The probability that the vertical faces have the same color painted is 0.6875
There are 6 faces on a cube.
Each face of the cube will either be red or blue.
The probability that one face will have red color = probability that the face will have blue color = 1/2
It is given that the cube is placed on a horizontal surface and the 4 vertical faces have the same color.
The painting of the faces of the cube clearly follows a binomial distribution.
Therefore the probability to color the faces of a cube
= P(4 faces are red, 2 faces blue) + P(4 faces are blue, 2 faces red) + P(5 faces blue) + P(5 faces red) + P(All faces blue) + P(all faces red)
For any binomial distribution
ⁿCₓ X pˣ (1 - p)ⁿ⁻ˣ
where
n = no. of sample
x = random variable
p = probability of success
Hence we get
⁶C₄ X 0.5⁴ 0.5² + ⁶C₄ X 0.5⁴ 0.5² + ⁶C₅ X 0.5⁵ 0.5 + ⁶C₅ X 0.5⁵ 0.5
⁶C₆ X 0.5⁶ + ⁶C₆ X 0.5⁶
= 15 X 0.015625 + 15 X 0.015625 + 6 X 0.015625 + 6 X 0.015625 + 0.015625
= 0.6875
Therefore we get the probability of having the four vertical faces of the same color to be 0.6875.
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Find the Error When graphing the equation y=−3x+2, a student plotted the y-intercept at 2, then moved down 3 units and to the left 2 units because the slope is negative, so both rise and run are negative. Find his error and correct it.
Which selections describe an error that the student made and give the correct response? Select all that apply.
Multiple select question.
A)
The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −31 .
B)
The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.
C)
The student plotted the y-intercept at 2, instead of at −3. The y-intercept should be −3, because when x=0, you get y=−3.
D)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the left 1 unit, because the slope is −3−1, not −3−2.
E)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 2 units, because the slope is −32, not −3−2.
F)
After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −31, not −3−2.
*also need this one*
Answer:
A, B, F
Step-by-step explanation:
You want to know the errors made in graphing y = -3x +2 by plotting the y-intercept of 2 and then plotting another point 3 down and 2 left of that.
PlotThe appropriate graph would be created by plotting the y-intercept at 2, then moving down 3 units and 1 unit right from there, because the slope is -3.
ErrorsThe y-intercept is correctly plotted at y=2.
The next point is incorrectly plotted down 3 units and 2 units left of the y-intercept. It should be plotted down 3 units and 1 unit right.
The slope is -3, or -3/1. For a negative slope, the rise or run, but not both, will be negative. We don't know the student's rationale for using 2 as the "run" in ...
slope = rise/run
The best error descriptors seem to be ...
A) The student used the y-intercept, 2, for the denominator of the slope. The slope should be −3 or −3/1 .
B) The student said that, because the slope is negative, both rise and run are negative. When the slope is negative, either the numerator is negative or the denominator is negative, not both.
F) After plotting the y-intercept at 2, the student moved down 3 units and to the left 2 units. The student should have moved down 3 units and the to the right 1 unit, because the slope is −3/1, not −3/−2.
<95141404393>
government employees: in 2013 about 66% of full-time law enforcement workers were sworn officers, and of those, 88.4% were male. females however make up 60.7% of civilian employees. choose one law enforcement worker at random and find the following. b. the probability that he is a male civilian employee
The probability that he is a male civilian employee is 0.13362.
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.
Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).
Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.
Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.
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The length of a rectangle is 5 yd longer than its width.
If the perimeter of the rectangle is 70 yd, find its length and width
Answer:
length is 20 yards, width is 15 yards
Step-by-step explanation:
Length = width + 5
2(W + 5) + 2(W) = 70
2W + 10 + 2W = 70
4W + 10 = 70
4W = 60
W = 60 ÷ 4
W = 15 yards
L = 15 + 5
L = 20 yards
how many three-digit positive integers leave a remainder of 2 when divided by 5 and a remainder of 6 when divided by 7?
There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.
The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.
The next number will be 107, and then 112,
The last 3 digit number to leave a remainder 2 when divided by 5 is 997
Therefore here we get an Arithmetic Progression
102, 107, 112, ..., 997
We know that for any term of an A.P
aₙ = a + (n - 1)d
where,
a = first term
n = the order number of that particular value
d = common difference
Here,
a = 102
d = 107 - 102
= 5
The number of 3 digit number for the above problem will be the value of n for 997
Hence we get
997 = 102 + (n - 1)5
or, 102 + 5n - 5 = 997
or, 5n + 97 = 997
or, 5n = 997 - 97
or, 5n = 900
or, n = 900/5
or, n = 180
Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7
The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104
The largest is 993
Therefore, just like before, we get the A.P
104, 111, 118, ..., 993
here,
a = 104
d = 7
aₙ = 993
Hence we get,
993 = 104 + (n - 1)7
or, 104 + 7n - 7 = 993
or, 97 + 7n = 993
or, 7n = 993 - 97
or, 7n = 896
or, n = 128
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2.2(s + 1) 14.7 = 5.1
Answer:-454/539
Step-by-step explanation:32.34(s+1)=5.1
32.34s+32.34=5.1
32.34s=5.1-32.34
32.34s=-27.24
s=-454/539
a train goes at a constant speed.it can travel 150 miles
in 2 1/2 hours. what distance will it travel in 2 hours.
PLEASE ANSWER
The distance traveled by the car in 2hours is 120miles
What is speed?Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
from the definition speed= distance/time
since the train has constant speed,therefore the speed of the car = 150/2 1/2
= 60miles/hour
Distance= speed×time
Therefore for a time of 2hours the train will cover
60×2= 120 miles
Therefore the distance covered in 2hours is 120miles
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Jerome tries to find the value of the expression 3 - 6 + 5 by first applying the commutative property. He rewrites the expression as 3 - 5 + 6. Explain, What is wrong with Jerome's approach?
The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
What is the commutative property of addition?Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.
On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.
Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
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f(x) = −3 x 2+ 18x − 27
Answer:
18x−33−f(x)=0
Step-by-step explanation:Solve for f by simplifying both sides of the equation, then isolating the variable.
a principal orders t-shirts and wants to check some of them to make sure they were printed properly. she randomly selects 222 of the 101010 boxes of shirts and checks every shirt in those 222 boxes. what type of sample is this?
This is an example of Cluster random sampling.
Cluster sampling refers to probability sampling when the population is divided into multiple smaller groups, also called clusters, and then further sampling is performed to check the data.
Here we can see that the principal had selected 222 boxes randomly over here. This implies that she had taken a group of boxes randomly. Then she proceeded to check every t-shirt in this box.
Therefore here we see that the population i.e the boxes were divided into smaller groups. The 222 boxes are the clusters here. Therefore we can conclude that the principal uses the cluster random sampling method.
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You have $8.50 and you need to make copies of a flyer at a store that charges
$0.35 per copy. Find the inequality that represents the number of copies you can
make. Use x as the variable.
What is the maximum number of copies you can afford to make?
copies
The required number maximum number of copies can be afforded x < 24.28.
Given that,
We have $8.50 and you need to make copies of a flyer at a store that charges $0.35 per copy.
Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number of copies be x,
According to the question,
0.35x < 8.50
x < 8.50 / 0.35
x < 24.28
Thus, the required number maximum number of copies can be afforded x < 24.28.
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solve the proportion: 3/5 = 7/x
Answer:
11.6666666 (infinitely)
Complete the statement.
48 cm = mm
The value of the 48 cm will be equal to 480 mm.
What is a unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that the number is 48 cm. Here 48 cm is the length of any object the value of 48 cm in the unit mm will be calculated as below,
1 cm = 10 mn
48 cm = 48 x 10 mm
48 cm = 480 mm
Therefore, the value of the 48 cm will be equal to 480 mm.
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What is the chance of getting a heart in a deck of cards and a six on a dice both at the same time?
I need this really fast pls
Assuming it is a standard deck of 52 cards and a standard dice of 6 faces.
There are 13 heart cards in a standard deck, therefore the odd of getting a heart is 13 : 52 = 1/4.
There is only 1 six in a standard dice, therefore the odd of getting a six is 1/6.
For these events to happen simultaneously, we multiply the chances.
Therefore, the chance of getting a heart in a deck of cards and a six on a dice is 1/4 x 1/6 = 1/24.
Answer:
heart from a deck of cards= 13/52 = 1/4
getting a six on a dice= 1/6 = 1/6
Step-by-step explanation:
heart from a deck of cards :
In the context of ordinary maths questions the answer is so obvious as to almost not be worth mentioning. There are 52 cards in an ordinary deck and 13 of them have heart pips, so 13/52 = 1/4.
six from a dice :
There is a 1/6 chance of rolling a 6. There are only 6 sides on a die, and only 1 of them is 6, so there is a 1/6 chance of rolling a 6.
at the same time is:
13/15 + 1/6 = 31/30 = 1/30
look at picture. 100 POINTSSS
The correct number in the function f (3) will be;
⇒ f (3) = 2
What is Line segment?
Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The graph is shown in figure.
Now,
Clearly, By the image of the graph;
At x = 3,
The function is defined as;
⇒ f (3) = 2
Thus, The correct number in the function f (3) will be;
⇒ f (3) = 2
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Click the two inequalities represented by the system of inequalities graph below.
The system of inequalities that best represent the shaded feasible region shown on the graph is
y < x + 1y < -x - 2How to determine the inequalities represented inequalities graphinformation gotten from the question include
inequality graph showing shaded regions
some interpretation on the information from the question include
shading below the is less thandotted lines mean the inequality do not have equal toThis interpretation removes the first and the last options since they contain the equal to sign
positive slope moves from bottom left to top right
y < x + 1
negative slope moves from top left to down right
y < -x - 2
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can 2 parabolas have the same vertex but different directions of opening?
Answer:
Step-by-step explanation:
Yes, of course!
A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!
12 < y (8 - y)
SHOW WORK PLS
Answer:
2<y<6
Step-by-step explanation:
12 < 8y-y^2
y^2 -8y +12 <0
(y-6)(y-2)<0
y < 6
y < 2
2. 6
- - +
- +. +
+. - +
2<y<6
given that x = 2 and y = -4, find the value of 3x + y
given that q = 3m - 2p, express m in terms of p and q.
[tex]\huge\mathcal {♨Answer♥}[/tex]
Answer is on the attachment...
☆...Hope this helps...☆
_♡_mashi_♡_
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equation that can be used to find the price of one tire patch is 22.20 - 4x = 1.90 and 4x + 1.90 = 22.20
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Rhyan paid using a gift card that had $22.20 on it.
Let x represent the cost of each tire patch needed for the mountain biking trip. Rhyan bought four tire patches and had $1.90 remaining. Hence:
22.20 - 4x = 1.90
4x + 1.90 = 22.20
The equation is 22.20 - 4x = 1.90
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Can anyone write the equation of the graph?
The equation of the absolute function graph given in the diagram is: y = |x - 3| + 5.
How to Find the Equation of the Graph of an Absolute Value Function?y = a|x – h| + k is the equation, in vertex form, that represents the absolute value function where:
The vertex of the graph of the absolute value function = (h, k) The graph opens up or opens down depends on the value of a.The vertex of the graph is (3, 5). This implies that:
(h, k) = (3, 5)
Substitute h = 3 and k = 5 into the equation in vertex form, y = a|x – h| + k:
y = a|x – h| + k
y = a|x - 3| + 5
To find the value of a, substitute a point on the graph, (5, 7), into the y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 - 5 = 2a [subtraction property]
2 = 2a
a = 1 [division property of equality]
Substitute a = 1 into the equation y = a|x - 3| + 5:
y = |x - 3| + 5
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This table shows the ratio of number of people to liters of ginger ale needed. A 2-column table has 4 rows. Column 1 is labeled People with entries 24, 12, 36, 48. Column 2 is labeled Ginger Ale (liters) with entries 4, A, B, 8. Find the missing values in the ratio table. A = B =
The missing values in the ratio table include the following:
A = 2
B = 6
What is a proportional relationship?In Mathematics, a proportional relationship can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the number of people.y represents the liters of ginger ale needed.k represents the constant of proportionality.In order for the ratio of the number of people to liters of ginger ale needed to have a proportional relationship, the variables x and y must have the same constant of proportionality.
Next, we would calculate the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 24/4
Constant of proportionality (k) = 6.
Now, we can determine the value of A and B:
A = x/k
A = 12/6
A = 2
For the value of B, we have:
B = x/k
B = 36/6
B = 6.
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Answer: A=2 and B=6
Step-by-step explanation: I hope this helped you
:D
A factory produces 270000 000 sweets every
week. How many sweets does the factory
produce in a year? Give your answer in
standard form
The factory produced 1.404 x 10⁶ sweets in a year
How to calculate the number of sweets the factory produce in a year?
Standard form is a way of writing very large numbers or very small numbers in a simpler form. It is also called scientific notation
Given that: The factory produces 270000000 sweets every
week.
To know how many sweets the factory produces in a year, we will multiply the quantity produced in a week by 52 since there are 52 weeks in a year. Thus:
Number of sweet in a year = Weekly production x 52
= 270000000 x 52 = 14040000000 sweets
To express 140400000000 in standard form, we will move the position of the decimal point to the back of the first number(1) and take note of the number of steps we take to get there. The number of steps will then be used as the power of 10:
14040000000 = 1.404 x 10⁶
Therefore, the number of sweets produced by the factory in a year in standard form is 1.404 x 10⁶ sweets
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Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options.
y = –Two-fifthsx – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –Two-fifths(x – 5)
y – 4 = Five-halves(x + 5)
The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2
The given equation of the line is
5x - 2y = -6
Ax + By = C1
Bx - Ay = C2
are perpendicular.
Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2
We have to find the value of C2
The line is passing through the point (5, -4)
Substitute the values in the equation and find the value of C2
2(5) + 5(-4) = C2
C2 = 10 -20
= -10
The equation will be 2x + 5y = -10
Rearrange the terms and make it slope intercept form
2x + 5y = -10
5y = -10 -2x
5y = -2x - 10
y = (-2/5)x - 2
Hence, equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2
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A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top. Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
A) What are the dimensions of the square to be cut from each corner?
B) What would the volume be of the open box?
Dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
What is Three dimensional shape?Three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
A piece of cardboard that is 25 inches by 20 inches is to be made into a box with an open top
Each corner will have a square of the same dimensions cut out to be folded into an open box with no top.
Let the cut squares will have side h then h is the height of the box and the two lengths are (25-2h) and (20-2h).
The dimensions of the box are (25-2h) and (20-2h)..
Volume of the box will be V=h(25-2h)(20-2h)
Hence, dimensions of the box are (25-2h) and (20-2h) and Volume of the box will be V=h(25-2h)(20-2h).
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Taub has a smart phone data plan that costs $20 per month that includes 8 GB of
data, but will charge an extra $10 per GB over the included amount. How much
would Taub have to pay in a month where she used 3 GB over the limit? How much
would Taub have to pay In a month where she used went over by T GB? (the equation)
Answer:
10t + 20
Step-by-step explanation:
a car is traveling at 57 mi/h before it enters into a skid. the drag factor of the road surface is 1.1, and the braking efficiency is 100%. how long might the average skid mark be to the nearest tenth of a foot?
The average skid mark for the car is 98.5 feet.
The average skid mark can be calculated by the formula -
S = ✓30Dfn, where s is speed of car, D is skid distance, f is drag factor and n is braking efficiency. Keep the values in formula to calculate the value of D.
57 = ✓30 × D × 1.1 × 1
Performing multiplication on Right Hand Side of the equation
57 = ✓D × 33
Taking square on both sides of the equation
D = 57² ÷ 33
Taking square on numerator on Right Hand Side of the equation
D = 3249 ÷ 33
Performing division on Right Hand Side of the equation
D = 98.45 feet
Rounding to the nearest tenth of a foot
D = 98.5 feet
Hence, the average skid mark is 98.5 feet.
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Please help!! I need to find the Length of Side EF and The scale factor from both triangles
The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.
What is Similarity?In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.
According to given data:For length of side DF, ratio of corresponding sides is equal.
⇒ [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]
⇒ DF = 3
Similarly for EF,
[tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]
⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]
⇒ EF = 2.25
At last, by using same concept of similarity scale factor is
[tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]
⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]
This is our scale factor for both triangle.
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Use the graphs of f and r to describe the transformation from the graph of f to the graph of r.
The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.
The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Here,
r(x)=4f(x)
So, r(x)=4(-1/4 x-2)
⇒ r(x)=-x-2
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Vertical: stretch
The graph of the functions is given below.
Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.
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11 Sand costs $98.90 per tonne.
This cost includes a tax of 15%.
Calculate the amount of tax paid per tonne of sand.
The amount of tax paid per tonne of sand is $14.835 as the sand costs $98.90 per tonne.
What is meant by percentage?In mathematics, a percentage is a value or ratio expressed as a fraction of 100.
The term percent is derived from the Latin per centum, which means "hundred" or "by the hundred." The sign for "percent" comes from the Italian expression per cento, which means "for a hundred." The "per" was frequently shortened as "p." and finally disappeared entirely. The "cento" was reduced to two circles divided by a horizontal line, from which the present "%" symbol was derived.
Given,
The cost of one Tonne of sand=$98.90
The tax on one Tonne=15%
The amount of tax per Tonne of sand is,
=(15/100)×98.90
=$14.835
Hence, the amount of tax paid per tonne of sand is $14.835.
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Translate the expression “the product of triple a number and 19”
Answer: 3x+19
Step-by-step explanation: