If the shaded trapezoid has an area of 9 square inches, what is the area, in square inches of this figure below?
(give a possible answer if you can)
Answers
Total shaded area is the sum of the areas of the two triangles is 64.5 in²
The area of each of the two triangles can be found from the formula ...
A = (1/2)bh
left triangle
A = (1/2)(9.8 in)(8.6 in) = 42.14 in²
right triangle
A = (1/2)(5.2 in)(8.6 in) = 22.36 in²
Total shaded area is the sum of the areas of the two triangles:
(42.14 +22.36) in² = 64.5 in²
Hence, total shaded area is the sum of the areas of the two triangles is 64.5 in²
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Related Questions
according to the national automobile dealers association, the mean price for used cars is $10,192. a manager of a kansas city used car dealer-ship reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. please formulate the hypotheses test to use to determine if the mean price of used cars from this dealer is statistically different than the national average.
Answers
If the p-value is less than α, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the mean price of used cars at this particular dealership is statistically different from the national average. If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.
To test whether the mean price of used cars at this particular dealership differs from the national mean, we can use a hypothesis test.
Let μ be the population mean price for used cars at the dealership, and let μ0 be the national mean price for used cars, which is given as $10,192.
We want to test the null hypothesis H0: μ = μ0 against the alternative hypothesis Ha: μ ≠ μ0, at a significance level of α = 0.05.
We can use a two-tailed t-test for the mean to test this hypothesis, assuming that the population standard deviation is unknown and using the sample standard deviation s as an estimate. The test statistic can be calculated as:
t = (X - μ0) / (s / √(n))
where X is the sample mean, s is the sample standard deviation, and n is the sample size.
Under the null hypothesis, the test statistic follows a t-distribution with n-1 degrees of freedom. We can then calculate the p-value associated with the observed test statistic, and compare it with the significance level α.
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Rework problem 27 in section 6.3 of your textbook (page 277) except use the data below instead of the data in your textbook: Assume that producing 1 unit of calcium requires 0.3 units of calcium, 0.2 units of hydrogen, and 0.5 units of sea salt; that producing 1 unit of hydrogen requires 0.8 units of calcium, 0.2 units of hydrogen, and 0.4 units of sea salt; and that producing 1 unit of sea salt requires 0.3 units of calcium, 0 units of hydrogen, and 0.6 units of sea salt. Find the production schedule that satisfies an external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt.
Answers
To rework problem 27 in section 6.3 with the given data, we need to use the same approach as in the textbook. We will use the matrix method to find the production schedule that satisfies the external demand.
Let x1, x2, and x3 be the number of units of calcium, hydrogen, and sea salt, respectively, that need to be produced to meet the external demand. Then the production constraints can be written as:
0.3x1 + 0.8x2 + 0.3x3 >= 57 (for calcium)
0.2x1 + 0.2x2 + 0x3 >= 32 (for hydrogen)
0.5x1 + 0.4x2 + 0.6x3 >= 13 (for sea salt)
We can write these constraints in matrix form as:
| 0.3 0.8 0.3 | | x1 | | 57 |
| 0.2 0.2 0 | * | x2 | >= | 32 |
| 0.5 0.4 0.6 | | x3 | | 13 |
Solving this system of inequalities, we get:
x1 = 150
x2 = 40
x3 = 25
Therefore, the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt is to produce 150 units of calcium, 40 units of hydrogen, and 25 units of sea salt.
To find the production schedule that satisfies the external demand for 57 units of calcium, 32 units of hydrogen, and 13 units of sea salt, we can set up a system of linear equations.
Let C, H, and S represent the production of calcium, hydrogen, and sea salt, respectively. We have:
1. 0.3C + 0.2H + 0.5S = 57 (calcium requirements)
2. 0.8C + 0.2H + 0.4S = 32 (hydrogen requirements)
3. 0.3C + 0H + 0.6S = 13 (sea salt requirements)
Solving this system of linear equations will give us the production schedule for calcium, hydrogen, and sea salt. Using a matrix solver or similar tool, we find the solutions:
C = 40
H = 20
S = 30
So, to satisfy the external demand, the production schedule should include 40 units of calcium, 20 units of hydrogen, and 30 units of sea salt.
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which is the most accurate way to estimate 33% of 71?
Answers
Answer:
71 is about 72, and 33% is about 1/3, so 33% of 71 is approximately 1/3 × 72 = 24.
.33 × 71 = 23.43, so the approximation is reasonable
Eduardo’s average speed on his commute to work was 55 miles per hour. On the way home, he hit traffic and only averaged 40 miles per hour. If the round trip took him 1.25 hours, which expression represents the distance, in miles, for his trip home that is missing from the table?
Answers
Answer:
40(1.25-t)
Step-by-step explanation:
There are 3 components to consider; time, speed and distance
Time and Speed are given.
The distance has to be calculated.
Speed to work = 55 miles per hour
Time to work = 1.25-T
Speed to home = 40 miles per hour
Time to home = 1.25-t
Total Time = T + t = 1.25
Distance for trip to home
Speed = Distance/Time
40 = Total Distance/1.25-t
Total Distance = 40(1.25-t)
Therefore, 40(1.25-t) is the correct answer.
!!
What’s the probability of a dice that is 6 as a fraction
Answers
Answer:
1/
Step-by-step explanation:
A standard dice has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Each outcome has a probability of 1/6 of occurring on a single roll of the dice, assuming the dice is fair and unbiased.
Since there is only one outcome on a standard dice that is 6, the probability of rolling a 6 is 1/6.
Therefore, the probability of a dice that is 6 as a fraction is 1/6.
The following frequency table shows the number of fish caught by each of Igor's family members. Number of fish Number of family members 0 0 1 3 2 1 3 0 4 4 What was the minimum number of fish that a family member caught?
Answers
The minimum number of fish that a family member caught is 1. Based on the given frequency table, the minimum number of fish that a family member caught can be determined by looking at the lowest "Number of fish" value with a non-zero "Number of family members" value.
Here's a step-by-step explanation:
1. Observe the frequency table:
Number of fish | Number of family members
-----------------------------------------
0 | 0
1 | 3
2 | 1
3 | 0
4 | 4
2. Identify the lowest "Number of fish" value with a non-zero "Number of family members" value. In this case, it's "1 fish" with "3 family members".
Therefore, the minimum number of fish that a family member caught is 1 fish.
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49-2/3*34=32-1/6*34 49 - 2/3 x 34=32 - 1/6 x 34
Answers
Find the z-score such that: (a) The area under the standard normal curve to its left is 0.5 z = (b) The area under the standard normal curve to its left is 0.9826 z = (c) The area under the standard normal curve to its right is 0.1423 z = (d) The area under the standard normal curve to its right is 0.9394 z =
Answers
(a) For an area of 0.5 to the left of the z-score under the standard normal curve, z = 0. This is because the standard normal curve is symmetric, and the area to the left of the mean (which is also the median and mode in this case) is 0.5.
(b) For an area of 0.9826 to the left of the z-score under the standard normal curve, you can look up the corresponding z-score in a standard normal (z) table, or use a calculator or software with an inverse cumulative distribution function. The z-score is approximately z = 2.13.
(c) For an area of 0.1423 to the right of the z-score under the standard normal curve, you first find the area to the left (1 - 0.1423 = 0.8577). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = 1.08.
(d) For an area of 0.9394 to the right of the z-score under the standard normal curve, find the area to the left (1 - 0.9394 = 0.0606). Then, look up the corresponding z-score in a standard normal (z) table or use a calculator. The z-score is approximately z = -1.55.
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the most basic distinction between types of data is that some data are quantitative while other data are qualitative. quantitative data generally consists of:
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The most basic distinction between types of data is that some data are quantitative while other data are qualitative. Quantitative data consists of numerical information that can be measured or counted, allowing for statistical analysis and objective comparisons. This type of data can be further classified into two subcategories: continuous data and discrete data.
Continuous data represent measurements that can take on any value within a specified range, such as height, weight, temperature, or time. These measurements can be represented using fractions or decimals and are typically collected using precise instruments like rulers or thermometers.
Discrete data, on the other hand, consist of distinct, separate values that can be counted or categorized. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, or the number of books sold in a month. Discrete data is often collected through surveys or counting processes.
In contrast, qualitative data are non-numerical and describe attributes, characteristics, or experiences. This type of data is typically obtained through observation, interviews, or open-ended survey questions. Examples of qualitative data include feelings, opinions, beliefs, or descriptions of events.
In summary, the primary distinction between types of data lies in their nature: quantitative data is numerical and allows for objective measurement, while qualitative data is descriptive and explores subjective aspects. Understanding the difference between these two types of data is essential for conducting accurate and meaningful research.
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a state politician is interested in knowing how voters in rural areas and cities differ in their opinions about gun control. for his study, 85 rural voters were surveyed, and 21 were found to support gun control. also included in the study were 85 voters from cities, and 57 of these voters were found to support gun control. let population 1 be the voters in rural areas and population 2 be the voters from cities. step 2 of 2: interpret the confidence interval obtained in step 1.
Answers
Interpret the Confidence Interval. Based on the information provided, we have the following data: Population 1 (Rural Voters): 85 surveyed, 21 support gun control, Population 2 (City Voters): 85 surveyed, 57 support gun control
Let's assume you've already calculated the confidence interval in Step 1. The confidence interval will show a range within which the true difference in support for gun control between rural and city voters is likely to fall.
To interpret the confidence interval, consider the following example:
Confidence Interval: (X1, X2)
If the entire interval is positive (X1 > 0 and X2 > 0), it indicates that city voters are more likely to support gun control than rural voters, with a certain level of confidence (usually 95% or 99%).
If the entire interval is negative (X1 < 0 and X2 < 0), it indicates that rural voters are more likely to support gun control than city voters, with the same level of confidence.
If the interval contains 0 (X1 < 0 and X2 > 0), it means there is not enough evidence to conclude that there is a significant difference in gun control support between rural and city voters at the chosen confidence level.
Remember to always provide the actual confidence interval values and the chosen confidence level in your interpretation.
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lassify the number as natural, whole, integer, rational, and/or irrational.
Select all terms that are correct.
Natural Whole Integer Rational Irrational
7√
Natural – square root of 7
Whole – square root of 7
Integer – square root of 7
Rational – square root of 7
Answers
The square root of 7 is classified as an irrational number.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.Rational numbers can also be classified as follows:
Whole: non-negative integer.Natural: positive integers -> whole except zero.Integers: positive and negative numbers that are not decimal.The square root of 7 is a non-exact square root, hence it is classified as an irrational number.
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In the petting zoo at the State Fair, the probability of randomly selecting a sheep from among all the animals in the zoo is 0.6. If
the rest of the animals are goats, and there are 80 animals in all, how many are goats?
Answers
Step-by-step explanation:
.6 of the animals are sheep .6 * 80 = 48 are sheep
the rest of the 80 are goats = 32 goats
Answer:
32 goats
Step-by-step explanation:
If the probability of selecting a sheep is 0.6, then the probability of selecting a goat is 1 - 0.6 = 0.4.
This means that 40% of the animals are goats.
To find the actual number of goats, we can set up an equation:
0.4 x 80 = number of goats
Simplifying this equation, we get:
32 = number of goats
Therefore, there are 32 goats in the petting zoo, and the remaining animals (48) are sheep.
there is another way to solve this problem.
Since we know that the total number of animals in the petting zoo is 80 and that 60% of them are sheep, we can calculate the number of sheep as follows:
Number of sheep = 0.6 x 80 = 48
We can then calculate the number of goats by subtracting the number of sheep from the total number of animals:
Number of goats = 80 - 48 = 32
So, we get the same answer as before, which is that there are 32 goats in the petting zoo.
Vector v has a magnitude of 30 and a direction θ = 45°. What are the magnitude and direction of 3v?
Answers
The requried magnitude of 3v is 90 and the direction of 3v is 225°.
To find the magnitude and direction of 3v, we can start by calculating the magnitude of 3v:
|3v| = 3|v| = 3(30) = 90
This means that the magnitude of 3v is 90.
To find the direction of 3v, we need to add 180° to the direction of v, since 3v is in the opposite direction to v. The direction of v is given as θ = 45°, so the direction of 3v is:
[tex]\theta_3v = \theta_v + 180^o = 45^o+ 180^o = 225^o[/tex]
Therefore, the magnitude of 3v is 90 and the direction of 3v is 225°.
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would a chi-square test based on a 2 ✕ 2 table using a level of 0.05 be statistically significant?p-value = 0.01a)Yes, because 0.01 < 0.05.b) Yes, because 0.01 < 3.84. c) No, because 0.01 < 3.84.d) No, because 0.01 < 0.05.
Answers
there is a statistically significant association between the two variables
a) Yes, because 0.01 < 0.05.
In a chi-square test for a 2x2 table, the degrees of freedom is 1. A p-value of 0.01 indicates that the probability of observing a chi-square statistic as extreme or more extreme than the one calculated under the null hypothesis (i.e., assuming no association between the two variables) is very low. Since 0.01 is less than the chosen level of significance of 0.05, we can reject the null hypothesis and conclude that there is a statistically significant association between the two variables
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Suppose you want to test the claim that a population mean equals 40. Please explain your answer.
(a) State the null hypothesis
(b) State the alternate hypothesis if you have no information regarding how the population means might differ from 40.
(c) Sate the alternate hypothesis if you believe (based on experience or past studies) that population mean may exceed 40.
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be less than 40.
Answers
In all cases, we use hypothesis testing to determine if the sample mean is significantly different from the hypothesized population mean of 40. The results of the test will help us make conclusions about the population mean based on the information gathered from the sample.
(a) State the null hypothesis:
The null hypothesis (H0) is the claim that there is no significant difference between the population mean and the value specified. In this case:
H0: µ = 40
(b) State the alternate hypothesis if you have no information regarding how the population means might differ from 40:
The alternate hypothesis (H1) is the claim that the population mean is different from the value specified. In this case:
H1: µ ≠ 40
(c) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may exceed 40:
If you believe that the population mean may be greater than 40, the alternate hypothesis would be:
H1: µ > 40
(d) State the alternate hypothesis if you believe (based on experience or past studies) that the population mean may be less than 40:
If you believe that the population mean may be less than 40, the alternate hypothesis would be:
H1: µ < 40
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true or false? the P(b | a) = P(a and b) / P(b)
Answers
True. This is known as Bayes' theorem, which states that the probability of an event A given the occurrence of another event B can be calculated as the probability of both events A and B occurring divided by the probability of event B occurring. It can be written as: P(A | B) = P(B | A) * P(A) / P(B).
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Calculate the area and circumference of a circle with diameter 8cm explain by step by step
Answers
Answer:
Area: 201.06 cm^2
Circumference: 50.265 cm
Step-by-step explanation:
Area of a circle: A=πr²
π≅3.1415
A=π(8)²
Area≅201.06 cm²
Circumference of a circle: C=2π²
C=2π(8)
C=50.265 cm
Answer:
Area = 50.27cm² , Circumference = 25.13cm
Step-by-step explanation:
First off, to find the area of a circle the formula is [tex]\pi[/tex]r², and in the equation you gave a diameter, so to get a radius divide the diameter by 2.
So therefore [tex]\pi[/tex]4² is your equation and the answer is 50.27cm²
Now to find the circumference. The formula to find circumference is 2[tex]\pi[/tex]r.
Again if you're given a diameter divide it by 2 to get the radius.
So 2[tex]\pi[/tex]4 is the equation, and the answer is 25.13 cm.
Please let me know if you have any more questions, or need any extra assistance!
Find the sin and cosin of a traingle with the opposite side=B, the adjacent side=A and the hyp=10
Answers
If triangle has opposite side as "B", adjacent side as "A" and hypotnuse as 10 units, then Sine is B/10 and Cosine is A/10.
The Sine is defined as the ratio of the opposite side to the hypotenuse:
So, sin(θ) = opposite/hypotenuse
In this case, the opposite-side is = B and the hypotenuse is = 10 units,
So we can write : sin(θ) = B/10,
Similarly, cosine is defined as the ratio of the adjacent-side to the hypotenuse : cos(θ) = adjacent/hypotenuse
In this case, the adjacent side is = A and the hypotenuse is = 10 units,
So, we can write : cos(θ) = A/10,
Therefore, the sine of the triangle is B/10 and the cosine of the triangle is A/10.
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The given question is incomplete, the complete question is
Find the Sine and Cosine of a triangle with the opposite side=B, the adjacent side=A and the hypotnuse=10 units.
as a teacher assistant you are calculating student greades. one student had the following test scores 85,93.91,81, what is the student's average score?
Answers
Answer: 87.5
Step-by-step explanation:
sum of values/number of values
85+93+91+81/4
350/4
87.5
find the inverse of the following matrices by writing them in the form i - d and using the sum-of-powers method on d. check the accuracy of your answer by using the determinant-based formula for the inverse of ~ 2-b)1-2 matrix (see section 3 .3) . (a) .7 - .2 - .4 .8 (b) . 6 .3 .2 .5 (c) .6 0 0 .5
Answers
A matrix is a rectangular array of numbers or other mathematical objects arranged in rows and columns.
(a) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.
A =
[0.7 -0.2 -0.4]
[0.8 0.0 0.0]
[0.0 0.0 1.0]
Let D = 0.3A, then we have:
I - D =
[0.7 - 0.3(0.7) - 0.3(-0.2) - 0.3(-0.4)]
[0.8 - 0.3(0.8) - 0.3(0.0) - 0.3(0.0)]
[0.0 - 0.3(0.0) - 0.3(0.0) - 0.3(1.0)]
=
[0.46 0.06 0.12]
[0.56 0.80 0.00]
[0.00 0.00 0.70]
Using the sum-of-powers method, we have:
(I - D)^(-1) =
[1.131 -0.509 -0.343]
[-0.951 1.509 0.000]
[0.000 0.000 1.429]
To check the accuracy of our answer, we can use the determinant-based formula for the inverse:
A^(-1) = (1/det(A)) * adj(A)
where det(A) is the determinant of A, and adj(A) is the adjugate of A. We have:
det(A) = (0.70.01.0) + (-0.20.00.0) + (-0.40.80.0) - (-0.40.0-0.2) - (0.70.80.0) - (-0.20.01.0) = 0.56
adj(A) =
[0.0 0.8 0.0]
[-0.4 0.0 0.28]
[0.28 -0.2 0.0]
So, we have:
A^(-1) = (1/0.56) *
[0.0 0.8 0.0]
[-0.4 0.0 0.28]
[0.28 -0.2 0.0]
=
[1.131 -0.509 -0.343]
[-0.951 1.509 0.000]
[0.000 0.000 1.429]
which is the same as the answer we obtained using the sum-of-powers method.
(b) To find the inverse of the matrix, we write it in the form I - D. Let A be the given matrix.
A =
[0.6 0.3]
[0.2 0.5]
Let D = 0.2A, then we have:
I - D =
[0.52 -0.12]
[-0.08 0.48]
Using the sum-of-powers method, we have:
(I - D)^(-1) =
[2.058 0.514]
[0.343 2.171]
To check the accuracy of our answer, we can use the determinant-based formula for the inverse:
A^(-1) = (1/det(A)) *
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3. Solve the equation (x + 3)² = 49
Answers
Answer:
x = 4, -10
Step-by-step explanation:
(x + 3)² = 49
[tex]\sqrt{(x + 3){2} }[/tex] = [tex]\sqrt{49}[/tex]
x + 3 = ± 7
x + 3 = 7
x = 4
x + 3 = -7
x = -10
So, the answer is x = 4, -10
need to solve by hand1.The yield of a manufacturing process was measured for ten consecutive production lots. The results (in fractional form) are summarized in the table at right. Compute the following sampl
Answers
The difference between the highest and lowest yield values.
Range = highest_ yield - lowest_ yield
Based on the information provided, I understand that you have a table with yield data for ten consecutive production lots. To compute the sample statistics, follow these steps:
1. Calculate the sample mean:
Add the yield values from the table and divide by the total number of production lots (10).
Mean = (yield_ 1 + yield_ 2 + ... + yield_ 10) / 10
2. Calculate the sample variance:
Subtract the mean from each yield value, square the result, and sum them. Divide the sum by the number of production lots minus 1 (9).
Variance = [(yield_1 - mean)^2 + (yield_2 - mean)^2 + ... + (yield_10 - mean)^2] / 9
3. Calculate the sample standard deviation:
Take the square root of the variance.
Standard deviation = √(variance)
4. Calculate the range:
Find the difference between the highest and lowest yield values.
Range = highest_yield - lowest_yield
Once you have calculated these sample statistics, you can better understand the yield performance of the manufacturing process and analyze the production data. Remember to use the actual yield values from your table when doing these calculations.
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4. There are ¾ as many boys as girls in a class of fifth-graders. If there are 132 students in the class, how many are girls?
Answers
Answer:
There should be 33 girls in the class.
Step-by-step explanation:
Take the total amount of students, 132, and multiply it by one-fourth, since three-fourths of the students are boys.
express x and y in terms of trigonometric ratios of θ. (express your answer in terms of θ only.)
Answers
To express x and y in terms of trigonometric ratios of θ, we need to use the definitions of sine, cosine, and tangent ratios.
Let's assume that θ is an acute angle in a right triangle with hypotenuse of length 1. Then, we have:
sin θ = opposite/hypotenuse = y/1 = y
cos θ = adjacent/hypotenuse = x/1 = x
tan θ = opposite/adjacent = y/x
Therefore, we can express x and y in terms of trigonometric ratios of θ as follows:
x = cos θ
y = sin θ
Alternatively, if we are given the value of one trigonometric ratio and we need to find the others, we can use the Pythagorean identity:
sin^2 θ + cos^2 θ = 1
From this, we can derive:
cos^2 θ = 1 - sin^2 θ
sin^2 θ = 1 - cos^2 θ
And then use the definitions of tangent and cotangent ratios:
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ = 1/tan θ
Hope this helps!
To express x and y in terms of trigonometric ratios of θ, we will use the basic trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). In a right-angled triangle, we have:
1. sin(θ) = opposite side / hypotenuse
2. cos(θ) = adjacent side / hypotenuse
3. tan(θ) = opposite side / adjacent side
Assuming x is the adjacent side and y is the opposite side in relation to angle θ, and the hypotenuse is denoted by r, we can express x and y in terms of trigonometric ratios of θ as follows:
Step 1: Solve for x using the cosine ratio:
x = r * cos(θ)
Step 2: Solve for y using the sine ratio:
y = r * sin(θ)
So, x and y are expressed in terms of trigonometric ratios of θ as x = r*cos(θ) and y = r*sin(θ).
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Drag each label to the correct location on the chart. Given: Prove: A coordinate system labeled 2, 1, 4, and 3, anticlockwise. Complete the flow chart to prove .
Answers
∠1 ≅ ∠2 ⇒ given
∠1 ≅ ∠3 ⇒ Vertical angles theorem.
∠2 ≅ ∠4 ⇒ Vertical angles theorem.
∠3 ≅ ∠4 ⇒ Transitive property of congruence
How to explain the angleGiven, ∠1 ≅ ∠2
∠2 ≅ ∠3 ⇒ Transitive property of congruence
We have to prove that ∠3 ≅ ∠4.
For that, here given the flow chart.
We have to complete the flow chart by using the given statements.
That is,
∠1 ≅ ∠2 ⇒ given
∠1 ≅ ∠3 ⇒ Vertical angles theorem.
∠2 ≅ ∠4 ⇒ Vertical angles theorem.
∠3 ≅ ∠4 ⇒ Transitive property of congruence
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k^4/(16k^6 5) use the comparison test or limit comparison test to determine whether the following series converges.
Answers
To use the comparison test or limit comparison test, we need to find a known series that either diverges or converges and is similar to the given series.
Using the comparison test, we can compare the given series to the series 1/n^2, which is a p-series with p=2 and converges.
To see if our series is smaller or larger than 1/n^2, we can simplify the given series by canceling out k^4 from the numerator and denominator:
k^4 / (16k^6 5) = 1 / (16k^2 5)
Now, we can compare 1 / (16k^2 5) to 1/n^2:
1 / (16k^2 5) < 1/n^2 for all k > 1
Therefore, since our series is smaller than a convergent series, it must also converge.
Alternatively, we can use the limit comparison test by finding the limit of the ratio of the given series to 1/n^2 as n approaches infinity:
lim (n→∞) [k^4/(16k^6 5) / (1/n^2)] = lim (n→∞) (n^2 / (16k^6 5))
This limit is zero for all k > 1, which means the given series and the series 1/n^2 have the same behavior and both converge.
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What is the distance between the points located at (15, −10) and (15, 22)?
12 units
-12 units
32 units
-32 units ??????
Answers
Answer:
C
Step-by-step explanation:
The distance between the two points can be found using the distance formula, which is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the two points are located at (15, -10) and (15, 22), so:
x1 = 15
y1 = -10
x2 = 15
y2 = 22
Substituting these values into the formula, we get:
d = √((15 - 15)^2 + (22 - (-10))^2)
= √(0 + 32^2)
= √1024
= 32
Therefore, the distance between the two points is 32 units.
You can also just do this by calculation how far the y points are from each other since the x axis are the same. I’m my head I just counted from -10 to 22, and new you could just add 10 to 22 to find the distance they are apart, so it’s 32.
unit 7 homework 13 polynomials and factoring
Answers
The answers to all parts are shown below.
1. 5a + 3 -4a² + 2a³
writing into standard form of polynomial
2a³- 4a² + 5a +3.
2. 7xy + x³ - y³ -5x²y²
writing into standard form of polynomial
= x³ - y³ - 5x²y² + 7xy
3. The degree of the polynomials are
3x+1 = 1 degree
5x² - 2 degree
10- 0 degree
3x³ -2x² + 10= 3 degree
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two sides of a triangle are equal in length and double the length of the shortest side. the perimeter of the triangle is 36 inches. x 2x 2
Answers
Answer:
Let's use "a" to represent the length of the shortest side. The remaining two sides are equal in length and double the length of the shortest side, thus we may represent them as "2a" according to the issue.
Because the perimeter of a triangle is equal to the sum of its sides' lengths, we may solve the following equation:
a + 2a + 2a = 36
We may simplify the left side of the equation as follows:
5a = 36
When we divide both sides by 5, we get:
a = 7.2
Now that we know the length of the shortest side, we can calculate the lengths of the other two sides:
2a = 14.4
As a result, the triangle's sides are 7.2 inches, 14.4 inches, and 14.4 inches.
To ensure that these lengths match the problem's requirements, we may check that the two larger sides are equal in length and twice the length of the shortest side:
14.4 = 2(7.2)
14.4 = 14.4
As a result, x = 7.2 inches and 2x = 14.4 inches is our solution.
The length of the shortest side is 7.2 inches, and the equal sides are each 14.4 inches (2x).The three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
Let's use x to represent the length of the shortest side. According to the problem, the other two sides are equal in length and double the shortest side, so they must be 2x each.
To find the perimeter of the triangle, we add up the lengths of all three sides:
x + 2x + 2x = 5x
We know that the perimeter is 36 inches, so we can set up an equation:
5x = 36
To solve for x, we divide both sides by 5:
x = 7.2
Now that we know the length of the shortest side, we can find the lengths of the other two sides:
2x = 2(7.2) = 14.4
So the three sides of the triangle are 7.2 inches, 14.4 inches, and 14.4 inches.
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We want to buld a box whose base is a square, has no top and will enclose 100m3. determine the dimensions of the box so that it will sue the minimum amount of material.
Answers
To build a box with a square base, no top, and a volume of 100 m³ that uses the minimum amount of material, we need to minimize the surface area while maintaining the volume.
Let x represent the side length of the square base, and h represent the height of the box.
Volume (V) = x²h = 100 m³
Surface Area (SA) = x² + 4xh
First, solve the volume equation for h:
h = 100/x²
Now, substitute this expression for h into the surface area equation:
SA = x² + 4x(100/x²) = x² + 400/x
To minimize the surface area, we'll find the derivative of the surface area equation with respect to x and set it equal to zero:
d(SA)/dx = 2x - 400/x²
Setting the derivative equal to zero and solving for x:
2x - 400/x² = 0
2x³ - 400 = 0
x³ = 200
x = (200)^(1/3) ≈ 5.85 m
Now, plug the value of x back into the equation for h:
h = 100/(5.85²) ≈ 2.93 m
So, the dimensions of the box that minimize the amount of material used are approximately 5.85 m × 5.85 m × 2.93 m.
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