Answer:
(a) A cross sectional study (b) The parameter can be computed as follows: Non-drinkers who agree exposed to obesity, Drinkers who are exposed or vulnerable to obesity (c) A postie relationship is established from the experiment between drinkers who are exposed to obesity and non drinkers who are exposed to obesity
Step-by-step explanation:
(a) The type of design is refereed to as a cross sectional study
(b) Now, because 50 men are beer drinkers out of 891 men.
Hence we can deduce form this that 500/891 gives us 0.56%.
This suggest that 0.56% men are beer drinkers out of which 325 have obesity, lets take for example 235/500 = 0.65% are exposed to obesity in which 80/ (89-500) = 80/491 = 0.16%
The non drinkers are 0.16% and are not exposed to obesity
Thus,
The parameters to be calculated is stated below:
Non-drinkers who agree exposed to obesityDrinkers who are exposed or vulnerable to obesity(c) The next step is to determine and explain the results.
In this case we can say there is a positive relationship between drinkers and non drinkers, since from the experiment 0.65% are exposed to obesity and 0.16$ non drinkers are exposed to obesity.
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
Find the m∠YAX in the figure below
Answer:
76
Step-by-step explanation:
The two angles are vertical angles so they are equal
3x+7 = 4x-16
Subtract 3x from each side
3x-3x+7 = 4x-3x-16
7 = x-16
Add 16 to each side
7+16 = x-16+16
23 =x
We want YAX
YAX = 3x+7
3*23+7
69+7
76
Write the number that is ten thousand more than
1,853,604,297:
Answer:
The answer would be 1,853,614,297
Please answer this correctly
Answer:
the base is 5 meters long.
Step-by-step explanation:
To find the a missing side when given the area you have to multiply the area by 2 which in this case would be 50 so 50/10 would be 5m which is your answer.
So the right answer is 5m
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
A company sells eggs whose individual weights are normally distributed with a mean of 70\,\text{g}70g70, start text, g, end text and a standard deviation of 2\,\text{g}2g2, start text, g, end text. Suppose that these eggs are sold in packages that each contain 444 eggs that represent an SRS from the population. What is the probability that the mean weight of 444 eggs in a package \bar x x ˉ x, with, \bar, on top is less than 68.5\,\text{g}68.5g68, point, 5, start text, g, end text?
Answer:
6.68% probability that the mean weight is below 68.5g.
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question:
[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]
Probability that the mean weight is below 68.5g:
This is 1 subtracted by the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 70}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that the mean weight is below 68.5g.
Answer:
P(x ∠ 68.5) = 0.07
Step-by-step explanation:
Got it right on khan.
True or False? A prism must have a triangular or rectangular base.
Answer: No
Step-by-step explanation:
Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.
Hope that helped,
-sirswagger21
The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.
Answer:
1651
Step-by-step explanation:
let s say that the price before the increase is x
to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09
and we know that this value is 1800
so
x*1.09=1800
<=>
x = 1800/1.09=1651.376147
to the nearest penny it gives 1651
Answer:
Hello!
Answer: 1651
I hope that was correct. Please let me know, thank you!
Step-by-step explanation:
Some college professors make bound lecture notes available to their classes in an effort to improve teaching effectiveness. A study of business student's opinions of lecture notes. Two groups of students were surveyed - 86 students enrolled in a promotional strategy class that required the purchase of lecture notes, and 35 students enrolled in a sales/retailing elective that did not offer lecture notes. At the end of the semester :"Having a copy of the lecture notes was helpful in understanding the material." Responses were measured on a nine-point semantic difference scale, where 1="strongly disagree" and 9=" strongly agree." A summary of the results is reported in the follow:
Classes Buying Lecture Notes Classes Not Buying Lecture Notes
n1=86 n2=35
X1=8.48 X2=7.80
S21=.94 S22=2.99
a. Describe the two populations involved in the comparison.
b. Do the samples provides sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students? Test using α=.01
c. Construct a 99% confidence interval for (μ1-μ2). Interpret the result.
d. Would a 95% confidence interval for (μ1-μ2) be narrow or wider than the one you found in part c? Why?
Answer:
Step-by-step explanation:
a) The number of students sampled in both populations are large. We can assume that the populations are normally distributed. The populations are also independent.
b) This is a test of 2 independent groups. Let μ1 be the mean responses of students buying lecture notes and μ2 be the mean responses of students not buying lecture notes.
The random variable is μ1 - μ2 = difference in the mean responses of students buying lecture notes and the mean responses of students not buying lecture notes.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
x1 = 8.48
x2 = 7.8
s1 = 0.94
s2 = 2.99
n1 = 86
n2 = 35
t = (8.48 - 7.8)/√(0.94²/86 + 2.99²/35)
t = 1.32
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [0.94²/86 + 2.99²/35]²/[(1/86 - 1)(0.94²/86)² + (1/35 - 1)(2.99²/35)²] = 0.0706/0.00192021883
df = 37
We would determine the probability value from the t test calculator. It becomes
p value = 0.195
c) Since alpha, 0.01 < than the p value, 0.195, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, the samples do not provide sufficient evidence to conclude that there is a difference in the mean responses of the two groups of the students.
d) The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 99% confidence interval, the z score is 1.2.58. This is determined from the normal distribution table.
x1 - x2 = 8.48 - 7.8 = 0.68
z√(s1²/n1 + s2²/n2) = 2.58√(0.94²/86 + 2.99²/35) = 1.33
The confidence interval is
0.68 ± 1.33
The upper boundary for the confidence interval is
0.68 + 1.01 = 2.01
The lower boundary for the confidence interval is
0.68 - 1.33 = - 0.65
We are confident that the difference in population means responses between the students buying lecture notes and the students not buying lecture notes is between - 0.65 and 2.01
d) For a 95% confidence interval, the z score is 1.96.
z√(s1²/n1 + s2²/n2) = 1.96√(0.94²/86 + 2.99²/35) = 1.01
The confidence interval is
0.68 ± 1.01
The upper boundary for the confidence interval is
0.68 + 1.01 = 1.69
The lower boundary for the confidence interval is
0.68 - 1.01 = - 0.33
Therefore, a 95% confidence interval for (μ1-μ2) would be narrower. This is seen in the values in both scenarios.
7. Find all geometric sequences such that the sum of the first two terms is 24 and the sum of the first
three terms is 26.
Answer:
Step-by-step explanation:
Let the first term is n, then the second term must be an where a is a common ratio, and the third term is a^2 n
so, n + an = 24
n + an + a^2 n = 26
solve for a, then solve for n
A magazine asks its readers to complete a survey on their favorite music and tv celebrities. Classify this sample
Answer:
All the elements in the sample share a common characteristic. All of them read the magazine, so we may have a biased sample. And we also have the bias of the fact that only the volunteers will respond to this survey, so this is a biased sample.
This type of sample is usually called convenience sampling, where the elements in the sample are the most readily available (and what is most readily available for a magazine than its own readers?)
Then the type of sample is a convenience sample and a biased sample.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
-1, 1
13, 15
Step-by-step explanation:
x and x+2 are the integers
x*(x+2)= 7(x+x+2) -1x²+2x= 14x+14-1x² - 12x -13= 0Roots of the quadratic equation are: -1 and 13.
So the integers pairs are: -1, 1 and 13, 15
A and b are similar shapes. B is an enlargement of a with scale factor 1.5 Work out the value of x, h and w
Answer:
x = 54°
h = 7.5cm
w= 6cm
Step-by-step explanation:
Find attached the diagrams as found at Maths made easy.
Similar shapes have same shapes but different sizes.
When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.
B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A
To determine the value of x, h and w, let's look at the relationship of A and B.
h = 1.5 × 5cm
h = 7.5cm
9cm = 1.5 × w
w = 9cm/1.5
w= 6cm
Since the angles do not change when a shape is enlarged, the value of x = 54°
x = 54°
Find the volume of the cone below.
Answer:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
Step-by-step explanation:
For this case we know that the volume of the cone is given by:
[tex] V =\frac{1}{3} \pi r^2 h[/tex]
For this case we know that the radius is r=7cm and the height is h =11cm. And replacing we got:
[tex] V=\frac{1}{3} \pi (7cm)^2 (11cm)= \frac{1}{3} \pi (49cm^2) (11 cm)=\frac{539}{3} \pi cm^3[/tex]
And the best option would be:
[tex] V = \frac{539}{3} \pi cm^3 [/tex]
If the point (7,6) lies on the graph of y = (x - 5)2 + k, where k is some constant, which other point must also
lie on the same graph?
Answer:
k = -4 (0, -14) also lies on the graph
Step-by-step explanation:
6 = (7 - 2)2 + k
6 = 10 + k
-4 = k
y = (0 - 5)2 - 4, y = -14
Solve for the unknown value
X=______Degrees
Answer:
Step-by-step explanation:
_______________________________
Hey!!
Solution,
X+61+42=180[ sum of angle in triangle]
or,X+103=180
or,X=180-103
X=77°
So the value of X is 77°
Hope it helps..
Good luck on your assignment
____________________________
Explain why the sum of the angle measures in any
triangle is 180º.
Answer: I think In short, the interior angles are all the angles within the bounds of the triangle. ... If you think about it, you'll see that when you add any of the interior angles of a triangle to its neighboring exterior angle, you always get 180—a straight line, A square has 4 90 degree angles so it adds to 360, think about how triangles having half the area of a square, just like how 180 is half of 360
hope this helped
Alguien me puede ayudar con en esto por favor !!!
Answer:
y=cosx
Step-by-step explanation:
cosx has a domain of all real numbers
The table represents a linear equation.
Which equation correctly uses point (-2, -6) to write the
equation of this line in point-slope form?
х
-4
-2
6
10
y
-11
-6
14
24
y-6 = {(x - 2)
• y-6 = (x - 2)
y +6 = } (x + 2)
y+6= {(x + 2)
Answer:
see below
Step-by-step explanation:
Considering the last two table entries, we can find the slope of the line to be ...
Δy/Δx = (24 -14)/(10 -6) = 10/4 = 5/2
The point-slope form of the equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
For (h, k) = (-2, -6) and m = 5/2, this is ...
y -(-6) = 5/2(x -(-2))
y +6 = 5/2(x +2) . . . . . matches the last choice
Answer:
d is the right choice
Step-by-step explanation:
Aunit cube is shown.
Select the true statements
A unit cube can have a length of 1 inch, a width of 1 inch, and a height of 2 inches
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have
the same volume
Aunit cube can be used to measure the weight of a rectangular prism.
A unit cube can be used to measure the volume of a rectangular prism.
Aunit cube can have a length of 4 feet, a width of 4 feet, and a height of 4 feet.
A unit cube can be used to determine the angle measures of a rectangular prism,
4 of 10 Answered
Session Timer: 11:03
Session Score: 259
Answer:
A unit cube has one cubic unit of volume.
Another unit cube with the same length, width and height as the unit cube shown would have the same volume
Step-by-step explanation:
A cube is a shape formed from the combination of a square.
A cube has equal sides.
But a unit cube has equal sides and equal volume to be equal to one, i.e unity.
What is the graph of 3x+5y=15
Answer: y= -15 - 3x/5 is the answer.
Step-by-step explanation:
Answer:
The second graph
Step-by-step explanation:
the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the youngest
Answer:
The age difference between oldest the youngest is of 48 years.
Step-by-step explanation:
We can solve this question using a system of equations.
I am going to say that:
Kissi's age is x.
Esinam's age is y.
Lariba's age is z.
The ratio of the ages of Kissi and Esinam is 3:5
This means that [tex]\frac{x}{y} = \frac{3}{5}[/tex], so [tex]5x = 3y[/tex]
That of Esinam and Lariba is 3:5
This means that [tex]\frac{y}{z} = \frac{3}{5}[/tex], so[tex]5y = 3z[/tex]
The sum of the ages of all 3 is 147 years
This means that [tex]x + y + z = 147[/tex]
What is the age difference between oldest the youngest
z is the oldest
x is the youngest.
First i will find y.
We have that, from the equations above: [tex]x = \frac{3y}{5}[/tex] and [tex]z = \frac{5y}{3}[/tex]
So
[tex]x + y + z = 147[/tex]
[tex]\frac{3y}{5} + y + \frac{5y}{3} = 147[/tex]
The lesser common multiple between 5 and 3 is 15. So
[tex]\frac{3*3y + 15*y + 5*5y}{15} = 147[/tex]
[tex]49y = 147*15[/tex]
[tex]y = \frac{147*15}{49}[/tex]
[tex]y = 45[/tex]
Youngest:
[tex]x = \frac{3y}{5} = \frac{3*45}{5} = 27[/tex]
Oldest:
[tex]z = \frac{5y}{3} = \frac{5*45}{3} = 75[/tex]
Difference:
75 - 27 = 48
The age difference between oldest the youngest is of 48 years.
Solve sin2x=-1/2 on the interval 0≤ angle≤360°
Answer:
x=135
Step-by-step explanation:
We know that sin(270) = -1/2
So 2x = 270
x = 135
A Pew Research study of 4726 randomly selected U.S. adults regarding scientific human enhancements, found that approximately 69% of the sample stated that they were worried about brain chip implants being used for improving cognitive abilities.
Required:
a. Show that the necessary conditions (Randomization Condition, 10% Condition, Sample Size Condition) are satisfied to construct a confidence interval. Briefly explain how each condition is satisfied.
b. Find the 90% confidence interval for the proportion of all U.S. adults that are worried about brain chip implants used for improving cognitive abilities.
(To show your work: Write down what values you are entering into the confidence interval calculator.)
c. Briefly describe the meaning of your interval from part (b).
Answer:
a)Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
b) The 90% confidence interval for the population proportion is (0.68, 0.70).
Step-by-step explanation:
a) Evaluating the necessary conditions:
Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]
b) We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.69.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]
The 90% confidence interval for the population proportion is (0.68, 0.70).
The circular area covered by a cell phone tower can be represented by the expression 225π miles2. What is the approximate length of the diameter of this circular area
Answer:
The length of the diameter of this circular area is of 30 miles.
Step-by-step explanation:
The area of a circular region can be represented by the following equation:
[tex]A = \pi r^{2}[/tex]
In which r is the radius. The diameter is twice the radius.
In this question:
[tex]A = 225\pi[/tex]
So
[tex]A = \pi r^{2}[/tex]
[tex]225\pi = \pi r^{2}[/tex]
[tex]r^{2} = 225[/tex]
[tex]r = \pm \sqrt{225}[/tex]
The radius is a positive measure, so
[tex]r = 15[/tex]
Area in squared miles, so the radius in miles.
What is the approximate length of the diameter of this circular area
D = 2r = 2*15 = 30 miles
The length of the diameter of this circular area is of 30 miles.
Hypothesis Test for Two Populations including:t-Test for μ1-μ1t-Test for μdF-Test forWe are interested in determining whether or not the variances of the sales at two small grocery stores are equal. A sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the followingStore A Store BnA=21 nB=16SA=28.284 SB=20Which of the following is critical values of F at 95% confidence?A. a and dB. 2.57C. 0.3891D. 0.3623E. 2.76
Answer:
The critical values of F at 95% confidence are 0.359 and 2.788.
Step-by-step explanation:
We are given that a sample of 21 days of sales at Store A and a sample of 16 days of sales at Store B indicated the following:
Store A Store B
nA = 21 nB = 16
SA = 28.284 SB = 20
And we are interested in determining whether or not the variances of the sales at two small grocery stores are equal.
AS we know that when we are interested in variances of two samples, we use F-test for doing hypothesis testing.
The test statistics for F-test is = [tex]\frac{S_A^{2} }{S_B^{2} } \times \frac{\sigma_B^{2} }{\sigma_A^{2} }[/tex] ~ [tex]F__n_A_-_1,_ n_B_-_1[/tex]
where, [tex]S_A[/tex] and [tex]S_B[/tex] are sample standard deviations.
Now, the critical values of F at 2.5% (because two-tailed test) level of significance from F-table at degrees of freedom (21 - 1, 16 - 1) = (20, 15) are given as;
2.788 for right-part and 0.359 for the left-part.
Simplify -2(-5) - 7 + 1(-3)
Answer:
Step-by-step explanation:
BRUH YOU STUPID
Answer:
0
[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]
hord
12 cm
5 cm
Resu
5 cm
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the
height of the prism is placed inside the prism, as shown in the figure.
SUME
The volume of the space outside the pyramid but inside the prism is
cubic centimeters,
Answer:
The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.
Step-by-step explanation:
To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.
The prism and pyramid's bases is 25 cm²
The pyramid's height is 12÷2 or 6 cm
The volume formula for a prism is l×w×h
The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h
The area of the prism is 5×5×12 or 300 cm³
The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³
300 cm³-75 cm³=225 cm³
The volume outside the pyramid but inside the prism is 225 cm³.
an=(−3n+4)n(−4n−8)n In this problem you must attempt to use the Root Test to decide whether the series converges. Compute L=limn→[infinity]|an|−−−√n Enter the numerical value of the limit L if it converges, INF if it diverges to infinity, MINF if it diverges to negative infinity, or DIV if it diverges but not to infinity or negative infinity. L= Which of the following statements is true? A. The Root Test says that the series converges absolutely. B. The Root Test says that the series diverges. C. The Root Test says that the series converges conditionally. D. The Root Test is inconclusive, but the series converges absolutely by another test or tests. E. The Root Test is inconclusive, but the series diverges by another test or tests. F. The Root Test is inconclusive, but the series converges conditionally by another test or tests. Enter the letter for your choice here:
Answer:
L = 3/4
Option A. The Root Test says that the series converges absolutely.
Step-by-step explanation:
By using the root test equation given in the question. L = 3/4
Since L < 1, the series converges absolutely.
For clarity of expression, the detailed calculation is contained in the attached file. Check the file attached for the complete calculation to this question.
someone pls pls pls help me
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A, 2/3C, -8D, 4E, -1/68. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46