a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The probability of getting a total of 7 = 6/36
The probability of getting total of 11 = 2/36
a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)
= 6/36 + 2/36
= 2/9
b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)
= 1- 2/ 9
= 7/9
c. Find the odds against rolling a sum of 7 or 11.
= 2/9
d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.
10 x 2/9 = 20/9
10 x 7/9 = 70/9
Thus, The money you will win $10.
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A. 2
C
C. 3
5
4
3
-3-2 A-10
-1
2
-2
-3
B
1
N
D
3 4
5
E
6
F
In the similarity
transformation of AACB
to AEFD, AACB was dilated by
a scale factor of [?], reflected
across the [ ], and moved
through the translation [ ].
B. 1/2
D. 1/3
Answer: x-axis
Step-by-step explanation:
If you visualize the line of reflection, it must be vertical. Option A is the only option that has a vertical line.
Which expression is equivalent to
The expression that is equivalent to the given expression is 16⁴
Evaluating an ExpressionFrom the question, we are to determine the expression that is equivalent to the given expression
The given expression is
[tex](\frac{1}{16} )^{-4}[/tex]
Evaluating
[tex](\frac{1}{16} )^{-4}[/tex]
[tex]= (16^{-1} )^{-4}[/tex]
[tex]= 16^{-1 \times -4}[/tex]
[tex]= 16^{4}[/tex]
Hence, the expression that is equivalent to the given expression is 16⁴
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What is the percentage of salt in the solution made of 9 on of water and 3 lb of salt
The percentage composition of salt in the solution is; 84.2%.
What is the percentage composition of salt?Since, it follows that there are 16 ounces in 1 pound. Then the 3 lb of salt is equivalent to; 3×16 = 48ounces.
Consequently, the percentage of salt in the solution as described is;
{48/57} × 100%
Percentage composition of salt is therefore;
= 84.2%.
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Three men and eight women are waiting to be interviewed for jobs. If they are all selected in random order, find the probability that all will be interviewed first.
The probability that all men will be interviewed first is; 1/55
How to find probability combination?To solve this question we will make use of the probability combination formula which is;
nCr = n!/(r! * (n - r)!)
Thus, since we want to find the probability that all men will be interviewed first, then we will use the formula;
3(3!)/((11C1) * (10C1) * (9C1)) = 18/990
Simplifying that fraction gives us; 1/55
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100 POINTS!!! To find the distance AB across a river, a distance BC of 319 m is laid off on one side of the river. It is found that B = 104.6° and C = 14.4°. Find AB.
Answer: AB = 90.7 meter
Given following:
BC = 319 meterangle B = 104.6°angle C = 14.4°Find angle A :
⇒ 180° - (104.6° + 14.4°)
⇒ 61°
Now, use sine rule:
[tex]\sf \dfrac{AB}{BC} = \dfrac{sin(C^{\circ })}{sin(A^{\circ \:})}[/tex]
[tex]\sf \dfrac{AB}{319} = \dfrac{sin(14.4) } {sin(61)}[/tex]
[tex]\sf AB = \dfrac{319 \ sin(14.4) } {sin(61)}[/tex]
[tex]\sf AB = 90.70464953 \quad \approx \quad 90.7 \ m \ (rounded \: to \: nearest \ tenth)[/tex]
Please help I am behind on this questions!!
Answer:
$83,802
Step-by-step explanation:
The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.
FormulaThe future value of an annuity due is given by the formula ...
FV = P(1 +r)((1 +r)^t -1)/r
where P is the annual payment, r is the annual interest rate, and t is the number of years.
This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).
ApplicationFor P=$1000, r = 0.06, and t = 30, the future value is ...
FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68
To the nearest dollar, the account value will be $83,802.
__
Additional comment
Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.
graph the solution set of this inequality 3x-2y <_ 12
The graph of the solution set for the inequality can be seen below.
How to graph the solution set?Here we have the inequality:
3x - 2y < -12
If we isolate y, we get:
3x + 12 < 2y
(3x + 12)/2 < y
(3/2)x + 6 < y
Now, we just need to graph the line y = (3/2)x + 6 with a dashed line (because the points on the line are not solutions).
And then we need to shade the region above the line.
The graph of the solution set can be seen below.
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How many surgeon are either office-based or ophthalmologist.?
Answer:
Is there a graph related to this question?
What is the equation of a parabola that has intercepts of x=-2 and x=6 and passes through point (8,6)?
Step-by-step explanation:
general form of a parabola :
y = ax² + bx + c
we have 3 points of the parabola to calculate the 3 variables :
the 2 intercepts are actually
(-2, 0)
(6, 0)
and then
(8, 6)
so, we get the 3 equations
0 = a(-2)² + b×-2 + c = 4a - 2b + c
0 = a×6² + b×6 + c = 36a + 6b + c
6 = a×8² + b×8 + c = 64a + 8b + c
from the 1st equation we get
c = -4a + 2b
using that in the 2nd equation we get
0 = 36a + 6b - 4a + 2b = 32a + 8b = 4a + b
b = -4a
therefore,
c = -4a + 2b = -4a + 2×-4a = -4a - 8a = -12a
using all that in the 3rd equation we get
6 = 64a + 8×-4a + -12a = 64a - 32a - 12a = 20a
a = 6/20 = 3/10 = 0.3
b = -4a = -4×3/10 = -12/10 = -1.2
c = -12a = -12×3/10 = -36/10 = -3.6
so, we have
y = 3/10 x² - 12/10 x - 36/10 = 3/10 × (x² - 4x - 12)
Select the correct answer from each drop-down menu. Which system of equations is represented by this graph? Graph shows system of equations plotted on a coordinate plane. A line goes through (minus 6, 0) and (0, minus 3). Another line goes through (0, 3) and (minus 4, minus 5). y = x + 3 y = x − 3 Reset
The equation of the line going through (-6, 0) and (0, -3) is y = -(1/2)x - 3
The equation of the line going through (0, 3) and (-4, -5) is y = 2x + 3
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The equation of the line going through (-6, 0) and (0, -3) is:
y - 0 = [(-3 - 0) / (0- (-6)](x - (-6))
y = -(1/2)x - 3
The equation of the line going through (0, 3) and (-4, -5) is:
y - 3 = [(-5 - 3) / (-4 - 0)](x - 0)
y = 2x + 3
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Answer:
2
-1/2
Step-by-step explanation:
Area of Rectangle: A = length*width
One side of a rectangle is twelve kilometers longer than three times another side of the rectangle. Find the
sides if we also know that the area of the rectangle is 135 km².
shorter side:
longer side:
Answer:
shorter side: 5 km
longer side: 27 km
Step-by-step explanation:
So you're already given the formula for the area of a rectangle, the next thing to do is assign length and width in terms of some unknown variable, which for convenience, I'll just say is x. So let's say one of the sides is x, the one that's the shorter side, since the longer side can be related to the shorted side, which is x. The longer side is 12km longer than 3 times the other side, so since the other side is x, it's length is (3x+12). So we simply multiply this by x, to get the area which is 135
"Known" Values: one side=x, other side=3x+12, area=135 km^2
[tex]135=x(3x+12)[/tex]
Distribute the x
[tex]135=3x^2+12x[/tex]
Subtract 135 from both sides
[tex]0=3x^2+12x-135[/tex]
Now since the equation is equal to zero, we can use the quadratic equation. In this case a=3, b=12, and c=-135
[tex]x=\frac{-12\pm\sqrt{12^2-4(3)(-135)}}{2(3)}[/tex]
Simplify denominator and multiply inside of the radical
[tex]x=\frac{-12\pm\sqrt{144+1,620}}{6}[/tex]
If you're confused where the negative went in the radical, it canceled out when multiply -4 by -135. Now add the stuff in the radical
[tex]x=\frac{-12\pm\sqrt{1,764}}{6}[/tex]
Simplify the radical
[tex]x=\frac{-12\pm 42}{6}[/tex]
Now you might think there are two solutions to this equation, but the thing is that one of the sides simply cannot have a "negative length", because in this context, x must be positive. So it's easy to see you have to use the positive sign, since using the negative sign would result in -12-42 over 6 which is certainly negative. So we can ignore that solution as it doesn't mean anything in this context. We only need the positive solution
[tex]x=\frac{-12+42}{6}[/tex]
Add values
[tex]x=\frac{30}{6}[/tex]
Divide
[tex]x=5[/tex]
Since the shorter side was 5, that's the solution to the shorter side, now to find the longer side we plug in 5 into the equation: [tex]3x+12[/tex] which becomes 3(5) + 12 = 15+12 = 27. This means the two lengths are 5 and 27
Step-by-step explanation:
let x = length of shorter side
[tex](3x + 12)(x)= 135[/tex] This is the equation
[tex]3x^2+12x=135[/tex] use distributive property to multiply out
[tex]3x^2+12x-135=0[/tex] subtract 135 from both sides to get in position to factor
[tex]3(x^2+4x-45)[/tex] factor out a 3
[tex]3(x-5)(x-9)[/tex] factor the resulting expression
[tex]x=5,9[/tex] two answers (we want one so see which one works)
Check both values of x
[tex]5*3+12=27[/tex]
[tex]27*5=135[/tex]
Therefore, we know the shorter side is 5 km and the longer side is 27 km.
At this point, we do not even need to check x=9
Change 192 feet to inches
Answer:
2304 inches
Step-by-step explanation:
please mark brainiest
Answer:
2304
Step-by-step explanation:
If you would like a step-by-step explanation, please just let me know. I sincerely hope this helps.
Can someone help me fully simplify this step by step pleaseeeee
[tex]2x - 7x + 2 + 1 - 2[/tex]
[tex]2x - 7x + 3 - 2[/tex]
[tex] - 5x + 1[/tex]
Question 10 of 15
What is the solution to the system of equations graphed below?
Answer:
(1,5)
Step-by-step explanation:
The solution to the system of equations is where the two graphs intersect.
The two lines intersect at x=1 and y =5
The point of intersection is (1,5)
Answer: (1, 5)
Step-by-step explanation: Over to the right one, up five; I hope this helps!
Key: (xGraph, yGraph) If a number is positive on the x axis, go right, if negative, go left. The same applies to the y graph, if the number is positve, go up, if negative go down. Your solution is where the two lines meet.
suppose that there are two types of tickets to show; advance and same -day. Advance tickets cost $35 and same-day tickets cost $30. For one performance, there were 50 tickets sold in all, and the total amount paid for them was $1650. How many tickets of each type were sold?
Answer:
#of advanced tickets (x) = 30
#of same-day tickets (y) = 20
Step-by-step explanation:
x-#of advanced tickets
y-#of same-day tickets
[tex]x+y=50,\\35x+30y=1650[/tex]
5x+30(x+y)=1650
5x+30(50)=1650
5x=150
x=30
y=20
If you stand 100 feet away from a flagpole, and the angle of elevation to the top of the pole is 31°, what is the height of the flagpole?
The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Trigonometric ratio is used to show the relationship between the sides and angles of a triangle.
Let h represent the height of the flagpole, hence:
tan(31) = h/100
h = 60.086 feet
The height of the flagpole with an angle of elevation to the top of the pole of 31° is 60.086 feet
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20. Find the solution to the system of linear equations below:
x - 3y = -5
2x + 5y = 12
O (-5, 12)
O (3,2)
O (-2,7)
O (1,2)
Answer:
The last option
Step-by-step explanation:
When you plug in 1 for the x and 2 for y, the answer is -5 for the first equation and is 12 for the second equation. I hope that helps!
If A and B are vectors such as A+3b=-3i+j and A-B=i-2j find A and B
Solve by elimination.
[tex](\vec A + 3\, \vec B) - (\vec A - \vec B) = (-3\,\vec\imath + \vec\jmath) - (\vec\imath - 2\,\vec\jmath)[/tex]
[tex]\implies 4\,\vec B = -4\,\vec\imath + 3\,\vec\jmath \implies \boxed{\vec B = -\vec\imath + \dfrac34\,\vec\jmath}[/tex]
[tex]\implies \vec A = \vec\imath - 2\,\vec\jmath + \vec B[/tex]
[tex]\implies \boxed{\vec A = -\dfrac54 \,\vec\jmath}[/tex]
An automobile travels 140 miles in 4 hours. Find the average rate of speed
Answer:
35mph
Step-by-step explanation:
divide 140/4=35
Number sense is an important concept for young for young children to know because it provides a foundation for understanding arithmetic.
a. true
b. false
Find the locus of a point P which moves so that the sum of squares of squares of its distance A(3,0)and B(-3,0) is 4 times the distance between A and B
Based on the calculations, the equation for the locus of these points is equal to x² + y² = 9.
How to find the locus of a point?First of all, we would determine the distance between points A and B as follows:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(-3 - 3)² + (0 - 0)²]
Distance = √[-9² + 0]
Distance = √81
Distance = 9.
Four (4) times the distance between points A and B is given by:
Distance = 9 × 4
Distance = 36.
Translating the word problem into a mathematical expression, we have:
a² + b² = 36
Also, from the distance formula we have:
a = √[(h + 3)² + (k - 0)²]
a² = h² + 6h + 9 + k²
Similarly, b² is given by:
b = √[(h - 3)² + (k - 0)²]
b² = h² - 6h + 9 + k²
Equating the equations, we have:
a² + b² = 36
h² + 6h + 9 + k² + h² - 6h + 9 + k² = 36
2h² + 2k² = 36 - 18
2h² + 2k² = 18
Dividing both sides by 2, we have:
h² + k² = 9 ⇒ x² + y² = 9.
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How many solutions does the system contain?
Answer: 2
Step-by-step explanation:
This system has 2 solutions because there are two points of intersection. See attached for where I pointed them out.
Write an equation that represents the transformations formed by the following items: (a) horizontally shifting the graph of f(x) = square root over x, 9 units to the right and then vertically shrinking the graph by a factor of 2/3.
(b) vertically stretching the graph of f(x) = square root over x by a factor of 8 and then vertically shifting the graph 4 units down.
(c) horizontally stretching the graph of f(x) = square root over x, by a factor of 7 and then vertically shifting the graph 5 units up
(d) reflection of the graph of f(x) square root over x, across the y-axis and then vertically shifting the graph 10 units down. Answer:
The equations of the transformed graphs are [tex]f(x) = \frac 23\sqrt{x - 3}[/tex], [tex]f(x) = 8\sqrt{x }-3[/tex], [tex]f(x) = \sqrt{\frac x7} + 5[/tex] and [tex]f(x) = \sqrt{-x} - 10[/tex]
How to transform the functions?The function #1
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is shifted right by 3 units.
So, we have:
[tex]f(x) = \sqrt{x - 3}[/tex]
It is shrunk vertically by a factor of 2/3
[tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \frac 23\sqrt{x - 3}[/tex]
The function #2
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched vertically by a factor of 8
[tex]f(x) = 8\sqrt{x }[/tex]
It is shifted down by 3 units.
So, we have:
[tex]f(x) = 8\sqrt{x }-3[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = 8\sqrt{x }-3[/tex]
The function #3
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is stretched horizontally by a factor of 7
[tex]f(x) = \sqrt{\frac x7}[/tex]
It is shifted up by 5 units.
So, we have:
[tex]f(x) = \sqrt{\frac x7} + 5[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{\frac x7} + 5[/tex]
The function #4
The function is given as::
[tex]f(x) = \sqrt{x}[/tex]
It is reflected across the y-axis
[tex]f(x) = \sqrt{-x}[/tex]
It is shifted down by 10 units.
So, we have:
[tex]f(x) = \sqrt{-x} - 10[/tex]
Hence, the equation of the transformed graph is [tex]f(x) = \sqrt{-x} - 10[/tex]
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The term can also be written as:
The correct expansion is the one in option b:
[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]
How to rewrite the term?Here we must use the logarithmic property:
[tex]Log(a) -Log(b) = Log(\frac{a}{b})[/tex]
Our expression in this case is:
[tex]Log_9(\frac{6}{11})[/tex]
Using the above property, we can rewrite the expression as:
[tex]Log_9(\frac{6}{11}) = Log_9(6) - Log_9(11)[/tex]
From this, we conclude that the correct option is B.
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A rectangular prism has a length of 3 1/2 inches, a width of 5inches, and a height of 1 1/2
Find three consecutive odd integers whose sum is 489
Answer:
162, 163, and 164.
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 489
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 489
3X + 3 = 489
3X + 3 - 3 = 489 - 3
3X = 486
3X/3 = 486/3
X = 162
Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.
162 + 163 + 164 = 489
We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.
Answer:
161, 163, 165
Step-by-step explanation:
x + x+2 + x +4 =489.
This is how we calculate three consecutive odd integers!
Combine like terms:
3x+6=489
3x=483
x=161
Three numbers are:
161, 161+2, 161+4.
161, 163, 165
add 37 +31 by counting in tens
Answer:
(30+30) +(7+1) = 68
Step-by-step explanation:
hope this helps you (ʘᴗʘ✿)
(06.02 LC)
Line AB contains points A (-2, 3) and B (4, 5). Line AB has a slope that is
What is the degree of the polynomial f(x) = (x − 1)(x + 1)(x + 3)
Step-by-step explanation:
Multiply the factors
[tex](x - 1)(x + 1)(x + 3)[/tex]
[tex]( {x}^{2} - 1)(x + 3)[/tex]
[tex]{x}^{3} + 3 {x}^{2} - x - 3[/tex]
The highest exponent is 3, so the degree is 3
First accurate answer gets brainliest
Answer: [tex]20x^2 + 47x+24[/tex]
Step-by-step explanation:
We just multiply the values on the edges like we are finding the area of a square, L * L = area.
4x * 5x = 20x^2
4x * 8 = 32x
3 * 8 = 24
3 * 5x = 15x
Next add the answers together
20x^2 + 47x + 24
Answer:
option 3
Step-by-step explanation:
you need to times (4x+3) by (5x+8)
so you basically need to expand the brackets and collect like terms