Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis.
What is null hypothesis?In statistical hypothesis testing, the null hypothesis is a statement about a population parameter that is assumed to be true until there is sufficient evidence to suggest otherwise. The null hypothesis is typically denoted by H0 and represents the status quo or default assumption.
The null hypothesis often takes the form of an equality or a statement of "no difference" or "no effect" between two or more groups, variables, or populations. For example, the null hypothesis could be that the mean score of a group of students on a test is equal to a certain value, or that there is no difference in the average height of males and females in a population.
We want to test the hypothesis that the mean amount of time spent in extracurricular activities per week is the same in the suburban and city school districts. Set up the null and alternative hypotheses is as given by:
Null hypothesis: u1 - u2 = 0
Alternative hypothesis: u1 - u2 ≠ 0
To test this hypothesis, we can use a two-sample t-test. We first calculate the test statistic:
t = ((x1 - x2) - (u1 - u2)) / √(s1²/n1 + s2²/n2)
where x1, s1, and n1 are the sample mean, standard deviation, and sample size for the suburban school district, and x2, s2, and n2 are the sample mean, standard deviation, and sample size for the city school district.
Plugging in the values, we get:
t = ((6 - 4) - 0) / √((3²/60) + (2²/40)) ≈ 3.14
This test's degrees of freedom are given by:
df = (s1²/n1 + s2²/n2)² / ( (s1²/n1)² / (n1 - 1) + (s2²/n2)² / (n2 - 1) )
Plugging in the values, we get:
df = ((3²/60) + (2²/40))² / ( (3²/60)² / 59 + (2²/40)² / 39 ) ≈ 93.24
Using a t-distribution table with 93 degrees of freedom and a level of significance of 0.05, we find the critical values to be approximately -1.98 and 1.98.
Since the calculated t-value (3.14) is greater than the critical value (1.98), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean amount of time spent in extracurricular activities per week is different between the suburban and city school districts.
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Can someone please help me on this i’ve been doing this for an hour
Step-by-step explanation:volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length
give the position of C on this number line
The position of C on the number line is 1/8th position.
Define the term number line?A number line is a visual representation of the real numbers as points or marks on a straight line. The number line is usually represented horizontally, with zero in the middle and positive numbers to the right of zero and negative numbers to the left of zero.
From the given number line, there are total 8 points between 0 to 1
That means, it's fractions of 8.
Location of point C is on the 1st point,
So, position of C on this number line = (1/8) ÷ (1-0) = 1/8
Therefore, In the number line, C is located in the 1/8th place.
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The perimeter of a square is 16 cm find length , diagonal and area
Answer:
Step-by-step explanation:
we have perimeter 16
for perimeter 4+4+4+4 we add together it's 16
for area we have 4 times 16
How many sides has a polygon if the sum of its
interior angles is 1440⁰
Answer:
10 sides
Step-by-step explanation:
We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:
S = (n - 2) x 180 degrees
If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:
1440 = (n - 2) x 180
Dividing both sides by 180, we get:
8 = n - 2
Adding 2 to both sides, we get:
n = 10
Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.
Please help me as I’m struggling
Therefore , the solution of the given problem of pie chart comes out to be number of adults who selected math (15) outnumbered the number of minors. (10).
Explain pie charts.
A pie chart, also referred to as a circle diagram, is a graphical representation of each of the values of a particular variable or a method to condense a collection of nominal data. (e.g. percentage distribution). A circle with many parts makes up this kind of chart. Each segment represents a particular group.
Here,
for a two-way table: Party A, Party B, and Party C
Men make up 12 8 % of the population while women make up 16 %.
Total 28 15 19
32 ladies make up the group, to start with.
b) 16 female voters plan to support Party A.
Math, English, and science are studied by adults aged 15 to twenty-one and by children aged ten to ten.
Total 25 24 31
15 people selected math.
b) Reeshma is mistaken. The number of adults who selected math (15) outnumbered the number of minors. (10).
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I need help somebody please
Answer: 54 square in
Step-by-step explanation:
I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation
on her way to visit her parents, jennifer drives 265 miles in 5 hours what is her average rate of speed in miles per hour?
Answer:
53 miles per hour
Step-by-step explanation:
To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:
average speed = total distance / total time
In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:
average speed = 265 miles / 5 hours
Simplifying the expression, we get:
average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.
Answer: 53 miles per hour
Step-by-step explanation:
To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:
Average speed = distance ÷ time
Average speed = 265 miles ÷ 5 hours
Average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed was 53 miles per hour.
13
Select the correct answer.
Solve the following equation for x.-
x²-36=0
Ο Α.
OB.
OC.
O D.
X = 1; x = -36
x= -1; x = 36
x = -6; x = 6
x=-18; x = 18
Answer:
C.
Step-by-step explanation:
x² - 36 = 0
x = 6
6² = 6 x 6 = 36
So..
36 - 36 = 0
As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.
What is the equation used in maths?To solve the equation [tex]x² - 36 = 0[/tex] , we can use the difference of squares formula:
A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.
[tex]a² - b² = (a + b)(a - b)[/tex]
In this case, a² = x² and b² = 36, so we can write:
[tex]x² - 36 = (x + 6)(x - 6)[/tex]
Setting this expression equal to 0 and solving for x, we get:
[tex](x + 6)(x - 6) = 0[/tex]
[tex]x + 6 = 0 or x - 6 = 0[/tex]
[tex]x = -6 or x = 6[/tex]
Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are [tex]x = -6[/tex] and [tex]x = 6.[/tex]
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(x+2)^2=-16 This equation had no solution, why not?
Answer:
It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).
Step-by-step explanation:
The normalized form of the equation
(x+2)^2= - 16
x^2 + 4x + 4 = - 16
x^2 + 4x + 20 = 0
We have in the form ax^2 + abx + c = 0
a = 1
b = 4
c = 20
Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64
Discriminant is negative, therefore, no Real solutions.
A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
What is circle graph?A circle graph, also known as a pie chart, is a type of chart that displays data as a circular diagram, divided into slices to represent proportions of a whole. Each slice of the circle represents a percentage of the total data being represented, and the entire circle represents 100% of the data.
According to question:Based on the circle graph, the percentage of students who prefer documentaries is 16% (as the percentage for documentaries is missing from the given options, we need to calculate it).
To find out the actual number of students who prefer documentaries, we need to multiply this percentage by the total number of students in the sample:
16% of 500 = (16/100) x 500 = 80
Therefore, 80 middle school students prefer the documentaries television genre.
None of the given options match exactly, but the closest one is 76.
Circle graphs are commonly used to show proportions or percentages of different categories within a dataset. They are useful for displaying data in a way that is easy to understand, and they are often used in business and finance, as well as in education and research.
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Jen’s assignment is to read at least 85 pages of a novel. Jen has read 31 pages. How many pages p does Jen have left to read? Write an inequality that represents this situation. Then solve the inequality
Jen has 54 pages left to read to meet her assignment requirement.
The inequality that represents this situation is p ≥ 85 - 31
To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.
The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:
p = 85 - 31
p = 54
Therefore, Jen has 54 pages left to read.
To represent this situation with an inequality, we can use:
p ≥ 85 - 31
This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).
Solving for p:
p ≥ 85 - 31
p ≥ 54
This means that Jen must read at least 54 more pages to meet her assignment requirement.
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PART X: Lost at sea
Suddenly, during your race, a powerful thunderstorm strikes. A wave washes over your boat, shorting out your navigation devices. They wouldn't be much use anyhow, because the lightning is interfering with all communications in the area.
When the storm ends and the sea is calm, you're safe, because you observed all safety precautions, but you have no idea how far off course you are. However, you do know:
* The height of a nearby landmark, which you remember from the tourist center you visited yesterday.
> Mykonos: The light in the Armenistis Lighthouse is 604 feet above sea level.
* The length of your thumb - it's about 2 inches long.
* That you can estimate lengths of less than a foot pretty accurately (to the nearest inch).
1. First, you close one eye and hold your thumb up to block your view of the landmark. You move your thumb nearer and farther from your eye until it just covers the landmark.
Make a sketch showing overlapping triangles ΔEBT and ΔELH to illustrate this situation, where your eye is E, the base of your thumb is B, the tip of your thumb is T, the bottom of the landmark is L, and the top of the landmark is H.
2. Explain why ΔEBT~ΔELH
3. When your thumb covers the landmark, you estimate that it is 10 inches from your eye. Label your drawing with the known measurements.
4. Solve for EL, the distance from your eye to the landmark. Show all work and justify each step.
Answer: 1. Here is a sketch of the overlapping triangles ΔEBT and ΔELH:
H
/|
/ |
/ |
/ |
/ θ |
/____|L
E
|
|
|
|
T
|
|
|
|
B
2. ΔEBT~ΔELH because they have the same shape (both are right triangles with angle θ in common) and their corresponding sides are proportional. Specifically, angle θ is shared by both triangles, angle EBT is a right angle, and angle ELH is a right angle. Therefore, by the Angle-Angle Similarity Theorem, the two triangles are similar. Corresponding sides are proportional because EB/EL = BT/LH (by definition of similar triangles).
3. We are given that BT (the length of the thumb) is about 2 inches. We are also told that the distance from the eye to the landmark (EL) is unknown, but that the distance from the eye to the thumb (EB) is 10 inches (estimated by the person). We are given that LH (the height of the landmark) is 604 feet, or 604*12=7248 inches (since there are 12 inches in a foot). Therefore, we can label the diagram as follows:
7248
/|
/ |
/ | EL
/ |
/ θ |
/____|L
E
|10
|
|
|
T
| 2
|
|
|
|
B
4. To solve for EL, we use the fact that the triangles are similar: EB/EL = BT/LH. Substituting in the known values, we get:
10/EL = 2/7248
5. Multiplying both sides by EL and dividing both sides by 2, we get:
EL = 7248*5 = 36240 inches
Therefore, the distance from the eye to the landmark is 36240/12 = 3020 feet (rounded to the nearest foot).
Step-by-step explanation:
3. Find the distance from A to B. A(-2,2) B (4,-2)
The distance from points A(-2, 2) to B (4, -2) is equal to √52 units.
How to calculate the distance between the two points?Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represents the data points (coordinates) on a cartesian coordinate.
Substituting the given points into the distance formula, we have the following;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance = √[(4 - (-2))² + (-2 - 2)²]
Distance = √[(6)² + (-4)²]
Distance = √(36 + 16)
Distance = √52 units.
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Can someone please help me with these, I wasn’t able to attend school cause I have Covid and I don’t know what’s going on. Please please help me
Answer: The answer for the first question goes as follows: Which one(s) have both pairs of opposite sides that are parallel? Rectangle, Rhombus, and square. Which one(s) have both pairs of opposite sides that are congruent? Rectangle, square, and rhombus. Which one(s) have all four sides congruent? Square and rhombus.
The answers to the second question are:
Circumference = pi * diameter. So, the distance around it is 100pi.Area of a circle = pi * r^2. So the area of the theater is 7854.0 ft^2.Step-by-step explanation:
Essentially, all of these parallelograms have different properties and properties that they share. For example, a property they share by the definition of a parallelogram is that all of them have two pairs of opposing sides that are parallel. Another property they share from the definition of a parallelogram is that opposite sides are congruent.
As such, rectangles, squares, and rhombuses have the properties that all parallelograms have because they are all parallelograms. However, they also have their own properties.
Rectangles: A rectangle has the properties of a parallelogram, as well as the property of having all of its angles be right angles. This also makes all of its angles congruent.Rhombuses: Rhombuses have the properties of a parallelogram, and they also have all four of their sides congruent. Squares: Squares are like rhombuses and rectangles put together. They have all of their angles as right angles and they have all four of their sides congruent.Second Question Explanation:
1. The question is describing a theater that has a circular base. Therefore, you can use the formula for the circumference of a circle, pi * diameter, to find the circumference (or distance around) the theater. The diameter is given to you: 100 ft. So just multiply that by pi.
2. The question is asking for the area of the theater. This means that you can use the formula for the area of a circle, A = pi * r^2. Note that it is asking you for the area, not the volume, so you would find the area of the circle, not the volume of the hemisphere. r represents the radius of the circle/theater. The diameter is given as 100 ft, and the radius is half of the diameter, so it is 50 ft. Now just plug the radius into the equation and you get the answer I showed.
Write this value in order , starting with the smallest 0. 2 1/2 2℅
0, 2%, 2 1/2 The values are ordered from smallest to largest, with 0 being the smallest, followed by 2%, and then 2 1/2.
0 is the smallest value because it represents nothing. It is the absence of a quantity, and therefore, it is always the smallest value.
2% is larger than 0 because it represents a percentage of a whole. Percentages are fractions out of 100, so 2% means 2 out of 100. It is larger than 0, but smaller than 2 1/2.
2 1/2 is the largest value because it represents a whole number and a fraction. It is larger than 2%, because 2 1/2 is equal to 250 out of 10,000 or 25 out of 1,000, which is a larger quantity than 2 out of 100.
Understanding the relative size of different values is an important skill in many areas, including mathematics, science, and finance. Being able to order values from smallest to largest helps us make sense of data and information, and it allows us to make informed decisions based on the relative size of different quantities. It is important to learn how to do this accurately and efficiently in order to be successful in these fields.
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identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. if sample data consist of weights measured in grams, what units are used for these statistics and parameters?
(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.
(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.
The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.
A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.
(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.
(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.
Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.
Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.
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Gerard wrote down the sum of squares of two (23?)2 + (1?2)² = 7133029 numbers, as shown. Unfortunately some of the digits cannot be seen because they are covered in ink. What is the last digit of the first number? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
Answer:
We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.
Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.
So, the last digit of the first number is 3. And the answer is (A) 3
Find the surface area of the rectangular prism.
6 km
4 km
4 km
Answer: 88km is your answer
Step-by-step explanation: We just had this on a test
the weights of bunches of bananas in the grocery store are normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. a random sample of four bunches is taken and the mean weight is recorded. which of the following is the mean of the sampling distribution for the mean of all possible samples of size four? a.0.89 b.1.27 c.3.54 d.5.53
The mean of the sampling distribution will be 3.54. Thus, the correct option is C.
The population means is equal to the mean of the sampling distribution for all feasible samples of size 4. In this instance, 3.54 pounds is shown as the population means.
This suggests that the mean weight of the population of banana bunches will be 3.54 pounds if we pick several random samples of size four, compute the mean weight for each sample, and then average those sample means.
The Central Limit Theorem, which asserts that the sampling distribution of the sample means approaches a normal distribution centered on the population mean as the sample size grows, is a fundamental idea in statistics.
Thus, the correct option is C.
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what is the probability of choosing a red card or a king from a deck of 52 cards? for this event, choosing a red card or choosing a king, where choosing a red card and choosing a king may occur jointly, which rule applies?
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection
How do we calculate the probability?The probability of choosing a red card or a king from a deck of 52 cards is 8/52 or 2/13. To calculate this, we first need to determine the number of cards that are either red or a king. There are 26 red cards in a deck of 52 cards, so the probability of choosing a red card is 26/52 or 1/2. There are four kings in a deck of 52 cards, so the probability of choosing a king is 4/52 or 1/13.
However, we need to be careful to avoid counting the red kings (two of which exist in a deck of 52 cards) twice. To account for this, we subtract the probability of choosing a red king from the sum of the probabilities of choosing a red card and a king. The probability of choosing a red king is 2/52 or 1/26, so the probability of choosing a red card or a king is:
P(red card or king) = P(red card) + P(king) - P(red king)
P(red card or king) = 26/52 + 4/52 - 2/52
P(red card or king) = 28/52
P(red card or king) = 2/13
The rule that applies here is the addition rule of probability, which states that the probability of the union of two events A and B is the sum of their individual probabilities minus the probability of their intersection (i.e., the probability that they occur jointly).
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I need some help with this
the solid is really just a right-cylinder missing a chunk.
so a full circle is 360°, now from the one in the picture above we're missing 90°, that means the cylinder is only using 270°, 360-90=270.
Well, 270° is just 3/4 of a full circle, and since the circle extends all the way down the solid cylinder, we can also say that's 3/4 of the volume of the cylinder, so hmmm let's just get the full volume of the cylinder with a radius of 6 and a height of 12 and then only grab 3/4 of it.
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=6\\ h=12 \end{cases}\implies V=\pi (6)^2(12)\implies V=432\pi \\\\\\ \stackrel{\textit{now let's just grab }\frac{3}{4}}{432\pi \cdot \cfrac{3}{4}}\implies 324\pi ~~ \approx ~~ \text{\LARGE 1017.88}[/tex]
I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes? a. S-(red,red), (red,black), (black,red), (black,black) b. S - fred,black) c. S-(0, 1, 2) d. none of the above
The option a. S-(red,red), (red,black), (black,red), (black,black) is the most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards
The most appropriate sample space S for the possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each (26 cards in the deck are red and 26 are black) is given by option a. S-(red,red), (red,black), (black,red), (black,black).
Sample space S in probability theory denotes the set of all possible outcomes of an experiment.
In other words, the sample space S represents all possible outcomes of an experiment under consideration. For instance, in the current scenario,
These four possible outcomes are independent and equally likely events, and the sample space S for the possible outcomes is given by option a. S-(red,red), (red,black), (black,red), (black,black).
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4.1.60-(15)+(-13 4.2.-2(3)+27 ÷(-3)
Answer:
-15
Step-by-step explanation:
4.1.60 - (15) + (-13) = 32
4.2. -2(3) + 27 ÷ (-3) = -2(3) - 9 = -15
Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns Select all that apply (Note that leading entries marked with an X may have any nonzero value and starred entries (*) may have any value including zero)
a. 0 0
0 0
b. 0 x
0 0
c. x *
0 0
d. x *
0 x
The possible echelon forms of the given matrix are:
A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.
This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.
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Solve for x. using the tangent lines.
50 deg
X
x =[?]^
This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
What is tangent?Tangent is a line or plane that touches a curve or surface at a single point. It is a measure of the steepness of a curve or surface at a particular point. It is equal to the ratio of the change in the y-coordinate to the change in the x-coordinate of a point on the curve. Tangent is used in many areas of mathematics and physics, including calculus, geometry, and mechanics. It is also used to describe the rate of change in a function, as well as to define the angle between two intersecting lines.
The tangent line equation for a line with a slope of 50 degrees is y = tan(50°)x.
To solve for x, you must rearrange the equation to isolate x on one side of the equation.
To do this, divide both sides of the equation by tan(50°), giving the equation x = y/tan(50°). This equation shows that the value of x is equal to the y-value divided by the tangent of 50°.
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Determine whether each of the following conditional statements is true or false. (a) If 10<7,10<7, then 3=43=4. (c) If 10<7,10<7, then 3+5=83+5=8. (b) If 7<10,7<10, then 3=43=4. (d) I…Determine whether each of the following conditional statements is true or false.(a) If 10<7,10<7, then 3=43=4.(c) If 10<7,10<7, then 3+5=83+5=8.(b) If 7<10,7<10, then 3=43=4.(d) If 7<10,7<10, then 3+5=83+5=8.
The given conditional statements are false, true, false, True.
They are determined by following:
(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.
Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.
The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.
If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.
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Edith's van can safely carry a maximum land of 920 kilograms.
She wants to use her van to carry
30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram
and
20 sacks of carots, each of mass 7. 5 kilograms to 1 decimal place
Can she definitely use her van safety in one journey?
You must show your working
(4 marks)
Yes, she can definitely use her van safety in one journey. The total weight is the weight of potatoes plus the weight of carots.
Given,
Number of sacks of potatoes = 30
Mass of each potato = 25
Total weight of Potatoes = 30 * 25
= 750
Number of sacks of carrots = 20
Mass of each Carot = 7.5
Total weight of Carrot = 20 * 7.5
= 150
(The total weight is the weight of potatoes plus the weight of carrots.)
So, total weight = 750 + 150
= 900
The maximum land which Edith can carry safely in the van is 920 kilograms.
∵ 900 < 920
∴ She can use her van safely.
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student completed the homework given that they failed the test?
Completed the homework
Did not complete the homework
Passed the test Failed the test
8
2
3
сл
The probability that a student completed the homework given that they failed the test is 3/8.
Describe Probability?Probability is a branch of mathematics that deals with the study of randomness and uncertainty in events. It involves the measurement and analysis of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
The concept of probability is used in many fields, such as statistics, physics, finance, and engineering, to make predictions and decisions based on incomplete information. It provides a framework for analyzing situations in which multiple outcomes are possible and assigns a quantitative value to the likelihood of each outcome.
To find the probability that a student completed the homework given that they failed the test, we need to use conditional probability.
Let A be the event that a student completed the homework and B be the event that a student failed the test.
We want to find P(A | B), the probability that a student completed the homework given that they failed the test.
Using the data from the table, we can see that the total number of students who failed the test is 8 (3 who completed the homework and 5 who did not).
Therefore, P(B) = 8/18 = 4/9 (the probability that a student failed the test)
Out of the 8 students who passed the test, 3 also completed the homework, so P(A and not B) = 3/18 = 1/6.
So, P(A | B) = P(A and B) / P(B) = (1/6) / (4/9) = 3/8.
Therefore, the probability that a student completed the homework given that they failed the test is 3/8.
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how many 5-letter passords can be made using the letters a thought z if... a) repetition of letters is allowed? b) repetition of letters is not allowed?
Answer:
Order is important: If allowed 11881376
Order is important:If rep. Is not allowed 7893600
Step-by-step explanation:
If the order isnt important and repetition is not allowed 65780
If order isn’t important and repetition is allowed 142506
Which operation is used to convert 245 liters to milliliters?
O Multiply by 1,000
O Multiply by 10,000
O Divide by 1,000
O Divide by 10,000
