Answers
Answer:
42, 12)
Step-by-step explanation:
Let the present ages of the father and son be x years and y years respectively.
According to the question,
Condition I,
Three years ago the sum of the ages of the father and his son was 48 years.
or,(x−3)+(y−3)=48
or,x−3+y−3=48
or,x−6=48−y
or,x=54−y - (i)
Condition II,
Three years hence the father's age will be three times the son's age,
or,(x+3)=3(y+3)
or,x+3=3y+9 - (ii)
Put value of x from equation (i) in equation (ii), we get,
or,(54−y)+3=3y+9
or,54−y=3y+9−3
or,54−6=3y+y
or,48=4y
or,y=484
∴y=12
Put the value of y in equation (i), we get,
or,x=54−12
∴x=42
So, (x,y) = (42, 12)
Therefore, the required present ages of the father and the son are 42 years and 12 years respectively.
Related Questions
Please Help:
Here are the statistics for the high temperatures in a city during October:
mean of 65.3 degrees Fahrenheit
median of 63.5 degrees Fahrenheit
standard deviation of 9.3 degrees Fahrenheit
IQR of 7.1 degrees Fahrenheit
Recall that the temperature C, measured in degrees Celsius, is related to the temperature F, measured in degrees Fahrenheit, by C=5/9(F−32).
a. Describe how the value of each statistic changes when 32 is subtracted from the temperature in degrees Fahrenheit.
b. Describe how the value of each statistic further changes when the new values are multiplied by 5/9.
c. Describe how to find the value of each statistic when the temperature is measured in degrees Celsius.
Answers
Answer:
a. Describe how the value of each statistic changes when 32 is subtracted from the temperature in degrees Fahrenheit.
a) The mean will change and other quantities remain same.
b) The mean, standard deviation and IQR change.
c) The standard deviation and IQR change.
a. When 32 is subtracted from the temperature in degrees Fahrenheit:
The mean would change by subtracting 32 from the original mean of 65.3.The median would remain the same since subtracting a constant value does not affect the relative order of the data points.The standard deviation would remain the same since it is a measure of dispersion and does not depend on the shift of the data.The IQR would remain the same since it is based on the order statistics (including the median) and is not affected by a constant shift.b. When the new values (obtained after subtracting 32) are multiplied by 5/9:
The mean would change by multiplying the new mean by 5/9.The median would remain the same since scaling by a constant value does not affect the relative order of the data points.The standard deviation would change by multiplying the new standard deviation by 5/9 since it is a measure of dispersion and scales with the data.The IQR would change by multiplying the new IQR by 5/9 since it is based on the order statistics and scales with the data.c. To find the value of each statistic when the temperature is measured in degrees Celsius:
The mean and median would remain the same since the Celsius scale and Fahrenheit scale have a linear relationship, and shifting or scaling the data does not affect their relative values.The standard deviation would change by multiplying the new standard deviation by 5/9 since it scales with the data.The IQR would change by multiplying the new IQR by 5/9 since it scales with the data.Learn more about IQR here:
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please help math 30 points
Answers
Answer:
144.288
Step-by-step explanation:
yes because I just took the tes
a team can row 40km in 2 hours when rowing with the current, but only 16km in 2 hours when rowing against the current. determine the teams rowing speed when there is no current
Answers
Based on the rowing speed of the team when rowing with the current and when rowing against, the team rowing speed when there is no current is 14 km/h.
What is the rowing speed without current?Assuming that x is the rowing rate and y is the rate of the current, the equations needed will be:
2 (x + y) = 40
2 (x - y) = 16
We can add the x-values of the equation to find the value of x which will be the rowing speed without current:
2x + 2x = 40 + 16
4x = 56
x = 56 / 4
x = 14 km /h
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find equations of the tangent line and of the normal line to the curve at the point . write the equations of the lines in the form .
Answers
The equations of the lines in the form y=mx+b are-
Tangent line: y = 240x - 215994Normal line: y = - 0.00417x + 9.75What is slope?A line's slope is described like the change in y coordinate to the change in x coordinate. The net y coordinate change is y, whereas the net x coordinate change is x.
Therefore the variation in y coordinate in relation to the variation in x coordinate is written as, dy/dx.
Now, as per the given conditions;
The equation of the line is y = (6 + 4x)²
Simplifying the equation;
y = (6 + 4x)²
= 36 + 48x + 16x²
y = 16x² + 48x + 36
Now, differentiate the equation to find the tangent slope;
dy/dx = 32x + 48
At the point (6,900),
dy/dx = 32(6) + 48 = 240
Let equation of the tangent at point (a,b) is;
(y - b) = m(x - a)
a = 6, b = 900, m = 240
y - 6 = 240(x - 900)
Write this in y = mx + b form,
y - 6 = 240x - 216000
y = 240x - 215994 (Equation of Tangent line)
The slope of the normal line = -(1/slope of the tangent line) (since they're both perpendicular to each other)
Slope of the normal line = -1/240
The, equation of the normal will become;
y - 6 = (-1/240)(x - 900)
y - 6 = (-x/240) + 3.75
y = (-1/240)x + 9.75
y = - 0.00417x + 9.75 (Equation of Normal line)
Thus, the equation for the normal and tangent has be found.
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The complete question is-
Find the equation of the tangent line and normal line to the curve y = (6 + 4x)² at the point (6,900). Write the equations of the lines in the form y=mx+b. Tangent line: y=
Normal line: y=
Solve the equation by graphing. If the exact roots cannot be found, state the consecutive integers between which the roots are located. If there are no roots, state no real solution. List all roots or consecutive integers in order from least to greatest. 2 x^ 2 + x = 11
Answers
The roots of the quadratic equation represented by the graph are; x = -2.5 and x = 2.5.
What is the Solution of the Quadratic Equation?
The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.
By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.
The roots are located between -3 and 3.
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Which expression is equivalent to the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power?
Answers
The equivalent expression is 5^(4) * 3^(-10)
What is an equivalent expression?Equivalent expressions are expressions having the same solution but different arrangement
Two expressions are said to be equivalent if they have the same value of solution irrespective of the variable(s) in them.
Now, let's represent the expression;
( 5^-2 × 3^5 )^-2
We simply by multiply the exponential value by the
5^-2(-2) × 3^5(-2)
5^4 × 3^- 10
Hence, the equivalent expression is 5^(4) * 3^(-10)
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Two different numbers are selected ffrom -2,-2,0,3,4,5 and multiplied together. what is the probability that the product is zero
Answers
Two numbers are drawn without replacement. The only way their product is zero is if one of these numbers is zero. The probability of this happening is
[tex]\dfrac{\dbinom11 \dbinom51}{\dbinom62} = \dfrac{1\cdot5}{15} = \boxed{\dfrac13}[/tex]
In other words,
• there is 1 zero in the list - we draw it with [tex]\binom11 = 1[/tex] way of doing so;
• there are 5 non-zero numbers in the list - we draw 1 of these, with [tex]\binom51 = 5[/tex] ways of doing so;
• there is a total of 6 numbers in the list - we draw 2 of these, with [tex]\binom62 = 15[/tex] ways of doing so.
On the other hand, if the numbers are drawn with replacement and independently of one another, then each number has the same probability of getting drawn each time. There are 6×6 = 36 possible outcomes, each with 1/36 probability of occurring. Their product is zero if at least one of the numbers drawn is zero. The probability of this happening is
[tex]\dbinom21 \dfrac16 \times \dfrac56 + \dbinom22 \left(\dfrac16\right)^2 = \dfrac{11}{36}[/tex]
That is,
• there is 1/6 chance of drawing a zero and 5/6 chance of not drawing a zero. This can selection can happen in [tex]\binom21=2[/tex] ways (zero is drawn first or last);
• there is 1/6 chance of drawing a zero for either selection. This can happen in [tex]\dbinom22=1[/tex] way (zero is drawn both times).
While the probabilities are close, they are not the same! Be careful with which interpretation you choose.
[tex]\dfrac13 = \dfrac{12}{36} > \dfrac{11}{36}[/tex]
a hotel chain charges $90 each night for the first two nights and $50 for each additional night's stay. the total cost t is a function of the number of nights x that a guest stays.
Answers
The total cost is T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}
What is algebra?Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/).
Given:
T(x)={a if x≤2, b if x > 2}
let us take
a= 90x, 0≤x≤2
and, b = 180 + 50x for x>2
Hence. the total cost be T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}
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In which number does the digit 6 have that is 10 times as great as the value of the digit 6 in 283,691
Answers
Answer:
486,732 hope this helps
The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling. A member of the staff maps the ceiling on a coordinate grid as shown, where each unit represents 1 meter. What is the approximate length of string lights the staff needs to decorate the ceiling?
Answers
The approximate length of string lights the staff needs to decorate the ceiling is 40.25
What is the approximate length of string lights the staff needs to decorate the ceiling?The complete question is added as an attachment
From the attached figure, we have the following coordinates
A = (5, 16)
B = (17, 10)
C = (14, 4)
D = (2, 10)
Calculate the lengths AB and BC using the following distance formula
d = √[(x2 - x1)^2 + (y2 - y1)^2]
This gives
AB = √[(5- 17)^2 + (16- 10)^2] = 13.4
BC = √[(14- 17)^2 + (4- 10)^2] = 6.7
The approximate length of string lights the staff needs to decorate the ceiling is then calculated as
P = 2 * (AB + BC)
This gives
P = 2 * (13.4 + 6.7)
Evaluate
P = 40.2
Hence, the approximate length of string lights the staff needs to decorate the ceiling is 40.25
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Answer: 40.25
Step-by-step explanation:
the set of all real numbers less than 50 or less than 50 set builder notation
Answers
Here is a simple example of set-builder notation set builder notation it says " the set of all x's, such that X is greater than 0".
SOMEONE PLEASE HELP ME I REALLY NEED HELP ON THIS
Answers
The volume of the square frustrum is 1018791.667 cubic feet, the volume of the pyramid is 22019.625 cubic feet and the volume of the Washington Monument is 1040811.292 cubic feet.
What is the volume of the Washington Monument?
The Washington Monument is an obelisc and the volume of the obelisc is the sum of the volumes of the square frustrum and the pyramid, that is:
V = V' + V'' (1)
V' = (1 / 3) · (a² + a · b + b²) · h (2)
V'' = (1 / 3) · b² · h' (3)
Where:
V' - Volume of the square frustrum, in cubic feet.V'' - Volume of the pyramid, in cubic feet.a - Length of the side of the lower base, in feet.b - Length of the side of the upper base, in feet. h - Height of the square frustrum, in feet.h' - Height of the pyramid, in feet.If we know that a = 55 ft, b = 34.5 ft, h = 500 ft and h' = 55.5 ft, then the volume of the Washington monumement is:
V' = (1 / 3) · (55² + 55 · 34.5 + 34.5²) · 500
V' = 1018791.667 ft³
V'' = (1 / 3) · 34.5² · 55.5
V'' = 22019.625 ft³
V = 1040811.292 ft³
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Solve the following equation for aa. Be sure to take into account whether a letter is capitalized or not.
d=
d=
\,\,Ma-N^3a
Ma−N
3
a
Answers
Answer:
a = [tex]\frac{d}{M-N^3}[/tex]
Step-by-step explanation:
d = Ma - N³a ← factor out a from each term on the right side
d = a(M - N³) ← isolate a by dividing both sides by M - N³ )
[tex]\frac{d}{M-N^3}[/tex] = a
Need help with this question ASAP please and youu??
Answers
Answer: (8, 8)
Step-by-step explanation:
y>x-7, y<=2x-8
1: 5>12-7
5>5 ==> Not true
2: 3>12-7
3>5 ==> Not true
3: -10>-6-7
-10>-13
-10<=2(-6)-8
-10<=-12-8
-10<=-20 ==> Not true
4: 8>8-7
8>1 ==> True
8<=2(8)-8
8<=16-8
8<=8 ==> True ==> (8, 8)
8y-2(y+4) pls help wil be rewarded with prize
Answers
Answer:
[tex] \large \sf \: 6y - 8[/tex]
Step-by-step explanation:
Let's simplify step-by-step.
8y−2(y+4)
Distribute:
=8y+(−2)(y)+(−2)(4)
=8y+−2y+−8
Combine Like Terms:
=8y+−2y+−8
=(8y+−2y)+(−8)
=6y+−8
=6y−8
Answer:
6y - 8
Step-by-step explanation:
This is a simplifying problem, so we just need to separate and link the like terms.
First we start with the parenthesis by distributing
-2*y + -2*4
-2y - 8
We can the put it back into the equation
8y - 2y + 8
8y and -2y are like terms so we can put them together to get 6y
6y +8
Find the equation of the line that is parallel to y=-2/3x and contains the point (4,-8)
Answers
Answer:
y = (-2/3)x + 16/3
Step-by-step explanation:
Any line parallel to y = (-2/3)x has the same slope: (-2/3).
Then, in this pattern, y = (-2/3)x + c, where c is the y-intercept.
If (4, -8) lives on this new line, then:
-8 = (-2/3)(4) + c, and
-8 = -8/3 + c
This last equation is equivalent to -24/3 + 8/3 + c => -16/3 = -c.
Therefore the y-intercept is 16/3 = c, and the desired equation is
y = (-2/3)x + 16/3
Convert the following decimal into a fraction.
0.83
Answers
Answer:
83/100
Step-by-step explanation:
To turn a decimal into a fraction, place decimal number over its place value.
Place value = 100
Decimal number = 83
Please solve the problem in the image!!!!!
Answers
Answer:
455 is the answer of your question
1. Is there a triangle with two right angles?
Answers
Answer:
A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible.
Answer:
No, it is not possible for a triangle to have two right angles because a triangle's angles add up to 180 degrees, and two right angles add up to 180. A triangle also has three angles, so the third angle cannot be 0 degrees.
(PLEASE I NEED THIS) Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y<2x-8
y>-1/2-3
Answers
The solution of the graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.
What is Inequality?
To compare two or more mathematical expression in a relation is called an Inequality.
Given that;
The solution sets are;
y < 2x - 8
y > -1/2 x - 3
Now, We draw graph of inequalities.
Then we get,
The graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.
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the length of a rectangle is four times its width. if the perimeter is at most 106 centimeters, what is the greatest possible value for the width? which inequality models this problem?
Answers
If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.
According to the statement
We have to find that the value of the width.
So, For this purpose, we all know that the
A rectangle may be a form of quadrilateral, whose opposite sides are equal and parallel.
From the given information:
the length of a rectangle is fourfold its width. if the perimeter is at the most 106 centimeters
Then
L = 4w --------The length of a rectangle is fourfold its width.
2w + 2L ≤ 106 ------- the perimeter is at the most 130 centimeters.
Now, if substitute the primary equation into the second inequality you may get
2w + 2 • (4w) ≤ 106.
Therefore, the inequality model becomes 2w + 2 • (4w) ≤ 106.
So, If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.
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Can somebody help me find this missing angle please.
Answers
Answer:
x = 96 degrees
Step-by-step explanation:
49 + 35 + x = 180
84 + x = 180
x = 180 - 84
x = 96 degrees
Helpp
Question 3 (Essay Worth 2 points)
(01.02 HC)
Is the expression x3 x3 x3 equivalent to x3 3.3? Why or why not? Explain your reasoning.
Answers
No the expression x³.x³.x³ is not equivalent to expression x³ˣ³ˣ³.
Given the expression:
x³.x³.x³
here we apply the law of exponent that, when bases are same powers are added.
Two exponential terms with the same base are multiplied, and while the base doesn't change, their powers are added. On the other hand, their powers are removed when two exponential expressions with the same base are split.
therefore, x³.x³.x³ = x ³⁺³⁺³
= x⁹
and in the second expression x³ˣ³ˣ³.
In this expression powers are multiplied.
= x³ˣ³ˣ³.
= x²⁷
therefore both expressions are not equivalent.
Hence the expressions are not equivalent.
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a. show one pair of corresponding points and two pairs of corresponding sides in the original and it’s copy.
b.what scale factor takes the original polygon to its smaller copy?
Answers
Answer:
1/4
Step-by-step explanation:
Let x = the scale factor
4x = 1 Divide both sides by 4
x = 1/4
an online retailer is shipping a shower curtain pole that is 13 feet long. their largest box is in the shape of a rectangular prism that is 10 ft × 9 ft × 8 ft. will the pole fit in the box?
Answers
Yes, the pole will fit in the box when kept diagonally.
In order to fit the pole in rectangular prism or cuboid, it has to be kept diagonally. Now, we need to calculate the length of body diagonal of cuboid. The length of body diagonal of cuboid should be greater than pole to fit it.
The length of body diagonal of cuboid can be calculated by the formula -
Diagonal = √(l² + b² + h²)
Keep the values in formula to find the diagonal of rectangular prism
Diagonal = √(10² + 9² + 8²)
Taking square of the three numbers to find the diagonal of rectangular prism
Diagonal = √100 + 81 + 64
Taking sum of numbers present on Right Hand Side of the equation
Diagonal = √245
Taking square root of the number
Diagonal = 15.65 feet
Hence, as the diagonal of rectangular prism is greater than shower curtain pole, it will definitely fit.
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HELP ASAP!!!
Solve for m in the following equation.
4m/3= 8
m= 10
m= 6
m= 2
m= 96
You buy three more than twice as many pounds of apples as bananas. If you bought seven pounds of apples, how many pounds of bananas did you buy?
What is the correct equation and solution for this problem?
3p – 2 = 7; p = 3 pounds
2p – 3 = 7; p = 5 pounds
3p + 2 = 7; p = 3 pounds
2p + 3 = 7; p = 2 pounds
Thank you!!
Answers
The value of the unknown variable, m in the equation 4m / 3 = 8 is 6. option B
How to solve for unknown in an equation?4m / 3 = 8
cross product4m = 8 × 3
4m = 24
divide both sides by 4m = 24/4
m = 6
let
pounds of apple = apounds of bananas = bthree more than twice as many pounds of apples as bananas.
a = 2b + 3
If you bought seven pounds of apples, how many pounds of bananas did you buy?
b = 7 pounds
a = 2b + 3
7 = 2b + 3
7 - 3 = 2b
4 = 2b
b = 4/2
b = 2 pounds
So therefore, the correct equation and solution for this problem is 2p + 3 = 7; p = 2 pounds. option D
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Write an absolute value equation that has the solutions x=-6 and x=10.
Answers
Answer:
[tex]r \times \cos( 0) = - 6 \\ r = - \frac{6}{ \cos(0) } \\ r = - 6 \sec(0) \\ \\ r \times \cos(0) = 10 \\ r = \frac{10}{ \cos(0) } \\ r = 10 \sec(0) [/tex]
5. Owen walked 5 miles in 4 hours. Fill out a table of
equivalent ratios and plot the points on the coordinate axes
provided.
F
Miles
5
40
Hours
4
36
6
n
P
Answers
Table:
Miles Hours
5 4
40 32
45 36
The ratio between Miles and Hours is 5:4
In the table, miles = 40 is got by 8 x 5 = 40
So corresponding hours = 8 x 4 = 32
In the table, hours = 36 is got by 9 x 4 = 36
So corresponding miles = 9 x 5 = 45
So the ratios are 5:4 , 40:32, 45:36
Graph can be plotted with number of miles in the x-axis and number of hours in y-axis.
The points to be plotted are (5, 4), (40,32) and (45, 36). Joint these points to get a straight line on the graph.
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Pleae help me with this problem.
Answers
Answer:
11) KI = 28
12) PR = 22
Step-by-step explanation:
You want the base segment lengths KI and PR, given relations between those segments and the corresponding midsegment of the triangle.
MidsegmentA midsegment is a line segment that joins midpoints of other line segments, usually the midpoints of triangle sides or opposite sides of a quadrilateral. In the case of a triangle, the midsegment is parallel to the third side, and half its length. This relation is used to solve these problems.
11)KI = 2·AB
(x +37) = 2(x +23) . . . . substitute given expressions
x +37 = 2x +46 . . . . . . eliminate parentheses
37 = x +46 . . . . . . . . . . subtract x
28 = x +37 . . . . . . . . . . subtract 9
The length of KI is 28 units.
12)PR = 2·HG
(x +30) = 2(19 +x) . . . . substitute given expressions
x +30 = 38 +2x . . . . . eliminate parentheses
22 = x +30 . . . . . . . . subtract (x+8)
The length of PR is 22 units.
__
Additional comment
As you can see here, there is no real reason to find the value of x, then substitute it back into the expression for the segment of interest. We can, and did, solve directly for the value of that expression.
As with any algebraic manipulation, any operation performed on one side of the equal sign must also be performed on the other side of the equal sign. When we say "subtract ()", we mean "subtract () from both sides of the equation."
In problem 11, x=-9. In problem 12, x=-8. Negative values of x work just fine, as long as the resulting segment lengths are positive.
a researcher records the repair cost for 1313 randomly selected stereos. a sample mean of $85.52$85.52 and standard deviation of $10.81$10.81 are subsequently computed. determine the 90�% confidence interval for the mean repair cost for the stereos. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
Answers
The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
What is the critical factor?The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;
Critical factor = (x-μ)/(s/√n)
where, x = sample mean repair cost
s = standard deviation of a sample
n = sample of stereos
μ = critical value
We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $85.52 and a standard deviation of $10.81 are subsequently computed.
Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.
So, the 90% confidence interval for the true mean repair cost, μ is ;
⇒ P(-2.015 < t₅ < 2.015) = 0.90
{As the critical value of t at 5 degrees of freedom are -2.015 & 2.015 with P = 5%}
⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90
⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90
⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90
90% confidence interval for
⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))
Here, x = $85.52, s = $10.81, and n = 13
⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))
⇒ μ = (79.47, 91.56)
Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.
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