribution. The sample mean is 12 and the sample standard deviation is 2. Use a level of significance of 0.05 to conduct a two-tailed test of the claim that the population mean is 11.5.
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
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person. Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents. Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
A. 8x = amount of broccoli needed
B. 4 people; 32÷8=4
Step-by-step explanation:
A. the variable (x) represents the amount of people.
B. 32 ounces divided by 8 ounces is enough for four people.
find 9 rational no. between 8/7 and 17/10.
Answer:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
Step-by-step explanation:
We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]
We make the denominators of both fractions same. So,
[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]
and
[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]
The rational number are:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
