60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
According to the question,
We have the following information:
3 digits integers are to be made from 1,2,3,4 and 5
So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.
Now, we have:
Total number of digits = 5
Number of digits to be made = 3
So, we have:
[tex]^{5} P_{3}[/tex]
Solving this expression:
5*4*3
60
Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
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the side lengths of the state flag of Michigan are in the ratio 4:7. if the flag is 28 feet long, what is its height?
If the side lengths of the state flag of Michigan are in the ratio 4:7. when the flag is 28 feet long the height will be 49 feet
How to calculate the height of the flagThe height of the flag is calculated using the scale factors, 4 : 7
if 4 is equivalent to 28 what would 7 be
4 / 7 = 28 / ?
4 * ? = 7 * 28
? = 7 * 28 / 4
? = 49 feet
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Given m \| nm∥n, find the value of x.
The value of x is 6.67 degrees.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
The (5x + 9)° angle on line m and the (7x - 9)° angle on line n are corresponding angles.
We have given that Line m and Line n are parallel.
t line is the transversal line on the two parallel lines, line m and line n.
We see that,
(5x + 9)° angle on line m is corresponding to the (7x - 9)° angle on line n.
So,
(5x + 9)° + (7x - 9)° = 180
12x = 180
x = 80 /12
x = 6.67
Thus, The value of x is 6.67 degrees.
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The length of a line is given as 12.2 cm, rounded to the nearest tenth of a cm.
a) What is the lower bound of the length of the line?
b)
What is the upper bound of the length of the line?
a) The lower bound of the length of the line is 12.12
b) The upper bound of the length of the line is 12.25
What is a lower bound?
The least value that would round up to the predicted value is the lower bound. The smallest value that would round up to the following anticipated value is the upper bound.
What is an upper bound?
A value that is greater than or equal to every element of a set of data.
What is the difference between the lower and upper bound?
An element of K that is greater than or equal to each element of S is known in mathematics as an upper bound or majorant of the subset S of some preordered set (K, ), especially in order theory. In addition, each element of K that is less than or equal to each element of S is characterized as a lower bound or minorant of S.
Here,
We have to find the lower bound and upper bound of 12.2
We get a lower bound = 12.12
and upper bound = 12.25
Hence, a) The lower bound of the length of the line is 12.12
b) The upper bound of the length of the line is 12.25
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the initial pressures for bicycle tires when first filled are normally distributed, with a mean of 70 pounds per square inch (psi) and a standard deviation of 1.2 psi. a random sample of 15 tires is drawn from this population. what is the probability that the mean tire pressure of the sample is less than 69 psi?
the probability that the mean tire pressure of the sample is less than 69 psi 0.2030
The formula of the z-score is z = (x - μ)/σ, where
x is the score
μ is the mean
σ is the standard deviation
given,
a mean of 70 pounds per square inch
μ = 70
the standard deviation of 1.2 psi.
σ = 1.2
the sample is less than 69
x=69
so on substituting
z=(69-70)/1.2
z=-1/1.2
z=-0.83
The value corresponding to the z score is 0.2030 i.e 20.30%
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There were 500 lions in an African nature
reserve. 3 years later there were 864 lions in
the same nature reserve.
a) Work out the percentage increase per year,
assuming that the number of lions increased
by the same percentage each year.
b) Use your answer to part a) to predict the
number of lions in the nature reserve after
another year.
Round your answer to the nearest integer.
The percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.
Given that, there were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let the percentage increase per year be x.
a) According to the question,
500(1+x)³=864
⇒ (1+x)³=864/500
⇒ (1+x)³=1.728
⇒ 1+x= 1.2
⇒ x =0.2
In percentage 20%
b) [tex]500(1+0.2)^1[/tex]
= $600
Hence, the percentage increase per year, assuming that the number of lions increased by the same percentage each year is 20%.
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Help right now please!
Andrew believes that the probability that he will win the tennis match is 39% What
is the probability that he will lose the match?
Answer:
39%
Step-by-step explanation:
Please help need it in the next 5 mins
Answer:
y = 4x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
here m = 4 , then
y = 4x + c ← is the partial equation
to find c substitute (2, 9 ) into the partial equation
9 = 8 + c ⇒ c = 9 - 8 = 1
y = 4x + 1 ← equation of line
1/3 Marks
10/29 Marks
Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
b)
How many sticks would be in pattern number n?
32
6n
The number of sticks in the sixth and nth patterns will be 32 and 5n + 2, respectively.
What is an arithmetic sequence?Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
In the first pattern, the number of sticks is 7. Then in each succession of the pattern, 5 sticks are added, then the number of sticks in the nth pattern will be given as,
aₙ = 7 + (n - 1) × 5
aₙ = 7 + 5n - 5
aₙ = 5n + 2
The number of sticks in the 6th pattern will be calculated as,
a₆ = 7 + (6 - 1) × 5
a₆ = 7 + 5 × 5
a₆ = 7 + 25
a₆ = 32
The number of sticks in the sixth and nth patterns will be 32 and 5n + 2, respectively.
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there are 280 counters in a bag
1/2 of the counters are red
2/5 of the counters are yellow
the rest are green
work out the number of green counters in the bag
Answer:
84 counters
Step-by-step explanation:
⅖ + ½ = 7/10
10 - 7 = 3
280 ÷ 10 × 3 = 84
Answer:
28
Step-by-step explanation:
1/2×280=140(red counters)
2/5×280=112(yellow counters)
140+112=252
280-252=28(green counters)
What set of reflections would carry hexagon abcdef onto itself? hexagon abcdef on the coordinate plane with point a at 0, 1, point b at negative 1, 0, point c at negative 2, 1, point d at negative 2, 3, point e at negative 1, 4, and point f at 0, 3. x‒axis, y = x, x‒axis, y = x y-axis, x‒axis, y-axis x‒axis, y-axis, y-axis y = x, x‒axis, y = x, y-axis
The correct answer to reflection of hexagon is Option B
y=x, x-axis, y=x, y-axis
What is hexagon?
6-sided polygon is called hexagon , it is type of polygon( a plane figure made up of lines).
Main body:
using point B(−3,1)
Across the line y=x(x,y)→(y,x)
so we get (1,−3)
Across the x-axis (x,y)→(x,−y)
we get (1,3)
Across the line y=x(x,y)→(y,x)
we get (3,1)
Across the y-axis (x,y)→(−x,y)
we get (−3,1)
Hence the option B is correct.
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if a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is . a. .20 b. 0 c. .03125 d. .50
The probability of getting all heads when flipping a coin four times is 1/16.
(HHHH), (HHHT), (HHTH), (HHTT), (HTHH), (HTHT), (HTTH), (HTTT), (THHH), (THHT), (THTH), (THTT), (TTHH), (TTHT), (TTTH), (TTTT) are some examples of spaces.
There were 16 total outcomes.
Probability going out of control
HHHH P(A) = P(getting all heads) = 1/16
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What is the solution of the following system?
Use the substitution method.
{y+7=3x6x−2y=12
Responses
The only solution is (14, 12) .
The only solution is , begin ordered pair 14 comma 12 end ordered pair, .
The only solution is (12, 14) .
The only solution is , begin ordered pair 12 comma 14 end ordered pair, .
There is no solution.
There is no solution.
There are an infinite number of solutions.
The given system of equations has no solution.
What is substitution method?
In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this procedure before the variable's value is substituted in the second equation.
Consider, the given system of equations,
y + 7 = 3x ..(1)
6x - 2y = 12 ..(2)
From equation (1),
y = 3x - 7.
Substitute value of (y) in inequation (2),
6x - 2(3x - 7) = 12
6x - 6x - 14 = 12
-14 = 12
It is not possible to solve -14 = 12.
Therefore, the given system of equations has no solution.
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Instructions
Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay.
Create and solve a story problem that would use this equation: y=5x+3 Be sure to define x, y, the constant, the coefficient and the variable.
A statement of the equation could be as; "John bought y oranges which are 5 times the apples more than 3".
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The information provided is that the real-world situation in which opposite quantities combine to make zero.
We have been given an equation as y = 5x + 3
A statement of equation could be as; "John bought y oranges which are 5 times the apples more than 3".
If the number of apple x is 6 then;
y = 5x + 3
y = 5(6) + 3
y = 33
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A train travels 1 kilometre in 1 minute 20 seconds At this rate, how many kilometres will the train travel in 1 hour?
The train will travel for approximately 50 kilometres in 1 hours.
How to find the time in hours the train covers?The train travels 1 kilometre in 1 minute 20 seconds.
At this rate the number of kilometres the train will travel in 1 hour can be calculated as follows;
Therefore, lets convert 1 minutes and 20 second to hours.
20 seconds = 0.333333 minutes
Hence,
60 minutes = 1 hour
1.33333 minutes = ?
cross multiply
time in hours = 1.3333 / 60
time in hours = 0.02222221666
Therefore,
0.02 hours = 1 km
1 hours = ?
number of kilometres the train will travel in 1 hours = 1 / 0.02 = 50 km
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9.34 billions of pounds
Hope that helps ;)
Solve the simultaneous equation
y = 2 - x 6x + 5y = 11
x + 2y = 2 2x + y = 1
The solution for the -
Simultaneous equation [1]
y = 2 - x
6x + 5y = 11
is (1, 1)
AND
Simultaneous equations [2]
x + 2y = 2
2x + y = 1
is (0, 1)
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have the following set of equations
Simultaneous equation [1]
y = 2 - x
6x + 5y = 11
Simultaneous equations [2]
x + 2y = 2
2x + y = 1
These are the equations of a straight line. Plotting the graphs and finding the point of intersection would give us the solution. It can be seen from the graphs that the solution is given for first set is of simultaneous equations as (1, 1) and the second set of simultaneous equations as (0, 1)
Refer to the two graphs attached.
Therefore, the solution for the -
Simultaneous equation [1]
y = 2 - x
6x + 5y = 11
is
(1, 1)
AND
Simultaneous equations [2]
x + 2y = 2
2x + y = 1
is
(0, 1)
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You have $20 and you make $5 an hour at your job. Your brother has $10 and makes $10 an hour at his job. Write and solve an equation to find out how many hours it will take for you and your brother to have the same amount of money.
Answer:
Let h = number of hours.
[tex]20 + 5h = 10 + 10h[/tex]
[tex]4 + h = 2 + 2h[/tex]
[tex]4 = 2 + h[/tex]
[tex]h = 2[/tex]
In 2 hours, we will have the same amount of money.
3.57x10^9 in scientific notation
Answer:
3.57 × 10⁹
Step-by-step explanation:
Scientific Notation:
a × 10ᵇ*Note: Your problem is already in scientific notation.
Answer: 3,570,000,000
Step-by-step explanation:
Your problem is already in scientific notation but if you are trying to turn it into a standard form, then that is the answer
an urn contains two red balls and three white balls. if a ball is chosen at random, what is the probability that it is white?
If an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white ball is 3/5
The number of red balls = 2 balls
The number of white balls = 3 balls
Total number of balls = 2 + 3
= 5 balls
The probability = Number of favorable outcomes / Total number of outcomes
Number of favorable outcomes = Number of white balls = 3
Total number of outcomes = 5
The probability = 3/5
Hence, if an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white is 3/5
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Makayla spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 5750 feet. Makayla initially measures an angle of elevation of 16^{\circ} ∘ to the plane at point AA. At some later time, she measures an angle of elevation of 31^{\circ} ∘ to the plane at point BB. Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary.
The distance the plane traveled from point A to point B is 10952 feet approx.
To solve this we have to use the Pythagoras theorem.
Given that the plane is at a constant height which can be supposed as the perpendicular (i.e 5750 feet) for the triangle which the plane , ground and the makayla make.
Now when the plane is at the A point then the angle of the elevation is 16°, so the distance from the makayla the plane is :
tanθ = P/B,
B(distance of makayla to plane on ground at point A) = P/tanθ ,
B = 5750 / tan 16°,
B = 5750/ 0.28;
B1 = 20535 feet approx
Similarly when the plane reach at the point B then the angle of the elevation is 31° then the distance from the makayla and the plane would be different, which will be :
tanθ = P/B,
B(distance of makayla to plane on ground at point B) = P/tanθ ,
B = 5750 / tan 31°
B = 5750 / 0.6
B2 = 9583 feet approx
now the distance traveled by the plane is B1 - B2 :
which is 20535 - 9583
10952 feet approx
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Answer:10483
Step-by-step explanation:
5 A pole 5 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Zoe measures the distance from
the pole to the stake and from the pole to the tower, as shown in the diagram below.
Find the length of the guy wire, to the nearest foot.
The length of the guys wire to the nearest foot is 56 feet.
How to find the length of the guy wire?The pole 5 ft tall is used to support the guy wire for the tower, which runs from the tower to a metal stake in the ground.
The situations forms a right angle triangle.
Therefore, the length of the guy wire can be found as follows:
Using trigonometric ratios, we can find the angle the guy wire made with the ground.
tan ∅ = opposite / adjacent
tan ∅ = 5 / 1
∅ = tan ⁻¹ 5
∅ = 78.690067526
∅ = 78.69°
Therefore, let's find the length of the guy wire using the angle.
cos 78.69° = adjacent / hypotenuse
0.1961172908 = 11 / h
h = 11 / 0.1961172908
h = 56.088884361
Therefore,
length of the guy wire = 56 feet
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Thando divided 1572 by a certain number,and got an answer of 104,remainder 12 what number did she divide 1572
The number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts.
Given:
The dividend = 1572,
The quotient = 104,
The reminder = 12
Calculate the divisor by the following formula,
Dividend = Divisor × quotient + Reminder
Substitute the values,
1572 = Divisor × 104 +12
Divisor = 15
Therefore, the number she divides the 1572 and got an answer of 104, the remainder of 12 is 15.
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A 0. 2 kg red ball is thrown horizontally at a speed of 4 m/s from a height of 3 m. A 0. 4 kg green ball is thrown horizontally from the same height at a speed of 8 m/s. Compared to the time it takes the red ball to reach the ground, the time it takes the green ball to reach the ground is.
The ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
By using the equations of motion we first find the acceleration and time of both the balls using [tex]v^{2} -u^{2} =2as[/tex] and [tex]v=u+at[/tex]
where,
v=final velocity,
u=intial velocity,
a=acceleration,
s=height,
t=time
For the red ball,[tex]v^{2} -u^{2} =2as[/tex], v=4m/s, u=0m/s, s=3m by substitiuting in the equation we get ,
[tex]4^{2} -0^{2} =2*a*3[/tex],
acceleration=a=16/6=8/3,
[tex]v=u+at[/tex] by substituting we get,
4=0+8/3*t,
time taken by the red ball to reach ground t=3/2
For the green ball,[tex]v^{2} -u^{2} =2as[/tex], v=8m/s, u=0m/s, s=3m by substituting in the equation we get ,
[tex]8^{2} -0^{2} =2*a*3[/tex],
acceleration=a=64/6=32/3,
[tex]v=u+at[/tex] by substituting we get,
8=0+32/3*t,
time is taken by the green ball to reach ground t=3/4
and their ratio of time red ball/green ball=(3/2)/(3/4)=2/1,
hence time to reach the ground is independent of their mass
therefore, the ratio of time that the red ball reaches the ground when compared with the green ball is 2:1
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In the diagram below of triangle ABC,
D is the midpoint of AC and E is the
midpoint of BC. If DE = 34 - 6x,
and AB = 28 - 4x, what is the measure
of DE?
A
Answer:
DE =
Submit Answer
D
C
E
B
Using midpoint theorem the value of DE is 4.
What is midpoint theorem?
According to the midpoint theorem, "The line segment of a triangle linking the midpoint of its two sides is said to be parallel to its third side and is also half the length of the third side."
Here using midpoint theorem we know that ,
=> DE = 1/2 AB
Here DE=34-6x and AB=28-4x.
=> 34-6x=1/2(28-4x)
=>68-12x=28-4x
=> 12x-4x=68-28
=> 8x = 40
=> x =5.
Now put x=5 into DE then,
=> DE=34-6(5)=34-30 = 4.
Therefore using midpoint theorem value of DE is 4.
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The perimeter of a rectangle is 72 inches. Its length is 6 inches greater than twice its width. Write and solve a system of equations that represents this situation.
f(x) =
g(x)=
solution:
Answer:
Step-by-step explanation:
first up, the perimeter is 4 side added up. so we do 72/4= which equals 18. we need to apply the 6 to the sides so we do 6/2=3 18/3=15 f=15 18+3= 21 one side is 15 & the other side is 21 to double check, 21+15*2= 72
Any help on this? ;-;
Answer:
last one: 20
Step-by-step explanation:
4 divided by 5 is 0.8
so is 20 divided by 25
URGENT
Two mechanics worked on a car. The first mechanic charged $115 per hour, and the second mechanic charged $55 per hour. The mechanics worked for a combined total of 25 hours, and together they charged a total of $2575. How long did each mechanic work?
The first mechanic worked 20 hours and the second mechanic worked 5 hours
The work charge of first mechanic = $115 per hour
The work charge of second mechanic = $55 per hours
Total number of hours they worked = 25 hours
The total amount they charged = $2575
Consider the number of hours that first mechanic work as x and second mechanic as y
Then the equations will be
x + y = 25
x = 25 -y
The second equation
115x + 55y = 2575
Here we have to use substitution method here
115(25-y) + 55y = 2575
2875 - 115y +55y = 2575
2875 -60y = 2575
60y = 2875 - 2575
60y = 300
y = 300 / 60
y = 5 hours
Then x = 25 - y
= 25 -5
= 20 hours
Hence, the first mechanic worked 20 hours and the second mechanic worked 5 hours
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Rite Aid sells 8 ounces of shampoo for $0.89 and Walgreens sells 12 ounces for $1.47 which is the better buy?
8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.
Answer:Rite aid
Step-by-step explanation:
8 ounces for $1.47. It comes out to $0.07 per ounce compared to $0.12 per ounce.
What is the slope of the line shown in the graph? Express your answer as an improper fraction or as an integer as appropriate. Show your work.
Write 8/5 as a mixed number.
Answer:1 3/5
Step-by-step explanation:
All you have to do is we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.
Answer:1 3/5
Step-by-step explanation: 8/5-5/5= 3/5 so that leaves you with 1 3/5
