The expected number of points as a function of a and b is C = b+a.
In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.
x1 = roll a 1 -> P1 = 1/6
x2 = roll a 2 -> P2 = 1/6
x3 = roll a 6 -> P3 = 1/6
x4 = roll a 1, 4 or 5 -> P4 = 1/2
E = P1*x1 + P2*x2 + P3*x2 + P4*x4
x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)
C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)
1/6*C = 1/6*b + 1/6a
Solving for C
C = b+a
Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability) that are the results that are going to affect your game.
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The Sum of the first 21 terms of the progression, -18, -15,-12........ is _____
Answer:
3
Step-by-step explanation:
18,15,12,..........
S
n
=45=
2
n
[2a+(n−1)d]
=>
2
n
[2×18+(n−1)(−3)]=45
=>
2
n
[36−3n+3]=45
=>n(39−3n)−90=0
=>39n−3n
2
−90=0
=>3n
2
−39n+90=0
=>n
2
−13n+30=0
=>n
2
−10n−3n+30=0
=>n(n−10)−3(n−10)=0
=>(n−10)(n−3)=0
=>n=10 or n=3
Hama is three times as old as David and the sun of their ages is 52. Determine their ages.
Using Algebra, Age of David is 13 years old, and Hama is 39.
Explain what algebra is.The area of mathematics known as algebra deals with symbols and the formulas used to manipulate them. These symbols, which are currently expressed as Latin and Greek letters, are used in elementary algebra to represent variables, or quantities without set values.
If David were n years old and Hamas was 3 years old, then:
n + 3n = 52
4n = 52
n = 13
3n = 3 * 13 = 39
13 plus 39 equals 52
David is 13 years old, and Hama is 39.
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Evaluate the expression. 12−{1+2[−1(3−8)]2} What is the value of the expression? Enter your answer in the box.
If the given mathematical expression 12−{1+2[−1(3−8)]2} is been evaluated , then it will become -18.
How can the expression be simplified?The mathematical expression can be simplified by first simplify the expression in the inner bracket one after the other.
The given mathematical expression is 12−{1+2[−1(3−8)]2}
then we can simplify one after the order by following the bracket one after the other, as :
12−{1+2[−1(3−8)]2}
12 - {1+2[-1(-5)]2}
Then we can further simplify the expression as :
12 - {3 [ 5 ] 2}
Then this can be further simplified as :
12 - {30}
This can be further simplified as :
-18
Therefore, the value of the expression given is -18
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1/4 Marks
a) Complete the prime factor trees for 16 and 40:
16
b)
2
2
8
2
4
17/31 Marks
2
2
40
What is the Lowest Common Multiple of 16 and 40?
82%
5
Answer:
Answer in photo!!! :))
Step-by-step explanation:
What is 40÷8175 PLEASE HELP ME H E L P
Answer:
Step-by-step explanation: 0.00489296636 if you divided by 40 to 8175 but if you wanted 8175 divided 40 it would equal 204.375 just letting you know i used a calculator so if these aren't it then i'm not sure
Which trigonometric ratio can be used to find the measurement of F using only the lengths shown.
The trigonometric ratio which can be used to find the measurement of F using only the lengths is: D. tangent only.
What is a tangent?In geometry, a tangent is also known as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
Mathematically, the tangent of an angle is given by this expression:
Cosθ = Adj/Hyp
Where:
Hyp represents the hypotenuse of a right-angled triangle.Adj represents the adjacent side of a right-angled triangle.θ is the angle.Since both the opposite side and adjacent side of this right-angled triangle are given, cosine is the trigonometric ratio which can be used.
For this right-angled triangle, the cosine of the angle (θ) is given by:
Cosθ = 9/F
F = 9/Cosθ
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A woman decides to start a small business making monogrammed cocktail napkins. She can set aside $1870 for monthly costs. Fixed costs are $1329.50 per month and variable costs are $3.70 per set of napkins. How many sets of napkins can she afford to make per month?
[tex] \: \huge \tt{\pink{A}{\orange{N}S{\green{W}{\blue{E}{\purple{R}}}}}} \\ \\ \: \: \: \tt \rightarrow {\blue{\fbox{147 \: sets}}} (approx)[/tex]
Step-by-step explanation:
Fixed costs = $ 1329.50 per month
Variable cost are $3.70 per set of napkins
Total cost she set aside = $1870 for monthly costs
Amount left for napkins = Total cost - Fixed Cost
= 1870 - 1329.50
= $540.50
$540.50 she can spend on napkinsCost for one set = $3.70
Let set of napkins = x
Total cost for napkins = $540.50
x × 3.7 = 540.50 x = 540.50 / 3.70x = 146.08 (approx) or 147 setsTherefore , she can afford to make 147 (approx) sets of napkins per month.
Sort the following transformations according to whether or not they preserve distances.
Preserves Distance
Does NOT Preserve Distance
A. Counter-clockwise rotation about the origin
B. A dilation of 1/5
C. A translation that moves a figure up 5 units
D. A reflection over the y-axis
E. A dilation of -4
The truth statements about the transformations are:
A. Counter-clockwise rotation about the origin ⇒ PreserveB. A dilation of 1/5 ⇒ Do not preserveC. A translation that moves a figure up 5 units ⇒ PreserveD. A reflection over the y-axis ⇒ PreserveE. A dilation of -4 ⇒ Do not preserveHow to determine the category of the transformation?There are four types of transformation, and they are:
DilationRotationReflectionTranslationThe representation of the types of transformation are:
Dilation: k(x, y)Rotation: rotation by anglesReflection: reflection across linesTranslation: (x + h, y + k)Of the above transformation, only the dilation transformation do not preserve side lengths or distance
Hence, the categories of the transformations are
(a), (c) and (d) ⇒ Preserve
(b) and (e) ⇒ Do not preserve
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Which of the following is an obtuse triangle? A. Triangle BB. Triangle CC. Triangle A D. Triangle D
Triangle b is a obtuse triangle.
What is a triangle ?A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.
A triangle has an obtuse angle if one of the inner angles is greater than 90 degrees. In an obtuse triangle, if one angle is greater than 90°, the total of the other two angles is also less than 90°.
As the triangle B have one interior angle as 126 degree which is greater than 90
so it follows the property of obtuse triangle
Hence, triangle b is a obtuse triangle.
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two cards are drawn without replacement from a standard deck of 52 playing cards. what is the probability of choosing a jack and then, without replacement, a face card? express your answer as a fraction or a decimal number rounded to four decimal places.
17. The area of the rectangle shown exceeds the area of the square by
2 cm². Find x.
y
X
x-1
18. The area of the square exceeds the area of the rectangle by 13 m².
Find y.
X
x + 2
y
X
y + 1
19. The area of the square is half the area of the rectangle. Find x.
y-3
2(x + 4)
(x - 2)
The values of the missing variables from the areas of rectangle and square are;
17) x = 4
18) y = 5
19) x = 4
What is the area of the rectangle and square?17) The formula for area of rectangle is;
A = Length * Width
Formula for area of square is;
A = side * side
Thus;
A_rect = (x - 1)(x + 2) = x² + x - 2
A_sq = x²
The area of the rectangle shown exceeds the area of the square by
2 cm². Thus;
x² + x - 2 - x² = 2
x - 2 = 2
x = 4
18) Area of the square; A_sq = y²
Area of the rectangle; A_rect = (y - 3)(y + 1) = y² - 2y - 3
The area of the square exceeds the area of the rectangle by 13 m². Thus;
y² - y² + 2y + 3 = 13
2y = 10
y = 5
19) The area of the square is half the area of the rectangle. Thus;
x² = ¹/₂(2(x² + 2x - 8))
x² = x² + 2x - 8
2x - 8 = 0
x = 4
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write an equation for the line will give brainliest
The equation of the line graph in slope intercept form is gotten as;
y = x + 3
What is the equation of the Line in Slope Intercept Form?The general formula for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, from the given straight line equation graph, we can see that the line crosses the x-intercept at x = -3 and crosses the y-intercept at y = 3. Thus;
When x = 0, y = 3
When y = 0, x = -3
Slope is gotten by using two points and their coordinates to get;
m = (3 - 0)/(0 - (-3))
m = 3/3
m = 1
Thus, the equation of the line is y = x + 3
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Write the formula for a meal that has a total cost of C
that is equal to the price of the food F plus 20% (for tip) of
the price of the food.
Answer:
C = F(0.20) + F
Step-by-step explanation:
C is the total cost. F(0.20) will reduce the value of the food to the tip amount required, and then adds the tip value to the price of the food, F.
Example inputs: let F be equal to 10
C = F(0.20) + F turns into C = 10(0.20) + 10
10(0.20) will cause 10 to be multiplied by the tip value, 20%, and 20% is equivalent to 0.20. Once you multiply 10 by 0.20, you get 2. After that, you add 2 to the price of food, which is 10, and you get a total cost of 12.
12 = 10(0.20) + 10
Patients in a study about a new medication were asked to rate their symptoms on a scale from 1 to 10 each hour, over a period of 8 hours after taking the medication. On the given scale, 1 represents symptoms being the least bothersome, and 10 represents them being the most bothersome. It is found that over this time period, the function y=0.5x2−3.6x+8.9 best models the patient's rating y, x hours after taking the medication.
What is the predicted rating 2.5 hours after taking a dose? Round your answer to two decimal places.
It is to be noted that the predicted rating after taking a dose in two decimal places is 5.53. See the explanation below.
What is the explanation for the above answer?Recall that we are given the expression:
y= 0.5x²−3.6x+8.9 .......................function 1
After 2.5 hours,
Predicted Rating (y) =
0.5 (2.5)² - 2.6 (2.5) + 8.9 [Substitute x into the function]
y= 0.5 (6.25) - 2.6 (2.5) + 8.9 [Expand the brackets]
y= 3.125 - 6.5 + 8.9
y= 5.525
Hence the predicted rating in two decimal places is 5.53. This means that the symptoms have been reduced by at least 50%.
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You want to hang three equally-suzed travel posters on a wall so that posters on the ends are each 3 feet from the end of the wall. You want the sapacing between posters to be equal. Wrte and somve an equation to determine how much space you should leave between the posters.
The equation is:
You Should leave ______ feet of space.
plss help me
Answer:
[tex]\frac{15-6-6}{2}[/tex] = x
You should have 1.5 feet of space between each picture.
Step-by-step explanation:
Let x be the spacing between the pictures
[tex]\frac{15-6-6}{2}[/tex] = x The total length - end spacing - the width of the posters. What is left is the blank spaces between the posters. Since there are 2 blank spaces, we will divide by 2 to find out the spacing between the two pictures. Which is 1.5 feet.
each side of a square is increasing at a rate of 2 cm/s. at what rate (in cm2/s) is the area of the square increasing when the area of the square is 64 cm2?
At 32 cm^2/s rate the area of the square is increasing when the area of the square is 64 [tex]cm^{2}[/tex]
As per given problem each side of a square is increasing at a rate of 2 cm/s. let side of square is x.so the area of it is A= [tex]x^{2}[/tex].now differentiating w.r.t time A
[tex]\frac{dA}{dt}[/tex]= 2x[tex]\frac{dx}{dt}[/tex]
when A=64 [tex]cm^{2}[/tex] x=8 cm
also given [tex]\frac{dx}{dt}[/tex]=2cm/s
so [tex]\frac{dA}{dt}[/tex]=2×2×8=32
So at 32 cm^2/s rate the area of the square is increasing when the area of the square is 64 [tex]cm^{2}[/tex]
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assume the cost of a gallon of milk is $2.70. with continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.
The time it would take the cost to be 4 times the current cost of a gallon of milk at an annual inflation rate of 6% is calculated to be 23.8 years.
To determine the time for the cost to be 4 times the current cost of a gallon of milk, we use the compound interest formula as follows;
A(t) = A(0) (1 + r)^t
Here A(t) is the cost of 4 times the current cost at time t
A(0) is the current cost
r is the interest rate
t is the time period
Therefore;
2.70 × 4 = 2.70( 1 + 0.06)^t
2.70 × 4 / 2.70 = (1.06)^t
4 = (1.06)^t
Taking log on both sides;
t × log(1.06) = log 4
t = log 4 / log(1.06)
t = 23.791 = 23.8 years
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Which expression is equivalent to quantity y raised to the negative second power times z raised to the seventh power end quantity over quantity z raised to the negative third power times y raised to the eighth power end quantity all raised to the negative second power? z raised to the tenth power over y raised to the tenth power y raised to the tenth power over z raised to the tenth power z raised to the twentieth power over y raised to the twentieth power y raised to the twentieth power over z raised to the twentieth power
The expression z raised to the twentieth power over y raised to the twentieth power is equivalent to the expression given in the question.
y raised to the negative second power = [tex]y^{-2}[/tex]
z raised to the seventh power = [tex]z^{7}[/tex]
Thus, in the numerator we have the expression- [tex]y^{-2} z^{7}[/tex]
In the denominator, we will have-
z raised to the negative third power = [tex]z^{-3}[/tex]
y raised to the eighth power = [tex]y^{8}[/tex]
denominator will be = [tex]z^{-3} y^{8}[/tex]
Thus, the expression becomes-
[tex](\frac{y^{-2 }z^{7} }{z^{-3} y^{8} })^{-2}[/tex]
Now, that we've decoded the expression, let us solve it-
[tex]({y^{-2 }y^{-8} z^{7} z^{3} )^{-2}[/tex]
= [tex]({y^{(-2-8) } z^{(7+3)})^{-2}[/tex]
= [tex]({y^{(-10) } z^{(10)})^{-2}[/tex]
= [tex]{y^{(-10*-2) } z^{(10*-2)}[/tex]
= [tex]{y^{(20) } z^{(-20)}[/tex]
= [tex]\frac{z^{20} }{y^{20} }[/tex]
= [tex](\frac{z}{y} )^{20}[/tex]
Thus, the expression z raised to the twentieth power over y raised to the twentieth power is equivalent to the expression given in the question above.
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8. Игральную кость кидают 6 раз. Какова вероятность того, что «шестерка» выпадет а) не менее трех раз; б) не более трех раз?ъ
Answer:
б) не более трех раз
john and maria are on the game show, "minute to win it" some of the numbers have slipped off the number line. help john and maria place the rational numbers back on the number line below.
\sqrt{16}
2/3
|-3|
2.47 x 10^{-2}
-1/4
The rational numbers arranged on a number line will graduate from the highest to the lowest (left to right) as follows:
√16|-3|2/32.47x10⁻²-1/4What is a rational number?A rational number is defined in mathematics as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q. For example, −4/7 is a rational number, as is every integer.
Note that a number line is defined as a horizontal line with evenly spaced numerical increments.
To get the order in which the numbers must be arranged, the trick is to convert the number for which you have doubt into their decimal forms or d integer forms.
A) √16 = 4
B) 2/3 = 0.6
C) |-3| = 3 {Reason: Absolute Value of any number must be its positive equivalent]
D) 2.47 x 10^{-2} = 0.0247
E) -1/4 = -0.25
Hence rearranged in descending order (from highest to lowest) we have:
On the number line, the first nubmer from the left will be √16, followed by |-3|, and so on.
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Q20. in an assorted colored lego box, 5/6 of the legos were red, and 2/3 of the remaining legos were green. if there were 18 legos, how many of the legos were green?
Answer:
2 legos were green
Step-by-step explanation:
Given- in an assorted colored lego box, 5/6 of the legos were red, and 2/3 of the remaining legos were green. if there were 18 legos,
let->
x number of the red ball then probability= x/18=5/6
=>x=15
then, 3 balls are other in which the green +remaining ball is present according to the question.
2/3 times of 3 are green legos==>
(2/3)*3=2 are green legos;
and the last ball 1 lego is remain.
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write 5 to the power of -3 in its simplest form without any indices
lol this is annoying
5 to the power of -3 in its simplest form without any indices is 1/125 or 0.008.
Exponents
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as [tex]6^4[/tex]. Here, 4 is the exponent and 6 is the base. This can be read as 6 is raised to power 4.
We know that,
[tex]a^{-b}=\frac{1}{a^b}[/tex]
Hence, we can write,
[tex]5^{-3}=\frac{1}{5^3}[/tex]
We know that the cube of 5 is 125.
Hence, we can write,
[tex]\frac{1}{5^3}[/tex] = 1/125
1/125 is the simplest form of fraction and is equal to 0.008 in decimal form.
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There is a close relationship between the air pressure inside a hurricane and its maximum
sustained wind speed: y = -0.932x + 973 where x is the air pressure in millibars (kPa) and y is the
wind speed in knots (nautical miles per hour).
The wind speed when the air pressure is 20kpa will be 954.36 miles per hour.
How to illustrate the information?From the information, there is a close relationship between the air pressure inside a hurricane and its maximum sustained wind speed: y = -0.932x + 973.
where x = the air pressure in millibars (kPa) l
y = wind speed in knots (nautical miles per hour).
Therefore, the wind speed when the air pressure is 20kpa will be calculated thus:
y = -0.932x + 973.
y = -0.932(20) + 973.
y = -18.64 + 973
y = 954.36
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There is a close relationship between the air pressure inside a hurricane and its maximum
sustained wind speed: y = -0.932x + 973 where x is the air pressure in millibars (kPa) and y is the
wind speed in knots (nautical miles per hour). Find the wind speed when the air pressure is 20kpa.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
1y is the answer!
Step-by-step explanation:
-6y+7y=1y
Answer:
-6y + 7y = 1y
Step-by-step explanation:
[tex]32 - 6y + 7y - 2y^2[/tex]
-6y + 7y = 1y
7y - 6y = 1y or y
the whole equation would be [tex]-2y^2+y+32[/tex]
Please help me please help me
( Please help + Will mark brainliest )
Answer the question in photo.
Answer:
3/2
Step-by-step explanation:
6/4 = 1.5
3/2 = 1.5
So we know 1.5 is the scale and it asks for it in fraction form which would be 3/2.
three cards are drwan at random, without replacement, from a standard deck of 52 playing cards. compute the (conditional) probability that the first card drawn is spade, given that the second and third cards have spades.
If the second and third cards have a spade then the probability that the first card drawn is a spade is 21.2%.
Probability can be described as a field of mathematics that determines how likely a thing is to happen. When there is uncertainty about the outcome of an event we consider the probabilities of certain results or outcomes.
There are a total of 13 spades in a deck of 52 playing cards. So if the second and third cards have spades then there are 11 spades remaining.
The formula for probability can be given as;
probability = number of favorable outcomes or events ÷ total number of outcomes or events
probability = 11 / 52 = 0.212
Converting it into percentage;
probability = 0.212 × 100 = 21.2%
Therefore, the probability that the first card drawn is a spade is calculated to be 21.2%.
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The large of two numbers is less than 3 times the small number if the sum of the numbers is 35 find the numbers
The numbers are 26 and 9 respectively.
What is an algebraic expression?An algebraic expression can best be defined as an arithmetic or mathematical expression that is known to consist of variables, coefficients, constants, factors as well as terms.
These expressions said to contain numerous arithmetic operations, which includes;
SubtractionBracketParenthesesMultiplicationAdditionDivision, with others inclusive.From the information given, we have that
Let the small number be x
The large number be y
y < 3x (1)
Also,
x + y = 35 equation 2
x = 35 - y
Substitute the value of x in equation 1
y < 3(35 - y)
expand the bracket
y < 105 - 3y
collect like terms
y + 3y < 105
4y < 105
Make 'y' the subject
y < 105/4
y < 26. 25
y = 26
substitute the value of y
x + y = 35
x + 26 = 35
x = 9
Hence, the values are 26 and 9
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PLEASE HELP! Marta is buying soft drinks for the class party. The table below shows the prices of 4 different packages of cola, the number of bottles in each package, and the ounces of cola per bottle.
The price of a 10-ounce bottle is $0.79
The price of a 12-ounce bottle is $0.99
The price of a 20-ounce bottle is $1.64
The price of the 64-ounce bottle is $4.98
Package price of 10-ounce bottles = $3.19
Number of bottles in the package = 4
Price per bottle = Package price/Number of bottles = 3.19/4
= $0.79
Package price of 12-ounce bottles = $5.99
Number of bottles in the package = 6
Price per bottle = Package price/Number of bottles = 5.99/6
= $0.99
Package price of 20-ounce bottles = $6.56
Number of bottles in the package = 4
Price per bottle = Package price/Number of bottles = 6.56/4
= $1.64
Package price of 64-ounce bottles = $4.98
Number of bottles in the package = 1
Price per bottle = Package price/Number of bottles = 4.98/1
= $4.98
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2. Find the parabola with equation y = ax² + bx whose tangent line at (1, 1) has equation y = 3x - 2.
Answer:
Step-by-step explanation: