It will take 3 tractors approximately 2.4 hours to plow the field.
Explanation:To find out how many hours it will take 3 tractors to plow the field, we can use the concept of work rates.
Given that 5 tractors can plow the field in 4 hours, we can set up a proportion:
5 tractors / 4 hours = 3 tractors / x hours
Cross-multiplying, we have:
5(x) = 3(4)
Simplifying, we get:
5x = 12
Dividing both sides by 5, we find that x = 2.4 hours.
Therefore, it will take 3 tractors approximately 2.4 hours to plow the field.
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It would take one tractor 20 hours to plow the field, so with the combined rate of three tractors, it will take them approximately 6.67 hours to plow the field together.
Explanation:The subject of this question is work-rate problems in Mathematics. To solve this problem, we must first determine the rate at which a single tractor can plow the field. If five tractors can plow a field in four hours, then one tractor would take five times as long, or 20 hours, to plow that same field alone.
Knowing this, we can now calculate how long it would take three tractors to plow the field together. Since one tractor takes 20 hours to plow the field, the rate of one tractor is 1 field per 20 hours. Therefore, three tractors would work at a rate of 3 fields per 20 hours, and so, it will take them 20/3, or approximately 6.67 hours to plow the field together.
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The ratio of girls to boys at a movie is 3:8. If there are 32 boys, how many girls are at the movie
Answer:
12
Step-by-step explanation:
8*4=32
So they simplified the ratio by dividing by 4, and we can multiply 3*4 to get the finishing number:
12
The final ratio would be 12:32
Answer:
twelve
Step-by-step explanation:
if the ratio of girls to boys is 3:8, the you have to multiply eight by four. Then, you multiply three by four because you need to keep it equal.
CAN SOMEONE HELP ME PLEASE ILL GIVE BRAINLEST..I need step to step equation thanks
Answer:
The required co-ordinate is (-2, -5).
Step-by-step explanation:
For a given point, reflection of a point (x, y) across a horizontal line y = k, the reflected co-ordinates will be: [tex]$ R_{y = k} = (x, 2k - y) $[/tex].
Here, (x, y) = (-2, 7) then reflection along the line y = 1, we get:
[tex]$ R_{y = 1} (-2, 7) = (-2, 2(1) - 7) $[/tex]
= (-2, -5)
The reflected point is (-2, -5).
what does this expression represent?
g3/10
A: a number divided by ten.
B: a number to the third power times by ten.
C: a number to the third power divided by ten.
D: a number to the second power divided by ten.
Answer:
Step-by-step explanation:
A: a number divided by ten. **g/10**
B: a number to the third power times by ten. **10g³**
C: a number to the third power divided by ten. **g³/10**
D: a number to the second power divided by ten. **g²/10**
answer: C
PLzz help easy math...............
Good evening ,
Answer:
A. 2n-1
Step-by-step explanation:
It’s an arithmetic series
with first term 1
Un = U₁ + r×(n-1)
= 1 + 2× (n-1)
= 1 + 2n -2
= 2n - 1.
:)
Answer:
A. 2n-1
Step-by-step explanation:
Find x.
300
043
00.
083
08
00
02 V3
Answer:
Therefore the value of x is 8 unit.
Step-by-step explanation:
Given:
In Right Angle Triangle ABC
angle B = 90°
angle C = 30°
AB = 4
To Find:
AC = Hypotenuse = ?
Solution:
In Right Angle Triangle ABC Sine Identity we have
[tex]\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\[/tex]
Substituting the given values we get
[tex]\sin 30 = \frac{AB}{AC}[/tex]
[tex]\dfrac{1}{2} =\dfrac{4}{x}\\\\\therefore x=4\times 2=8\\\\\therefore x =8[/tex]
Therefore the value of x is 8 unit.
a+ 1/2 b+ 2/5 + 3/2 a+ 1/4 b simplify the expression
You hope to reach $10,000 savings in 6 years in an account paying 1.5%. What is the present value?
All answers will include a $sign.
Answer:
[tex]P=\$9,174.31[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested or present value
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=6\ years\\ P=?\\ A=\$10,000\\r=1.5\%=1.5/100=0.015[/tex]
substitute in the formula above
[tex]10,000=P(1+0.015*6)[/tex]
solve for P
[tex]10,000=P(1.09)[/tex]
[tex]P=10,000/(1.09)[/tex]
[tex]P=\$9,174.31[/tex]
Move 1 match stick in the number 369 to make the biggest number
Given number is 369. The number 3 is made of 5 match sticks, 6 is made of 6 match sticks and 9 is also made of 6 match sticks.
Let us try the possibilities of moving 1 match stick to make the biggest number.
(a) If the left upper match stick from 9 is moving to right upper position of 6, then the number will be 383.
(b) If the left bottom match stick from 6 is moving to left bottom position of 9, then the number will be 358.
(c) If the right upper match stick from 9 is moving to right upper position of 6, then the number will be 385.
(d) If the right upper match stick from 9 is moving to left upper position of 3, then the number will be 965.
The above four trials are shown in the below attachment.
Among these four possibilities, 965 is the biggest number.
A produce store offers red and green apple. In one morning they sold 77 apples total. If 7 of the apples they sold were red, what is the ratio of green apples sold to red apples apples sold?
Answer:1:10 is the ratio
Step-by-step explanation:if 7 are red then there are only 70 green left so there are 7 red to every 70 green or reduced is 1:10
Answer:
10:1
Step-by-step explanation:
70 green apples were sold, and 7 red apples were. So, the ratio of green to red would be 70:7. Reduce it and you get 10:1
Listen to the subtraction word problem jane has nine counters three of her counters are red the rest of her counters are yellow
Answer:6 of her counters are yellow.
9-3=6
A cuboid is of dimensions 72 cm x 66 cm x 56 cm. Find the total number of small cubes
with side 12 cm that can be placed in the given cuboid.
Answer:
154 small cubes.
Step-by-step explanation:
We are given the dimensions of the cuboid as 72 cm × 66 cm × 56 cm.
So, length of the cuboid, l = 72 cm
Breadth of the cuboid, b = 66 cm
Height of the cuboid, h = 56 cm
Capacity of cuboid = l × b × h = 72 × 66 × 56 = 266112 cm³
Now, we have to find the number of small cubes of side 12 cm each that can be placed in the given cuboid.
Now, length of each side of each small cube, s = 12 cm
Volume of each small cube = s³ = (12)³ = 12 × 12 × 12 = 1728 cm³
For calculating the number of small cubes that can be placed in the given cuboid, we will divide the capacity of given cuboid by volume of each small cube.
Required number of cubes = [tex]\frac{Capacity\; of\; cuboid}{volume\; of\; each\; small\; cube}[/tex]
⇒ Number of cubes = [tex]\frac{266112}{1728}=154[/tex]
∴ 154 small cubes each of side 12 cm can be placed inside the given cuboid of dimensions 72 cm × 66 cm × 56 cm.
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games. His friend victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed. If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games
Answer:
Kyle
Step-by-step explanation:
Kyle:
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.
Victor:
Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed. If Victor spends 5 hours doing homework or reading, then he could play
[tex]30\cdot 5=150[/tex] minutes
that is
[tex]120+30=2[/tex] hours [tex]30[/tex] minutes (less than 3 hours).
Hence, if both boys spend the same amount of time on homework and reading this week, then Kyle will have more time to play video games.
Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. q2+11q
Answer:
[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]
Step-by-step explanation:
We have been given an expression [tex]q^2+11q[/tex]. We are asked to complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.
We know that a perfect square trinomial is in form [tex]a^2+2ab+b^2[/tex].
To convert our given expression into perfect square trinomial, we need to add and subtract [tex](\frac{b}{2})^2[/tex] from our given expression.
We can see that value of b is 11, so we need to add and subtract [tex](\frac{11}{2})^2[/tex] to our expression as:
[tex]q^2+11q+(\frac{11}{2})^2-(\frac{11}{2})^2[/tex]
Upon comparing our expression with [tex](a+b)^2=a^2+2ab+b^2[/tex], we can see that [tex]a=q[/tex], [tex]2ab=11q[/tex] and [tex]b=\frac{11}{2}[/tex].
Upon simplifying our expression, we will get:
[tex](q+\frac{11}{2})^2-\frac{11^2}{2^2}[/tex]
[tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex]
Therefore, our perfect square would be [tex](q+\frac{11}{2})^2-\frac{121}{4}[/tex].
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
The standard form of a quadratic equation is expressed as [tex]ax^2+bx+c=0[/tex]
Given the equation [tex]q^2+11q[/tex], we need to add a constant value that will make the expression a perfect square.
To complete the square, we will add the square of the half of the coefficient of q to the equation
Coefficient of q = 11
Half of the coefficient = 11/2
Square of the result = (11/2)² = 121/4
Adding 121/4 to the equation will make it a perfect square to have [tex]q^2+11q + \frac{121}{4}[/tex]
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If Gary spends 10 hours per week on the internet and 9 hours per week playing video games. If Gary has 5 hours of free time per day what percent of his free time is used on video games and the internet?
54 % of his free time is used on video games and internet
Solution:
Given that Gary spend 10 hours per week on the internet and 9 hours per week playing video games
Gary has 5 hours of free time per day
We know that, 1 week = 7 days
5 hours of free time per day, So for 1 week get,
7 x 5 = 35 hours of free time per week
Time spent per week on internet and video game = 10 + 9 = 19 hours per week
The percent of free time used on video games and internet is:
[tex]percent = \frac{\text{ Time spent per week on internet and video game }}{\text{ 35 hours of free time per week}} \times 100[/tex]
[tex]percent = \frac{19}{35} \times 100 = \frac{1900}{35}\\\\percent = 54.286 \approx 54[/tex]
Thus 54 % of his free time is used on video games and internet
What are the solutions to x2 + 8x + 7 = 0?
Answer:
x=-1, -7
Step-by-step explanation:
x^2+8x+7=0
factor out the trinomial,
(x+1)(x+7)=0
zero property,
x+1=0, x+7=0
x=0-1=-1,
x=0-7=-7
Which statements are true regarding the area of circle
D? Select two options
18 cm
The area of the circle depends on the square of the
radius
The area of circle D is 36
cm
The area of circle Dis 3240 cm?
The area of the circle depends on the square of pi.
The area of the circle depends on the central angle
Question:
Which statements are true regarding the area of circle D? Select two options.
The area of the circle depends on the square of the radius.
The area of circle D is 36Pi centimeters squared.
The area of circle D is 324Pi centimetres squared
The area of the circle depends on the square of pi.
The area of the circle depends on the central angle.
Answer:
The following statements are true regarding the area of circle D:
The area of the circle depends on the square of the radius The area of circle D is 324Pi centimetersStep-By-Step Explanation:
As we know, the formula for area of the circle is given by,
[tex]A=\pi r^{2}[/tex]
Where, r = radius of the circle. In figure, CD = radius = 18 cm
So, the circle area can be measured as
[tex]A=\pi(18)^{2}=324 \pi \mathrm{cm}^{2}[/tex]
From this, concluding that the circle area depends on radius square and its value is [tex]324 \pi \mathrm{cm}^{2}[/tex]. Hence, the statement given in option A and C are correct (reveals that option B is incorrect).
As the Pi is constant, the circle radius cannot depend on Pi value and Option D also incorrect. The area of sector of circle only depends on ratio of central angle to entire circle (So option E also incorrect).
Jennifers math scores for the third quarter were 78, 89, 93, 73, 99, 87, 92, and 89. What is the range of her scores
The range of Jennifer's math scores for the third quarter is 26.
Explanation:The range of Jennifer's math scores for the third quarter can be determined by subtracting the lowest score from the highest score. In this case, the lowest score is 73 and the highest score is 99. Therefore, the range is 99 - 73 = 26.
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Which expression is equivalent to
2/3(9x-6)+4(1/2 x -- 1/2)
1/2 and 3/4 are fractions
Answer:
Given expression [tex]\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})[/tex] is equivalent to the expression [tex]2(4x-3)[/tex].
Step-by-step explanation:
Given expression is [tex]\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})[/tex]
To simplify the expression:
[tex]\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=\frac{18x-12}{3}+\frac{4x-4}{2}[/tex]
Taking LCM 6 to the above expression we get
[tex]=\frac{(18x-12)2+3(4x-4)}{6}[/tex] (Applying multiplication rules)
[tex]=\frac{36x-24+12x-12}{6}[/tex] ( doing sums to the terms)
[tex]=\frac{48x-36}{6}[/tex]
[tex]=8x-6[/tex]
We can take common number 2 outside to the above expression
[tex]=2(4x-3)[/tex]
Therefore [tex]\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})=2(4x-3)[/tex]
Therefore given expression [tex]\frac{2}{3}(9x-6)+4(\frac{1}{2}x-\frac{1}{2})[/tex] is equivalent to the expression [tex]2(4x-3)[/tex].
mateo has 6.5 cups of sugar. how many batches of cookies can he make if each batch requires 3/4 cups of sugar?
The requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Mateo has 6.5 cups of sugar.
Each batch requires 3/4 cup of sugar,
Batches of cookies can he make,
= total cups of sugar/ 1 beach requires cups of sugar
= 6.5 / [3/4]
= 8.67 batches of cookies can be made.
Thus, the requried batch of sugar that can be made by 6.5 cups of sugar is 8.67 batches.
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A CD costs $15.50 before tax. What is the total cost after a 6% sales tax is added?
Answer:
16.43
Step-by-step explanation:
(6% /100%)* 15.50
= 16.43
Answer: $16.43
Step-by-step explanation:
How many seconds are in 250 days?
Quite an interesting question, let us see.
60 seconds in a minute60 x 60 seconds in an hour60 x 60 x 24 seconds in a day60 x 60 x 24 x 250 seconds in 250 days60 x 60 x 24 x 250 = 21,600,000
answer: 21,600,000
Step-by-step explanation: First, let's convert days to hours by multiplying 250 by the conversion factor of 24 to get 6,000 hours. Next we can convert hours to minutes by multiplying 6,000 by the conversion factor 60 to get 360,000 minutes. Finally, we convert minutes to seconds by multiplying 360,000 by the conversion factor 60 to get 21,600,000.
So, there are 21,600,000 seconds in 250 days.
Starting from point a, find the point that would cut the line segment created by the points A (-1,4) and B (5,4) into a ratio of 3:4
The coordinates of points are: (11/7 , 4)
Step-by-step explanation:
The formula for a point which divides a line in ration m:n is given by:
[tex]P(x,y) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]
Here
(x1,y1) = (-1,4)
(x2,y2) = (5,4)
m = 3
n = 4
So putting the values in the formula
[tex]P(x,y) = (\frac{(3)(5)+(4)(-1)}{3+4},\frac{(3)(4)+(4)(4)}{3+4})\\= (\frac{15-4}{7},\frac{12+16}{7})\\=(\frac{11}{7}, \frac{28}{7})\\=(\frac{11}{7} , 4)[/tex]
The coordinates of points are: (11/7 , 4)
Keywords: Ratio, fraction
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Name the largest angle in the figure.
AXC
DXA
BCD
Answer:
DXAStep-by-step explanation:
In a figure like this, the largest angle is formed from the two outermost points, which are D and A. Since the vertex is X, the angle is DXA.
I'm always happy to help :)The points (–2, 4) and (–2, –2) are vertices of a heptagon. Explain how to find the length of the segment formed by these endpoints. How long is the segment?
Answer:
The segment is 6 units long.
Step-by-step explanation:
The points (–2, 4) and (–2, –2) are vertices of a heptagon. We have to explain how to find the length of the segment formed by these endpoints.
If two points at the ends of a straight line PQ are P([tex]x_{1},y_{1}[/tex]) and Q([tex]x_{2},y_{2}[/tex]), then the length of the segment PQ will be given by the formula
[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]
Now, in our case the two points are (-2,4) and (-2,-2) and the length of the segment will be
[tex]\sqrt{(- 2 - (- 2))^{2} + (4 - (- 2))^{2}} = 6[/tex] units. (Answer)
The length of the segment is 6 units.
It is given that,
Points (–2, 4) and (–2, –2) are vertices of a heptagon.To find the length of the segment formed by these endpoints.
Explanation:
The distance formula is used to find the length of the segment formed by two endpoints.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(-2-(-2))^2+(-2-4)^2}[/tex]
[tex]d=\sqrt{(0)^2+(-6)^2}[/tex]
On further simplification, we get
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
Thus, the length of the segment is 6 units.
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sharif ran a 2 mile race at an average speed of 8 miles per hour. if arif ran the same race at an average speed of 6 mile per hour, how many minutes longer than sharif did arif take to complete the race?
Divide miles ran by speed to get time:
2 miles / 8 miles per hour = 0.25 hours = 15 minutes.
2 miles / 6 miles per hour = 0.33 hours = 20 minutes.
20 minutes - 15 minutes = 5 minutes longer.
Final answer:
After calculating the time taken by each runner to complete the 2-mile race, we find that Arif took 5 minutes longer than Sharif to finish.
Explanation:
To determine how many minutes longer Arif took to complete the race compared to Sharif, we need to calculate the time each runner took to complete the 2-mile race. First, we calculate Sharif's time. Since speed is distance divided by time, we can rearrange the formula to find time: time = distance/speed.
For Sharif:
Distance = 2 miles
Speed = 8 miles per hour
Time = 2 miles / 8 mph = 0.25 hours
Convert Sharif's time from hours to minutes by multiplying by 60 minutes per hour (0.25 hours * 60 minutes/hour = 15 minutes).
For Arif:
Distance = 2 miles
Speed = 6 miles per hour
Time = 2 miles / 6 mph = 0.333... hours
Convert Arif's time from hours to minutes (0.333... hours * 60 minutes/hour = 20 minutes).
Now, to find the difference in time, subtract Sharif's time from Arif's time:
Difference = Arif’s time - Sharif's time = 20 minutes - 15 minutes = 5 minutes
Arif took 5 minutes longer than Sharif to complete the race.
plz answer !! I need your help
Answer:
110°
Step-by-step explanation:
Angles of a quadrilateral add up to 360:
70 + 40 + ∠B + ∠O = 360
∠B + ∠O = 250
The central angle between A and C is double the angle B. And, it plus angle O add up to 360.
Therefore:
2∠B + ∠O = 360
Solve the system of equations. Subtracting the first equation from the second:
∠B = 110
A company wants to give a coffee cup to each of its employees. If there are 533 employees and the cups must be ordered in boxes of 12, how many boxes should the company buy?
Answer:
45
Step-by-step explanation:
533÷12=44R5
44R5≈45
7. On a scale drawing of a planned office space, one inch represents 6 feet.
How wide is the conference room if the width in the drawing is 3 inches?
Answer:
The width of the conference room = 18 feet
Step-by-step explanation:
Given:
Scale drawing of a planned office space is represented as
1 in : 6 feet
To find the width of the conference room if the width in the drawing is 3 inches.
Solution:
Scale is the representation of ratio of lengths in the drawing to the actual length.
The scale given here means that 1 inch length in the drawing corresponds to 6 feet length actually.
Thus, in order to find the actual length of 3 inches, we can use unitary method
If 1 inch in drawing corresponds to = 6 feet
∴ 3 inches in drawing corresponds to = [tex]3\times 6 \ft[/tex] = 18 feet
Thus, width of the conference room = 18 feet
Bill is building a sand box for his son to play in. The length is 2 feet more than the width. He has 20
feet of boards. What are the dimensions of his sand box?
Final answer:
To find the dimensions of Bill's sand box, use the given constraints and solve for the width and length using a simple equation.
Explanation:
Bill's sand box dimensions:
Let the width be x.
Length = x + 2.
Given 20 feet of boards, 2x + 2(x + 2) = 20.
Solving the equation, x = 4 feet (width) and length = 6 feet.
Jason and Michael are playing a game. For each question answered correctly, they earn 5 points. For each incorrect response, they lose five points. If Jason answers three questions incorrectly, what will be his final score?
Answer:
- 15 points
Step-by-step explanation:
For each question answered correctly, they earn 5 points and for each incorrect response, they lose five points.
Therefore, the score after answering the wrong one will reduce by 5 points.
Let us assume that the initial score of Jason is zero and he answers three questions incorrectly.
Therefore, Jason's final score will be [0 - (5 × 3)] = - 15 points. (Answer)