Given the word problem:
The numerator of the expression is the product of 5 and the sum of x and y and The denominator is the product of negative 8 and x.
The numerator will be the value on top in a fraction.
Here, the numerator is the product of 5 and the sum of x and y ==> 5(x + y)
The denominator is the value below in a fraction.
Here, the denominator is the product of negative 8 and x ==> -8x
Therefore, the expression that fits this description is:
[tex]\frac{5(x+y)}{-8x}[/tex]Consider the following function. Complete parts (a) through (e) below.f(x)=x²-2x-8The vertex is.(Type an ordered pair.)c. Find the x-intercepts. The x-intercept(s) is/are(Type an integer or a fraction. Use a comma to separate answers as needed.)d. Find the y-intercept. The y-intercept is(Type an integer or a fraction.)e. Use the results from parts (a)-(d) to araph the quadratic function.
Given the function:
[tex]f(x)=x^2-2x-8[/tex]It is a quadratic function where:
a=1
b= -2
c= -8
The x-coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]Substitute a and b:
[tex]x=-\frac{-2}{2(1)}=\frac{2}{2}=1[/tex]Substituting in the original equation to obtain the y-coordinate, we obtain:
[tex]y=(1)^2-2(1)-8=1-2-8=-9[/tex]So, the vertex is (0, -9)
c. For the intercept at x we make y = 0:
[tex]0=x^2-2x-8[/tex]And solve for x by factorization:
[tex]\begin{gathered} (x-4)(x+2)=0 \\ Separate\text{ the solutions} \\ x-4=0 \\ x-4+4=0+4 \\ x=4 \\ and \\ x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]So, the x-intercepts are:
(-2, 0) and (4,0)
Answer: (-2,0), (4,0)
d. For the intercept at y we make x = 0:
[tex]y=(0)^2-2(0)-8=-8[/tex]So the y-intercept is (0, -8)
Answer: (0, -8)
e. Graphing the function:
Explain how to estimate the product ofof 12 3/8 x 6 7/8Use complete sentences in your answer.
Given:
12 3/8 x 6 7/8
We can round 12 3/8 down to 12 because converting 12 3/8 to decimal will give 12.375.
We can round up 6 7/8 which is equivalent to 6.875 to 7
Hence, the estimate is 12 x 7 = 84
A science fair poster is a rectangle 36 inches long and 24 inches wide what is the area of the poster in square feet with sure to include the correct unit in your answer
Okay, here we have this:
Considering the provided information, we are going to calculate the area of the rectangle ins square inches and after we are going to convert it to square feet, so we obtain the following:
Area of the rectangle=36 inches * 24 inches = 864 square inches
Now, let's convert it to square feet, then we have:
[tex]\begin{gathered} 864in^2\cdot\frac{1ft^2}{144in^2} \\ =6ft^2 \end{gathered}[/tex]Finally we obtain that the area in square feet of the rectangle is 6 square feet.
Point O is the center of this circle. What is m
The value of the angle ∠CAB subtended at the circumference of the circle is 48° .
It is given that the center of the circle is at O.
∠AOB = 96° .
We know that the angle subtended by an arc at the center is twice that subtended at the circumference.
Therefore ∠CAB = 1/2 of ∠AOB
or, ∠CAB = 1/2 × 96°
or, ∠CAB = 48°
An arc is any segment of a circle's circumference. The angle formed by the two line segments joining a point to an arc's endpoints at any given position is known as the arc's angle.
The circle in the following illustration features an arc that subtends an angle at both the center O and a point on the circumference AB is a chord.
The angle of an arc at the center of a circle is twice as large as its angle elsewhere on the circle's edge.
Therefore the value of ∠CAB is 48° .
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How can I draw a histogram to illustrate the information? How do I calculate the median age of the population?
We can see from the question that we have 8 class intervals, and they are all of the same lengths. We have the frequency for age in each interval.
We need to remember that a histogram is similar to a bar plot. However, it does not have any description on the x-axis. Instead, it will have the given class intervals.
In this case, we have that the class intervals do not overlap, and it is easier to graph the histogram as follows:
1. We need to graph the class intervals on the x-axis, and then we have to draw the frequencies for each interval on the y-axis.
Which choice best represents the sum of (5 + 8x -3) and (9x -6)1: 17x + -42: 17x + 43: x + 144: x + - 14
We can solve the expression as:
[tex]\begin{gathered} (5+8x-3)+(9x-6) \\ 2+8x+9x-6 \\ 17x-4 \end{gathered}[/tex]The answer is 1. 17x-4.
Julia has been measuring the length of her baby's hair. The first time it was 6 cm long and after one month it was 2 cm longer. If the hair continues to grow at this rate, determine the function that represents the hair growth and graph it.
Given that,
The length of baby's hair at first time = 6cm
After a month, the length was 2 cm longer = 6 + 2 = 8 cm
As mentioned in the question, the hair continues to grow at this rate. Therefore, after two months, the length would be = 8 + 2 = 10 cm
It results in a sequence with a common difference of 2,
6, 8, 10, 12, ............
If a sequence has a common difference, it is called an arithmetic sequence. In such sequences, the nth term is calculated as:
an = a1 + (n-1)*d
Here,
a1 = first term = 6
d = common difference = 2. (8-6 or 10 - 8 = 2)
Now, put all the values in the equation,
an = a1 + (n-1)*d
an = 6 + (n-1)*2
an = 6 + 2n - 2
an = 2n + 4
an = 2(n+2)
Hence, the function that represents growth is an = 2(n+2).
By varying the value of 'n', you can get the values of 'an'. Both will generate ordered pairs that will help you in plotting. For example:
n = 1
an = 2(n+2) = 2(1+2) = 2 (3) = 6
=> ordered pair (1, 6)
n = 2
an = 2(n+2) = 2(2+2) = 2 (4) = 8
=> ordered pair (2, 8)
n = 3
an = 2(n+2) = 2(3+2) = 2 (5) = 10
=> ordered pair (3, 10)
n = 4
an = 2(n+2) = 2(4+2) = 2 (6) = 12
=> ordered pair (4, 12)
With the ordered pairs, you can plot the graph.
6) What is the equation of the following graphed function?Is the vertex a maximum or minimum?What are the solutions to the function?What is the y-intercept?уmobruo uove56$ x
If we know the roots (solutions) we can find the equation of the second-degree function using the formula above:
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]In this case, a = -1, x1 = 2 and x2 = 4. Therefore the equation will be:
[tex]f(x)=-1(x-2_{})(x-4_{})[/tex][tex]f(x)=-x^2+6x-8[/tex]The vertex is maximum (see that the function has a clear max value).
The solutions to the function are the roots (place in the x-axis where the function cross). They are 2 and 4.
The y-intercept is the point with the format (0,y). Thus to find this point we can substitute 0 into the function:
[tex]f(0)=-0^2+6\times0-8[/tex][tex]f(0)=-8[/tex]The y-intercept will be y = -8.
See attached pic of problem. I have to show cancelling of units and answer has to show proper number of significant figures.
We have that 1 cubic meter is equivalent to 1.308 cubic yards. Then, we can use a rule of three to find the value in yards of 1.37 cubic meters:
[tex]\begin{gathered} 1m^3\rightarrow1.308yd^3 \\ 1.37m^3\rightarrow x \\ \Rightarrow x=\frac{(1.37m^2)(1.308yd^3)}{1m^3}=1.37(1.308yd^3)=1.792yd^3 \\ \Rightarrow x=1.792yd^3 \end{gathered}[/tex]therefore, 1.37m³ is equivalent to 1.792yd³
The number of calories burnes by a 90-pound cyclist is proportional to the numer of hours the cyclist rides. the equation to represent this relationship is Y=225×. What is the constant of proportionality?
Answer
Constant of proportionality = 225
Explanation
If y varies directly as x, this can be written as
y ∝ x
Introducing the constant of variation, k, we have
y ∝ x
y = kx
So, for this question,
y = 225x
Constant of proportionality = 225
Hope this Helps!!!
What is numeral value of 3/4 + 5/8
The given expression is
[tex]\frac{3}{4}+\frac{5}{8}[/tex]We have to sum these fractions with the cross-rule. The image below shows this method.
can someone please help me with this please explain (and if you can please add an example)
Given: A square pyramid with a base length of 5 inches and a height of 9 inches.
Required: To find the volume of the given square pyramid.
Explanation: The volume of the square pyramid is given by the formula
[tex]V=\frac{a^2\times h}{3}[/tex]Where a is the base length, and h is the height of the square pyramid.
Hence,
[tex]\begin{gathered} V=\frac{5^2\times9}{3} \\ =75\text{ in}^3 \end{gathered}[/tex]Final Answer: The volume of the square pyramid is 75 cubic inches.
2. Yan also has three times as many apples as Xavier. Write a second expression for how many apples Yanhas.
For this case, let be "x" the number of apples Xavier has and "y" the number of apples Yan has.
According to the information given in the exercise, you know that Yan has three times as many apples as Xavier. In other words, to find the number of apples Yan has, you need to multiply the number of apples Xavier has by 3.
Then, knowing the above, you can write the following equation:
[tex]y=3x[/tex]Therefore, you can determine that an expression that represents how many apples Yan has, is the one shown below:
[tex]3x[/tex]Match these equation balancing steps with the description of what was done in each step.Step 1:12x - 6 = 10 6x - 3 = 5 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 2: 6x - 3 = 5 6x = 8 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2 Step 36x = 8 x= 4/3 -Add 3 to both sides -Divide both sides by 6 -Divide both sides by 2
Step 1:
6x - 3 = 5
[tex]\begin{gathered} \text{add 3 to both sides} \\ 6x-3+3=5+3 \\ 6x=8 \end{gathered}[/tex]step 2:
6x = 8
[tex]\begin{gathered} \text{Divide both sides by 6} \\ \frac{6x}{6}=\frac{8}{6} \\ x=\frac{4}{3} \end{gathered}[/tex]Step 3:
x = 4/3
[tex]\begin{gathered} \text{divide both sides by 2} \\ x=\frac{8}{6}=\frac{4}{3} \end{gathered}[/tex]
Two points A(0,-4), B(2,-1)determine line AB.What is the equation of the line AB? y= _1_x + _2_What is the equation of the line perpendicular to lineAB, passing through the point (2,-1)? y= _3_x + _4
1.
Let:
[tex]\begin{gathered} (x1,y1)=(0,-4) \\ (x2,y2)=(2,-1) \\ so\colon \\ m1=\frac{y2-y1}{x2-x1}=\frac{-1-(-4)}{2-0}=\frac{3}{2} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m1(x-x1) \\ y-(-4)=\frac{3}{2}(x-0) \\ y+4=\frac{3}{2}x \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]2.
If two lines are perpendicular, then:
[tex]\begin{gathered} m1\times m2=-1 \\ \frac{3}{2}\times m2=-1 \\ m2=-\frac{2}{3} \end{gathered}[/tex]Let:
[tex](x1,y1)=(2,-1)[/tex]Using the point slope equation:
[tex]\begin{gathered} y-y1=m2(x-x1) \\ y-(-1)=-\frac{2}{3}(x-2) \\ y+1=-\frac{2}{3}x+\frac{4}{3} \\ y=-\frac{2}{3}x+\frac{1}{3} \end{gathered}[/tex]The US consumes an average of 5.25 million metric tons of bananas per year. There are 317 million people in the US and there are 1000 kg in 1 metric ton. How many kilogram of bananas are consumed per person in a year? Round answer (except last one) to three significant digits. 365 days in a year.
The US consume 5.25 million metric tons of banana per year.
This is equivalent to 5.25 million x 1000kg = 5250 000 000 kg
US population = 317 million = 317 000 000
The number of kilogram of bananas consumed per person per year
= 5250 000 000 kg / 317 000 000
=16.6 kg
Therefore, the number of kilogram of bananas that are consumed per person per year is 16.6kg
Find the real and imaginary solution of (w^3) - 1000=0
Explanation
Given
[tex]w^3-1000=0[/tex]We will have;
[tex]\begin{gathered} w^3=1000 \\ \mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2} \\ therefore;\text{ }w=\sqrt[3]{1000},\:w=\sqrt[3]{1000}\frac{-1+\sqrt{3}i}{2},\:w=\sqrt[3]{1000}\frac{-1-\sqrt{3}i}{2} \\ hence;w=10,w=10\times\frac{-1+\sqrt{3}i}{2},\:w=10\times\frac{-1-\sqrt{3}i}{2} \\ w=10,\:w=-5+5\sqrt{3}i,\:w=-5-5\sqrt{3}i \end{gathered}[/tex]Answer: Option D
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Write an inequality for the word problem and answer the question about the inequality. Eric has an equal number of dimes and quarters that total less than 4 dollars. Could he have 12 dimes
Let
x -----> number of dimes coin
y -----> number of quarters coin
we have that
x=y ------> equation 1
and
0.10x+0.25y < 4 ------> inequality 1
substitute equation 1 in inequality 1
0.10x+0.25x < 4
solve for x
0.35x<4
x < 11.4
For 12 dimes
the value of x=12 not satisfy the inequality
that means
He couldn't have 12 dimes
A principal of $600 earns 3.2% interest compounded monthly. What is the effective interest (growth) rate? (Hint: make the equation look like abt.) About how long does it take to reach $1000?
Answer:
Explanation:
The formula for calculating the effective interest rate is expressed as
R = (1 + i/n)^n - 1
where
R is the effective interest rate
i is the nominal rate
n is the number of compounding periods in a year
From the information given,
n = 12 because it was compounded monthly
i = 3.2% = 3.2/100 = 0.032
Thus,
R = (1 + 0.032/12)^12 - 1
R = 0.03247
Multiplying by 100, it becomes 0.03247 x 100
Effective interest rate = 3.25%
We would apply the formula for calculating compound interest which is expressed as
A = a(1 + r/n)^nt
where
a is the principal or initial amount
t is the number of years
A is the final amount after t years
From the information given,
A = 1000
a = 600
n = 12
We want to find t
By substituting these values into the formula, we have
1000 = 600(1 + 0.032/12)^12t
1000/600 = (1.00267)^12t
Taking natural log of both sides, we have
ln (1000/600) = ln (1.00267)^12t = 12tln(1.00267)
12t = [ln (1000/600)]/ln (1.00267) = 191.5758
t = 191.5758/12
t = 16
It takes 16 years for the amount to reach $1000
Find the sum of the interior angles of the shape. Use the remaining angles to solve for x. Polygons Help91°120°899Sum of interior angles =degreesX =degrees
Solution
For this case we have 4 sides
Then the sum of the interior angles is givne by
[tex]180(n-2)=180(4-2)=180\cdot2=360\text{ }[/tex]Sum of interior angles is 360º
And if we solve for x we can do this:
360-91-120-89= 60
x= 60 º
The question is in the picture. Using the answer choice word bank, fill in the proportion to find the volume of the larger figure.
It is given that two similar solids have surface areas of 48 m² and 147 m², and the smaller solid has a volume of 34 m³.
It is required to find the volume of the larger solid.
Recall that the if the scale factor of similar solids is a/b, then the ratio of their areas is the square of the scale factor:
[tex]\frac{\text{ Area of smaller solid}}{\text{ Area of larger solid}}=\frac{a^2}{b^2}[/tex]Substitute the given areas into the equation:
[tex]\frac{48}{147}=\frac{a^2}{b^2}[/tex]Find the scale factor a/b:
[tex]\begin{gathered} \text{ Swap the sides of the equation:} \\ \Rightarrow\frac{a^2}{b^2}=\frac{48}{147} \\ \text{ Reduce the fraction on the right with }3: \\ \Rightarrow\frac{a^2}{b^2}=\frac{16}{49} \\ \text{ Take the square root of both sides:} \\ \Rightarrow\frac{a}{b}=\frac{4}{7} \end{gathered}[/tex]Recall that if the scale factor of two similar solids is a/b, then the ratio of their volumes is the cube of the scale factor:
[tex]\frac{\text{ Volume of smaller solid}}{\text{ Volume of larger solid}}=\left(\frac{a}{b}\right)^3[/tex]Let the volume of the larger solid be V and substitute the given value for the volume of the smaller solid:
[tex]\frac{34}{V}=\left(\frac{a}{b}\right)^3[/tex]Substitute a/b=4/7 into the proportion:
[tex]\begin{gathered} \frac{34}{V}=\left(\frac{4}{7}\right)^3 \\ \\ \Rightarrow\frac{34}{V}=\frac{4^3}{7^3} \\ \\ \Rightarrow\frac{34}{V}=\frac{64}{343} \end{gathered}[/tex]Find the value of V in the resulting proportion:
[tex]\begin{gathered} \text{ Cross multiply:} \\ 64V=343\cdot34 \\ \text{ Divide both sides by }64: \\ \Rightarrow\frac{64V}{64}=\frac{343\cdot34}{64} \\ \Rightarrow V\approx182.22\text{ m}^3 \end{gathered}[/tex]Answers:
The required proportion is 34/V =64/343.
The volume of the larger solid is about 182.22 m³.
in the function y=-2(x-1)+4 what effect does the number 4 have onthe graph, as compared to the graph of the function 7OA. t shifts the graph down 4 unitsO B. t shifts the graph 4 units to the leftOcHshifts the graph up 4 unitsOD.t shifts the graph 4 units to the right
Given:
y = -2(x - 1) + 4
The effect the number 4 has on the graph of the function is that there will be a vertical shift of 4 units up.
+4 here indicates a vertical shift of 4 upwards
ANSWER:
C) It shifts the graph up 4 units
15x²y/(x+1)^3* (x+1)/24x^5y
The simplified value of the given expression in the form of a fraction is [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .
The given expression is: [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
we will use the properties of exponents to simplify the expression.
Taking the powers of the like terms and combining we get :
[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]
[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]
[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]
Therefore we get the simplified equation for the expression.
Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.
A variable is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.
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A cylinder shaped above ground pool is 4.5 deep. If the diameter of the pool is 16 ft, determine the capacity of the swimming pool in cubic feet. Write your awnser in terms of pi
For this exercise you need to use the following formula for calculate the volume of a cylinder:
[tex]V=\pi r^2h[/tex]Where "r" is the radius and "h" is the height of the cylinder.
In this case you can identify that:
[tex]h=4.5ft[/tex]You know that the diameter of the pool is 16 feet. Since the radius is half the diameter:
[tex]\begin{gathered} r=\frac{16ft}{2} \\ \\ r=8ft \end{gathered}[/tex]Knowing the radius and the height of the pool, you can substitute them into the formula and then you have to evaluate, in order to find the capacity of the swimming pool in cubic feet:
[tex]\begin{gathered} V=\pi(8ft)^2(4.5ft) \\ V=288\pi\text{ }ft^3 \end{gathered}[/tex]The answer is:
[tex]288\pi\text{ }ft^3[/tex]Roselle has three cups of popcorn and 6 oz of soda for a total of $246 calories. Carmel has one cup of popcorn and 14 oz of soda for a total of $274 calories. determine the number of calories per cup of popcorn and per ounce of soda
Let 'x' be the number of calories per cup of popcorn, and 'y' be the number of calories per ounce of soda.
Given that 3 cups of popcorn and 6 oz of soda constitute 246 calories,
[tex]3x+6y=246[/tex]Also given that 1 cups of popcorn and 14 oz of soda constitute 274 calories,
[tex]x+14y=274[/tex]Solve the equations using Elimination Method.
Subtract 3 times equation 2 from equation 1,
[tex]\begin{gathered} (3x+6y)-3(x+14y)=246-3(274) \\ 3x+6y-3x-42y=246-822 \\ -36y=-576 \\ y=16 \end{gathered}[/tex]Substitute this value in equation 1, to obtain 'x' as,
[tex]\begin{gathered} 3x+6(16)=246 \\ 3x+96=246 \\ 3x=150 \\ x=50 \end{gathered}[/tex]Thus, the solution of the system of equations is x=50 and y=16.
Therefore, there are 50 calories per cup of popcorn, and 16 calorie per ounce of soda.
The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. Thewater output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in atotal water output of 1025 L. How long was each sprinkler used?Note that the ALEKS graphing calculator can be used to make computations easier.Х5?Hill family's sprinkler: hoursStewart family's sprinkler: [hoursM
The Hill family and the Stewart family each used their sprinklers last summer. The water output rate for the Hill family's sprinkler was 15 L per hour. The
water output rate for the Stewart family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a
total water output of 1025 L. How long was each sprinkler used?
Let
x ------> the number of hours of Hill family's sprinkler
y ------> the number of hours of Stewart family sprinkler
so
we have that
x+y=55 -------> x=55-y ------> equation 1
15x+25y=1025 ------> equation 2
Solve the system
Substitute equation 1 in equation 2
15(55-y)+25y=1025
solve for y
825-15y+25y=1025
10y=1025-825
10y=200
y=20
Find the value of x
x=55-20) -----> x=35
therefore
Hill family's sprinkler: 35 hoursStewart family's sprinkler:20 hoursIn AOPQ, OQ is extended through point Q to point R, m PQR = (7x – 19)º, mZOPQ = (2x – 3)°, and mZQOP = (x + 16). Find mZPQR.
Solution
For this case we can do the following:
m < PQR = 7x -19
m < OPQ= 2x-3
m < QOP= x+16
We need to satisfy that:
(180- m Replacing we got:
(180- 7x +19) + 2x -3 + x+16= 180
-7x +2x +x = -19+3 -16
-4x = -32
x= 8
Then m
6. 6.5 ounces →g7.45 miles → km8.2.3 miles → cmCovert #6#7#8
Answer:
6. 184.275 gr
7. 72 km
8. 368000 cm
Explanation:
To make these conversions, we need to know the following relationships:
1 ounce = 28.35 gr
1 mile = 1.6 km
1 km = 100000 cm
Then, we can convert each expression as follows:
6.5 oz x 28.35gr / 1 oz = 184.275 gr
45 mi x 1.6 km / 1 mi = 72 km
2.3 mi x 1.6 km/ 1 mi = 3.68 km x 100000 cm/ 1km = 368000 cm
Therefore, the answers are:
6. 184.275 gr
7. 72 km
8. 368000 cm
Two number cubes are rolled what is the probability that the sum of the numbers rolled is either a 1 and a 4 in either order
The first thing we have to know is that a cube with numbers is a dice that has 6 faces and that its numbers go from 1 to 6, so the probability that the sum of both dice gives 1 is zero, since the minimum that we are going to give is 2
[tex]P(sum=1)=0[/tex]Now for the sum of both dice of 4 we have the following combinations
• 1 and 3
,• 3 and 1
,• 2 and 2
We have 3 combinatorics that we have to get the probability of each of the combinations in order to find our final probability
[tex]\begin{gathered} P(1|3)=P(1)P(3)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(3|1)=P(3)P(1)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \\ P(2|2)=P(2)P(2)=\frac{1}{6}\cdot\frac{1}{6}=\frac{1}{36} \end{gathered}[/tex]The probability that the sum of 4 would be the sum of the probabilities of the combinatorcs
[tex]\begin{gathered} P(sum=4)=P(1|3)+P(3|1)+P(2|2) \\ P(sum=4)=\frac{1}{36}+\frac{1}{36}+\frac{1}{36} \\ P(sum=4)=\frac{3}{36} \\ P(sum=4)=\frac{1}{12} \end{gathered}[/tex]What is the probability of getting a 1 and a 4 in either order?The probability of getting any number on a die will be 1/6 if we can get a 1 or a 4 then our population will be 2/6
[tex]\begin{gathered} P(1|4)=\frac{2}{6} \\ P(4|1)=\frac{2}{6} \\ P(1\&4)=\frac{2}{6}\cdot\frac{2}{6} \\ P(1\&4)=\frac{4}{36} \\ P(1\&4)=\frac{1}{9} \end{gathered}[/tex]7/5-6/5+3/2=17/10=1 7/10
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
[tex]\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{14+15}{10}-x=\frac{6}{5}[/tex]that is:
[tex]\frac{29}{10}-x=\frac{6}{5}[/tex]solving for x, we obtain:
[tex]\frac{29}{10}-\frac{6}{5}=x[/tex]that is:
[tex]x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}[/tex]so that, the blank space would be:
[tex]\frac{17}{10}[/tex]and the complete expression would be:
[tex]\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}[/tex]