There are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).
Assuming that the distance between adjacent lattice points is equal to 1 unit, we can find the number of paths from [tex]a$ to $b$[/tex] consisting of exactly six line segments by using the concept of permutations and combinations.
To reach [tex]b$ from $a$[/tex] using exactly 6 line segments, we need to make 3 horizontal and 3 vertical moves, with each move covering a distance of 1 unit. The order in which we make these moves is important.
Out of the 6 moves, we can choose 3 moves to be horizontal and the remaining 3 to be vertical. The number of ways of doing this is given by the combination formula:
[tex]$C(6,3) = \frac{6!}{3!3!} = 20$[/tex]
Once we have selected the 3 horizontal moves and 3 vertical moves, we can arrange them in any order. The number of ways of doing this is given by the permutation formula:
[tex]$P(6,6) = 6! = 720$[/tex]
Therefore, the total number of paths from[tex]$a$ to $b$[/tex]consisting of exactly six line segments (vertical, horizontal or inclined) is given by the product of the number of ways of choosing 3 horizontal moves out of 6, and the number of ways of arranging the 6 moves:
[tex]$20 \times 720 = 14,400$[/tex]
Hence, there are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).
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There are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or inclined).
We can use the concept of permutations and combinations.
First, we need to consider the possible directions for each line segment:
vertical, horizontal, and inclined (assume inclined in both the top-right and bottom-right directions).
So there are 4 possible directions for each segment.
Since we have 6 line segments, we need to find the total number of paths that can be formed by arranging the 4
directions for the 6 segments.
We can use the formula for permutations with repetition, which is [tex]n^r[/tex], where n is the number of possible directions (4)
and r is the number of segments (6).
Plug in the values into the formula:
[tex]4^6[/tex] = 4096.
So, there are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or
inclined).
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Maya weighed 15 packages. Their mean weight was 5 pounds. What was the total weight of the 15 packages?
Answer:
75lbs
Step-by-step explanation:
if the mean of the packages was 15 then all the items averaged to 5 pounds each meaning they had a total of 15*5 or 75lbs
Draw triangle PQR where PQ has length 4 cm PR has length 3.5 cm and angle RPQ is 32° 
A triangle has two sides measuring 4 cm and 8 cm. Which lengths cannot be the length of the third side
The length of the third side of a triangle cannot be 15 cm
The correct answer is an option (b)
We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.
For example if a, b, c represents the side of a triangle then by above theorem a + b ≥ c
Here, the two sides of a triangle measure 4 cm and 8 cm.
Let a = 4 cm and b = 8 cm and c represents the third side of a triangle.
Using triangle inequality theorem,
a + b ≥ c
4 + 8 ≥ c
12 ≥ c
This means that the third side of the triangle must be less than or equal to 12 cm.
Thus, the correct answer is an option (b)
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The complete question is:
A triangle has two sides measuring 4 cm and 8 cm. Which lengths cannot be the length of the third side
a) 7 cm
b) 15 cm
c) 10 cm
d) 5 cm
Surface are. Help!!!!!!!!
The surface areas of the prisms are listed below:
Case 1: 94 in²
Case 2: 72 cm²
Case 3: 40.5 m²
Case 4: 39.1 mm²
Case 5: 130 ft²
Case 6: 136 m²
How to find the surface area of a prism
In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:
Rectangle
A = b · h
Triangle
A = 0.5 · b ·h
Where:
A - Areab - Widthh - HeightNow we proceed to determine the surface areas:
Case 1
A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)
A = 40 in² + 24 in² + 30 in²
A = 94 in²
Case 2
A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²
A = 12 cm² + 20 cm² + 15 cm² + 25 cm²
A = 72 cm²
Case 3
A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)
A = 10.5 m² + 21 m² + 9 m²
A = 40.5 m²
Case 4
A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)
A = 16 mm² + 6 mm² + 17.1 mm²
A = 39.1 mm²
Case 5
A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)
A = 100 ft² + 10 ft² + 20 ft²
A = 130 ft²
Case 6
A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)
A = 24 m² + 70 m² + 42 m²
A = 136 m²
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what is the mode of the data represented in this line plot?
Answer:6
Step-by-step explanation:
A rectangle and a triangle below have the same height and base measurements. Find the area of the rectangle and the right triangle, and then compare the areas
The area of rectangle is ____ square inches. The area of the triangle is __ square inches . The area of the triangle is ___ the area of the rectangle
The area of the rectangle is 48 in².
The area of the triangle is 24 in².
The area of the triangle is half the area of the rectangle.
How to calculate the area of a rectangle and a triangle?To calculate the area of a rectangle, we multiply the length of the rectangle by its width. And to calculate the area of a triangle we multiply the base of the triangle to the height of the triangle and divide by 2.
To calculate the area of the rectangle, we use the formula below
Formula:
A = LW....................... Equation 1Where:
A = Area of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 6 inW = 8 inSubstitute into equation 1
A = 6×8A = 48 in²Also, the area of the triangle is given by the formula below
A' = bh/2.................. Equation 2Where:
A' = Area of the triangleb = Base of the triangle = 6 inh = Height of the triangle = 8 inSubstitute into equation 2
A' = (6×8)/2A' = 24 in²Hence, the area of the triangle is half the area of the rectangle.
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Austin collected 30 9/10 kilograms of grass for recycling in exactly 2/3 of the class he collectible was the total amount in kilograms of blue grAss
Answer: Let's call the total amount of grass that Austin collected "G" in kilograms. We know that he collected 30 9/10 kilograms, which can be written as a mixed number or an improper fraction:
30 9/10 = 309/10
So, we have:
G = 309/10
We also know that 2/3 of the grass he collected was blue grass. So, let's call the amount of blue grass "B" in kilograms. We can set up an equation based on the information given:
B = (2/3)G
Substituting G = 309/10, we get:
B = (2/3)(309/10)
B = 206/5
B = 41 1/5
Therefore, the total amount of blue grass Austin collected was 41 1/5 kilograms.
Step-by-step explanation:
What happens when the function f(x) = 2 sin(2) is transformed by the rule g (w) = - f(x)?
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
O f(x) is reflected over the y-axis.
O f(x) is reflected over the x-axis.
• f(x) is compressed toward the y-axis by a factor of 1/2 and is reflected over the y-axis
Answer:
• f(x) is stretched away from the x-axis by a factor of 2 and is reflected over the x-axis.
Step-by-step explanation:
The function f(x) = 2sin(2x) has an amplitude of 2 and a period of π/2. When we apply the rule g(w) = - f(x), we are reflecting the graph of f(x) over the x-axis and then taking its opposite. This means that the amplitude of g(w) will still be 2, but the graph will be reflected and stretched away from the x-axis by a factor of 2.
I hope it helps you
Adding and subtracting decimals
1) 34.12 - 41.23 + 14.01
2) -34.12 + 41.23 - 14.01
Combine all positive numbers:
Combine all negative numbers:
Rewrite:
(look at the picture)
Answer:
1Step-by-step explanation:
calculate the probability of obtaining a sample result of 168 out of 200 or less if the company's claim is true. (use a table or technology. round your answer to four decimal places.)
The cumulative probability of obtaining a sample result will be approximately 0.0001
We have to apply Formula of Binomial Distribution:
P(X ≤ 168) = ΣP(X = i) for i = 0, 1, 2, .., 168, here in a sample of size n, P(X = i) is the probability of getting exactly i success
We assume that company's claim is true, 0.8 is the probability of success for each trial
P(X = i) = (200 choose i)×[tex]0.8^{i}[/tex] ×[tex]0.2^{200- i}[/tex]
By using this, we can easily find that cumulative probability is 0.0001
So, the probability is very low, this means that company's claim of an 80% success rate can be incorrect
So, further analysis may be needed to draw some conclusions and results
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PLEASE is due very soon please explain 50pts
Answer:
3
Step-by-step explanation:
Because same numbers = same y intercept but I'm not sure
Answer:
1) The image has the same slope, different y-intercept
Step-by-step explanation:
You want the relationship between the line 3x -5y = 4 and its image dilated by a factor of 5/3 centered at the origin.
DilationDilation about the origin multiplies every coordinate by the dilation factor. Dilation does not change slopes or angles, but it changes lengths by the dilation factor.
Dilation of a lineWhen the equation of a line is written in standard form, the dilation of it effectively multiplies the constant by the dilation factor.
The given line has intercepts ...
ax +by = c
x-intercept = c/a = 4/3
y-intercept = c/b = -4/5
If these values are multiplied by the dilation factor 5/3, they become ...
x-intercept' = (5/3)(4/3) = 20/9 = 2 2/9
y-intercept' = (5/3)(-4/5) = -4/3 . . . . . note the y-intercept has changed
SlopeThe slope of the given line can be determined from its intercepts:
m = (-y intercept)/(x intercept) = -(-4/5)/(4/3) = 3/5
Since both of these intercepts are multiplied by the same dilation factor, their ratio remains unchanged. The slope of the dilated line is the same.
EquationEffectively, the dilated line's equation is ...
3x -5y = 4(5/3)
3x -5y = 20/3
__
Additional comment
The original (dashed) line and its dilated image are shown in the attachment.
The coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).
Find the equation of the line parallel to PQ that passes through the point (6, -1).
The equation of the line parallel to PQ that passes through the point (6, -1) is y = (-5/6)x + 4.
What is the equation of the line parallel to PQ that passes through the point (6, -1)?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given that: the coordinates of P are (-3, 8) and the coordinates of Q are (9, -2).
We can find the slope of line PQ.
m = (y2 - y1) / (x2 - x1)
Where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively.
m = (-2 - 8) / (9 - (-3))
m = -10 / 12
m = -5/6
Since we want the equation of a line parallel to PQ, it will have the same slope.
Hence, the equation of the line can be written as:
y - y1 = m(x - x1)
where (x1, y1) is the point (6, -1) and m is the slope we found earlier.
Plugging in the values, we get:
y - (-1) = (-5/6)(x - 6)
y + 1 = (-5/6)x + 5
y = (-5/6)x + 5 - 1
y = (-5/6)x + 4
Therefore, the equation of the parallel line to PQ is y = (-5/6)x + 4.
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A rectangular prism has a length of 10 inches, a width of 4 inches, and a height of 3.7 inches. What is the volume of this rectangular prism?
Answer:
I believe it's 148.
Step-by-step explanation:
You must do L x W x H to find the volume of a rectangular prism or cube.
A teacher surveyed her class after they had taken a vocabulary test. Eighteen of the students claimed they had studied
at least one hour for the test. The remaining twelve students admitted that they had not studied for the test at all. The
test results (expressed as a percent) for the two groups are shown below.
Studied: 88, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 84
Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89
1. Calculate the range and Interquartile range for each set of data.
2. Using complete sentences, compare the data sets based on your results in part A.
NEED THIS ASAP PLEASE
Find the value of x. If a segment looks like a tangent, it is a tangent.
The value of x in the circle is 19.5 .
What is secant line of circle?
A secant is a straight line that intersects a circle at least twice in different places. We can draw an endless number of secants on a circle since a circle has an infinite number of points around its perimeter.
Here the given circle using formula for secant line ,
(A+B).B = (C+D).D
Here A = x , B = 8 , C= 12 and D=10. Then,
=> (x+8).8= (12+10).10
=> 8x+64 = 22*10
=> 8x+64 = 220
=> 8x = 220-64 = 156
=> x = 156/8 = 19.5
Hence the value of x in circle is 19.5.
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All relationships have equal weight; none is stronger than any other. true or false?
False. While all relationships should be valued and respected, it's unrealistic to say that they all have equal weight. Some relationships may be closer and more intimate than others, or may require more time and energy to maintain.
Additionally, some relationships may have greater consequences or impact on our lives than others. It's important to prioritize and nurture our relationships based on their individual significance and value to us.
In the context of relationships, the term "weight" refers to the importance or influence of a particular relationship. Not all relationships have equal weight because the significance of each relationship varies based on factors such as trust, communication, shared experiences, and emotional connections.
Some relationships are naturally stronger and more influential than others due to these factors, making them more valuable and impactful in a person's life. In contrast, weaker relationships may not have the same level of trust, connection, or influence, making them less important overall. It is essential to recognize and nurture the stronger relationships in one's life to maintain a healthy support system and overall well-being.
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Find the exact value of x
Answer:9
Step-by-step explanation:
NEED HELP FAST PLEASE HURRY INDEED OF HELP
Answer:
Step-by-step explanation:
Hopefully this is right.
Area = (pi)r²
Which is pi times the the radius squared
The radius is 2, so 2² is 4, So we multiply 3.14, which is pi, by 4.
Multiply 3.14 by 4, and the answer is 12.56, the question says round to the nearest tenth, so the final answer will be 12.6
My math teacher back in 7th grade gave us this sentence to help us memorize the equations.
Cherry Pie Delicious (C=(pi)d), Apple Pie Are Too (A=(pi)r²)
Do the same with the other two questions, and the answer for question two will be 3.14, rounded to the nearest tenth will be 3.1
Question three do the same as well, and the answer will be 660.185, rounded will be 660.2
Hope this helps!
A piece of machinery is designed in a shape of a triangular prism. It must be coated in Teflon before it is placed in the machine. How many square inches of Teflon will be needed to completely to cover the machinery
We would need 168 square inches of Teflon to completely cover the triangular prism machinery.
To calculate the surface area of a triangular prism, we need to find the area of each face and then add them up. Let's assume that the triangular bases of the prism have base b and height h, and that the length of the prism is l.
The surface area of the triangular bases is (1/2)bh for each base, so the total area is (1/2)bh + (1/2)bh = bh.
The lateral surface area of the prism is the area of the three rectangular faces. Each rectangular face has length l and height h, so the total lateral surface area is 3lh.
Therefore, the total surface area of the triangular prism is
bh + 3lh
To determine how much Teflon is needed to cover the machinery, we need to know the dimensions of the triangular prism. Once we have those dimensions, we can calculate the surface area using the formula above and then use that value to determine the amount of Teflon required.
Let's say the base of the triangular prism is 4 inches and the height is 6 inches, and the length of the prism is 8 inches. Then the surface area of the triangular prism is
bh + 3lh
= (4 in. x 6 in.) + 3(8 in. x 6 in.)
= 24 in² + 144 in²
= 168 in²
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What is the area of a right triangle with a height of 6-yards and a base of 22 yards?
O 34 yds²
O 68³
yds²
O 132 yds²
O
137/ yds²
Answer:
68 3/4 yds
Step-by-step explanation:
trust me :)
Answer:
see below
Step-by-step explanation:
area of triangle formula = 1/2 base * height
so 1/2*6*22 =66
not sure why there's no choice of 66
Write linear equation in slope intercept form:1/4x+y=-2/7
The given linear equation in slope intercept form is y = -1/4(x) - 2/7.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.By making "y" the subject of formula, we have the following:
1/4x + y = -2/7
y = -1/4(x) - 2/7
By comparison, we have the following:
Slope, m = -1/4.
y-intercept, c = -2/7.
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I need help with this problem I am having trouble understanding
The distance that the fish was able to travel in all was 23. 9 meters .
How to find the distance traveled ?The distance from Harry to the fish' s hole can be found by the Pythagorean theorem:
a ² + b ² = c ²
7 ² + 7 ² = c ²
49 + 49 = c²
98 = c²
c = 9. 9
The total distance that the fish traveled can then be found by summing the distance it already traveled with the distance to Harry's:
= 14 + 9. 9
= 23. 9 meters
The fish traveled approximately 23.9 meters in all, rounded to the nearest tenth.
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HELPPPPPPPPPPPP PLSSSSSSS
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the 1000-pound legal limit, and the standard deviation to be less than 40. A random sample of 31 helmets was tested and the sample mean and variance were found to be 825 pounds and 2350 pounds2, respectively. The manufacturer wants to know if the data provides sufficient evidence to indicate that the standard deviation is significantly less than 40.
Step 1 of 5: Calculate the test statistic for this problem. Round your answer to two decimal places.
Step 2 of 5: Determine the p-value for a lower one-sided alternative hypothesis (left-tail test). The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 3 of 5: What is the rejection region at the 10% level of significance for the test on the variance for a left-tailed alternative hypothesis? The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 4 of 5: State your conclusion using a significance level of 0.05. The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 5 of 5: Calculate a 90% confidence interval for the variance of force on the helmets. Round your answers to four decimal places.
Step 1: The test statistic is 56.56.
Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.
Step 5: The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]
What is Variance?In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.
Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: [tex]σ^{2}[/tex] ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb[tex]s^{2}[/tex]. The test statistic is:
chi-square = (n - 1) *[tex]s^{2}[/tex] / [tex]σ^{2}[/tex]
where n is the sample size, [tex]s^{2}[/tex] is the sample variance, and [tex]σ^{2}[/tex] is the population variance under the null hypothesis.
Substituting the given values, we have:
chi-square = (31 - 1) * 2350 / 1600 = 56.56
Rounding to two decimal places, the test statistic is 56.56.
Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.
Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.
Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.
Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:
[(n - 1) * [tex]s^{2}[/tex]/ chi-square upper, (n - 1) * [tex]s^{2}[/tex] / chi-square lower]
where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:
chi-square upper = 45.722
chi-square lower = 18.307
[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]
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PLEASE HELP AND SHOW WORK! EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!!!
The height of the cylinder, given the volume and the diameter of the base, would be 2, 592.46 feet
How to find the height of the cylinder ?The given diameter of the base is 10 inches, so we need to find the radius first. The radius is half the diameter:
Radius (r) = Diameter / 2 = 10 inches / 2 = 5 inches
We also need to convert the radius from inches to feet since the volume is given in cubic feet:
5 inches = 5/12 feet = 0.4167 feet
Volume of a cylinder:
Volume (V) = πr²h
450π = π x (0.4167)^2 x h
450 = (0.4167)^2 x h
h = 450 / (0.4167)^2 = 2, 592.46 feet
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the manager of a sawmill wants to find out what percentage of the boards that the mill produced are defective.which sampling methods are likely to be biased?select each correct answer.responseson 1 day, an hour after the sawmill begins production, 30 boards in a row are selected and examined.on 1 day, an hour after the sawmill begins production, 30 boards in a row are selected and examined.the manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week were defective. results from the first 5 customers to respond are tallied.the manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week were defective. results from the first 5 customers to respond are tallied.the manager selects 20 boards at random each day for 5 days and examines them.the manager selects 20 boards at random each day for 5 days and examines them.every 40th board produced over the course of 1 week is selected and examined.
Sampling methods that may be biased for finding the percentage of defective boards in a sawmill production are: selecting 30 consecutive boards, emailing customers and relying on their responses, and selecting every 40th board produced. So, the correct answer is A, B and D.
The biased sampling methods are Examining 30 consecutive boards one hour after production begins may be biased because it only captures a snapshot of the production at that specific time, and the boards selected may not be representative of the entire batch produced during the day.
Emailing customers to ask about defective boards may be biased because the response rate may vary among customers, and customers who experienced a higher or lower number of defective boards may be more likely to respond.
Selecting 20 boards at random each day for 5 days and examining them is less likely to be biased, as long as the selection process is truly random and representative of the entire production.
Selecting every 40th board produced over the course of one week is also less likely to be biased if the production process is consistent and there are no patterns or variations in the production that would affect the quality of every 40th board. So, the correct answer for biased is A, B and D.
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How many times can 3.6 go into 80
Answer:
22.2
Step-by-step explanation:
Answer:
3.6 can go into 80 22 times.
Step-by-step explanation:
it is known that roughly 2/3 of all human beings have a dominant right foot or eye. is there also right-sided dominance in kissing behavior? an article reported that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left.
It is possible that there is right-sided dominance in kissing behavior, based on the reported study. The fact that in a random sample of 127 kissing couples, both people in 79 of the couples tended to lean more to the right than to the left suggests a pattern of right-sided dominance.
However, it is important to note that this study alone is not conclusive evidence of right-sided dominance in kissing behavior.
Further research would be needed to confirm whether there is a consistent pattern of right-sided dominance in kissing behavior across different populations and cultures. It is also possible that other factors, such as social or psychological factors, could influence the direction in which people lean during a kiss. Therefore, it is important to approach this topic with caution and not draw any firm conclusions based on a single study.
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The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Can u show me working it how to do this please. Thanks
Answer:
To write a possible quadratic inequality, we first need to determine which quadratic function has roots at x = -0.5 and x = 1.5.
We know that the solution to the quadratic inequality is x < -0.5 or x > 1.5, which means that the parabola associated with our quadratic function should not intersect the x-axis between x = -0.5 and x = 1.5.
One quadratic function with roots at x = -0.5 and x = 1.5 is:
(x + 0.5)(x - 1.5) ≤ 0
To see why this is the case, we can use a graphing calculator to graph the quadratic function y = (x + 0.5)(x - 1.5) and observe that the function is negative (i.e., has a y-value less than zero) when x is less than -0.5 or greater than 1.5.
Alternatively, we can use the fact that the product of two factors is less than or equal to zero if and only if one factor is positive and the other is negative.
Since (x + 0.5) is positive for x > -0.5 and negative for x < -0.5, and (x - 1.5) is positive for x > 1.5 and negative for x < 1.5, the inequality (x + 0.5)(x - 1.5) ≤ 0 is true for x < -0.5 or x > 1.5, but false for -0.5 < x < 1.5.
Therefore, a possible quadratic inequality that satisfies the given set of values for x is:
(x + 0.5)(x - 1.5) ≤ 0
What is the value of x in the equation 2x + 3 = 11?
Answer: x=4
Step-by-step explanation:
Isolate x using opposite operations.
2x + 3 = 11
2x = 8
x = 4
Answer:
4
Step-by-step explanation:
subract 3 from 11
2x=8
divide by 2
x=4