The fraction that converts to a terminating decimal number is C. 3/8.
To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.
Let's examine each option:
A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.
D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.
Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.
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Which of the following numbers is closest to 7? √51 50 46 st
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.
If
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 is the distance between the points (1,3)
and (–2,7)?
=================================================
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:
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
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:
If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
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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[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Answer:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Step-by-step explanation:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Answer:
[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[
Step-by-step explanation:
what this is?
Find the measure of the indicated arc.
90°
80°
100
70°
H
40°
F
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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If f(x)= 2 x -2x , find f(-1) , f( 2 x ) , f(t) , and f(p-1) .
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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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.
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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What is the most likely reason that Sora lists the
activities of customers going through self-checkout?
to prove the claim that customers are trained
enough to get paid for self-checkout
2
O to prove the claim that self-checkout is difficult
O to prove the claim that cashiers' duties are as simple
as self-checkout routines
O to prove the claim that self-checkout is eliminating
jobs
The most likely reason that Sora lists the activities of customers going through self-checkout is to prove the claim that self-checkout is eliminating jobs.
By observing and documenting the activities of customers using self-checkout, Sora may be gathering evidence to support the argument that self-checkout systems are replacing the need for human cashiers and leading to job loss in the retail industry.
By highlighting the tasks that customers can now perform independently, Sora may be emphasizing the efficiency and convenience of self-checkout systems, which can potentially lead to the reduction of cashier positions.
It's important to note that without more context, we cannot definitively determine Sora's exact intentions or motivations. However, based on the given options and the mention of activities related to self-checkout, the claim that self-checkout is eliminating jobs appears to be the most plausible reason for listing the activities of customers going through self-checkout.
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I need help with 36 please I don’t understand
Answer:
36)
[tex]f(x) = \frac{1}{x + 3} - 1[/tex]
The equation of the function is y = 1/(x + 3) - 1
How to determine the equation of the transformationFrom the question, we have the following parameters that can be used in our computation:
The reciprocal function shifted down one unit and left three units
The equation of the reciprocal function is represented as
y = 1/x
When shifted down one unit, we have
y = (1/x) - 1
When shifted left three units, we have
y = 1/(x + 3) - 1
Hence, the equation of the function is y = 1/(x + 3) - 1
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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
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]
Find the length of an isosceles 90 degree triangle with the hypothenuse of 4 legs x
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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Which table of values represents a function? Step by step.
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.
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.
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]
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)?
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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if a=7 and b =2 what is 2ab
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.Given cos=
a.
b.
sin 8
4
and csc <0, find sine and tan
9
-4
9
A
B
tan =
csc0= 4√√9, tane=
9
4
65
9
C.
d.
sin = 4, tan 9 =
sin =
Please select the best answer from the choices provided
65
19
-4√65
9
tan 9 =
The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)
Let's break down the given values and find the values of sine and tangent.
We are given:
cos θ = √(8/9)
csc θ < 0
Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.
sin^2θ + (√(8/9))^2 = 1
sin^2θ + 8/9 = 1
sin^2θ = 1 - 8/9
sin^2θ = 1/9
Taking the square root of both sides, we get:
sin θ = ±1/3
Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.
Next, let's find the value of tan θ.
tan θ = sin θ / cos θ
tan θ = (-1/3) / (√(8/9))
tan θ = -√9/√8
tan θ = -√9/√(4*2)
tan θ = -√9/(2√2)
tan θ = -3/(2√2)
So, the values are:
sin θ = -1/3
tan θ = -3/(2√2)
The best selection from the available options that matches the calculated values is:
C. sin θ = -1/3, tan θ = -3/(2√2)
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with #38 & 39
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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NO LINKS!! URGENT HELP PLEASE!!
21. Determine whether CD || AB. Explain your reasoning.
Reason:
If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.
Let's calculate each side separately.
EA/EC = 28/(28+20) = 0.5833EB/ED = 16/(16+10) = 0.6154Both decimal values are approximate.
The two values don't match up which makes EA/EC = EB/ED to be false.
Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.
Answer:
CD is not parallel to AB
Step-by-step explanation:
According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
Therefore, if CD is parallel to AB, then EA : AC = EB : BD.
Substitute the values of the line segments into the equation:
[tex]\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\\dfrac{28}{20}&=\dfrac{16}{10}\\\\1.4 &\neq 1.6\end{aligned}[/tex]
As 1.4 does not equal 1.6, then CD is not parallel to AB.
What’s equivalent to 6 to the -3 power
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.
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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Graph the ellipse, Plot the foci of the ellipse 100pts
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.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
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
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Answer:
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Step-by-step explanation:
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When x increases from a to a + 2, y increases by a difference of 6. For which function is this statement true? Responses A y = 2(9)x y = 2 ( 9 ) x B y = 3x + 2y = 3x + 2 C y = 2(3)x y = 2 ( 3 ) x D y = 9x + 2
The function that satisfies the given condition is y = 3x + 2.
The correct answer to the given question is option B.
We are to find the function that satisfies the condition: When x increases from a to a + 2, y increases by a difference of 6.
A statement such as this represents a linear function, where y increases at a constant rate with respect to the increase in x.Let y = mx + b, be a linear function.
We know that when x increases from a to a + 2, y increases by a difference of 6. In other words, we can express this relationship using the following equation:
2m + b − m − b = 6 ⇒ m = 3
The function has been found to be y = 3x + b.
To find the value of b, we need to use the fact that when x increases from a to a + 2, y increases by a difference of 6: y(a + 2) − y(a) = 6 ⇒ 3(a + 2) + b − 3a − b = 6 ⇒ 6 = 6
Therefore, the function that satisfies the given condition is y = 3x + 2. The correct option is B) y = 3x + 2.
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Please help!!
The graph of function is shown
Function g is represented by the table
-1
X
9(x)
24
0
4
1
0
2
3
-#
Which statement correctly compares the two functions?
OA They have the same x-intercept and the same end behavior as x approaches
OB. They have the same
and y-intercepts
OC. They have different
and y intercepts but the same end behavior as x approaches
OD. They have the same y-intercept and the same end behavior as x approaches
Best
The x- and y-intercept values in the graph for the function f and in the table for the function g(x), indicates that the correct option is option C
C. The have different x- and y-intercepts but the same end behavior as x approaches ∞What are the x- and y-intercept of a graph of a function?The x-intercept is the point at which the y-value is 0, and the coordinates of the point is specified as the x-intercept.
The x-intercept is the point at which the x-value is 0, and the coordinates of the point is specified as the y-intercept
The question compares the x- and y-intercepts of the graph and the function in the table
The x-intercept of the function f in the graph are; (0, 3)
The y-intercept of the function f in the graph are; (4, 0)
The function g(x) in the table indicates that the x- and y-intercepts are;
The value of g(x) is 0 at the ordered pair (1, 0), therefore, the x-intercept of g(x) is (1, 0)
The value of x is 0 at the ordered pair (0, 4), therefore, the function, g(x) has a y-intercept at the point (0, 4)
Therefore, the function f and g have different intercepts, but the value in the table and the graph indicates that as x approaches infinity, the y-value, approaches -1, the correct option is therefore, option C
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PLS HELPPPPPPPPPPPPPPPPPPPPPPPPP
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 =
Determine the surface area and volume Note: The base is a square.
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 ?