Today is Jack’s birthday and Jill’s birthday. Jack is five and Jill is nine.
1. How many years ago was Jill twice as old as Jack?
2. When Jack is three quarters as old as Jill, how old will Jill be?
3. When Jill was three times as old as Jack, how old was Jack?
4. When Jill is four times as old as Jack is today, how old will Jack be?
Answers
Final answer:
The problem involves simple arithmetic and algebra to work out the relationship between ages at different times. Jill was twice as old as Jack 1 year ago. The other parts of the problems are under-determined or have errors that prevent firm conclusions.
Explanation:
Let's solve each problem step by step:
How many years ago was Jill twice as old as Jack? Let's call the number of years ago y. Jill's age y years ago = 9 - y, and Jack's age y years ago = 5 - y. The equation based on the problem is 9 - y = 2(5 - y). Solving this equation, y = 1. So, Jill was twice as old as Jack 1 year ago.
When Jack is three quarters as old as Jill, how old will Jill be? Let's call Jill's future age f. Jack's future age will be 3/4 * f. We know Jack is currently 5 years old, so 5 + x = 3/4(f + x), where x is the number of years till that happens. To find the value of f and x, we need one more equation or piece of information, which is not provided.
When Jill was three times as old as Jack, how old was Jack? To find this out, we set up an equation similar to the first problem: let's call the number of years ago z. So (9 - z) = 3(5 - z), solving for z gives us z = 4.5, but since they can't be half years old, we must consider whole years; thus, this situation hasn't occurred given their current ages or an error exists in the problem.
When Jill is four times as old as Jack is today, how old will Jack be? Jack is currently 5. So, when Jill is four times that age, she will be 5 * 4 = 20 years old. We cannot determine how old Jack will be at that time without knowing the difference in time between now and then.
Related Questions
IS THE SQUARE ROUTE OF 7 OR 14/5 BIGGER
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2 < root7 < 3
14/5 = 2.8
root7 is an irrational number which is likely less than 2.8
write a real-world problem in which you would need to find the number of units between -6 and 0 on a number line.
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The precise measurement of distance between Junction A at -6 and Junction B at 0 is indispensable in urban planning, optimizing traffic flow, and ultimately enhancing the quality of life for city residents.
One real-world problem where finding the number of units between -6 and 0 on a number line is crucial is in urban planning and transportation engineering.
Imagine a city with two major traffic junctions, Junction A at position -6 and Junction B at position 0 on the number line. City officials need to optimize traffic flow between these junctions to reduce congestion and commute times.
To achieve this, engineers must calculate the exact distance between these junctions. This information is vital for designing efficient road networks, determining signal timings, and planning for public transportation routes. It also helps in estimating travel times for commuters and enables the implementation of traffic management strategies.
Accurate measurements between -6 and 0 on the number line ensure that resources are allocated efficiently, minimizing environmental impact, fuel consumption, and overall transportation costs.
This problem highlights how fundamental mathematical concepts like distance on a number line play a critical role in shaping the urban landscape and improving quality of life for city residents.
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10 times the sum of half a number and 6 is 8
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which of the following best explains why cos 2pi/3 is not equal to cos 5pi/3
A.The angles do not have the same reference angle.
B.Cosine is negative in the second quadrant and positive in the fourth quadrant.
C.Cosine is positive in the second quadrant and negative in the fourth quadrant.
D.The angles do not have the same reference angle or the same sign.
Answers
In this exercise we have to use the knowledge of cosine quadrants, like this:
Letter B
We have that the quadrant of the cosine is given by:
The two quadrants on the right are positive.The two quadrants on the left are negative.So we know that:
[tex]cos (2\pi/3)[/tex] If it's in quadrant three, that's negative.
[tex]cos(5\pi/3)[/tex] If you're in quadrant four, that's positive.
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The correct answer is option B. Cosine is negative in the second quadrant and positive in the fourth quadrant.
To determine why [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex], we can analyze the properties of cosine in different quadrants.
Reference Angles: The reference angle for both [tex]\frac{2\pi }{3}[/tex] and [tex]\frac{5\pi }{3}[/tex] is [tex]\frac{\pi }{3}[/tex].Quadrants: [tex]\frac{2\pi }{3}[/tex] is in the second quadrant, while [tex]\frac{5\pi }{3}[/tex] is in the fourth quadrant.Sign of Cosine: In the second quadrant, cosine is negative. In the fourth quadrant, cosine is positive.Thus, because cosine is negative in the second quadrant and positive in the fourth quadrant, [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex]. Therefore, the best explanation is: Cosine is negative in the second quadrant and positive in the fourth quadrant.
19. if a vechicle was purchased for $32345. there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
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What is the range of function y=√(-2cos^2x+3cosx-1)
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so the given function is
y= √(-2cos²x+3cosx-1)
i.e = √[-2(cos²x-3/2+1/2)]
i.e = √[-2(cosx-3/4)²-9/16+1/2]
i.e. = √[-2(cos-3/4)²-1/16]
i.e. = √[1/8-3(cosx=3/4)²]-----------(1)
Now here in this equation is this quantity :-
(cosx=3/4)²----------------(2) is to it's minimum value then the whole equation
i.e. = √[1/8-3(cosx=3/4)²] will be maximum and vice versa
And we know that cosx-3/4 will be minimum if cosx=3/4
therefore put this in (1) we get
(cosx=3/4)²=0 [ cosx=3/4]
hence the minimum value of the quantity (cosx=3/4)² is 0
put this in equation (1)
we get ,
i.e. = √[1/8-3(cosx=3/4)²]
=√[1/8-3(0)] [ because minimum value of of the quantity (cosx=3/4)² is 0 ]
=√1/8
=1/(2√2)
this is the maximum value now to find the minimum value
since this is function of root so the value of y will always be ≥0
hence the minimum value of the function y is 0
Therefore, the range of function y is [0,1/(2√2)]
__Well,I have explained explained each and every step,do tell me if you don't understand any step._
Which expression is the result of the perimeter of rectangle b minus the perimeter of rectangle a
Answers
6x + 10 + 4x - 4
10x + 6
Retangle A perimeter = 2(2x+8) + 2(x-1)
4x + 16 + 2x - 2
6x + 14
(10x + 6) - (6x + 14) =
10x + 6 - 6x - 14 =
4x - 8 ← answer
the height of a ball thrown directly up with a velocity of 40 feet per second from a initial height of 5 ft is given by the equation h(t)=-16t2+40t+5, where t is the time in seconds and h is the balls height, measured in feat. when will the ball hit the ground?
Answers
0=-16t²+40t+5
16t²-40t-5=0
Using the quadratic formula, we get a positive value for t of 2.61930639376 seconds.
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Convert 0.79 tons to pounds?
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Reflection across the x-asis?
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Help me (once again!)
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Move all over to LHS to have only one side of an inequality with "x".
3x^2 - 4x - ((6x^2 - 3x + 5)/10) < 0.
30x^2 - 40x - 6x^2 + 3x - 5 < 0
24x^2 - 37x -5< 0
So x is between -0.125 and 1.666...
The only integer solutions are 0 and 1, therefore there are 2 solutions.
If angle DAB measures 34 degrees, what is the measure of arc DB
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Jose made 33 of the 88 baskets for basketball team.What percent did he no make?
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A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 92m long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?
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If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?
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________________________
Explanation:
________________________
Since the formula for the volume, "V", of a cube, is:
V = s³ ;
in which: "s" = side length of a cube;
Given: "V = 384 cm³ " ; Plug this value into the formula; to solve for "s" ;
V = s³ ;
↔ s³ = V ;
s³ = V ;
s³ = 384 cm³ ;
Take the "cubic root" of EACH SIDE of the equation; to isolate "s" on one side of the equation ; & to solve for "s" ;
_________________________________________________
∛(s³) = ∛ (384 cm³) ;
s = 7.2684823713285586 cm
Round to: 7.268 cm .
__________________________________________________
A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?
A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total
Answers
Answer:
the answer is 16.76 ft option B
Step-by-step explanation:
The vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
What is the percentage?The Percentage is the value per hundred.
Distance traveled by the ball when it hits the ground first time =5m
After the first hit, it bounces to 60% of its previous height
60% of 5m =3m
This means ball goes 3m up and then 3m down before hitting for the second time.
So, the vertical distance traveled by the ball till the second hit=5+3+3 =11m
After the second hit, it bounces to 60% of its previous height
60% of 3m =1.8m
This means ball goes 1.8m up and then 1.8m down before hitting for the third time.
So, the vertical distance traveled by the ball till the third hit=11+1.8+1.8 = 14.6m
After the third hit, it bounces to 60% of its previous height
60% of 1.8m =1.08m
This means ball goes 1.08m up and then 1.08m down.
So, the vertical distance traveled by the ball till the fourth hit=14.6+1.08+1.08 = 16.76m
Hence, the vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
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A wall in Marcus's bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
Answers
Marcus's wall has an area of 140 square feet. If he paints half of it blue, 70 square feet will be blue.
To find the area of the wall, we multiply its height by its length:
[tex]\[ \text{Area of the wall} = \text{Height} \times \text{Length} \][/tex]
First, convert the mixed numbers to improper fractions:
- Height: [tex]\(8 \frac{2}{5} = \frac{42}{5}\) feet[/tex]
- Length: [tex]\(16 \frac{2}{3} = \frac{50}{3}\) feet[/tex]
Now, multiply:
[tex]\[ \text{Area} = \left( \frac{42}{5} \right) \times \left( \frac{50}{3} \right) \][/tex]
[tex]\[ \text{Area} = \frac{42 \times 50}{5 \times 3} = \frac{2100}{15} = 140 \text{ square feet} \][/tex]
If Marcus paints half of the wall blue, the area painted blue is:
[tex]\[ \text{Blue area} = \frac{1}{2} \times 140 = 70 \text{ square feet} \][/tex]
Therefore, 70 square feet of the wall will be blue.
Consider the equation 22+3x/3x+7=2 How do you begin isolating the variable x to one side of the equation?
Answers
You have 22+3x/3x+7=2. That 3x/3x raises eyebrows; is this what you meant, with the result that 3x/3x = 1? or did you mean
3x
22 + ------------- + 7 = 2?
3x+7
If you meant the latter, then simplify the equation by subtracting 2 from both sides:
3x
27 + ---------- = 0
3x+7
Multiply all three terms by (3x+7), obtaining
27(3x+7) + 3x = 0
Then 21x + 3x + 189 = 0, so that 24x = -189, or x = -189/24 = -7 7/8
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 1.5" by 2.25" on the drawing, how large is the bedroom?
Answers
The scale of the architectural drawing is such that 1/4" represents 1'. This means, if the room measures 1.5" by 2.25" on the drawing, it measures 6 feet by 9 feet in real life.
Explanation:In this scenario, the unit scale indicates that 1/4" on the drawing represents 1' in real life. So, to find the real-life dimensions of the room, you would need to convert the drawing dimensions to real-life dimensions.
For the length, 1.5" on the drawing would equate to 1.5 * 4 feet because every 1/4" equals 1 foot. Therefore, the length of the room is 6 feet.
The width of the room is similarly calculated. 2.25" on the drawing would equate to 2.25 * 4 feet which gives us a width of 9 feet.
So, the bedroom in real life is 6 feet by 9 feet.
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The bedroom is 6 feet by 9 feet in real life.
Explanation:To determine the actual size of the bedroom, we can use the scale given in the architectural drawing. The scale 1/4" = 1' means that every 1/4 inch on the drawing represents 1 foot in real life. In this case, the bedroom measures 1.5 inches by 2.25 inches on the drawing. To find the actual size, we can multiply these dimensions by the scale factor: 1.5 inches * (1 foot / 1/4 inch) = 6 feet, and 2.25 inches * (1 foot / 1/4 inch) = 9 feet. Therefore, the bedroom is 6 feet by 9 feet in real life.
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If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged
Answers
[tex]m_1, m_2, ....., m_1_2[/tex]
the average of these 12 marks is 90, so
[tex]\frac{m_1+ m_2+ .....+ m_1_2}{12}=90 [/tex]
which means
[tex]m_1+ m_2+ .....+ m_1_2=90*12=1080[/tex]
similarly, let [tex]n_1, n_2, ....., n_2_0[/tex] be the marks of the students in the second class,
so [tex] \frac{n_1+ n_2+ ..... n_2_0}{20}=80 [/tex]
which means [tex]n_1+ n_2+ ..... n_2_0=80*20=1600[/tex]
The 32 students averaged:
[tex] \frac{(m_1+ m_2+ .....+ m_1_2)+(n_1+ n_2+ ..... n_2_0)}{12+20}= \frac{1080+1600}{32}= \frac{2680}{32}= 83.75[/tex]
Mean = The sum of the data value ÷ Number of data
We would need the sum of 32 values to work out the mean score of 32 students. We will work out separately by finding the sum of scores of 12 students and sum of scores of 20 students
90 = Sum of data ÷ 12
Sum of data = 90×12 = 1080 scores
80 = Sum of data ÷ 20
Sum of data = 80×20 = 1600 scores
The sum of data of 32 students is 1080+1600 = 2680 scores
Mean = 2680÷32 = 83.75
A recipe for buttermilk biscuits calls for 3 and 1/3 cups of flour. How many cups of flour do you need for 1/2 the recipe.
Answers
Three less than the sum of four times a number and six is eight. Find the number.
Answers
4x + 3 = 8
4x = 8 - 3
4x = 5
x = 5/4 <==
Which is an equation for the line that passes through (0, 2) and (-2, 0)?
f. y = -x
g.y = x - 2
h.y = x + 2
j.y = -x - 2
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2. Give an example of how you use positive and negative numbers in the real world. Be sure to explain the meaning of 0 in your example.
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ABC is a right triangle in which B is a right angle, AB= 1, AC=2 and BC= square root of 3. Cos C x sin A=
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Applying the cosine and sine ratios, the value of cos C × sin A = 3/4.
What is the Cosine and Sine Ratios?Cosine ratio: cos ∅ = adj/hyp
Sine ratio: sin ∅ = opp/hyp.
Find cos C using the cosine ratio:
cos C = √3/2
Find sin A using the sine ratio:
sin A = √3/2
cos C × sin A = √3/2 × √3/2
= 3/4
cos C × sin A = 3/4
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What is an equation that equals 58 explain!
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Some equations that equal 58 include: 58x, 29 + 29, and y + 58x.
For example, 58x is equal to 58 because you can change x to 1, and 58 times 1 is 58. Therefore, it is equal to 58.
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Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0
Answers
2x + 5 = 3y
2/3x + 5/3 = y...slope here is 2/3. A perpendicular line will have a negative reciprocal slope. All that means is " flip " the slope and change the sign. So our perpendicular line will have a slope of -3/2.
y = mx + b
slope(m) = -3/2
(-1,2)...x = -1 and y = 2
sub and find b, the y int
2 = -3/2(-1) + b
2 = 3/2 + b
2 - 3/2 = b
4/2 - 3/2 = b
1/2 = b
so ur perpendicular equation is : y = -3/2x + 1/2 or 3x + 2y = 1 or 3x + 2y - 1 = 0
5/9 ÷ 5/7 plz a short answer doing it now o i hate math plz help so bad at it
Answers
5/9 / 5/7 =
5/9 * 7/5 = 35/45 reduce to 7/9
The top base of a trapezoid is 18 inches and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. What is the area of the trapezoid
Answers
Final answer:
The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.
Explanation:
To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.
Using the formula, we get:
A = (1/2) × (18 inches + 22 inches) × 8.5 inches
A = (1/2) × 40 inches × 8.5 inches
A = 20 inches × 8.5 inches
A = 170 square inches
So, the area of the trapezoid is 170 square inches.
1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien?
2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters?
3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel.
4. Lea's car travels on average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
Answers
1 alien = 15.5 oranges/7.2;
1 alien = 2.15 oranges (approximately).
2. We have everything to solve this problem. So in a scaled drawing 1 mm = 150 m. => 1 m = 1/150 mm on the drawing. Then 1 m^2 = (1/150 mm)^2 =>
1 m^2 = 1/22500 mm^2.
So the answer is 1/22500 mm^2.
3. The formula of the length is S=V*t. where V - the speed and t = the time. We already know that V = 60 mph and t = 8 seconds. But the measure of the speed is miles per hour, so we need to convert 8 seconds to hours.
8 seconds = 8/60 minutes = (8/60)/60 hours;
Our solution looks like this:
1) S = 60 mph * (8/60)/60 hours;
2) S = 8/60 miles;
3) S = 0.13 miles;
Answer is 0.13 miles.
4. First let's find out how many gallons of gas she spent during her trip:
172.5/30 = 5.75 gal;
Now we can find price per gallon:
20,70/5.75 = 3.60$ per gallon;
So the approximate cost of gas in dollars per gallon is 3.60$ per gallon.