Answers
The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).
a = 10 feet
b = 20 feet
Using the Pythagorean theorem, we can calculate c as follows:
c^2 = a^2 + b^2
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
To find c, we take the square root of both sides:
c = √500
c ≈ 22.36
Rounding the answer to the nearest whole number, we get c ≈ 22.
Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
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Related Questions
if a=7 and b =2 what is 2ab
Answers
Answer: 28
Step-by-step explanation:
If [tex]a = 7[/tex] and [tex]b = 2[/tex], then [tex]2ab[/tex] can be worked out as follows:
[tex]\Large 2ab = 2 \times a \times b[/tex]
Substituting the values of [tex]a[/tex] and [tex]b[/tex], we get:
[tex]2 \times 7 \times 2 = 28[/tex]
Therefore, [tex]2ab[/tex] is equal to 28 when [tex]a = 7[/tex] and [tex]b = 2[/tex].
________________________________________________________
The answer is:
28Work/explanation:
To evaluate the expression [tex]\sf{2ab}[/tex], I begin by plugging in 7 for a and 2 for b:
[tex]\large\pmb{2(7)(2)}[/tex]
Simplify by multiplying.
[tex]\large\pmb{2*14}[/tex]
[tex]\large\pmb{28}[/tex]
Therefore, the answer is 28.What is the sum of the series?
Answers
Determine the surface area and volume Note: The base is a square.
Answers
The volume of the can is approximately 304 cubic centimeters.
To determine the surface area and volume of the can, we need to consider the properties of a cylinder with a square base.
Surface Area:
The surface area of the can consists of three parts: the square base and the two circular faces.
a) Square Base:
The base of the can is a square, so its area is given by the formula:
Area = side^2.
Since the diameter of the can is 8 centimeters, the side of the square base is also 8 centimeters.
Therefore, the area of the square base is 8 cm [tex]\times[/tex] 8 cm = 64 square centimeters.
b) Circular Faces:
The can has two circular faces, one at the top and one at the bottom.
The formula for the area of a circle is[tex]A = \pi \times r^2,[/tex] where r is the radius. The radius of the can is half the diameter, which is 8 cm / 2 = 4 cm.
Thus, the area of each circular face is [tex]\pi \times (4 cm)^2 = 16\pi[/tex] square centimeters.
To find the total surface area, we sum the areas of the square base and the two circular faces:
Total Surface Area = Square Base Area + 2 [tex]\times[/tex] Circular Face Area
[tex]= 64 cm^2 + 2 \times 16\pi cm^2[/tex]
≈ [tex]64 cm^2 + 100.48 cm^2[/tex]
≈[tex]164.48 cm^2[/tex]
Therefore, the surface area of the can is approximately 164.48 square centimeters.
Volume:
The volume of the can is given by the formula:
Volume = base area [tex]\times[/tex] height.
Since the base is a square, the base area is equal to the side^2, which is 8 cm [tex]\times[/tex] 8 cm = 64 square centimeters.
The height of the can is the height we calculated earlier, which is approximately 4.75 centimeters.
Volume = Base Area [tex]\times[/tex] Height
[tex]= 64 cm^2 \times4.75[/tex] cm
≈ 304 [tex]cm^3[/tex]
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Which function is graphed ?
Answers
An arithmetic sequence has the first term Ina and a common difference In 3. The 13th term in the sequence is 8 ln9. Find the value of a.
Answers
The value of a is 8 ln 9 - 36. Given an arithmetic sequence that has the first term Ina and a common difference In 3. The 13th term in the sequence is 8 ln 9.
We need to find the value of a.
Step 1: Finding the 13th term. Using the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Substituting the given values, we get:an = a1 + (n - 1)d 13th term, a 13 = a1 + (13 - 1)3a13 = a1 + 36 a1 = a13 - 36 ...(1)Given that a13 = 8 ln 9.
Substituting in equation (1), we get: a1 = 8 ln 9 - 36.
Step 2: Finding the value of a. Using the formula for the nth term again, we can write the 13th term in terms of a as: a13 = a + (13 - 1)3a13 = a + 36a = a13 - 36.
Substituting the value of a13 from above, we get:a = 8 ln 9 - 36. Therefore, the value of a is 8 ln 9 - 36.
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Let X_1,…,X_n be a random sample. For S(X_1,…,X_n )=1/(1/n ∑_(i=1)^n▒〖(x_i-c)〗^2 ) , find its asymptotic distribution where EX^k=α_k.
Answers
The asymptotic distribution of the estimator S(X₁, ..., Xₙ) is a standard normal distribution, denoted as N(0, 1).
To find the asymptotic distribution of the estimator S(X₁, ..., Xₙ), we can use the Central Limit Theorem (CLT). However, we need some additional assumptions to apply the CLT, such as the finite variance of the random variables.
Given that E(Xᵢ^k) = αₖ for all k, we can assume that the random variables Xᵢ have a finite variance. Let's denote the variance of Xᵢ as Var(Xᵢ) = σ².
First, let's simplify the estimator S(X₁, ..., Xₙ):
S(X₁, ..., Xₙ) = 1 / (1/n ∑ᵢ (Xᵢ - c)²)
Notice that the numerator is a constant and doesn't affect the asymptotic distribution. So, we can focus on analyzing the denominator.
Let's calculate the expected value and variance of the denominator:
E[1/n ∑ᵢ (Xᵢ - c)²] = 1/n ∑ᵢ E[(Xᵢ - c)²] = 1/n ∑ᵢ (Var(Xᵢ) + E[Xᵢ]² - 2cE[Xᵢ] + c²)
= 1/n (nσ² + α₁ - 2cα₁ + c²) (using the fact that E[Xᵢ] = α₁ for all i)
Var[1/n ∑ᵢ (Xᵢ - c)²] = 1/n² ∑ᵢ Var[(Xᵢ - c)²] = 1/n² ∑ᵢ (Var(Xᵢ - c)²) = 1/n² ∑ᵢ (Var(Xᵢ))
= 1/n² (nσ²) = σ²/n
Now, let's apply the CLT. According to the CLT, if we have a sequence of independent and identically distributed random variables with a finite mean (μ) and a finite variance (σ²), the sample mean (in this case, our denominator) converges in distribution to a standard normal distribution as the sample size approaches infinity.
Therefore, as n approaches infinity, the asymptotic distribution of S(X₁, ..., Xₙ) will follow a standard normal distribution.
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PLS HELPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
The correct option is the 3rd one
angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,
angle 2 = angle 3 = angle 6 = angle 7 = 120 degrees
Step-by-step explanation:
To solve this, we only need to look at the top two angles, 1 and 2
Since line l is a line, angle 1 and 2 must sum to 180,
Since angle 1 = 60 degrees, then,
angle 1 + angle 2 = 180
60 + angle 2 = 180
angle 2 = 120 degrees
the only option that corresponds to this is the third option,
angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,
angle 2 = angle 3 =
You're a marketing analyst for Wal-
Mart. Wal-Mart had teddy bears on
sale last week. The weekly sales
($ 00) of bears sold in 10 stores
was:
8 11 0 4 7 8 10 583
At the .05 level of significance, is
there evidence that the average
bear sales per store is more than 5
($ 00)?
Answers
Based on the data and the one-sample t-test, at the 0.05 level of significance, there is sufficient evidence to conclude that the average bear sales per store at Wal-Mart is significantly higher than $500
.
To determine if there is evidence that the average bear sales per store at Wal-Mart is more than $500 at the 0.05 level of significance, we can conduct a one-sample t-test. Let's go through the steps:
State the null and alternative hypotheses:
Null hypothesis (H₀): The average bear sales per store is equal to or less than $500.
Alternative hypothesis (H₁): The average bear sales per store is greater than $500.
Set the significance level (α):
In this case, the significance level is given as 0.05 or 5%.
Collect and analyze the data:
The weekly sales of bears in 10 stores are as follows:
8, 11, 0, 4, 7, 8, 10, 583
Calculate the test statistic:
To calculate the test statistic, we need to compute the sample mean, sample standard deviation, and the standard error of the mean.
Sample mean ([tex]\bar X[/tex]):
[tex]\bar X[/tex] = (8 + 11 + 0 + 4 + 7 + 8 + 10 + 583) / 8
[tex]\bar X[/tex] ≈ 76.375
Sample standard deviation (s):
s = √[Σ(x - [tex]\bar X[/tex])² / (n - 1)]
s ≈ 190.687
Standard error of the mean (SE):
SE = s / √n
SE ≈ 60.174
Now, we can calculate the t-value:
t = ([tex]\bar X[/tex] - μ₀) / SE
Where μ₀ is the hypothesized population mean ($500).
t = (76.375 - 500) / 60.174
t ≈ -7.758
Determine the critical value:
Since we are conducting a one-tailed test and the alternative hypothesis is that the average bear sales per store is greater than $500, we need to find the critical value for a one-tailed t-test with 8 degrees of freedom at a 0.05 level of significance. Looking up the critical value in the t-distribution table, we find it to be approximately 1.860.
Compare the test statistic with the critical value:
Since -7.758 is less than -1.860, we have enough evidence to reject the null hypothesis.
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Which of the following numbers is closest to 7? √51 50 46 st
Answers
Answer:
Step-by-step explanation:To determine which of the given numbers is closest to 7, we can calculate the absolute difference between each number and 7 and choose the number with the smallest absolute difference.
Let's calculate the absolute differences:
Absolute difference between √51 and 7:
|√51 - 7| ≈ 7.13 - 7 ≈ 0.13
Absolute difference between 50 and 7:
|50 - 7| = 43
Absolute difference between 46 and 7:
|46 - 7| = 39
Comparing the absolute differences, we can see that the number closest to 7 is √51. The absolute difference between √51 and 7 is the smallest among the given options.
Therefore, √51 is the number closest to 7.
Which table of values represents a function? Step by step.
Answers
Answer:
A
Step-by-step explanation:
For a table of values to be a function, all inputs must have one unique output. The only table that doesn't violate this is table A.
Notice that while two different inputs (-4 and 1) have the same output of 7, it is still a function because both outputs of 7 are associated with two different inputs.
A camera sensor with a fixed size of 720 × 680 is used in the system described in the article. For a sensor of these dimensions, calculate
i.the resolution in pixels in scientific notation to 4 significant figures
ii.the resolution in megapixels, rounded to the nearest thousandth of a megapixel
iii.the aspect ratio of the sensor, cancelled down to its lowest terms
Answers
Resolution = 720 × 680 = 489,600 pixels.
In scientific notation to 4 significant figures, the resolution would be approximately 4.896 × 10^5 pixels.
ii. To find the resolution in megapixels, we divide the total number of pixels by 1 million:
Resolution in megapixels = 489,600 pixels / 1,000,000 = 0.4896 megapixels.
Rounded to the nearest thousandth of a megapixel, the resolution would be approximately 0.490 megapixels.
iii. The aspect ratio of the sensor can be found by dividing the width by the height and canceling down to its lowest terms:
Aspect ratio = 720 / 680 = 36 / 34.
Therefore, the aspect ratio of the sensor in its lowest terms is 18:17.
The pixel resolution is 4.896 x 10^5 pixels; in megapixels, it's approximately 0.490; and the aspect ratio is 18:17.
Explanation:First, let's calculate the resolution in pixels: Resolution is simply the width times the height of the sensor. Specifically for this question, multiply 720 by 680. This gives us 489600 pixels for the resolution - in scientific notation to 4 significant figures we have 4.896 x 10^5.
Next, to calculate the resolution in megapixels, we need to divide the resolution by 1 million (since one megapixel is equal to 1 million pixels). So, 489600/1,000,000 is approximately 0.490 megapixels when rounded to the nearest thousandth of a megapixel.
Finally, the aspect ratio is the relationship of the width to the height of an image or screen. For a 720 x 680 sensor, if we divide 720 by 680, the result would be approximately 1.0588. However, we want this ratio in its simplest form, so we should use the greatest common divisor (GCD). In this case, the GCD of 720 and 680 is 40, so by dividing both dimensions by 40, we get an aspect ratio of 18:17.
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Help please
The box plot represents the scores on quizzes in a science class. A box plot uses a number line from 70 to 86 with tick marks every one-half unit. The box extends from 76 to 80.5 on the number line. A line in the box is at 79. The lines outside the box end at 72 and 84. The graph is titled Science Quizzes, and the line is labeled Scores On Quizzes. Determine which of the following is the five-number summary of the data. Min: 72, Q1: 79, Median: 80, Q3: 82, Max: 84 Min: 75, Q1: 77.5, Median: 80, Q3: 81.5, Max: 85 Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84 Min: 73, Q1: 77, Median: 78, Q3: 80.5, Max: 85
Answers
Answer:
The five-number summary of the data represented by the given box plot is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84. Therefore, the correct option is: Min: 72, Q1: 76, Median: 79, Q3: 80.5, Max: 84.
Step-by-step explanation:
Find the measure of the indicated arc.
90°
80°
100
70°
H
40°
F
Answers
The measure of an arc in a circle is determined by the central angle that subtends it. Let's analyze each given measure of the indicated arcs:
90°: A 90° arc spans one-fourth of the entire circle since a full circle has 360°.
80°: An 80° arc is smaller than a quarter of the circle but larger than a sixth since 360° divided by 4 is 90°, and by 6 is 60°. Therefore, it lies between these two values.
100°: A 100° arc is slightly larger than a quarter of the circle but smaller than a third, as 360° divided by 4 is 90°, and by 3 is 120°.
70°: A 70° arc is smaller than both a quarter and a sixth of the circle, falling between 60° and 90°.
H: The measure of an arc denoted by "H" is not provided, so it cannot be determined without further information.
40°: A 40° arc is smaller than a sixth of the circle but larger than a twelfth, as 360° divided by 6 is 60°, and by 12 is 30°.
F: Similarly, the measure of the arc denoted by "F" is not provided, so it remains unknown without additional data.
Thus, the measures of the indicated arcs are as follows: 90°, between 60° and 90°, between 90° and 120°, between 60° and 90°, unknown (H), between 30° and 60°, and unknown (F).
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with #38 & 39
Answers
The chords arc theorem and the angles of intersecting chords theorem indicates that we get;
a. CD = 32
b. [tex]m\widehat{BD}[/tex] = 55°
c. [tex]m\widehat{CD}[/tex] = 110°
d. [tex]m\widehat{AB}[/tex] = 125°
What is the angle of intersecting chords theorem?The angle of intersecting chords theorem states that the angle formed by the intersection of two chords in a circle is half the sum of the measure of the intercepted arcs.
The diameter of the circle AB indicates that we get;
PB is the perpendicular of the chord CD
CE = DE = 16
CD = CE + DE = 16 + 16 = 32
The chords CB and BD are congruent, therefore, according to the chords arc theorem, the arcs the chords intercepts are congruent.
Therefore; (4·x + 7)° = (5·x - 5)°
4·x + 7 = 5·x - 5
5·x - 4·x = 7 + 5 = 12
x = 12
[tex]m\widehat{BD}[/tex] = (5·x - 5)° = (5 × 12 - 5)° = 55°
[tex]m\widehat{BC}[/tex] = [tex]m\widehat{BD}[/tex] = 55°
[tex]m\widehat{CD}[/tex] = [tex]m\widehat{BC}[/tex] + [tex]m\widehat{BD}[/tex] = 55° + 55° = 110°
The angle of intersecting chords theorem indicates that we get;
90° = (1/2) × ((5·x - 5)° + m[tex]\widehat{AC}[/tex])
90° = (1/2) × ((4·x + 7)° + m[tex]\widehat{AD}[/tex])
Therefore; 2 × 90° = (4·x + 7)° + m[tex]\widehat{AD}[/tex]
(4·x + 7)° = 55°
Therefore; 2 × 90° = (4·x + 7)° + m[tex]\widehat{AD}[/tex] = 55° + m[tex]\widehat{AD}[/tex]
180° = 55° + m[tex]\widehat{AD}[/tex]
m[tex]\widehat{AD}[/tex] = 180° - 55° = 125°
m[tex]\widehat{AD}[/tex] = 125°
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Anna volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday, 382 people went to The Youth Wing, 461 people went to Social Issues, and 355 went to Fiction and Literature. On Sunday, the library had 800 total visitors. Based on what Anna had recorded on Saturday, about how many people should be expected to go to The Youth Wing? Round your answer to the nearest whole number.
Answers
Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.
Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:
[tex]\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}[/tex]
Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}[/tex]
Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}[/tex]
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800[/tex]
Calculating the proportion:
[tex]\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}[/tex]
Calculating the estimated number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800[/tex]
Simplifying the equation:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}[/tex]
Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:
[tex]\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254[/tex]
Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
ecorded the sizes of the shoes in her family's cupboa
the modal size?
8, 7, 8, 8.5, 7, 8.5, 7
Answers
The modal sizes of shoes in the family's cupboard are 8 and 7.
To determine the modal size of shoes in the family's cupboard, we need to find the shoe size that appears most frequently in the given data. Let's analyze the sizes:
8, 7, 8, 8.5, 7, 8.5, 7
To find the mode, we can create a frequency table by counting the number of occurrences for each shoe size:
8 | 3
7 | 3
8.5 | 2
From the frequency table, we can see that both size 8 and size 7 appear three times each, while size 8.5 appears two times. Since both size 8 and size 7 have the highest frequency of occurrence (3), they are considered modal sizes. In this case, there is more than one mode, and we refer to it as a bimodal distribution.
To determine the mode, we performed a frequency count of each shoe size in the given data. We counted the number of occurrences for sizes 8, 7, and 8.5. Based on the frequency counts, we identified the sizes with the highest frequency, which turned out to be 8 and 7, both occurring three times. Thus, they are the modal sizes in the data set.
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What is the distance between the points (1,3)
and (–2,7)?
Answers
=================================================
Explanation
I'll use the distance formula.
[tex](x_1,y_1) = (1,3) \text{ and } (x_2, y_2) = (-2,7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-2))^2 + (3-7)^2}\\\\d = \sqrt{(1+2)^2 + (3-7)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]
The distance is 5 units.
Answer:
5
Step-by-step explanation:
Graph the ellipse, Plot the foci of the ellipse 100pts
Answers
Answer:
Step-by-step explanation:
The general equation for an ellipse with center (h, k) is:
[tex]\boxed{\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1}[/tex]
If a > b, the ellipse is horizontal.
If b > a, the ellipse is vertical.
Given equation:
[tex]\dfrac{(x-5)^2}{4}+\dfrac{(y+5)^2}{9}=1[/tex]
As b > a, the ellipse is vertical. Therefore:
b is the major radius and 2b is the major axis.a is the minor radius and 2a is the minor axis.Vertices = (h, k±b)Co-vertices = (h±a, k)Foci = (h, k±c) where c² = b² - a²Comparing the given equation with the standard form, we get:
[tex]h = 5[/tex][tex]k = -5[/tex][tex]a^2=4 \implies a=2[/tex][tex]b^2=9 \implies b=3[/tex]Therefore:
[tex]\textsf{Center}= (5, -5)[/tex][tex]\textsf{Major axis}=2 \cdot 3 = 6[/tex][tex]\textsf{Minor axis}=2 \cdot 2 = 4[/tex][tex]\textsf{Vertices:} \;\;(h, k \pm b)=(5,-5 \pm 3)=(5,-8)\;\;\textsf{and}\;\;(5,-2)[/tex][tex]\textsf{Co-vertices:}\;\;(h \pm a, k)=(5 \pm 2, -5)=(3, -5)\;\; \textsf{and}\;\;(7, -5)[/tex]To graph the ellipse:
Plot the center at (5, -5).Plot the vertices at (5, -8) and (5, -2). The distance between them is the major axis.Plot the co-vertices at (3, -5) and (7, -5). The distance between them is the minor axis.If f(x)= 2 x -2x , find f(-1) , f( 2 x ) , f(t) , and f(p-1) .
Answers
The values of f(-1), f(2x), f(t), and f(p-1) all simplify to 0. Therefore, f(-1) = f(2x) = f(t) = f(p-1) = 0.
To find the values of f(-1), f(2x), f(t), and f(p-1), we substitute the given values into the function f(x) = 2x - 2x and simplify.
f(-1):
Substituting x = -1 into f(x):
f(-1) = 2(-1) - 2(-1) = -2 + 2 = 0
f(2x):
Substituting x = 2x into f(x):
f(2x) = 2(2x) - 2(2x) = 4x - 4x = 0
f(t):
Substituting x = t into f(x):
f(t) = 2(t) - 2(t) = 2t - 2t = 0
f(p-1):
Substituting x = p-1 into f(x):
f(p-1) = 2(p-1) - 2(p-1) = 2p - 2 - 2p + 2 = 0
The values of f(-1), f(2x), f(t), and f(p-1) all simplify to 0. Therefore, f(-1) = f(2x) = f(t) = f(p-1) = 0.
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NO LINKS!! URGENT HELP PLEASE PLEASE!!!
Answers
Answer:
[tex]\textsf{12)} \quad \text{a.}\;\;m \angle 1 = 107^{\circ}, \quad \text{b.}\;\;m \angle 2 = 107^{\circ}, \quad \text{c.}\;\;m \angle 3 = 73^{\circ}[/tex]
[tex]\textsf{13)} \quad EC = 6[/tex]
[tex]\textf{14)}\quad \text{a.}\;\;x = 33, \quad \text{b.}\;\; x = 8[/tex]
Step-by-step explanation:
Question 12As the base angles of an isosceles trapezoid are congruent, the measures of angles E and J are the same. Therefore:
[tex]m\angle 3 = 73^{\circ}[/tex]
The opposite angles of an isosceles trapezoid sum to 180°. Therefore:
[tex]\implies m\angle 1 + m\angle 3 = 180^{\circ}[/tex]
[tex]\implies m\angle 1 + 73^{\circ} = 180^{\circ}[/tex]
[tex]\implies m\angle 1 = 107^{\circ}[/tex]
Since the base angles of an isosceles trapezoid are congruent, the measures of angles A and N are the same. Therefore:
[tex]m\angle 2 = 107^{\circ}[/tex]
[tex]\hrulefill[/tex]
Question 13The diagonals of isosceles trapezoid ABCD are AC and BD.
Point E is the point of intersection of the diagonals. Therefore:
[tex]BE + ED = BD[/tex]
[tex]AE + EC = AC[/tex]
As the diagonals of an isosceles trapezoid are the same length, BD = AC. Therefore:
[tex]AE + EC = BD[/tex]
Given BD = 20 and AE = 14:
[tex]\implies AE + EC = BD[/tex]
[tex]\implies 14 + EC = 20[/tex]
[tex]\implies 14 + EC - 14 = 20 - 14[/tex]
[tex]\implies EC = 6[/tex]
[tex]\hrulefill[/tex]
Question 14The midsegment of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides (legs) of the trapezoid.
The formula for the midsegment of a trapezoid is:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Midsegment of a trapezoid}\\\\$M=\dfrac{1}{2}(a+b)$\\\\where:\\ \phantom{ww}$\bullet$ $M$ is the midsegment.\\ \phantom{ww}$\bullet$ $a$ and $b$ are the parallel sides.\\\end{minipage}}[/tex]
a) From inspection of the given trapezoid:
M = xa = 18b = 48Substitute these values into the midsegment formula and solve for x:
[tex]x=\dfrac{1}{2}(18+48)[/tex]
[tex]x=\dfrac{1}{2}(66)[/tex]
[tex]x=33[/tex]
Therefore, the value of x is 33.
b) From inspection of the given trapezoid:
M = 15a = 22b = xSubstitute these values into the midsegment formula and solve for x:
[tex]15=\dfrac{1}{2}(22+x)[/tex]
[tex]30=22+x[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
Find the length of an isosceles 90 degree triangle with the hypothenuse of 4 legs x
Answers
The length of the hypotenuse in the isosceles 90-degree triangle is √(2).
In an isosceles 90-degree triangle, two legs are equal in length, and the third side, known as the hypotenuse, is longer. Let's denote the length of the legs as x and the length of the hypotenuse as 4x.
According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we have:
[tex]x^2 + x^2 = (4x)^2.[/tex]
Simplifying the equation:
[tex]2x^2 = 16x^2.[/tex]
Dividing both sides of the equation by [tex]2x^2[/tex]:
[tex]1 = 8x^2.[/tex]
Dividing both sides of the equation by 8:
[tex]1/8 = x^2[/tex].
Taking the square root of both sides of the equation:
x = √(1/8).
Simplifying the square root:
x = √(1)/√(8),
x = 1/(√(2) * 2),
x = 1/(2√(2)).
Therefore, the length of each leg in the isosceles 90-degree triangle is 1/(2√(2)), and the length of the hypotenuse is 4 times the length of each leg, which is:
4 * (1/(2√(2))),
2/√(2).
To simplify the expression further, we can rationalize the denominator:
(2/√(2)) * (√(2)/√(2)),
2√(2)/2,
√(2).
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A sample of gas stored at ST has a volume of 3.56 L. The gas is heated to 400 K and has a pressure of 125 kPa. What is the volume of the gas after it is heated?
Answers
The volume of the gas after it is heated is approximately 0.0417 liters.
To find the volume of the gas after it is heated, we can use the combined gas law, which relates the initial and final conditions of a gas sample. The combined gas law is expressed as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
Where:
P₁ and P₂ are the initial and final pressures of the gas (in kPa)
V₁ and V₂ are the initial and final volumes of the gas (in liters)
T₁ and T₂ are the initial and final temperatures of the gas (in Kelvin)
Given:
Initial volume (V₁) = 3.56 L
Initial temperature (T₁) = ST (which is typically 273.15 K)
Final temperature (T₂) = 400 K
Final pressure (P₂) = 125 kPa
Now we can plug these values into the combined gas law equation and solve for V₂:
(P₁V₁) / T₁ = (P₂V₂) / T₂
(1 * 3.56) / 273.15 = (125 * V₂) / 400
(3.56 / 273.15) = (125 * V₂) / 400
Cross-multiplying and solving for V₂:
3.56 * 400 = 273.15 * 125 * V₂
1424 = 34143.75 * V₂
V₂ = 1424 / 34143.75
V₂ ≈ 0.0417 L
As a result, the heated gas has a volume of approximately 0.0417 litres.
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If
Answers
Answer:
I pass my classes.
Step-by-step explanation:
I had to add this sentence or else it wouldnt allow me to send it.
Answer:
In math, the word "if" can be used for piecewise functions. In piecewise functions, you can see equations where f(x) = x+3 IF x>0 and f(x) = -x IF x<0.
What’s equivalent to 6 to the -3 power
Answers
x^-1 =1/x^1=1/x
Similarly,
x^(-a)=1/(x^a)
Therefore
6^(-3)=1/(6^3)=1/(6*6*6)=1/216
If the manager of a bottled water distributor wants to estimate, 95% confidence, the mean amount of water in a 1-gallon bottle to within ±0.006 gallons and also assumes that the standard deviation is 0.003 gallons, what sample size is needed?
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of compact fluorescent light bulbs to within ±250 hours and also assumes that the population standard deviation is 900 hours, how many compact fluorescent light bulbs need to be selected?
If the inspection division of a county weighs and measures department wants to estimate the mean amount of soft drink fill in 2-liter bottles to within ± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.08 liters, what sample size is needed?
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 52 minutes. What sample size is needed if the executive wants to be 95% confident of being correct to within ±5 minutes?
Answers
n = (Z * σ / E)^2
where:
n = required sample size
Z = Z-value for the desired confidence level (for 95% confidence, Z ≈ 1.96)
σ = standard deviation
E = desired margin of error
Let's calculate the sample sizes for each scenario:
1. Bottled Water:
Z ≈ 1.96, σ = 0.003 gallons, E = 0.006 gallons
n = (1.96 * 0.003 / 0.006)^2 ≈ 384.16
Since we can't have a fraction of a sample, we round up to the nearest whole number. Therefore, a sample size of 385 bottles is needed.
2. Compact Fluorescent Light Bulbs:
Z ≈ 1.96, σ = 900 hours, E = 250 hours
n = (1.96 * 900 / 250)^2 ≈ 49.96
Again, rounding up to the nearest whole number, a sample size of 50 light bulbs is needed.
3. Soft Drink Fill:
Z ≈ 1.96, σ = 0.08 liters, E = 0.01 liters
n = (1.96 * 0.08 / 0.01)^2 ≈ 122.76
Rounding up, a sample size of 123 bottles is needed.
4. Digital Media Consumption:
Z ≈ 1.96, σ = 52 minutes, E = 5 minutes
n = (1.96 * 52 / 5)^2 ≈ 384.16
Rounding up, a sample size of 385 consumers is needed.
Please note that the sample sizes calculated here assume a simple random sampling method and certain assumptions about the population.
```
n = (Z^2 * σ^2) / E^2
```
where:
- Z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence)
- σ is the population standard deviation
- E is the desired margin of error
Substituting the given values, we get:
```
n = (1.96^2 * 52^2) / 5^2
n ≈ 385.07
```
Rounding up, we get a required sample size of 386.
Therefore, the advertising executive should sample at least 386 individuals to estimate the mean time that consumers spend with digital media with a margin of error of ±5 minutes and 95% confidence level.
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
what this is?
If the left-hand limit of is equal to the right-hand limit of as x approaches 10, the limit of as x approaches 10 is and the value of k is .
Answers
The limit of f(x) as x approaches 10 is 315 and The value of k is 250.
The function f(x) is a piecewise function, so we need to evaluate it separately for x < 10 and x >= 10.
[tex]f(x)= { \frac{(0.1x(2)+20x+15,x < 10)}{(0.25x(3)+k,x > 10)}[/tex]
For x < 10, the function is equal to 0.1x^2 + 20x + 15. So the left-hand limit of f(x) as x approaches 10 is equal to 0.1(10)^2 + 20(10) + 15 = 315.
For x >= 10, the function is equal to 0.25x^3 + k. So the right-hand limit of f(x) as x approaches 10 is equal to 0.25(10)^3 + k = 250 + k.
Since the left-hand limit and the right-hand limit are equal, the limit of f(x) as x approaches 10 is also equal to 315, and the value of k is equal to 250.
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Calc II Question
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y axis.
Y = e^(-x^2)
Y = 0
X = 0
X = 1
Correct answer is pi (1 - (1/e))
I'm just not sure how to get to that answer
Answers
Answer:
[tex]\displaystyle \pi\biggr(1-\frac{1}{e}\biggr)[/tex]
Step-by-step explanation:
Shell Method (Vertical Axis)
[tex]\displaystyle V=2\pi\int^b_ar(x)h(x)\,dx[/tex]
Radius: [tex]r(x)=x[/tex]
Height: [tex]h(x)=e^{-x^2}[/tex]
Bounds: [tex][a,b]=[0,1][/tex]
Set up and evaluate integral
[tex]\displaystyle V=2\pi\int^1_0xe^{-x^2}\,dx[/tex]
Let [tex]u=-x^2[/tex] and [tex]du=-2x\,dx[/tex] so that [tex]-\frac{1}{2}\,du=x\,dx[/tex]Bounds become [tex]u=-0^2=0[/tex] and [tex]u=-1^2=-1[/tex][tex]\displaystyle V= -\frac{1}{2}\cdot2\pi\int^{-1}_0e^u\,du\\\\V= -\pi\int^{-1}_0e^u\,du\\\\V=\pi\int^0_{-1}e^u\,du\\\\V=\pi e^u\biggr|^0_{-1}\\\\V=\pi e^0-\pi e^{-1}\\\\V=\pi-\frac{\pi}{e}\\\\V=\pi\biggr(1-\frac{1}{e}\biggr)[/tex]
If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answers
Answer:
39°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the other angle be x , then
x + 54° + 87° = 180°
x + 141° = 180° ( subtract 141° from both sides )
x = 39°
that is the other angle is 39°
In a triangle, the sum of all angles is always 180°. To find the third angle in a scalene triangle where two angles are known, subtract the known angles from 180°. In this case, subtracting 54° and 87° from 180° gives a third angle of 39°.
Explanation:The question refers to finding the third angle in a scalene triangle, where we know two of the angles. A scalene triangle is a triangle where all three sides are of a different length, and therefore all three angles are also different. The sum of the angles in any triangle is always 180°.
To find the third angle in the triangle, you can use the equation: Angle C = 180° - Angle A - Angle B.
So, we subtract the known angles from 180°: Angle C = 180° - 54° - 87° = 39°.
Therefore, the third angle in this scalene triangle is 39°.
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Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
Answers
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50