The age of the father is 57 years old
Calculating mean of a populationTotal age = Average age x Population
Average of the four children = 15
Population = 4
Total age of the four children = 15 x 4
Total age of the four children = 60 years
If the parents are added:
Population = 6
Average age = 25
Total age = 25 x 6
Total age = 150 years
Total age of the parents = 150 - 60
Total age of the parents = 110 years
The father is 4 years older than his wife
Let the age of the father be x
The age of the wife = x - 4
x + x - 4 = 110
2x = 114
x = 114/2
x = 57
Therefore, the age of the father is 57 years old
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A train leaves the station at 11 a.m. traveling at the rate of 40 miles per hour. A faster train leaves the same station at 1 p.m. that afternoon and travels in the same direction on a parallel track at a rate of 60 miles per hour. At what time will the faster train overtake the slower one
The faster train overtake the slower on 5 p.m.
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time.
Let the number of hours after 1pm at which faster train will overtake slower train be x.
At overtaking point,
Distance travelled by slower train = Distance travelled by faster train
Given :
Speed of slower train = 40 miles per hourSpeed of faster train = 60 miles per hourTime taken by faster train = xTime taken by slower train = x + 2.On equating distances we get
40 x ( x + 20) = 60 x (x)
40x + 80 = 60x
20x = 80
x = 4.
∴The faster train overtake the slower on 1 + 4 = 5 p.m.
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How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s
65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
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Need help understanding how to find the answer to problem
Answer:
3.Tan(45)=n/2
1=n/2
n=2
Cos(45)=2/m
1/√2=2/m
m=2√2
5.Sin(60)=x/14
√3/2=x/14
14√3/2=x
x=7√3
Cos(60)=y/14
1/2=y/14
y=7
5. Where is the graph increasing?
Answer:
Increases from points 0x,-6y to 2x,-3y.
Step-by-step explanation:
Ann invested $9000 in an account that earns 4.7% interest compounded annually . how much did ann have in the account after 5 years
The correct answer is FV = $11,323.38
What is compound interest explain?
Compound interest is when you earn interest on both the money you've saved and the interest you earn. So let's say you invest $1,000 (your principal) and it earns 5 percent (interest rate or earnings) once a year (the compounding frequency).FV = PV x [1 + R]^N, where FV=Future Value, PV=Present Value, R=Interest rate per period, N=Number of periods.
FV = 9,000 x [1 + 0.047]^5
FV = 9,000 x 1.047^5
FV = 9,000 x 1.258152857750007
FV = $11,323.38
Therefore , the answer is $11,323.38.
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verbal scale uses a representative fraction to describe the ratio between the map and the real world
Verbal scale uses a representative fraction to describe the ratio between the map and the real world is a "true" statement.
What is verbal scale/expression?A verbal scale is also known as a "word statement" or a "scale expression," and it is one of the possibilities for entering "scale text" in the ArcGIS software.
It is presented as a relationship between map distance and ground distance that is stated in common units that both parties can agree upon.
Uses of the verbal scale:
Verbal scales are widely employed on large-scale maps and planning documents, most frequently by civil engineers, just like representative fractions. On some smaller-scale maps, you can discover them, although not as frequently as you can with representative fractions. The verbal scales have already been calculated in some common map scales, so you might utilize those. The best treatment of verbal scales and the other scale indications may be found in Map Use by Kimerling, Muehrcke, and Muehrcke.To know more about the verbal expression(scale), here
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The complete question is-
Verbal scale uses a representative fraction to describe the ratio between the map and the real world.(True/False).
I'J'is a translation of IJ Write the translation rule.
Answer:
(x+6), (y+9)
Step-by-step explanation:
The x coordinate of J goes from -7 to -1, so it is translated x+6
The y coordinate of j goes from -8 to 1, which is a difference of 9, so it's translated y + 9
WILL MAKE BRAINLIEST
5. If m2ABC= 180°, is the angle right, straight, obtuse, or acute?
obtuse
acute
straight
right
Based on the estimated cost of college from step 1, determine how you are going to pay for college. You will need to do some research to learn about the various methods used to pay for college costs.
Complete the table below to document your financial needs.
Source Estimated Need
grants
loans
scholarships
work-study
other
This is a budgeting exercise. Based on the estimated cost of college which was set at $58,000, the following steps indicate how I intend to pay for college:
Scholarship - 70% = $40,600Work Study - 17.2% = $10,000Loan - 12.76% = $7, 400$58,000
What is budgeting?Budgeting is simply the process of outlining the total expense requirements of an individual person or a corporate entity and how those expenses will be satisfied and efficiently allocated.
From the above, the total sum of $58,000 will be satisfied from three sources:
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Which of the following is the MOST accurate definition of standard deviation
The average of a set of scores
The typical amount by which scores differ from the mean of a set of scores
The average of the sum of squared deviations from the mean
The mean absolute deviation of the sum of the squared deviation from the average
The MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average. Option 4
Definition of standard deviation
Standard deviation can be defined as a statistic tool that measures the dispersion of a dataset in relation to its mean and is calculated as the square root of the available variance of the set.
It is calculated as the square root of the given variance.
Thus, the MOST accurate definition of standard deviation is the mean absolute deviation of the sum of the squared deviation from the average.
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Kevin was asked to determine the length of side XZ. His work is shown.
Triangle X Y Z is shown. Angle Y Z X is 90 degrees and angle Y X Z is 34 degrees. The length of hypotenuse X Y is 18.
cos(34°) =
(XZ)cos(34°) = 18
XZ =21.7
Which error did Kevin make?
He has the side lengths in the wrong place in the cosine ratio.
He multiplied both sides by the length of XZ instead of dividing by XZ.
He should have used the sine ratio.
He should have used the tangent ratio.
Answer:
The answer is A) He has the side lengths in the wrong place in the cosine ratio.
Answer:
A. He has the side lengths in the wrong place in the cosine ratio.
Step-by-step explanation:
got it right on edge23
An owner of a large car lot believes that fuel prices are going to rise significantly and wonders how this rise might affect demand for the high performance vehicles. Specifically, the owner is investigating a link between how fast a car can go from 0 to 60 miles per hour (measured in seconds) and the car's economy as measured in miles traveled per gallon used (mpg). If fast cars, which are normally high in demand, are associated with higher mpg then there will be much less demand if gas prices rise as predicted. The owner gathers data on 20 vehicles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. "mpg" 0 to 60 time (seconds) 28 7.7 25 8.2 25 8.6 22 7.4 22 8 21 6.9 21 7.5 21 7.4 21 7.8 21 8.8 20 6.1 20 6.9 20 7.2 20 7.5 20 7.5 20 7.5 20 7.7 19 6.7 19 7.9 19 8.5
The correlation coefficient r between the two data sets is 0.33
How to determine the correlation coefficient r?From the table of values, we make use of the following representations:
Represent the mpg on the x axisRepresent the time on the y axisUsing the above representations, we can now plot our data values in the Excel software
From the Excel application, we have the following summary:
X Values
∑ = 424
Mean = 21.2
∑(X - Mx)2 = SSx = 101.2
Y Values
∑ = 151.8
Mean = 7.59
∑(Y - My)2 = SSy = 8.238
X and Y Combined
N = 20
∑(X - Mx)(Y - My) = 9.54
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
This gives
r = 9.54 / √((101.2)(8.238))
Evaluate
r = 0.3304
Approximate
r = 0.33
Hence, the correlation coefficient r between the two data sets is 0.33
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__________ notation encodes a real number as a mantissa multiplied by a power (exponent) of 2.
Answer:
Step-by-step explanation:
floating point
Which
expression is equivalent to
(x^6y^8)^3/x^2y^2
Answer: [tex]x^{16}y^{22}[/tex]
Step-by-step explanation:
[tex]\frac{(x^6 y^8)^3}{x^2 y^2}=\frac{x^{18}y^{24}}{x^2 y^2}=x^{16}y^{22}[/tex]
Suppose you drop a ball from a height of 10 feet. after the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0.85an – 1. what is a1? feet what is the height the ball rebounds to after its third bounce? round your answer to three decimal places. feet
The maximum height of the ball after its third bounce is equal to 3.568 feet.
What is the maximum height of a ball at the third bounce?
In this question we are aware that the maximum height reached by the ball decreases linearly after each bounce. To determine that height, we must take advantage of the recursive formula described in statement:
n = 0
a₀ = 10 ft
n = 1
a₁ = 0.85 · 10 - 1
a₁ = 8.5 - 1
a₁ = 7.5 ft
n = 2
a₂ = 0.85 · 7.5 - 1
a₂ = 5.375 ft
n = 3
a₃ = 0.85 · 5.375 - 1
a₃ = 3.568 ft
The maximum height of the ball after its third bounce is equal to 3.568 feet.
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The first one is 10 feet.
The second one is 6.141 feet.
Step-by-step explanation: Edge 2023
Area=
Help me please thanks so much :)
Answer:
48π
Step-by-step explanation:
To find the area of the shaded region, find the area of the large circle and the small circle then subtract.
Large circle:
8²π=64π
Small circle:
4²π=16π
Now subtract 16 from 64.
64-16=48
The area of the shaded region is 48π.
Hope this helps!
PLEASE HELP WILL GIVE BRAINLIEST
Arrange the tiles on both boards to find the value of x.
Board sum: 3x + (-5) = 1
What x value solves the equation?
3x - 5 = 1
X =
Answer: x = 2
Step-by-step explanation:
3x - 5 = 1
add 5 to both sides
3x - 5 (+5) = 1 (+5)
3x = 6
divide by 3 on both sides
3x/3 = 6/3
x = 2
Figure TUVS is a parallelogram.
Parallelogram T U V S is shown. Angle U is (4 x + 9) degrees and angle V is (6 x minus 29) degrees.
Which angles equal 91°?
angles T and V
angles S and U
angles U and V
angles S and T
Angles T and V of the parallelogram are equal to 91°.
Calculating the Value of x
In the parallelogram TUVS, adjacent angles U and V are given as,
U = 4x+9
V = 6x-29
Since U and V are adjacent angles, and as per the properties of a parallelogram, sum of adjacent angles is equal to 180°.
4x+9 + 6x-29 = 180
10x - 20 =180
10x = 200
x = 20
Calculating the Angles of the Parallelogram
∠U = 4x + 9
∠U = 4(20) + 9
∠U = 80 + 9
∠U = 89°
∠V = 6x - 29
∠V = 6(20) - 29
∠V = 120 - 29
∠V = 91°
According to the properties of a parallelogram, opposite angles are of equal measure.
∴ ∠T = ∠V and ∠S = ∠U
⇒ ∠T = 91° and ∠S = 89°
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Answer:
angles t and v
Step-by-step explanation:
edge
Solve the system of equations 2x-2y=-14 and 3x-y=-1 by combining the equations.
The solution to the system of equations is x = 3 and y = 10
How to solve the equations?The system is given as:
2x-2y=-14
3x-y=-1
Multiply (1) by 1 and (2) by 2
So, we have:
1(2x-2y=-14)
2(3x-y=-1 )
This gives
2x - 2y=-14
6x - 2y=-2
Subtract the equations
-4x = -12
Divide by -4
x = 3
Substitute x = 3 in 3x-y=-1
3(3)-y=-1
Evaluate
9 - y = -1
Solve for y
y = 10
Hence, the solution to the system of equations is x = 3 and y = 10
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Evaluate the following expression by applying the appropriate properties (24) 3 (31.7)/ 172
−3/7×14/15×7/12×(−30/35)
=(−3/7×14/15)×(7/12×−30/35)
On further calculation, we get
=−2/5×−1/2
We get,
=1/5.
Property 1:
If a/b is a rational number and m is a non-zero integer then a/b =(a*m)/(b*m). In other words, we can say that the rational number remains unaltered if we multiply both the numerator and denominator with the same integer. Ex: 2/3 = 2*2/3*2 = 4/6, 2*3/3*3 = 6/9, 2*4/3*4 = 8/12.
Math Properties
Commutative Property.
Associative Property.
Distributive Property.
Identity Property.
Inverse Property.
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Sumaya's smoothie store is planning to sell an extra-large size. the extra-large size will have three times the volume of the small size (the small size is (8,4) ). it will cost twice as much as the small size.
which coordinate pair represents the volume and cost of the extra-large size?
The coordinate pair that represents the volume and cost of the extra-large size is (24, 8).
A coordinate plane is a plane that can be used to represent the position of a point. The plane consists of x-axes and y-axes. The position of a point is referenced from the origin.
The small size of a pizza is represented by the coordinate pair (8, 4) ⇒ (volume, cost)
Since the volume of the extra-large size will have three times the volume of the small size, hence:
Volume of extra-large size = 8 * 3 = 24
The cost of an extra large is twice as much as the small size, hence:
Cost of extra large = 4 * 2 = 8
A coordinate plane is a graphing and outline machine for factors and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants inside the coordinate plane. The point at which these strains join is known as the starting place (0, zero).
Coordinates are written as (x, y) meaning the point on the x-axis is written first, followed by the point on the y-axis. a few children can be taught to keep in mind this with the phrase 'along the hall, up the stairs, that means that they must observe the x-axis first after which the y.
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PLRASE HELPPP PLS IM STUCK
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Dalvin took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $2 per mile. The total fare was $30.80, not including the tip. Which tape diagram could be used to represent the context if mm represents the number of miles in the taxi ride?
Answer:
The equation should be 2.5x+1.8=59.3
Step-by-step explanation:
The number of miles in the taxi ride is 10
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
Dalvin took a taxi from his house to the house. The taxi company charged a pick-up fee of $4.80;
The fare per mile is $2
The total fare was $30.80, not including the tip;
Let the number of mile is x
Total fare = pick up fee + fee per mile
30.80 = 4.80 + 2x
2x = 26
x = 13
Therefore, the number of miles by algebra Dalvin took a taxi will be 13
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To solve this system of equations using substitution, what could be substituted in place of y in the first equation? 4x = 5 − 2y y − 2x = 7
Answer:
y = [tex]-\frac{4x-5}{2}[/tex]
Step-by-step explanation:
Step 1: Switch sides
5 - 2y = 4x
Step 2: Subtract 5 from both sides
5 - 2y - 5 = 4x - 5
Step 3: Simplify
-2y = 4x - 5
Step 4: Divide both sides by -2
[tex]\frac{-2y}{-2} = \frac{4x}{-2} - \frac{5}{-2}[/tex]
Step 5: Simplify
y = [tex]-\frac{4x-5}{2}[/tex]
B.) what fraction of the cost is spent on food and entertainment? food- 17% entertainment- 24% they have 3000 dollars
The quantity spent on amusement = 720
quantity spent on food = 510
they have got 3000 for vacation.
amount spent on food = 17% of 3000
⇒ 17/one hundred*3000
17*30= 510
amount spent on amusement = 24% of 3000
⇒ 24/100*3000
24*30= 720
A person would possibly account for a terrible temper or general rude conduct by explaining that bad site visitors affected the morning travel, for example. someone who is exceeded over for a promotion would possibly rationalize the frustration by means of claiming to not have desired so much responsibility in the end.
To carry into accord with cause or reason something to appear reasonable especially: to characteristic (one's actions) to rational and creditable motives without evaluation of proper and especially unconscious motives he attempted to rationalize his merciless behavior. intransitive verb.
Ego protection wherein apparently logical motives are given to justify unacceptable behavior that is influenced by subconscious instinctual impulses. In the psychoanalytic concept, such conduct is considered to be a defense mechanism.
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Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.
1/5n+3/5n=7/9
Can you help?
The value of n from the given expression is 35/36
Solving linear equationGiven the equation below expressed as:
1/5n+3/5n=7/9
Find the LCM
(n+3n)/5 = 7/9
4n/5 = 7/9
Cross multiply
4n * 9 = 5* 7
36n = 35
n = 35/36
Hence the value of n from the given expression is 35/36
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What is the simplified form of tan (pi÷4-x)
Answer:
π/4 − x
Step-by-step explanation:
I hope its correct
id love some help!!!
Answer:
Circle:circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
[tex] \sf{formula \: to \: find \: the \: area \: is}[/tex][tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]
[tex] \sf{formula \: to \: find \: perimeter \: of \: circle \: is}[/tex][tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]
Continue to Question.If the radius is 2 inches and
Use 3,14 for π So:
[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]
[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]
[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]
So, The Area of circle is 12.56inches²Christopher decides that another road to be named Saturn Avenue is needed that will go past
the cleaners and be perpendicular to Sunshine Avenue. Determine the slope of the equation
of the line that represents Saturn Avenue. [Show your work. Draw and label Saturn Avenue
on the coordinate plane. (Optional)
Slope of the equation of the line that represents Saturn Avenue: slope =
y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. This can be obtained by using the formula for finding the equation of the line.
Find the equation of the line:
Equation of a line can be determined using the formula,
y = mx + c
where m is the slope of the line and c is the y - intercept.
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
Here in this question draw the line passing through cleaners and perpendicular to Planet Drive.
The point where x = 0 is (0, 4)
This means that y - intercept is 4
By considering two points on the line we can find the slope of the equation,
Consider the points (8, 4) and (16, 4)
m = rise/run = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)
m = (4 - 4)/(16 - 8) = 0/8 = 0
So we got that,
y - intercept of the line = 4 slope of the line = 0Putting in the equation of line we get,
y = mx + c
⇒ y = (0)x + 4 ⇒ y = 4
Hence y = 4 is the equation of the line that represents Saturn Avenue given that Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive.
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Question: Christopher decides that another road to be named Saturn Avenue is needed that will go past the cleaners and be perpendicular to Planet Drive. Determine the equation of the line that represents Saturn Avenue. Show your work. Draw and label Saturn Avenue on the coordinate plane.