An equation in slope-intercept form for the perpendicular bisector of the line segment with endpoints (-1, -8) and K (5, 4) is y = 2x - 6.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 + 8)/(5 + 1)
Slope (m) = 12/6
Slope (m) = 2.
At data point (-1, -8) and a slope of 2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2x + 2
y = 2x - 6.
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The rear windshield wiper blade on a car has a length of 8 inches. The blade is mounted on a 16 inch arm, 8
inches from the pivot point. If the wiper turns through an angle of 130 degrees, how much area is swept
clean?
blade
square inches.
The area swept clean by the wiper blade is approximately 239.3 square inches.
To find the area swept clean by the bladeWe need to find the area of the circular sector that is swept out by the blade as it rotates through an angle of 130 degrees. The radius of the circular sector is the length of the wiper arm, which is 16 inches.
The formula for the area of a circular sector is
A = (θ/360) × πr^2
Where
θ is the central angle of the sector (in degrees)r is the radius of the circle π is the constant pi (approximately 3.14)In this case, θ = 130 degrees and r = 16 inches, so we can plug these values into the formula to get:
A = (130/360) × 3.14 × (16)^2
Simplifying this expression, we get:
A ≈ 239.3 square inches
Therefore, the area swept clean by the wiper blade is approximately 239.3 square inches.
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when flipping a coin 4 times. How many favorable outcomes are there for two heads and two tails (in any order)?
There are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.
How many favorable outcomes are there for heads and tailsWhen flipping a coin 4 times, there are 2 possible outcomes (heads or tails) for each flip.
Therefore, there are a total of 2^4 = 16 possible outcomes for 4 coin flips.
To find the number of favorable outcomes for getting two heads and two tails (in any order), we can use combinations.
We need to choose 2 coin flips out of 4 to be heads, which can be done in C(4,2) = 6 ways.
Once we have chosen the positions for the heads, the remaining positions must be tails.
So there are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.
These outcomes are:
HH-TT
HT-HT
TH-HT
TT-HH
HT-TH
TH-HT
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about how much money
The cost of the car with 60,000 miles would be = $13,000 approximately.
How to determine the cost of cars according to mileage?To calculate the cost of the car form the given graph above is to draw a straight line that connects most of the points of interception.
From the graph, the most appropriate point of interception would be on $13,000 since each line in y-axis represents a thousand dollars.
Therefore, the cost of the car with 60,000 miles would be = $13,000 approximately.
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The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
The best measure of variability for the data is A. The range is the best measure of variability, and it equals 8.
How to find the range ?The range is the difference between the highest value and the lowest value in the dataset. In this case, the highest number of rose bouquets is 9, and the lowest is 1. This is the data shown on the line plot.
Range = Highest Value - Lowest Value
Range = 9 - 1
Range = 8
The range is the best measure of variability, and it equals 9. The IQR is used when there are outliers that can affect the data.
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In ΔDEF, the measure of ∠F=90°, EF = 2. 3 feet, and FD = 2. 9 feet. Find the measure of ∠D to the nearest tenth of a degree
In ΔDEF, the measure of angle D = 38.4°
Here in triangle DEF the measure of angle F = 90°
This means that ΔDEF is a right triangle and DE is the hypotenuse.
We need to find the measure of angle D.
Consider the tangent of angle D.
tan(D) = opposite side/ adjacent side
tan(D) = EF / FD
Here, EF = 2.3 feet, and FD = 2.9 feet.
So above equation becomes,
tan(D) = 2.3 / 2.9
tan(D) = 0.79310
D = arctan(0.7931)
D = 38.42°
Therefore, the measure of ∠D = 38.4°
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Suppose a charity received a donation of 29.9 million. If this represents 43% of the charity's donated funds, what is the total amount of its donated funds?
sorry to bother but can yall help me with this?
My rabbit Nibbles lives in a moveable pen and helps to keep the grass short. The pen is rectangular and measures 3m by 2m, as shown in the diagram, where the arrow indicates North. On successive days, the pen is moved 1m East, 2m South, 1m West and 2m North.
What is the total area, in square metres, of the region of grass which Nibbles can nibble?
Answer:
We can break down the total area of grass that Nibbles can nibble into two parts: the original rectangular pen, and the additional grass that Nibbles can reach as the pen is moved.
The area of the original rectangular pen is:
A1 = length x width = 3m x 2m = 6 square meters
To calculate the area of the additional grass, we can visualize the movements of the pen. The pen moves 1 meter to the east, 2 meters to the south, 1 meter to the west, and 2 meters to the north. This creates an irregular pentagon shape, as shown in the diagram below:
```
+-------+
| |
| |
E |
+----+---+ |
| S|
| |
| |
| |
| |
| |
+-----------+
W
```
To calculate the area of this irregular pentagon, we can divide it into two triangles and one rectangle:
- The east and west sides of the pen form a rectangle with dimensions 1m x 2m, for an area of 2 square meters.
- The south side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.
- The north side of the pen creates a right triangle with legs of 2m and 1m, for an area of (1/2) x base x height = 1 square meter.
Therefore, the total area of grass that Nibbles can nibble is:
A = A1 + 2 + 1 + 1 = 10 square meters.
So the answer is 10 square meters.
y=400(0.99)x growth or decay
The given function of the growth decay is decreasing.
What in mathematics is an exponential?
The formula for an exponential function, often known as an exponential function, is f (x) = axe, where "x" is a variable and "a" is a constant that serves as the function's basis and must be greater than 0.The transcendental number, abbreviated e, which is roughly equivalent to 2.71828, is the most often used exponential function basis.
We have given that,
Y=400(.99)^x
Exponential growth is a process that increases quantity over time. decreases over time, and is said to be undergoing exponential decay instead.
Therefore, The given function of the growth decay is decreasing.
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How many home runs did the player with 154 hits have?
How many was he predicted to have?
can someone do this i don’t understand
A good way to solve for lines and segments will be to know the equations and properties of the shapes that we are provided with.
How to solve for lines and segmentsTo get the answers for the lines and segment, you can begin by applying the following steps:
Identify the given information: Determine what information is provided about the line or segment. For example, you may be given the coordinates of two points on the line or segment, or the slope and y-intercept of a line.Find the equation: Use the information provided to find the equation of the line or segment. For a line, the general equation is y = mx + b, where m is the slope and b is the y-intercept. For a segment, you may need to use the distance formula or midpoint formula to find the endpoints, and then find the equation of the line that passes through those points.Check for intersections: If you need to find the intersection of two lines or segments, set their equations equal to each other and solve for the variables. If the lines or segments do not intersect, they are parallel or skew.Find lengths and angles: Once you have the equations and intersection points, you can use geometry and trigonometry to find lengths and angles of the lines and segments.Learn more about lines and segments here:
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PLEASE ANSWER!! WILL GIVE BRAINLIEST
Answer:
the correct answer is option D
Complete the table.
f(u) = u² + 2u + 3 f(u) U
-20 -10 0 10
Explain.
Answer: see below
Step-by-step explanation:
To complete the table, we need to evaluate the function f(u) = u² + 2u + 3 for the given values of u.
f(u) U
-20 (-20)² + 2(-20) + 3 = 403
-10 (-10)² + 2(-10) + 3 = 117
0 0² + 2(0) + 3 = 3
10 10² + 2(10) + 3 = 123
The table can be filled as follows:
f(u) U
403 -20
117 -10
3 0
123 10
The function f(u) = u² + 2u + 3 is a quadratic function, which has a parabolic shape. The coefficient of u² is positive, which means the parabola opens upward. The vertex of the parabola is at the point (-1, 2), which is the minimum point of the function.
As u increases or decreases from 0, the function increases. This is reflected in the table, where we see that the values of f(u) increase as u moves away from 0.
The table gives us a set of ordered pairs that represent the function f(u) for the given values of u. These ordered pairs can be plotted on a coordinate plane to draw the graph of the function.
Activity#2<br />Directions: Solve the following problems. Show your complete solutions. <br /><br />1. The diagonals of a Kite have lengths of 12 and 15 cm. Find the area of a Kite. <br />2. Given parallelogram ABCD, angle A and angle B measures (x+30) and (3x-90) respectively. Determine the measure of each angle. <br />3. One lateral face of the roof of the school building is trapezoid in shape. <br />One of the bases of this trapezoid is 6 m longer than the other base. Find<br />the length of the two bases if the median measures 19 m. <br />4. Given Isosceles Trapezoid CLUB, if m<C = 4x+3 and m<L = 5x-15, then find the value of x. <br />5. SPIN is a trapezoid with median AB. If the length of AB is 18cm and SP is 6, then find the length of NI. <br />
The length of NI is 8.5 cm.
Find the area of a kite by using formula?The area of a kite can be found using the formula: Area = (d1 * d2)/2, where d1 and d2 are the lengths of the diagonals.
Substituting the given values, we get:
Area = (12 * 15)/2
Area = 90 square cm
Therefore, the area of the kite is 90 square cm.
In a parallelogram, opposite angles are equal. So, we have:
Angle A = Angle C (opposite angles)
Angle B = Angle D (opposite angles)
Also, sum of adjacent angles in a parallelogram is 180 degrees. So, we have:
Angle A + Angle B = 180 degrees
(x+30) + (3x-90) = 180
4x - 60 = 180
4x = 240
x = 60
Therefore, Angle A = x + 30 = 90 degrees, and Angle B = 3x - 90 = 90 degrees.
Let the shorter base of the trapezoid be x. Then, the longer base is x+6 (as given in the problem).
The median of a trapezoid is the average of the two bases. So, we have:
Median = (x + x + 6)/2 = 19
2x + 6 = 38
2x = 32
x = 16
Therefore, the shorter base of the trapezoid is 16 m and the longer base is 22 m.
In an isosceles trapezoid, opposite angles are supplementary. So, we have:
Angle C + Angle L = 180 degrees
4x + 3 + 5x - 15 = 180
9x - 12 = 180
9x = 192
x = 21.33
Therefore, the value of x is 21.33.
In a trapezoid, the median is the average of the two bases. So, we have:
AB = 18 (given)
Median = (SP + NI)/2
But SP = NI (opposite sides of a trapezoid are equal)
So, Median = 2SP/2 = SP
Therefore, SP = Median = 19/2 = 9.5 cm
Also, AB = SP + NI
18 = 9.5 + NI
NI = 8.5 cm
Hence concluded that the length of NI is 8.5 cm.
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Suppose that we would like to determine the proportion of U.S. citizens who have brown hair. To estimate this, we randomly select 100 people and we find that 63 of them have brown hair. Construct a 95% confidence interval for the proportion of people with brown hair in the U.S.
we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:
[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]
where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.
In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:
[tex]Confidence Interval = 0.63 ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]
Simplifying the expression inside the square root, we get:
[tex]Confidence Interval= 0.63 ± 0.098[/tex]
Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:
[tex]\frac{63}{100} = 0.63[/tex](0.532, 0.728)
This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
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¿Cuál es la aceleración que adquiere un objeto que tiene una masa de 12 Kg y es empujado con una fuerza de 20N?
The acceleration acquired by the object of mass 12 Kg and is pushed with a force of 12 N, is given by 5/3 m/s².
We know that from the first law of Newton's Law that,
F = m*a
where 'F' is applied force; 'm' is mass of object and 'a' is acceleration.
Let the acceleration acquired by the object be 'A'.
Mass of the object is (m) = 12 Kg
The force applied (F) = 20 N
So from Newton's First Law of Motion we get,
F = m*a
20 = 12*A
A = 20/12
A = 5/3
Hence the acceleration will be 5/3 m/s².
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The question is in another language. The question is in English will be -
''What is the acceleration acquired by an object that has a mass of 12 Kg and is pushed with a force of 20N?''
7 Find in degrees. 19 0 [?] degrees Round to the nearest hundredth.
Answer:
Θ ≈ 21.62°
Step-by-step explanation:
using the sine ratio in the right triangle
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{19}[/tex] , then
Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{7}{19}[/tex] ) ≈ 21.62° ( to the nearest hundredth )
LOOK AT PHOTO
5x+3> 10
The smallest integer value of x that would be a solution in the inequality would be x = 2.
How to find the smallest integer ?To find the smallest integer value of x that satisfies the inequality 5x + 3 ≥ 10, first solve the inequality for x:
Subtract 3 from both sides:
5x ≥ 7
Divide by 5:
x ≥ 7/5
The inequality states that x must be greater than or equal to 7/5, which is equal to 1.4. Since we are looking for the smallest integer value, we should round up to the next integer, which is 2. Therefore, the smallest integer value of x that satisfies the inequality is x = 2.
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Please help, will give brainliest
Answer:
1. Mean : 85.6
2. Median : 90
3. Mode : 95
4. Range : 35
Step-by-step explanation:
1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.
2. To find the median, line up all the numbers in order from least to greatest. Like so :
60,75,75,90,90,95,95,95,95
In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.
3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.
4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do [tex]95-60[/tex] and you will get an answer of 35.
Hope this helps!
Answer:
Mean: 85.6
Median: 90
Mode: 95
Range: 35
Step-by-step explanation:
Mean: Add up all the value and divide by the number of values you have.
75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770
770 / 9 = 85.6
Median: Rearrange in increasing order + look at middle number
60, 75, 75, 90, 90, 95, 95, 95, 95
Mode: Number that shows up the most.
95 shows up 4 times.
Range: Maximum - Minimum.
95 - 60 = 35.
Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for either 24 hours or 48 hours. Here are the resulting bacterial counts for each condition. The value of the correlation between bacterial count after 24 hours and bacterial count after 48 hours
The bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.
To find the correlation between the bacterial count after 24 hours and 48 hours, we would need the actual numerical values of the bacterial counts for each strain. Without that information, we cannot calculate the correlation coefficient. However, it is important to note that a positive correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours also increases. A negative correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.
The complete question is-
Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition:
24 hr: 66, 71, 93, 102, 62
48hr: 110,123,146,136,113
If we had plotted bacterial count at 35 degrees Celsius on the y-axis instead of the x-axis, the value of the correlation coefficient would be
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Can someone show me step by step of how to do this please and correctly
What is the area of the circle? Approximate using pi equals 22 over 7 and round to the nearest square yard.
a circle with radius labeled 18 yards
57 square yards
113 square yards
1,018 square yards
2,037 square yards
Points earned on this question: 0
find the slope of (-7,2) and (-4,1)
Answer:
-1/3
Step-by-step explanation:
Use the formula [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] to find the slope given the 2 points:
1-2
------
-4-(-7)
-1/3 is your slope
Find the slope of the line through the pair of points. D(3, 5), J(8, 7)
20 POINTS
Answer:
2/5
Step-by-step explanation:
slope= y2-y1 / x2-x1
in this case:
y2=7 y1=5 x2= 8 x1=3
plug that into the formula above to get the answer
slope= 2/5 or 0.4
Find the surface of each pyramid
The surface area of the given pyramid is 203 in²
Calculating the surface area of a square PyramidFrom the question, we are to calculate the surface area of the given square pyramid
From the given information, the base of the pyramid is 7 in
and
The slant height of the pyramid is 11 in
The surface area of a pyramid can be calculated by using the formula
A = a² + 2al
Where A is the area of the pyramid
a is the side base
and l is the slant height
From the given information,
a = 7 in
and
l = 11 in
Thus,
Surface area = 7² + 2(7)(11)
Surface area = 49 + 154
Surface area = 203 in²
Hence,
The surface area is 203 in²
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Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at negative 5 comma 3, negative 5 comma 6, negative 9 comma 6, negative 9 comma 3, negative 7 comma 1.
50 POINTS ASAP Determine the line of reflection.
Reflection across x = −4
Reflection across y = 1
Reflection across the x-axis
Reflection across the y-axis
Answer:
The correct line of reflection that maps the polygon ABCDE to its image polygon A' B' C' D' E' is:
C. Reflection across the x-axis
Explanation:
The given vertices of the original polygon ABCDE are:
A(-3, 3)
B(-3, 6)
C(1, 6)
D(1, 3)
E(-1, 1)
The given vertices of the image polygon A' B' C' D' E' are:
A'(-5, 3)
B'(-5, 6)
C'(-9, 6)
D'(-9, 3)
E'(-7, 1)
Comparing the coordinates of the original polygon ABCDE and its image polygon A' B' C' D' E', we can see that the y-coordinates are negated, while the x-coordinates remain the same. This indicates that the reflection is happening along the x-axis, as it is the line that reverses the y-coordinates while keeping the x-coordinates unchanged.
Therefore, the correct line of reflection is the x-axis, as shown by option C. Reflection across the x-axis.
Double-check this answer i wrote.
a one-hectare forest community is sampled in early august. the sample yields 12 small trees, 4 types of vines, as well as 17 native shrubs that represent 10 species. what can be estimated from the sample for the shrubs in the forest community?
Based on the sample of a one-hectare forest community in early August, an estimate can be made for the total number and diversity of shrub species present in the community.
From the sample of the one-hectare forest community, several estimates can be made for the shrubs in the forest community:
Abundance: The abundance of shrubs in the one-hectare forest community can be estimated by multiplying the number of shrubs in the sample by 10 (the number of species represented by the sample). Therefore, an estimate of the total number of shrubs in the one-hectare forest community would be 17 x 10 = 170 shrubs.
Species richness: The sample contained 10 species of shrubs. This can be used as an estimate of the total number of shrub species in the one-hectare forest community.
Diversity: The diversity of the shrub community in the one-hectare forest can be estimated using the data on species richness and abundance. The most commonly used metric for estimating diversity is the Shannon-Wiener diversity index, which takes into account both the number of species and their relative abundance.
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I need some help please
Step-by-step explanation:
'3' is greater than 0 so we use the second portion of f(x)
f(3) = x+1
= 3 + 1 = 4
Find the equation of the line shown ?
Answer:
y=2x+3
Step-by-step explanation:
find x
look for points (2,7), (3,9), (0,3)
(x2-x1), (y2-y1)
x - distance from 7 and 9: (9-7=2)
y - distance from 2 and 3: (3-2=1)
Rise(y) over run (x) = 2/1=2
so X=2
y=2x
Because we see the line passes the point (0,3) we know the b in y=mx+b = 3
To prove:
try a point
(2,7)
y=mx+b (plug-in)
7=2(x)+3 (isolate x, subtract 3 to 7)
4= 2x (isolate x, divide by 2)
x=2
2=2 ( compare x to original coordinate: (2,7))
consider the experiment of rolling a die whose sample space is (1,2,3,4,5,6). if two dice are rolled simultaneously, what is the probability that a prime number turns up on one of the dice and a composite number on the other?
Therefore, the probability of getting a prime number on one die and a composite number on the other die when rolling two dice simultaneously is 1/6 or approximately 0.1667.
What is probability?Probability theory is a branch of mathematics that deals with the study of random events and the analysis of their outcomes. It is widely used in statistics, science, engineering, finance, and many other fields to model and predict the behavior of complex systems.
Here,
There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled simultaneously. We need to count the number of outcomes where one die shows a prime number and the other die shows a composite number.
Prime numbers in the sample space are 2, 3, and 5. Composite numbers are 4, 6, and any number greater than 1 that is not prime.
So, there are three possible outcomes where one die shows a prime number and the other die shows a 4 or 6:
(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)
Therefore, there are a total of 6 possible outcomes where one die shows a prime number and the other die shows a composite number.
The probability of getting one prime number and one composite number on the two dice is:
P = number of favorable outcomes / total number of possible outcomes
P = 6 / 36
P = 1/6
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