We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .
According to our question-
Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,
with at least two of the five numbers being consecutive.
I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).
Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.
Hence, multiplication principle we come to know that there are 13×(123).
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Use point-slope form to write the equation of a line that passes through the point (1,-3)(1,−3) with slope -\frac{5}{3}−
3
5
.
Answer:
y + 3 = (-5/3) × (x - 1)
Step-by-step explanation:
5
(1, -3); m = - -------
x₁, y₁ 3
y - y₁ = m(x - x₁)
y - (-3) = (-5/3)(x - 1)
y + 3 = (-5/3)x + (5/3)
-3 -3
--------------------------------
y = (-5/3)x - (4/3) :Slope-intercept form
I hope this helps!
simplify 4m square-5mn square+8m square -6n square m -m square.
question: 4m^2 - 5mn^2 + 8m^2 - 6n^2m - m^2
answer:
11m^2-11mn^2 (see pictures)
P & P contractors was paid $562 by the Rogers family to build a fence. Six workers worked on the fence and each worker was to be paid the same. P & P Contractors took $148 dollars before any workers were paid. How many dollars did each worker make?
Answer: $69
Step-by-step explanation: 562-148=414 & 414/6=69
a food truck only sells two types of sandwiches ham and chicken.
the food trucks charges 350 for ham sandwiches and four for chicken sandwiches.
two nights ago the food truck sold $415 worth of sandwiches the food truck sold 110 sandwiches.
the system of equations written below represents the Food Truck Sale of sandwiches H + C equals 110 3.50 H + 4 C = 415.
how many chicken sandwiches did they sell ?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The number of chicken sandwiches is 60.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 6 is an equation.
We have,
Number of ham sandwiches = H
Number of chicken sandwiches = C
Cost of ham sandwiches = $3.50
Cost of chicken sandwiches = $4
Now,
The total number of sandwiches = 110
The total amount earned = $415
Now,
The two equations are:
H + C = 110 _____(1)
3.50H + 4C = 415 _____(2)
From (1) we get,
C = 110 - H _____(3)
Now,
Putting (3) in (2) we get,
3.50H + 4(110 - H) = 415
3.50H + 440 - 4H = 415
-0.5H = 415 - 440
-0.5H = -25
H = 25/0.5
H = 50
Now,
Putting H = 50 in (3) we get,
C = 110 - H
C = 110 - 50
C = 60
Thus,
The number of chicken sandwiches is 60.
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BRAINLIEST !!! The data below are the heights of mothers (x values) and their corresponding
daughters (y values)
X Y
63 59
67 65
64 65
60 61
65 65
67 67
59 61
60 63
58 60
72 71
63 62
a. Calculate the correlation coefficient of the data.
b. Based on the correlation coefficient, is there a correlation between the heights of
daughters and mothers? Explain your answer.
Answer:
a. The correlation coefficient of the data is 0.817.
b. Yes, there is a correlation between the heights of daughters and mothers. The correlation coefficient of 0.817 indicates a strong positive correlation, meaning that as the height of the mother increases, the height of the daughter also increases.
Davis can read 4/5 of a page in one minute. How many pages can he read in 4 1/2 minutes?
Simplify your answer completely.
Answer: I believe it is 18/5
or Decimal Form:
3.6
or Mixed Number Form:
3 3/5
Step-by-step explanation
4/5 x 4 1/2
Speedometer readings for a vehicle (in motion) at 7-second intervals are given in the table. t (sec) v (ft/s) 0 7 14 21 28 Estimate the distance traveled by the vehicle during this 35-second period using the velocities at the beginning of the time intervals. distance traveled feet Give another estimate using the velocities at the end of the time periods. distance traveled feet License Points possible: 1 This is attempt 1 of 1.
Another estimate is given as L6, R6, and M3 using the velocities at the conclusion of the time periods.
The table provides speedometer readings of velocity for a moving vehicle at 7-second intervals. t (sec) v (ft/s) 0 7 14 21 28 Using the speeds at the start of the time intervals, calculate the distance the car went during this 35-second span. travel distance in feet
Just figure out the rectangles' surface areas. Always draw the picture; it will be really helpful.
L6 = 10(0+9+31+56+71+68) \sR6 = 10(9+31+56+71+68+50) \sM3 = 20(9+56+68)
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When 27 is subtracted from the square of a number, the result is 6 times the number. Find the negative solution, please! I need help-
Hence, the negative solution is [tex]x=-3[/tex].
What is the equation?
The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Here given that,
When [tex]27[/tex] is subtracted from the square of a number, the result is [tex]6[/tex] times the number.
So we can write the equation is
[tex]x^2-27=6x\\x^2-6x-27=0\\x^2-9x+3x-27=0\\x(x-9)+3(x-9)=0\\(x+3)(x-9)=0\\x=-3,9[/tex]
Hence, the negative solution is [tex]x=-3[/tex].
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The function below has at least one rational zero. Use this fact to find all zeros of the function h(x) = 7x4 - 9x3 - 41x2 + 13x + 6. If more than one zero, separate with commas. Write exact values, not decimal approximations.
Assuming that h(x) = 7x4 - 9x3 - 41x2 + 13x + 6 and h(-2) = 7, (-2) 4 - 9(-2) (-2) 3 - 41(-2) (-2) 2 + 13(-2) + 6 = 7(16) - 9(-8) (-8) - 41(4) + 13(-2) + 6 = 0;
This indicates that (x + 2) is a synthetic polynomial factor.
(7x4 - 9x3 - 41x2 + 13x + 6) ÷ (x + 2):
The balance is zero.
A polynomial of degree 3 makes up the quotient: g(x) = 7x3 - 23x2 + 5x + 3.
The Rational Zeros Theorem shows that p: 1, 3, which are factors of the constant term 3, and q: 1, 7, which are factors of the leading coefficient 7, respectively
All potential outcomes are p/q: 1, 3, 1/ 7, and 3/7 g(3) = 7. (3)
3 - 23(3) +(3)
By artificial division:
The balance is zero.
The polynomial quotient is quadratic.
7x2 - 2x - 1 = 0
Equation for quadratics = [-b (b2 - 4ac)]/2a
x = -(-2) ± √[(-2)2 - (4 × 7 × -1)]/ (2 × 7) = (2 ± √32)/14 = (1 ± 2√2)/7
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A chart which is intended to show the relative values of a set of variables in comparison to each other is a _____.
a. column chart
b. scatter plot
c. pie chart
d. line chart
I need help with this please
Answer:
He spent 4&1/10 hours
Step-by-step explanation:
2&1/2+1&3/5
=5/2+8/5
=25/10+16/10
=41/10
4&1/10
A line with a slope of –12 passes through the points (–3,–6) and (r,–10). What is the value of r?
The value of r is r = -8/3, for a line that has slope -12, passes through points (-3, -6) and (r, -10)
What is slope ?Slope is a notation that shows that a surface of which one end or side is at a higher level than another surface.
Slope formula = (y₂-y₁)/(x₂-x₁)
Given that,
A line that has slope -12, passes through points (-3, -6) and (r, -10).
To find the slope of the line that passes through points (-3, -6) and (r, -10),
Use slope formula,
m = (y₂-y₁) / (x₂-x₁)
m = (-10 + 6) / r - (-3)
m = -4 / (r+3)
Since a line that has slope -12 passes through the points (-3, -6) and (r, -10),
Therefore, both will have the same slope,
-4 / (r+3) = -12
r + 3 = 1/3
r = 1/3 - 3
r = -8/3
The required value of r is -8/3.
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. y―cos x, y= ????x, x= π/2
A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x
Given that,
We have to draw the area that the provided curves surround. Choose x or y as the integration direction. Label the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x
We know that,
y=eˣ, x=π/2, y=cos x
Now area of the shaded region is
A=[tex]\int\limits^\pi/2_ x=0 \int\limits^e^{2} _y=cosx {dy} \, dx[/tex]
A=[tex]\int\limits^\pi/2_0 {e^{x}-cosx } \, dx[/tex]
Now we integrate with respect to x.
A=[eˣ-sinx]₀π/2
A=[e to the power of π/2- sin(π/2)]-[e⁰-sin(0)]
A=[e to the power of π/2-1]-[1-0]
A=[e to the power of π/2-1-1]
A=[e to the power of π/2-2]
Therefore, A=[e to the power of π/2-2] when the height and breadth of a typical approximate rectangle that you have drawn. then locate the region's area. y=eˣ, x=π/2, y=cos x
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In the diagram, BCD is
BC=5 cm, AB = 12 cm,
AD= 13
straight line,
AC = 13 cm and ABC = 90°.
Find
(a) tan BAC
(b) cos ACD.
Give both answers as fractions.
Step-by-step explanation:
where is the diagram?
please
Determine whether the pair of lines appear to be parallel or perpendicular.
1. The lines are perpendicular because they are always the same distance apart and never intersect.
2. The lines are parallel because they are always the same distance apart and never intersect.
3. The lines are parallel because they intersect at a right angle.
4. The lines are perpendicular because they intersect at a right angle.
Answer:
4
Step-by-step explanation:
The lines are perpendicular because they intersect at a right angle.
I need help with this linear equation.
The linear equation of the relationship is L = -8t + 40.
The amount Austin paid back each week is: $8.
How to Write a Linear Equation?A linear equation is straight line graph, which can be expressed as y = mx + b, in slope-intercept form. In the slope-intercept form, we have:
The value of m as the slope of the linear equation.The value of b as the initial value or y-intercept.Slope = change in y / change in x.
Using two pairs of values from the table given, (1, 32) and (2, 24):
Slope (m) = (32 - 24) / (1 - 2)
m = 8/-1
m = -8.
Find the y-intercept (b) by substituting m = -8 and (x, y) = (1, 32) into y = mx + b:
32 = -8(1) + b
32 = -8 + b
32 + 8 = b
40 = b
b = 40
Substitute b = 40 and m = -8 into L = mt + b:
L = -8t + 40
Using the linear equation, the amount Austin paid back each week is: $8.
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The graph of y = f(x) is transformed to the graph of y = 2f(x - 1).
Describe fully the two single transformations which have been combined to give the resulting transformation.
Answer:
Stretches vertically by 2, shifts right by 1
Step-by-step explanation:
changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)
What is 1 plus 1?????????
Answer:
2
Step-by-step explanation:
you take 1 and add 1 to it... and bam... 2
Answer:
2
Step-by-step explanation:
1+1=2 because 2-1=1 :0
Cody has $1400 in a savings account that earns 4 % annually. How much will he have total after 3 years?
Answer: $4368
Step-by-step explanation:
Find 4% of 1400 by taking 1400 times 0.04 = $56
So a year he has 1456$
After 3 years just need to take 1456 times 3 = $4368
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What is the surface of a rectangular prism with the length of 5 cm, width of 4 cm and height of 2 cm?
The surface area of the rectangular prism is 76cm^2
What are the basics of geometry?Geometry is the study of various mathematical or actual-world shapes, figures, and sizes. In geometry, we study various angles, transformations, and figure-to-figure similarities. The fundamental concepts of geometry primarily depend on point, line, angle, and plane.
What are the 3 types of geometry?The three most popular types of geometry are solid geometry (which deals with objects like the line, sphere, and polyhedron) and spherical geometry. Plane geometry deals with objects like the point, line, circle, triangle, and polygon.
According to the question:-
The surface area of the rectangular prism is:_
surface area= 2*(lb+bh+hl)
=2*(5*4+4*2+2*5)
=76 cm^2
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The required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph. Company A is cheaper if the time is less than 4 hours.
As per the given question, we can write the linear functions as:
A(t) = 50t + 100
B(t) = 25t + 200
We can determine time t when both companies charge the same rate by equating the two equations.
50t + 100 = 25t + 200
Subtract 25t from both sides and subtract 100 from both sides
25t = 100
Divide both sides by 25
t = 4
At 4 hours both companies charge the same rate. So Company A is cheaper if the time is less than 4 hours.
After 4 hours, company B is cheaper.
Since both functions are linear, we only need two points to plot each one onto a graph.
Thus, the required linear functions are A(t) = 50t + 100 and B(t) = 25t + 200 which are represented in the attached graph.
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7 times X equals 8 times X
Answer: X=0
Step-by-step explanation: X is equal to zero. This is the only way the equation can be true.
what is eguilvilt to -2 with the power of 4 over -2 with the power of 2
By using exponent properties we will find the equivalent expression:
(-2)⁴/(-2)² = (-2)² = 4
How to get an equivalent expression?Here we need to use the exponent property:
xⁿ/xᵇ = xⁿ⁻ᵇ
Here the expression we have is:
(-2)⁴/(-2)²
Using the above property we can rewrite the expression as:
(-2)⁴/(-2)² = (-2)⁴⁻² = (-2)²
Now we can solve this:
(-2)² = (-2)*(-2) = 4
Then the equivalent expression is 4.
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help pleaseee!!!! !!!
Answer:
x=2173
Step-by-step explanation:
Factor each polynomial
Answer: (2x + 5) (4x^2 -10 + 25)
Step-by-step explanation:
I use the equation a^3 + b^3 = (a+b) ( a^2 -ab + b^2)
You can factor the answer (2x + 5) (4x^2 -10 + 25) out to check and will get 8x^3 +125
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The sum of the measures of the angles of any triangle is 180 degrees . In a certain triangle, the largest angle measures 55degrees less than twice the medium angle, and the smallest angle measures 25 degrees less than the medium angle. Find the measures of each of the three angles.
Each of the three angles measures 75°, 65°, and 40°.
What is an angle measure?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.
Here, we have
Let the largest angle be x degrees, the median y, and the smallest z.
x = 2y - 55
z = y - 25
x + y + z = 180
Substituting for x in the last equation:
2y - 55 + y + z = 180
3y + z = 235
From the second equation:
- y + z = -25 Subtract this from the last equation:
4y = 260
y = 65 degrees
z = 65 - 25 = 40 degrees.
and x = 180 - 65 - 40 = 75 degrees.
Hence, each of the three angles measures 75°, 65°, and 40°.
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The measures of each of the three angles are 40,65 and 75 degrees.
What is angle ?
In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle.
Give that:
Let us consider X,Y,Z re the largest ,medium and smallest angle in the triangle.
Sum of the measures of the angles of any triangle is 180 degrees .
X + Y + Z = 180 degree
The largest angle measures 55degrees less than twice the medium angle,
Z = 2Y - 55 degree
The smallest angle measures 25 degrees less than the medium angle,
X = Y - 25 degree
Now ,replace X by (Y - 25) and Z by (2Y - 55) in the first equation
Y - 25 +Y + 2Y - 55 = 180 degree
4Y = 180 + 25 + 55
4Y = 260
Y = 65 Degree of the medium angle
X = 65 - 25
X = 40 Degree of the smallest angle
Z = 2 * 65 -55
= 130-55
Z = 75 Degree of the largest angle.
40 + 65 + 75 = 180
180 = 180
Hence proved.
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Add.
(7v–4)+(–4v3–v2–8v–5)
Answer:
-4v³ - v² - v - 9
Step-by-step explanation:
1. Subtract the numbers
7v - 4 - 4v³ - v² - 8v - 5
7v - 9 - 4v³ - v² - 8v
2. Combine like terms
7v - 9 - 4v³ - v² - 8v
-v - 9 - 4v³ - v²
3. Rearrange Terms
-v - 9 - 4v³ - v²
-4v³ - v² - v - 9
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
What are z-scores?How closely a value relates to the mean of a set of values is expressed by a Z-score.
The Z-score is created using standard deviations from the mean.
A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.
So, in order to determine how far the raw score deviates from the mean, the Z score is used.
The following steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
The graph of the normal distribution indicates:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.
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the width of a rectangle is 6 centimeters less than the length. the perimeter is 148 centimeters. find the length and width.
The rectangle has a length of 40 cm and width of 34 cm.
Given,
The length of a rectangle = x cm
The width of the rectangle = x - 6 cm
The perimeter of the rectangle = 148 cm
We have to find the length and width of the rectangle;
Here,
Perimeter of rectangle = 2(length + width)
That is,
148 = 2(x + x - 6)
148/2 = 2x - 6
74 = 2x - 6
74 + 6 = 2x
x = 80/2
Length, x = 40 cm
Width, x - 6 = 40 - 6 = 34 cm
Therefore,
The length of the rectangle is 40 cm and the width of the rectangle is 34 cm
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A bus leaves Deltaville at 11:32 it’s a travels at an average speed of 42 km/h if it arrives in eastwich at12:42 what is the distance between the two towns ?
Answer:
7.14 km
Step-by-step explanation:
the total time that the bus takes to travel from Deltaville to Eastwick 12:42 - 11:32 = 00:10
Convert to hours 00:10 / 60 minutes/hour = 0.17 hours.
distance = speed * time
distance = 42 km/h * 0.17 hours
distance = 7.14 km