draw segment XZ with Y in between X and Z. Label the following information. , , XY=7x,YZ=6x-11, and XZ=83 What is the value of x?

The sum of 15 and 60 using the greatest common factor and the distributive property is 15(1+4).

Greatest common factor, as the name implies, is greatest among all common factors among the quantities given.

We can factorize the quantities in smallest relative factors possible (one level of factors over which all quantities can form themselves), and collect as many common factors as we could. Those will together compose GCF(Greatest common factor).

Given;

(15+60)

The common factor of 15 and 60 = 15

Taking 15 common;

=15(1+4)

Therefore, the answer by taking factor will be 15(1+4).

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The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates to calculate the sum of the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

The maximum value that can be represented in 2 bits for A(A[1:0]) is 3, and the maximum value that can be represented in 2 bits for B[1:0] is also 3. The maximum possible value of Y is 9, which requires 4 bits to represent. The truth table for the multiplier is shown below:

A[1] A[0] B[1] B[0] Y[3] Y[2] Y[1] Y[0]

0    0    0    0    0     0     0     0

0    0    0    1    0     0     0     1

0    0    1    0    0     0     1     0

0    0    1    1    0     0     1     1

0    1    0    0    0     0     0     0

0    1    0    1    0     0     0     1

0    1    1    0    0     0     1     0

0    1    1    1    0     0     1     1

1    0    0    0    0     0     0     0

1    0    0    1    0     0     0     1

1    0    1    0    0     0     1     0

1    0    1    1    0     0     1     1

1    1    0    0    0     1     0     0

1    1    0    1    0     1     0     1

1    1    1    0    0     1     1     0

1    1    1    1    1     1     1     1

The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates as follows:

Y[2] = A[1] * B[1] + (A[1] + B[1]) * (A[0] * B[0])

This can be simplified to Y[2] = A[1] * B[1] + A[0] * B[0]. That is, the third bit of output Y[2] is equal to the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

The third bit of output, Y[2], can be implemented using AND, OR, and NOT gates to calculate the sum of the product of the first bits of both inputs, A[1] and B[1], plus the product of the second bits of both inputs, A[0] and B[0].

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Important to detect outliers in data set, Z-score (3 std dev from mean) and IQR methods are commonly used, choosing right method and threshold crucial for accurate data analysis.

it is more than 3 standard deviations away from the mean. This method is known as the Z-score method or the standard deviation method for detecting outliers. It provides a way to quantify how far away a data point is from the mean in terms of standard deviations. However, it is important to note that the 3 standard deviation threshold is just a general guideline and may not always be appropriate. Other methods, such as the interquartile range (IQR) method, can also be used to detect outliers in a data set.

It's essential to detect outliers as they can greatly impact the analysis and interpretation of data, so choosing the appropriate method and threshold for identifying outliers is crucial.

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a. Qualitative    b. Quantitative discrete    c. Quantitative discrete   d. Qualitative

Question a is qualitative because it does not ask for a numerical answer but rather for a yes or no response. Question b is quantitative discrete because it requires a numerical answer from the respondent, but the answer is limited to a range of possible values (0-30 days). Question c is quantitative discrete because it requires a numerical answer from the respondent, but the answer is limited to a range of possible values (0-7 days). Question d is qualitative because it does not ask for a numerical answer but rather for a yes or no response. All of these questions are part of the Gallup-Healthways Well-Being Index survey, which is used to track trends in U.S. residents' health and wellbeing on a regular basis. The survey covers six areas of health and wellness, and the questions used to measure the Index provide both qualitative and quantitative data.

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Answer:

x ≈ - 2.70 or x ≈ 2.03

Step-by-step explanation:

Given:

[tex]1.5x^2+x-8.2=0[/tex]

Solve:

Multiply both sides by 10:

[tex]1.5x^2\cdot \:10+x\cdot \:10-8.2\cdot \:10=0\cdot \:10[/tex]

[tex]15x^2+10x-82=0[/tex]

Quadratic Formula: [tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Using the Quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Knowing that;

quadratic equation of the form: [tex]ax^2+bx+c=0[/tex]

a = 15

b = 10

c = -82

Plug it in:

[tex]=\frac{-10\pm \sqrt{10^2-4\cdot \:15\left(-82\right)}}{2\cdot \:15}[/tex]

[tex]=\frac{-10\pm \:2\sqrt{1255}}{2\cdot \:15}[/tex]

Separate the solutions since there are two:

[tex]x_1=\frac{-10+2\sqrt{1255}}{2\cdot \:15},\:x_2=\frac{-10-2\sqrt{1255}}{2\cdot \:15}[/tex]

[tex]=\frac{-10+2\sqrt{1255}}{30}[/tex]

[tex]=\frac{-5+\sqrt{1255}}{15}[/tex]

[tex]x=\frac{-5+\sqrt{1255}}{15},\:x=-\frac{5+\sqrt{1255}}{15}[/tex]

Which as a decimal is:

[tex]x=-\frac{5+\sqrt{1255}}{15}[/tex] ⇒ [tex]\left\mathrm Decimal}:\quad x=-2.69506\dots \right[/tex]

[tex]x=\frac{-5+\sqrt{1255}}{15}[/tex]    ⇒   [tex]\left\mathrm{Decimal}:\quad x=2.02839\dots \right[/tex]

Rounding:

-2.69506.. ≈ -2.70

2.02839..  ≈ 2.03

Hence, x ≈ - 2.70 or x ≈ 2.03.

RevyBreeze

After several hours of observation, he determined the lab dish had 1953125 bacteria.

A number system is defined as a system of writing to express numbers.

Given that A lab technician observed 5 bacteria growing in a lab dish.

One hour later he observed 25 bacteria.

Every hour he notice about 5 times as many as the hour before.

After several hours of observation, he determined the lab dish had 5 to the power of 9 bacteria.

5⁹

Five to the power of nine

1953125

Hence, After several hours of observation, he determined the lab dish had 1953125 bacteria.

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Answer:
The inverse of a function is the reflection of a function over the line y=x. Therefore, this will reflect the function over the line of symmetry.

As the line of symmetry in this case is the x-axis, the inverse function can be found by switching the x and y values.

So we have f(x) = 1.5x + 100, and the inverse function is therefore y=1.5x+100

Please let me know if this helps. :)

The value of 1+1 in base 10 is 2 and its value in base 2 is 10

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the sum.

For example if there 20 apples, 30mangoes and 40 cashews in a basket. The total number of fruits in the basket is obtained by adding all the fruits together.

This is means the total number of of fruit = 20+30+40 = 90 fruits.

Therefore 90 fruits are in the basket.

Similarly, the addition of 1 and 1 will give

1+1 = 2. This answer is in base 10.

1+1 can also be in base two and 1+1 in base 2 = 10

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For the function, the x-intercept of g(x) is at (5,0).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Given f(x) = ln(x)

and g(x) = -f(x - 4)

the function is

g(x) = -ln(x - 4)

when x = 5

g(x) = -ln(5 - 4)

g(x) = -ln1

g(x) = 0

the coordinates are (5, 0)

Hence the x-intercept is (5, 0).

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Answer:

57 degrees

Step-by-step explanation:

The sides of the rectangle in question number 1 are 4.5 units and 13.5 units. The sides of the rectangle in question number 2 are 6 units and 12 units.

Let's call the width of the rectangle in question number one as "w". Since the length of the rectangle is three times as long as its width, the length can be represented as 3w.

The perimeter of the rectangle is 36 units, so if we add up the lengths of all four sides, we get:

2w + 2(3w) = 36

2w + 6w = 36

8w = 36

w = 4.5

So the width of the rectangle is 4.5 units. Since the length is three times the width, the length is 3 × 4.5 = 13.5 units. So the sides of the rectangle are 4.5 units and 13.5 units.

Let's call the width of the rectangle in question number 2 as "p". Since the length of the rectangle is twice as long as its width, the length can be represented as 2p.

The area of the rectangle is given as 72 square units, so we can use the formula for the area of a rectangle to find the value of p:

A = l × w

72 = 2p × p

72 = 2p²

36 = p²

p = 6

So the width of the rectangle is 6 units. Since the length is twice the width, the length is 2 × 6 = 12 units. So the sides of the rectangle are 6 units and 12 units.

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Answer:

a + c = 1250

$7.00a + $5.50c = $7979

Step-by-step explanation:

Making the system of equations for the number of tickets involved how many attended and who attended

It's showing 1250 attended and children and adults showed up. Let's a = adults and c = children

a + c = 1250 <--- that's saying adults + children equal 1250

For $ earned, it involves how much each ticket was and the total cost

Looks like we have prices for a and c and the total cost which was 7979. Since adults were 7.00, we'll call that 7.00a. And for children it was 5.50, we'll call that 5.50c

Putting it together 7.00a + 5.50c = 7979 because all the $7.00 tickets plus all the $5.50 tickets cost $7979

The value of n/p = 5n/3p.

It is a branch of mathematics that deals with the occurrence of a random event.

Let's assume that the total number of numbers in the list is T. Therefore, p + n = T.

The probability of picking a positive number is 3/5.

So p/T = 3/5.

Ratio of the number of negative numbers to the number of positive numbers is n/p.

Divide the two equations we get

n/p = (n/T) / (p/T) = (n/T) / (3/5) = (5/3) * (n/T) = 5n/3p

Hence, the value of n/p = 5n/3p.

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The solution set of the inequality is (-7.5, 1), and the correct graph is the one in option A.

Here we want to solve the inequality below:

-10 < 2x + 5 < 7

To solve this, we need to isolate the variable x, then we will get:

-10 < 2x + 5 < 7

-10 - 5 < 2x < 7 - 5

-15 < 2x < 2

-15/2 < x < 2/2

-7.5 < x < 1

So the solution set is (-7.5, 1)

So the graph of this will be a number line that starts at -7.5 and ends at 1, that would be the one in option a.

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The equation that compares dollar amounts to be received or paid at different dates is the Time Value of Money (TVM) equation.

The time value of money(TVM) equation enables us to compare dollar amounts to be received or paid at various dates. This equation takes into account the concept of the opportunity cost of money and accounts for the changes in the value of money over time due to inflation and other factors. The equation calculates the present value of a future amount, or the future value of a present amount, based on an interest rate. This helps in making financial decisions by comparing the value of money at different points in time.

The equation used to compare dollar amounts received or paid at different time periods is called time value of money. This equation takes into account the effect of inflation, investment return, and the time period for which the money is being held, to calculate the present or future value of a sum of money. It helps to determine the equivalent value of money at a certain point in time, considering the opportunity cost of not having access to the money.

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The complete question is:

The formula that enables us to compare the amount of money that will be received or paid at various dates is the

Time value money.

Taylor rule.

interest-rate parity equation.

yield curve.

The system of equations has its solution to be (4, 0)

From the question, we have the following parameters that can be used in our computation:

. 3x + 4y = 12

2x + y = 8

Make y the subject

y = 8 - 2x

So, the second equation becomes

3x + 4(8 - 2x) = 12

Open the brackets

This gives

3x + 32 - 8x = 12

So, we have

-5x = -20

Divide

x = 4

Recall that

y = 8 - 2x

So, we have

y = 8 - 2(4)

y = 0

Hence, the solution is (4, 0)

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Answer:

60 + 5x = 125 - 10x

Step-by-step explanation:

Jeter- 60 + 5x

Callie- 125 - 10x

Set them equal to each other to find out when they will equal the same amount

Answer:

The answer can be expressed in multiple forms

[tex]4.\overline3\overline3[/tex] weeks

[tex]4\frac{1}{3}[/tex] weeks

Step-by-step explanation:

Lets write down what we are given

Jeter Initial Amount = $60.00

Callie Initial Amount = $125.00

Deposit/Withdrawal Per Week

Jeter + $5.00

Callie - $10.00

We can set up an expression for Jeter's money

[tex]60+5w[/tex]

We can set up an expression for Callie's money

[tex]125-10w[/tex]

[tex]w[/tex] represents the number of weeks

We can set each expression equal to each other to find out when they will have the same amount of money.

[tex]60+6w=125-10w[/tex]

Lets solve for [tex]w[/tex].

Add [tex]10w[/tex] to both sides of the equation.

[tex]60+5w+10w=125-10w+10w[/tex]

Combine like terms and simplify.

[tex]60+15w=125[/tex]

Subtract 60 from both sides of the equation.

[tex]60+15w-60=125-60[/tex]

Evaluate the subtraction and simplify..

[tex]15w=65[/tex]

Divide both sides of the equation by 15.

[tex]\frac{15w}{15}=\frac{65}{15}[/tex]

Simplify the left side by cancelling the common factor of 15.

[tex]w=\frac{65}{15}[/tex]

[tex]w=\frac{13}{3}[/tex]

[tex]w=4.3333[/tex]

[tex]w=4\frac{1}{3}[/tex]

The radian measure of angle A is -13π/18.

The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can also be used to represent the angle, with the middle letter indicating the location of the angle (i.e.its vertex).

Given an angle A = -130°

to find the radian measure,

we know that,

1° = π/180 radians

-130° = -130(π/180)

-130° = -13π/18

Hence the value in radian is -13π/18.

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The scale factor to produce figure {2} from figure {1} is -

{K} = 4/3.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller. Mathematically, we can write -

{K} = A/B

Given are two right triangles as figure {1} and {2}.

We can write the scale factor as the ration of the lengths of the legs as -

{K} = 4/3

Therefore, the scale factor to produce figure {2} from figure {1} is -

{K} = 4/3.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 298000}}{\left( \cfrac{16}{100} \right)298000}\implies 47680[/tex]

Answer:

2

Step-by-step explanation:

y inverse 3 in mathematics

The total cost of either plan is, 42

The number of DVD's rented is, 31

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Plan 1- membership fee of $11 and charges $1 for every DVD

Plan 2- $42 per month for unlimited DVD rentals

The two plans cost the same amount

The total cost of either plan = ?

The number of DVD's rented = ?

Suppose, the number of DVD's is n

So, cost in plan 1,

=  membership fee  +  n x (charges $1 for every DVD)

=   11 + n x 1

=   11 + n

And, cost in plan 2,

=  42

According to given condition,

cost is equal in both cases,

11 + n = 42

n = 31

Hence, the total cost and number of DVD's are respectively,  45 & 31

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The coordinates of the vertex of the following parabola is (0,6).

The given equation of the parabola is [tex]& y=-3 x^2+6 \\[/tex]

The point where the parabola and its axis of symmetry intersect is called the vertex of a parabola. It is used to determine the coordinates of the point on the parabola's axis of symmetry where it crosses it.

The standard form of a parabola is [tex]y=ax^{2} +bx+c.[/tex]

The vertex form of a parabola is [tex]y = a(x-h)^{2} + k[/tex].

[tex]$$\begin{aligned}& y=-3 x^2+6 \\& y-6=-3 x^2 \\& y-6=-3(x-0)^2\end{aligned}$$[/tex]

The vertex formula is used to find the vertex of a parabola. The formula to find the vertex is (h, k) = (-b/2a, -D/4a), where D = [tex]b^{2} -4ac[/tex].

Now comparing the above equation by the equation of parabola

⇒[tex]$$y-b=4(x-a)^2 \cdots$$[/tex]

With vertex (a, b)

So a=0 and b=6.

So vertex of above parabola is[tex]$(\mathbf{0}, \mathbf{6})$[/tex].

Therefore, the vertex of the given parabola [tex]$\mathbf{y}=-\mathbf{3} \mathbf{x}^{\mathbf{2}}+\mathbf{6}$ is $(\mathbf{0}, \mathbf{6})$[/tex].

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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. [tex]& y=-3 x^2+6 \\[/tex]

The equation of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

y = - kx + (6k - 3).

The general equation of a straight line is -

y = mx + c

where -

{m} → slope

{c} → y - intercept

Given is the line that passes through the point (6, -3) and has a slope of {m} = - k.

We can write the general equation as -

y = mx + c

Now -

{m} = - k                     .... Eq { 1 }

We can write -

y = - kx + c

For the point (6, - 3), we can write -

- 3 = - 6k + c

{c} = 6k - 3                           .... Eq { 2 }

We can write the equation of the line as -

y = - kx + (6k - 3)

Therefore, the equation of the line that passes through the point (6, -3) and has a slope of {m} = - k is →

y = - kx + (6k - 3).

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The given of the system of equation is has  No solution, parallel lines.

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

A1x+B1y+C1=0

A2x+B2Y+C2=0

1. One solution:

There will be one solution to the system of equations,  If we have:

[tex]\frac{A_1}{A_2} not\ equal to \ B_1/B_2[/tex]

2. Infinitely Many Solutions: (Identical lines in the system)

the ratio of A1 and A2 equal to ratio of B1 and B2 and equal toC1 and C2

3. No Solution:(Parallel lines)

the ratio of A1 and A2 equal to ratio of B1 and B2 but not equal ltoC1 and C2

Now, let us discuss the system of equations one by one:

a) A1=2, B1=-4 , C1=-12

A2=-3 , B2= 6 ,C2 = 15

Therefore, no solution i.e. parallel lines.

The complete question is-

Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15

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The possible sequences of rolls are [tex]6^7[/tex].

It is the total number of possible outcomes from a given set.

We have,

Standard six-sided die:

The number of times the dice are rolled = 7 times.

Now,

Number of sides in a dice = 6

So,

The total possible outcomes.

= [tex]6^7[/tex]

Thus,

The possible sequences of rolls are [tex]6^7[/tex].

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Answer:

105

Step-by-step explanation:

First off, please don't simply copy this for your homework, as the only person that is harmed is you.

(7)        (3)

(4)   x   (2)    = 35 * 3 = 105

^

Is the ways to choose the positions of the 4

------------^

Is the way to choose the positions of the 1s and 2s.

Answer:

Answer:

-0.05 per share  (loss)

Step-by-step explanation:

2 years net loss = 1 mm

so EPS (earnings per share) = -1/20 = -0.05 per share loss

The required simplified value of the measure of the multiplication factor x in the circle is 2.25.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Arc VW = 12x + 25 °
∠VXW = 52°

According to the question,
Arc VW = ∠VXW
12x + 25 = 52
x = 52 - 25 / 12
x = 2.25

Thus, the required simplified value of the measure of the multiplication factor x in the circle is 2.25.

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Answer:

[tex]\sf 1. \quad \dfrac{3}{8}[/tex]

[tex]\sf 2. \quad \dfrac{7}{24}[/tex]

Step-by-step explanation:

Spinner 1 is divided into 6 congruent sections.

There are 3 red sections, 2 blue sections and 1 yellow section.

Therefore, the probability of spinning each of the three colors is:

    [tex]\bullet \quad \sf P(R_1)=\dfrac{3}{6}=\dfrac{1}{2}[/tex]

    [tex]\bullet \quad \sf P(B_1)=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

    [tex]\bullet \quad \sf P(Y_1)=\dfrac{1}{6}[/tex]

Spinner 2 is divided into 3 sections of differing sizes.

The red section is half of the spinner. The blue and yellow sections are quarters of the spinner.

Therefore, the probability of spinning each of the three colors is:

    [tex]\bullet \quad \sf P(R_2)=\dfrac{1}{2}[/tex]

    [tex]\bullet \quad \sf P(B_2)=\dfrac{1}{4}[/tex]

    [tex]\bullet \quad \sf P(Y_2)=\dfrac{1}{4}[/tex]

If each spinner is spun once, then:

The probability that both spinners both show red is:

[tex]\sf P(R_1)\;and\;P(R_2)=\dfrac{1}{2} \times \dfrac{1}{2}=\dfrac{1}{4}[/tex]

The probability that both spinners both show blue is:

[tex]\sf P(B_1)\;and\;P(B_2)=\dfrac{1}{3} \times \dfrac{1}{4}=\dfrac{1}{12}[/tex]

The probability that both spinners both show yellow is:

[tex]\sf P(Y_1)\;and\;P(Y_2)=\dfrac{1}{6} \times \dfrac{1}{4}=\dfrac{1}{24}[/tex]

Therefore, the probability that both spinners show the same colour is:

[tex]\sf P(R_1\;\&\;R_2)\;or\;P(B_1\;\&\;B_2)\;or\;P(Y_1\;\&\;Y_2)=\dfrac{1}{4}+\dfrac{1}{12}+\dfrac{1}{24}=\dfrac{9}{24}=\dfrac{3}{8}[/tex]

If each spinner is spun once, the probability of getting a red from spinner 1 and a blue from spinner 2 is:

[tex]\sf P(R_1)\;and\;P(B_2)=\dfrac{1}{2} \times \dfrac{1}{4}=\dfrac{1}{8}[/tex]

The probability of getting a blue from spinner 1 and a red from spinner 2 is:

[tex]\sf P(B_1)\;and\;P(R_2)=\dfrac{1}{3} \times \dfrac{1}{2}=\dfrac{1}{6}[/tex]

Therefore, the probability of getting a red-blue combination is:

[tex]\sf P(R_1\;\&\;B_2)\;or\;P(B_1\;\&\;R_2)=\dfrac{1}{8}+\dfrac{1}{6}=\dfrac{7}{24}[/tex]