Based on the sample data and the hypothesis test, Bill McWaffle should not take a public position on the issue of gambling legalization.
Using the normal approximation, we can calculate the test statistic, which follows a standard normal distribution under the null hypothesis. The test statistic is given by:
Z = (p - p₀) / √(p₀(1 - p₀) / n),
where p₀ represents the proportion specified under the null hypothesis, which is 0.65 in this case.
Substituting the values into the formula, we have:
Z = (0.34 - 0.65) / √(0.65(1 - 0.65) / 200) ≈ -9.91.
Looking up the z-value in a standard normal distribution table or using statistical software, we find that the critical value for a one-sided 99 percent confidence level is approximately 2.33.
Since the test statistic (Z = -9.91) is much smaller (in absolute value) than the critical value (2.33), we have strong evidence to reject the null hypothesis. This means that the proportion of constituents in favor of legalization is significantly less than 65 percent.
This decision ensures that he does not risk alienating a large segment of voters, as the data does not provide sufficient evidence to support a clear majority opinion of at least 65 percent in favor of legalization.
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In circle
�
H,
�
�
=
6
HI=6 and the length of
�
�
⌢
=
4
�
IJ
⌢
=4π. Find m
∠
�
�
�
∠IHJ
In circle HI=6 and the length of IJ =4π. The measure of ∠IHJ is 60 degrees.
In a circle, the measure of an angle formed by a chord and a tangent at the point of contact is half the measure of the intercepted arc.
Given that IJ is a chord of the circle, and its length is 4π, we can determine the measure of the intercepted arc using the formula:
Arc length = (central angle / 360 degrees) * circumference of the circle
The circumference of the circle is 2π times the radius, and the radius is half the diameter. Since HI is given as 6, the diameter is 2 * 6 = 12. Therefore, the circumference is 2π * 6 = 12π.
Now, we can calculate the measure of the intercepted arc:
4π = (central angle / 360 degrees) * 12π
Simplifying the equation, we get:
4 = (central angle / 360)
To find the measure of the angle IHJ, we solve for the central angle:
central angle = 4 * 360 = 1440 degrees
Since the measure of ∠IHJ is half the measure of the intercepted arc, ∠IHJ = 1440 / 2 = 720 degrees.
However, angles in a circle are measured from 0 to 360 degrees, so we need to find the equivalent angle within this range:
720 - 360 = 360 degrees
Therefore, the measure of ∠IHJ is 360 degrees, or equivalently, 60 degrees.
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Toasters again In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
The number of trials is n = 10,000 and we want to find the probability of having fewer than 450 faulty toasters, which is equivalent to finding the probability of having 0, 1, 2, ..., 449 faulty toasters.
Using a binomial distribution calculator or software, we can find that the probability of having 0 faulty toasters is about 0.0379, the probability of having 1 faulty toaster is about 0.1584, the probability of having 2 faulty toasters is about 0.3095, and so on. If we add up all these probabilities for 0 to 449 faulty toasters, we get a total probability of about 0.9999.
Therefore, the probability of having fewer than 450 faulty toasters is about 0.9999 or 99.99%. This means that it is highly likely that fewer than 450 toasters need to be returned in a batch of 10,000.
I'll provide a general explanation using the given terms:
1. First, determine the defect or return rate. Let's assume it is given as "p" (e.g., 0.05 would represent a 5% defect rate).
2. Next, find the expected number of defective toasters in the batch by multiplying the total number of toasters (10,000) by the defect rate "p": Expected_Defects = 10,000 * p.
3. Then, use a statistical method, such as the binomial distribution or normal approximation, to calculate the probability of having fewer than 450 defective toasters. This will involve finding the cumulative probability (sum of probabilities) for 0 to 449 defective toasters.
4. Finally, the resulting probability will represent the chances that fewer than 450 toasters need to be returned in the batch of 10,000.
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A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively.
a. Draw the density function.
b. Determine P(35 < X < 45).
c. Draw the density function including the calculation of the probability in part (b).
Use the Standard Normal Distribution to answer the
following problems:
A normal distribution has a mean of 30 and a standard
deviation of 4. Find the probability that a randomly
selected x-value from the distribution is in the given
interval. Represent your answer as a decimal to the
nearest ten-thousandth place.
Between 24 and 32
Between 31 and 37
Between 20 and 35
At least 27
At least 19
At most 29
The probabilities of the normal distribution are:
Between 24 and 32 is 0.7745.
Between 31 and 37 is 0.2580.
Between 20 and 35 is 0.8962.
At least 27 is 0.7734.
At least 19 is 0.9970.
At most 29 is 0.4013.
We have,
To find the probabilities using the standard normal distribution, we need to standardize the given values using the formula z = (x - μ) / σ, where z is the standardized value, x is the given value, μ is the mean, and σ is the standard deviation.
Between 24 and 32:
Standardized value for 24: z = (24 - 30) / 4 = -1.5
Standardized value for 32: z = (32 - 30) / 4 = 0.5
Using a standard normal distribution table or a calculator, we can find the corresponding probabilities:
P(24 < x < 32) = P(-1.5 < z < 0.5)
Between 31 and 37:
Standardized value for 31: z = (31 - 30) / 4 = 0.25
Standardized value for 37: z = (37 - 30) / 4 = 1.75
P(31 < x < 37) = P(0.25 < z < 1.75)
Between 20 and 35:
Standardized value for 20: z = (20 - 30) / 4 = -2.5
Standardized value for 35: z = (35 - 30) / 4 = 1.25
P(20 < x < 35) = P(-2.5 < z < 1.25)
At least 27:
Standardized value for 27: z = (27 - 30) / 4 = -0.75
P(x ≥ 27) = P(z ≥ -0.75)
At least 19:
Standardized value for 19: z = (19 - 30) / 4 = -2.75
P(x ≥ 19) = P(z ≥ -2.75)
At most 29:
Standardized value for 29: z = (29 - 30) / 4 = -0.25
P(x ≤ 29) = P(z ≤ -0.25)
Using a standard normal distribution table or a calculator, you can look up the probabilities corresponding to the standardized values and find the answers to each of the above expressions.
So,
Between 24 and 32:
P(24 < x < 32) = P(-1.5 < z < 0.5) ≈ 0.7745
Between 31 and 37:
P(31 < x < 37) = P(0.25 < z < 1.75) ≈ 0.2580
Between 20 and 35:
P(20 < x < 35) = P(-2.5 < z < 1.25) ≈ 0.8962
At least 27:
P(x ≥ 27) = P(z ≥ -0.75) ≈ 0.7734
At least 19:
P(x ≥ 19) = P(z ≥ -2.75) ≈ 0.9970
At most 29:
P(x ≤ 29) = P(z ≤ -0.25) ≈ 0.4013
Thus,
The probabilities of the normal distribution are:
Between 24 and 32 is 0.7745.
Between 31 and 37 is 0.2580.
Between 20 and 35 is 0.8962.
At least 27 is 0.7734.
At least 19 is 0.9970.
At most 29 is 0.4013.
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what is the cross section formed by a plane that contains a vertical line of symmetry for a tetrahedron
The cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.
What is tetrahedron?A tetrahedron is a three-dimensional geometric shape with four triangular faces. If a plane containing a vertical line of symmetry intersects a tetrahedron, the resulting cross section would depend on the orientation and position of the plane relative to the tetrahedron.
In general, there are several possible cross sections that can be formed by a plane containing a vertical line of symmetry for a tetrahedron. The specific shape and characteristics of the cross section would vary based on the angle and position of the intersecting plane.
For example, if the plane intersects the tetrahedron perpendicular to its vertical line of symmetry, the resulting cross section would be a vertical slice through the tetrahedron. This cross section would typically be a polygon with sides formed by the intersecting edges of the tetrahedron's faces.
On the other hand, if the intersecting plane is at an angle to the vertical line of symmetry, the resulting cross section would have a different shape. It could be a tilted polygon or even a curved shape, depending on the orientation of the intersecting plane and the specific angles of intersection.
In summary, the cross section formed by a plane containing a vertical line of symmetry for a tetrahedron can take various shapes, including polygons or curved shapes, depending on the orientation and angle of the intersecting plane.
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Can I hv help with this pls!!
The conversion of the recurring decimals 0.027 and 0.037 to fractions in its simplest form are 0.243/9 and 0.333/9
How to convert recurring decimals to fractions?Let
the fraction = x
0.027
Multiply by 10
0.027 × 10 = x
= 0.27
Subtract 0.027 from 0.27
0.27 - 0.027 = x
0.243 = x
divide by 9
0.243/9 = x
0.037
= 0.037 × 10
= 0.37
Subtract 0.037 from 0.37
0.333 = x
divide by 9
x = 0.333/9
Hence, 0.243/9 and 0.333/9 is the fraction for the recurring decimals 0.027 and 0.037.
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if the probability of winning a carnival game was 2/5 and max played it five times, write an expression that would calculate the probability he won the first three games and lost the last two. use exponents to express your final answer, but do not evaluate.
suppose a data set has a variance of 72.25 what is the standard deviation of this data set
Answer:
8.5
Step-by-step explanation:
Standard deviation = √variance = √72.25 = 8.5
How many ways can you arrange the word Campfire?
Using permutations, the word CAMPFIRE can be arranged in 40,320.
What is permutation?A permutation is the number of ways in which a data set can be arranged or ordered.
Order is important in permutations, unlike in combinations.
The word to be arranged in different ways = CAMPFIRE
The number of letters in CAMPFIRE = 8
The formula for permutations is: n! / (n - r)!.
In this formula:
n is the number of letters in the word
r is the number of letters to be arranged
n = 8
r = 8
8! / (8 - 8)!
= 8! / 0!
= 8! / 1 = 8!
= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 40,320
Thus, the word CAMPFIRE can be arranged in 40,320 ways based on the permutation formula.
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the of a node is the height of its right subtree minus the height of its left subtree. question 24 options: a) balance factor b) depth c) length d) degree
a) balance factor
The balance factor of a node in a binary tree is defined as the height of its right subtree minus the height of its left subtree. It is commonly used in balance algorithms for maintaining balanced binary trees, such as AVL trees.
What is balance factor?
The balance factor is a keyword that represents the measure of the height difference between the left and right subtrees of a node in a binary tree. It is calculated by subtracting the height of the left subtree from the height of the right subtree
Certainly! In a binary tree, the balance factor of a node is a measure of the difference in height between its right subtree and left subtree. It is calculated by subtracting the height of the left subtree from the height of the right subtree.
The balance factor helps in determining the balance or imbalance of a node in a binary tree. It is used as a criterion for tree balancing algorithms, such as the AVL tree. By checking the balance factor of each node, these algorithms ensure that the tree remains balanced and avoids degeneration into a skewed or unbalanced structure.
A balance factor of 0 indicates that the heights of the left and right subtrees are equal, meaning the node is balanced. A positive balance factor means the right subtree is taller than the left subtree, indicating a right-heavy or right-skewed tree. Conversely, a negative balance factor implies the left subtree is taller, indicating a left-heavy or left-skewed tree.
By maintaining balanced trees using the balance factor, efficient search and retrieval operations can be achieved, ensuring optimal performance in various tree-based data structures.
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Which equation represents a line which is perpendicular to � = 0 x=0? � = − � x=−y � = − 5 x=−5 � = � + 2 y=x+2 � = 1 y=1
The equation y=1 represents a line Perpendicular to x=0.
The equation x=0 represents a vertical line passing through the point (0,0) on the x-axis. A line perpendicular to this line will be a horizontal line passing through the point (0, c) where c is a constant.
So, the equation of the line perpendicular to x=0 is y = c, where c is any constant.
Among the given options, the equation that represents a horizontal line is:
� = 1 y=1
Therefore, the equation y=1 represents a line perpendicular to x=0.
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If the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], what is nullity(A)?
If the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.
To determine the nullity of matrix A, we need to find the number of linearly independent vectors that satisfy the equation Ax = 0. Since the set {u1, u2, u3} spans R3, we know that any vector in R3 can be expressed as a linear combination of these three vectors. Thus, the equation Ax = 0 has a nontrivial solution if and only if the three vectors u1, u2, and u3 are linearly dependent. If they are linearly dependent, then one of them can be expressed as a linear combination of the other two, and we can eliminate that vector from the matrix A. This means that the nullity of A is equal to the number of linearly dependent vectors in the set {u1, u2, u3}. Since the set spans R3, it must contain three linearly independent vectors, and therefore the nullity of A is 0.
In summary, if the set {u1, u2, u3} spans R3 and A = [u1 u2 u3], then the nullity of A is 0, meaning there are no linearly independent vectors that satisfy the equation Ax = 0.
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a farmer has 312 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a common side. the common side divides the total area in half. what is the maximum area for each pig pen?
The maximum area for each pig pen is 156 square feet. The total length of fencing available is 312 feet. We also know that the two pig pens share a common side, so we can assume that the other three sides of each pen are independent rectangles.
The length of the common side "x" and the width of each pen "y". Since the total area is divided in half by the common side, we can write an equation:
2(xy/2) = x*y
xy = 156
A = xy
y = 156/x
Substituting this expression for y into the formula for the area, we get:
A = x(156/x)
A = 156 - x^2/2
This is a quadratic equation in standard form, with a = -1/2, b = 0, and c = 156. The vertex of the parabola is at x = -b/2a = 0, which means that the maximum area occurs when x is at the midpoint of the fencing available, which is 156/2 = 78
feet.
y = 156/78 = 2
The dimensions of each pig pen are 78 feet by 2 feet, and the maximum area of each pen is:
A = 78*2 = 156 square feet.
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For every 1 million cleared by a client, the client control banking officer receives a commission of 15000. If a loan worth 34000000 is cleared, how much commission does the credit control officer receive
The credit control officer's commission for clearing a loan worth 34000000 would be 510000 based on a commission rate of 15000 for every 1 million cleared.
If a loan worth 34000000 is cleared, the credit control officer would receive a commission based on the total amount cleared. Since the commission rate is 15000 for every 1 million cleared, we can calculate the commission by dividing the loan amount by 1 million and multiplying it by the commission rate.
So, 34000000 divided by 1000000 equals 34. This means that there are 34 million-dollar increments in the loan amount. Multiplying 34 by the commission rate of 15000 gives us a commission of 510000.
Therefore, the credit control officer would receive a commission of 510000 for clearing a loan worth 34000000. It is important to note that this commission may be subject to taxes and other deductions depending on the credit control officer's employment terms and local laws.
In conclusion, the credit control officer's commission for clearing a loan worth 34000000 would be 510000 based on a commission rate of 15000 for every 1 million cleared.
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Which expression is equal to x−9x−4+x2−x+5x−4 ?
Responses
x2−42x−8
x2−4x−4
x2−x−42x−8
x2−x−4x−4
Please help me thanks
Answer: Choice B
Step-by-step explanation:
The formula for the area of a circle is πr², and the radius is 1/2 of the diameter.
In the circle shown, the diameter is 18 m. Since the radius is half the diameter, the circle's radius is 9 m.
Inputting this value into this equation gives us π·9², or 81π. Putting this into a calculator or solving it with an approximation of pi gives us a number close to 254.46 m².
The closest option to that is B, so that is your answer.
the single factor anova tests for mean differences between 3 or more groups by comparing ____
The single factor ANOVA tests for mean differences between 3 or more groups by comparing the variance within groups to the variance between groups.
It examines whether the differences between the means of the groups are greater than what would be expected due to chance. The ANOVA test uses the F-statistic to calculate the ratio of the variance between groups to the variance within groups. If the F-statistic is significant, it indicates that there is a significant difference in the means between the groups, and post-hoc tests can be conducted to determine which specific groups differ significantly. In conclusion, the single factor ANOVA tests are an essential statistical tool for determining whether there are significant differences between multiple groups and are used widely in various fields of research.
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5. Jake drew a model on grid paper
of a kite that he wants to make.
Each grid line represents 10 cm.
His drawing has coordinates (1,
5), (3, 6), (5, 5), and (3, 0). Sketch
Jake's kite, and calculate the area
of the real kite.
Based on the information given ,it should be noted that the area of the real kite will be 1615.548 cm²
How to calculate the areaThe given coordinates are:
(1, 5) -> (10 cm, 50 cm)
(3, 6) -> (30 cm, 60 cm)
(5, 5) -> (50 cm, 50 cm)
(3, 0) -> (30 cm, 0 cm)
Base = Distance between (10 cm, 50 cm) and (30 cm, 0 cm)
= ✓((30 cm - 10 cm)² + (0 cm - 50 cm)²)
= ✓(400 + 2500)
= ✓(2900) cm
Height = Distance between (30 cm, 60 cm) and (30 cm, 0 cm)
= 60 cm - 0 cm
= 60 cm
Area of Triangle 1 = (1/2) * Base * Height
= (1/2) * ✓(2900) cm * 60 cm
= 1615.548 cm²
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what will be the shape of the sampling distribution of the difference in sample proportions, and why?
The sampling distribution of the difference in sample proportions will be approximately normal, provided that the sample sizes are large enough and certain conditions are met.
The shape of the sampling distribution can be determined by the Central Limit Theorem (CLT), which states that when sampling from a population, the sampling distribution of a sample statistic approaches a normal distribution as the sample size increases. In the case of the difference in sample proportions, the CLT applies if the sample sizes are large enough for each proportion and if the samples are independent.
When these conditions are met, the sampling distribution of the difference in sample proportions will be approximately normal. The exact shape of the distribution will depend on the population proportions and the sample sizes, but it will be symmetric and bell-shaped. This allows for the use of statistical tests and confidence intervals based on the normal distribution to make inferences about the difference in proportions.
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let f(x)=x^3, g(x)=sqrt x, and h(x)=x/3. Find each of the following.
h(f(g(1/2)))
h(f(g(x)))
The value of the functions are;
h(f(g(1/2))) = (√1/2)³/3
h(f(g(x))) = = (√x)³/3
How to determine the valueIt is important to note that a function is an equation that shows the relationship between two variables
From the information given, we have that;
f(x) = x³
g(x) = √x
h(x) = x/3
To determine the composite function, we need to substitute the value of one function as the value of x in the other, we have that
f(g(1/2) =
g(1/2) = √1/2
Substitute the value
f(g(1/2) = (√1/2)³
Now, substitute the value as x in h(x)
h(f(g(1/2))) = (√1/2)³/3
f(g(x)) = (√x)³
Then, h(f(g(x))) = = (√x)³/3
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Th graph shows a relationship between the balance of a gift card, y, and the number of lunches purchased with the gift card x. Write an equation in slope intercept form to represent this situation.
The equation in slope intercept form to represent this situation is y = -7.5x + 30
Writing the equation in slope intercept form to represent this situation.From the question, we have the following parameters that can be used in our computation:
The graph
A linear equation si represented as
y = mx + c
Where
m = slope
c = y when x = 0
From the graph, we have
c = 30
So, we have
y = mx + 30
Using the other points, we have
4m + 30 = 0
So, we have
m = -7.5
This gives
y = -7.5x + 30
Hence, the equation in slope intercept form to represent this situation is y = -7.5x + 30
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in an election, suppose that 45% of voters support a new tax on fast food. if we poll 105 of these voters at random, the probability distribution for the proportion of the polled voters that support a new tax on fast food can be modeled by the normal distibution pictured below. complete the boxes accurate to two decimal places
The normal distribution curve represents the probability distribution for the proportion of voters who support the new tax on fast food when polling 105 voters at random.
Since the proportion of voters who support a new tax on fast food follows a normal distribution, we can model it using the normal distribution curve. Given that 45% of voters support the tax, the mean proportion of voters who support the tax is 0.45.
The standard deviation can be calculated using the formula:
Standard Deviation = sqrt[(p * (1 - p)) / n]
where p is the proportion of voters who support the tax (0.45) and n is the sample size (105).
Substituting the values, we get:
Standard Deviation = sqrt[(0.45 * (1 - 0.45)) / 105] ≈ 0.0497 (rounded to four decimal places)
Now, we can complete the boxes:
Mean = 0.45 (given)
Standard Deviation = 0.0497 (calculated)
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URGENT!!
In words I need the answer to this for my geometry class
Create a conditional and it’s converse where the conditional is TRUE but the converse is False.
The conditional statement with a false converse is :
Conditional: If an animal is a dog, then it is a mammal.Converse: If an animal is a mammal, then it is a dog.How to write the statement ?A conditional statement consists of an if-then structure, and its converse can be formed by swapping the hypothesis and conclusion. To illustrate, "If A, then B," becomes "If B, then A" in converse form. Our aim is to devise a truthful condition while simultaneously ensuring that its converse yields a falsehood.
Thus, for instance, we may use the fact that all dogs are classified as mammals to offer a valid conditional statement; regrettably, such a proposition fails under converse statement, since not all mammals share this canine trait. Consider cats, elephants, and whales - they render our converse false.
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Dominic's grandfather is teaching him how to make cornbread. Dominic pours it into the pan shown. Dominic's grandfather tell him he should stop when it is 1/2 inch from the top, to allow room for the cornbread to rise in the oven. what is the volume?
Answer:
Step-by-step explanation:
Answer:
115.5
Step-by-step explanation:
did the iready
assume condition one has two values, condition two has five values, condition three has three values, and condition four has two values; the number of rules required for the decision table is sixty. T/F
False. assume condition one has two values, condition two has five values, condition three has three values, and condition four has two values; the number of rules required for the decision table is sixty.
The number of rules required for a decision table can be calculated by multiplying the number of values in each condition. In this case, condition one has two values, condition two has five values, condition three has three values, and condition four has two values. The total number of rules would be the product of these values: 2 x 5 x 3 x 2 = 60.
Therefore, the statement "the number of rules required for the decision table is sixty" is true.
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40% of jams 60 classmates enjoy watching football . 35% of his 20 relatives enjoy football . how many more classmates enjoy football ?
out of jams 60 classmates, 40% OR 24 Classmates enjoy watching football. out of jams 20 relatives, 35% or 7 relatives enjoy watching football. therefore there are 25-7=17 more classmates who enjoy football than relatives
►Solving equation x+1 3 || X 2 can anyone please give me a question and the answers which is related to algebra solving equation
The solution for the given equation is x = 2.
Given is an equation, x+1 / 3 = x/2, we need to solve it,
So, in the questions like this, our first step should be of cross-multiplication,
x+1 / 3 = x/2
Cross-multiplying,
2(x+1) = 3x
Using the distributive law,
2x+2 = 3x
Combining the like terms,
3x-2x = 2
x = 2
There can be many equations made like this,
For example,
1) 9 = 3 + x/4
Solution = 9-3 = x/4
6 = x/4
x = 24
2) 2x+2 / 4 = x-3 / 3
Using Cross-multiplying,
6x+6 = 4x-12
2x = -12-6
2x = -18
x = -9
Hence there are many equations made.
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what is the ratio for COS A?
The ratio of cos A in the right triangle is 12 / 13.
How to find the angle of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the ratio of cos A using trigonometric ratios.
Using cosine ratio,
cos A = adjacent / hypotenuse
Therefore,
adjacent side = 12
hypotenuse side = 13
cos A = 12 / 13
Therefore, the ratio is 12 / 13
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if y varies inversely with x, and y = 60 when x =3, find y when x = 18
Answer:
y=10
Step-by-step explanation:
y is inversely proportional to x or y=k. 1/x
where k = constant
or x.y =k where y=60 x=3,
3*60 =180=k
Now, when x=18;
18*y = 180 y=180/18
y=10.
Pepe tiene 2 veces la edad de su hermano. Hace 4 años tenía cuatro veces la edad de su hermano, que edad tiene cada uno?
The solution is: the present age of the man is 40 years and the present age of the son is 8 years.
Let us assume the age of the son now = x
Then
The age of the man now = 5x
Now we have to calculate the age of the son and father 9 years ago
Age of the son 4 years ago = x - 4
Age of the man 4 years ago = 5x - 4
Then
5x - 4 = 9(x - 4)
5x - 4 = 9x - 36
5x - 9x = -36 + 4
- 4x = - 32
MUltiplying both sides of the equation by -1 we get
4x = 32
x = 32/4
= 8
So the present age of the son is 8 years
Present age of the man = 5x
= 5 * 8
= 40 years
So the present age of the man is 40 years and the present age of the son is 8 years.
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complete question:
A man is five times as old as his son. Four years ago, he was nine times as old. Find their present ages.
