Answer:
C. ∠ZXY and D. YX
Step-by-step explanation:
C. ∠ZXY
because the middle letter is always the angle or the turning point of an angle and also it is in order based on the diagram. The angle won't change even if you look at it on a different point of view or if the diagram was flipped.
D. YX
because the line YX is a true statement because XY or YX is on the same line that goes on and on. You can tell because there's arrows on the end of the line.
What is the radius of the red circle? What is the radius of the blue circle?
Red Circle:
First find the diameter
We can do that by counting the squares
Diameter:4
The radius is half of the diameter
4/2=2
Radius of the Red Circles:2
Blue Circle:
Diameter: 2
2/2=1
Radius of the Blue Circle:1
if p=-6 and q = 4 what is the smallest subset containing the value of the expression below? p^2 +q/ -|p|-q
The value of the given expression is -4, which is integer. Therefore, option B is the correct answer.
The given expression is (p²+q)/(-|p|-q).
Here, p=-6 and q=4.
Substitute p=-6 and q=4 in the given expression we get
((-6)²+4)/(-|-6|-4)
= 40/(-10)
= -4
Therefore, option B is the correct answer.
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1_Escribe cómo se lee los siguientes números.
789.406=
973.002=
1003.576=
3.322.010=
Answer:
setesientos ochenta y nueve mil cuatrosientos seis
novecintos setenta y Tres mil dos
un millon Tres mil quinientos setenta y seis
tres millones tresientos veintidos mil diez
:)
Write this equation in slope-intercept form by isolating the y-variable. 12x = 4y y= x
Answer:
3x
Step-by-step explanation:
I took the the answer so I know it
Answer: 3
Step-by-step explanation: On Edge!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad. The probability of drawing a bag with bad potatoes is less than 1. The probability of drawing a bag with good potatoes is greater than 0. What is the probability of drawing a bag with bad potatoes? what is the expected probability of the complement of the event?.
Probability of drawing bad potatoes = 0.1
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0
The probability of drawing a bag with bad potatoes as a decimal .
The probability is 20% which means 20 by hundred , which means there is a chance of being its ok.
probability of bad potatoes = 2/20
=1/10
=0.1
To find the probability of the outcomes = Number of favourable outcome / Number of total outcome.
Probability of event 1 and 2
probability of event 1 =Number of favourable outcome / Number of total outcome.
probability of event 2 = 1 -( probability of event 1)
probability of good potatoes = 1- ( probability of bad potatoes)
Probability of the given event( probability of the bad potatoes = 1-(0.1)
Thus,
Probability of the bad potatoes in the 2 of the bags are=0.9
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An animal starts from rest and accelerates to its top speed in 7 seconds. It continues at this speed for 9 seconds and then slows to a stop in a further 4 seconds. Calculate the total distance that the animal travelled
Answer:
hggffffxdfffdsddfdohgfffdedss
109. Effect of Gravity on Earth If a rock falls from a height of 20 meters on Earth, the height H (in meters) after r seconds is approximately H(x) = 20 - 4.9r? (a) What is the height of the rock when x = 1 second? When r = 1.1 seconqds? When x = 1.2 seconds? (b) When is the height of the rock 15 meters? When is it 10 meters? When is it 5 meters? (c) When does the rock strike the ground?
We have the expression for the height H of the rock in function of the time r, when it falls from a height of 20 meters:
\(H(r)=20-4.9\cdot r^2\)When r = 1 second, we have:
\(H(1)=20-4.9(1)^2=20-4.9\cdot1=20-4.9=15.1\)When r = 1.1 seconds, we have:
\(H(1.1)=20-4.9(1.1)^2=20-4.9\cdot1.21=20-5.929=14.071\approx14\)When r = 1.2 seconds, we have:
\(H(1.2)=20-4.9(1.2)^2=20-4.9\cdot1.44=20-7.056=12.944\approx13\)To know the time for each height, we have to work with the equation like this:
\(\begin{gathered} H=20-4.9r^2 \\ 4.9r^2=20-H \\ r^2=\frac{20-H}{4.9} \\ r=\sqrt{\frac{20-H}{4.9}} \end{gathered}\)Then, we can calculate at which time the height is 15 meters:
\(r=\sqrt{\frac{20-15}{4.9}=\sqrt{\frac{5}{4.9}}}=\sqrt{1.02}\approx1.01\)When the height is 10 meters, r is:
\(r=\sqrt{\frac{20-10}{4.9}=\sqrt{\frac{10}{4.9}=}}\sqrt{2.04}\approx1.43\)When the height is 5 meters, r is:
\(r=\sqrt{\frac{20-5}{4.9}=\sqrt{\frac{15}{4.9}=}}\sqrt{3.06}\approx1.75\)The rock hits the ground when H=0. This happens when r is:
\(r=\sqrt{\frac{20-0}{4.9}=\sqrt{\frac{20}{4.9}=}}\sqrt{4.08}\approx2.02\). The slope of the aggregate expenditure line (model) is equal to:
MPC
APC
MPS
APS
The correct option is MPC. The slope of the aggregate expenditure line is equal to the marginal propensity to consume (MPC.)
Aggregate expenditure is the total spending in an economy on final goods and services at a particular price level and time. This expenditure comprises four types of spending, which are:
Investment expenditure (I)Government expenditure (G)Consumption expenditure (C)Net exports (NX)Therefore, the formula for aggregate expenditure can be given as: AE = C + I + G + NX.
Aggregate expenditure can be calculated by adding the consumption expenditure, investment expenditure, government expenditure, and net exports. The marginal propensity to consume (MPC) is the amount that consumer spending rises when disposable income rises by $1. The formula for MPC is:
MPC = Change in consumption / Change in disposable income
Therefore, the slope of the aggregate expenditure line is equal to the marginal propensity to consume (MPC). Therefore, the correct option is MPC.
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Ricarda earns $25 allowance each week. How can she mentally compute her total earnings after 7 weeks?
Answer:
25w
Step-by-step explanation:
Let w represent the number of weeks and 25 is the amount she gets each week, so 25(7)=175.
Answer: $175
Step-by-step explanation: She could do 25x8(25x4x2) which is 200 and then subtract 25.
A nutrition researcher wants to determine the mean fat content of hen's eggs. She collects a sample of 40 eggs. She calculates a mean fat content of 23 grams with a sample standard deviation of 8 grams. From these statistics, she calculates a 90% confidence interval of 20.9 grams to 25.1 grams. What can the researcher do to decrease the width of the confidence interval?
a. increase the confidence level
b. decrease the confidence level
c. decrease the sample size
d. none of the above
To decrease the width of the confidence interval, the researcher can take the following steps:
1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.
2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.
Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.
The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.
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How much does the state spend in tax dollars altogether?
a. 20 million dollars
b. 12 million dollars
c. 24 million dollars
d. 48 million dollars
Answer:
24 mill
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65. PLS NEED ASAP!!
Answer: Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase
Step-by-step explanation:
Answer:
its B and C
Step-by-step explanation:
CREATE AN EXPRESSION & SOLVE.
Kiera thinks of a number.
She subtracted 4 from it.
Then she multiplied that
answer by 3. She got a final
answer of 24. What was her
starting number?
Answer:
24/3-4
Answer is 12
Step-by-step explanation:
To find the answer, you have to work backwards. You also have to use PEMDAS. Since she multiplied her answer to get 24, you have to work backwards and divide by 3 first. You will get the number 8 after that because 24/3 is 8. Since she also subtracted 4, you have to work backwards and add 4. That gives you an original number of 12.
Answer:
12
Step-by-step explanation:
explanation: if you go backwards you divide 24 by 3 getting 8, then you add 4 to that and then you get 12.
Kuta Software - Infinite Pre-AlgebraFind each product.1) (3n + 2)(n + 3) 2) (n − 1)(2n − 2)3) (2x + 3)(2x − 3) 4) (r + 1)(r − 3)5) (2n + 3)(2n + 1) 6) (3p − 3)( p − 1)7) (3p + 3)(3p + 2) 8) (k − 2)(k − 3)9) (v − 1)(3v − 3) 10) (2x − 3)(3x + 3)
The product of each is
1) (3n + 2)(n + 3) = 3n² + 11n + 6
2) (n − 1)(2n − 2) = 2n² − 4n + 2
3) (2x + 3)(2x − 3) = 4x² − 9
4) (r + 1)(r − 3) = r² − 2r - 3
5) (2n + 3)(2n + 1) = 4n² + 8n + 3
6) (3p − 3)(p − 1) = 3p² − 6p + 3
7) (3p + 3)(3p + 2) = 9p² + 15p + 6
8) (k − 2)(k − 3) = k² − 5k + 6
9) (v − 1)(3v − 3) = 3v² − 6v + 3
10) (2x − 3)(3x + 3) = 6x² − 3x − 9
We have to determine the product of each.
1) (3n + 2)(n + 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(3n + 2)(n + 3) = n(3n + 2) + 3(3n + 2)
Simplify
(3n + 2)(n + 3) = 3n² + 2n + 9n + 6
(3n + 2)(n + 3) = 3n² + 11n + 6
2) (n − 1)(2n − 2)
To find the product we use Distributive property.
a(b + c) = ab + bc
(n − 1)(2n − 2) = 2n(n − 1) − 2(n − 1)
(n − 1)(2n − 2) = 2n² − 2n − (2n − 2)
Simplify
(n − 1)(2n − 2) = 2n² − 2n − 2n + 2
(n − 1)(2n − 2) = 2n² − 4n + 2
3) (2x + 3)(2x − 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(2x + 3)(2x − 3) = 2x(2x + 3) − 3(2x + 3)
(2x + 3)(2x − 3) = 4x² + 6x − (6x + 9)
Simplify the bracket
(2x + 3)(2x − 3) = 4x² + 6x − 6x - 9
(2x + 3)(2x − 3) = 4x² − 9
4) (r + 1)(r − 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(r + 1)(r − 3) = r(r + 1) − 3(r + 1)
(r + 1)(r − 3) = r² + r − 3r - 3
(r + 1)(r − 3) = r² − 2r - 3
5) (2n + 3)(2n + 1)
To find the product we use Distributive property.
a(b + c) = ab + bc
(2n + 3)(2n + 1) = 2n(2n + 3) + 1(2n + 3)
(2n + 3)(2n + 1) = 4n² + 6n + 2n + 3
(2n + 3)(2n + 1) = 4n² + 8n + 3
6) (3p − 3)(p − 1)
To find the product we use Distributive property.
a(b + c) = ab + bc
(3p − 3)(p − 1) = p(3p − 3) − 1(3p − 3)
(3p − 3)(p − 1) = 3p² − 3p − 3p + 3
(3p − 3)(p − 1) = 3p² − 6p + 3
7) (3p + 3)(3p + 2)
To find the product we use Distributive property.
a(b + c) = ab + bc
(3p + 3)(3p + 2) = 3p(3p + 3) + 2(3p + 3)
Simplify the bracket
(3p + 3)(3p + 2) = 9p² + 9p + 6p + 6
(3p + 3)(3p + 2) = 9p² + 15p + 6
8) (k − 2)(k − 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(k − 2)(k − 3) = k(k − 2) − 3(k − 2)
(k − 2)(k − 3) = k² − 2k − 3k + 6
(k − 2)(k − 3) = k² − 5k + 6
9) (v − 1)(3v − 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(v − 1)(3v − 3) = 3v(v − 1) − 3(v − 1)
(v − 1)(3v − 3) = 3v² − 3v − 3v + 3
(v − 1)(3v − 3) = 3v² − 6v + 3
10) (2x − 3)(3x + 3)
To find the product we use Distributive property.
a(b + c) = ab + bc
(2x − 3)(3x + 3) = 3x(2x − 3) + 3(2x − 3)
(2x − 3)(3x + 3) = 6x² − 9x + 6x − 9
(2x − 3)(3x + 3) = 6x² − 3x − 9
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The complete question is:
Find each product.
1) (3n + 2)(n + 3)
2) (n − 1)(2n − 2)
3) (2x + 3)(2x − 3)
4) (r + 1)(r − 3)
5) (2n + 3)(2n + 1)
6) (3p − 3)( p − 1)
7) (3p + 3)(3p + 2)
8) (k − 2)(k − 3)
9) (v − 1)(3v − 3)
10) (2x − 3)(3x + 3)
Farris Pharmacy has a uniform yearly demand for 200 bottles of Zithromax antibiotics. Suppose that their yearly ordering and storage costs C(x) ar given by the tunction C(x)=5x+ x
8,000
Where X is the number of bottles they place in each order. You may assume that one shipment arrives just as the previous shipment is sold. How much doesit cost the pharmacy to store one bottle?
The cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.
The given function is c(x)=5x+8000/x
We can calculate the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics by using the provided equation C(x).
To find the cost of storing one bottle, we will simply set x equal to 1. Therefore, C(1) = 5(1) + 8,000/1 = 8,005.
This means that the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.
Therefore, the cost for Farris Pharmacy to store one bottle of Zithromax antibiotics is 8,005.
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If n is an integer, what is the possible value of n for which 1,116n is the square of an integer? Explain.
E. 24
F. 28
G. 31
H. 33
Answer:
G.31
Step-by-step explanation:
when n = 31
1116n = 1116*31 = 34596
34596 is square of 186.
= 186^2
= 34596
and other values (24,28,33) of n does not give square during 1,116n but 31 gives.
Hence, 31 is the possible value of n for which 1,116n is the square of an integer(186).
Which line is parallel to the line Y = X +7?
A. X-y=5
B. X+y=-2
C. Y=1
D. X=1
Answer:
a
Step-by-step explanation:
y=1 has a slope of 0,
x=1 has an indefinite slope,
x+y has a negative slope, so
x-y would be the only oneeft
The diameter of a cylinder is 5 yd. The height is 4 yd. What is the volume of the cylinder
Answer:
25 pi square yd OR rounded pi to 3.14: 78.5 square yd
Step-by-step explanation:
Use the formula volume of cylinder = base area × h to determine the value of the base area.
Diameter: 5 yd
Height: 4 yd
(5/2)^2 Pi x 4 = 25 pi square yd.
Answer:
78.5 yd
Step-by-step explanation:
= \(\pi\)r²h
= (3.14)(2.5)²(4)
= (3.14)(6.25)(4)
= 19.625 x 4
= 78.5 yd
A sweater was on sale at 40% off the regular price. Ella saved $20 by buying the sweater on sale. What was the regular price of the sweater?
Answer:
$60
Step-by-step explanation:
i-ready
A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle isA1+√32B5−2√3C 2D 1+√3
An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.
A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.
The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.
Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.
From the diagram, let GH be x. The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3
\(\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}\)
By Pythagoras' theorem, from ΔHEF,
\(\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}\)
The radius of the circle (HE) is 2-√3+√3=2.
The answer is 2 cm. Therefore, option C is correct.
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If a public utility company is considered a monopolist, which of the following is not true? A. The company's demand curve and supply curve are upward sloping. B. Its price must be higher than its marginal revenue. C. For the company to practice price discrimination, there should not be any resale of its product. D. Its profit maximizing quantity is determined where its marginal revenue equals its marginal cost.
For the company to practice price discrimination, there should not be any resale of its product, is not true if a public utility company is considered a monopolist. This is because price discrimination involves charging different prices to different groups of customers based on their willingness to pay. Resale of the product can actually facilitate price discrimination as it allows different customers to buy the product at different prices and then resell it to others. The other options are true for a monopolist, such as having upward sloping demand and supply curves, charging a price higher than its marginal revenue, and determining profit maximizing quantity at the point where marginal revenue equals marginal cost.
Let's analyze each statement:
A. The company's demand curve and supply curve are upward sloping.
This statement is NOT true for a monopolist. A monopolist faces a downward sloping demand curve, which means that they can increase the quantity sold by lowering the price. The supply curve does not apply in the traditional sense for monopolists, as they have the power to set both the price and quantity produced.
B. Its price must be higher than its marginal revenue.
This statement is true for a monopolist. Under a monopoly, the price charged by the company is higher than its marginal revenue due to the downward-sloping demand curve.
C. For the company to practice price discrimination, there should not be any resale of its product.
This statement is true. In order for a monopolist to successfully engage in price discrimination, they must prevent the resale of their product, ensuring that consumers cannot undercut the monopolist's pricing strategy.
D. Its profit maximizing quantity is determined where its marginal revenue equals its marginal cost.
This statement is true. A monopolist maximizes its profit by producing the quantity where marginal revenue equals marginal cost, and then setting the price based on the demand curve at that quantity.
So, the statement that is NOT true for a public utility company considered as a monopolist is: A. The company's demand curve and supply curve are upward sloping.
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the sum of a particular two digit number is 11. if this number's digits are reversed, the number is decreased by 63. what is this number?
The required number is 94.
Let the digit on unit's place be 'x'
Digit on ten's place be 'y'
Therefore,
Original number = 10y + x
Given, the sum of the digits = 11
=> x + y = 11 →(I)
When the digits are reversed, new number = 10x + y
Therefore,
(10y + x) - (10x + y) = 63
10y + x - 10x - y = 63
9y - 9x = 63
=> y - x = 7 →(II)
Adding (I) and (II) we get
2y = 18
y = 9
Substituting the value of y in (I) we get
x + 9 = 11
x = 2
Therefore,
Original number = 10y + x = 10(9) + 4 = 94
The required number is 94.
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The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y.
After the common factor is removed, the remaining factor is a
.
The expression x²y - 2xy - 24y can be factored by first factoring out a common factor of y, After the common factor is removed, the remaining factors are, (x - 6) & (x - 4)
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression x²y - 2xy - 24y
Now taking common factor y from all the terms,
⇒ y(x² - 2x - 24)
Now considering another factor (x² - 2x - 24)
⇒ (x² - 2x - 24)
⇒ x² - 6x + 4x -24
⇒ x(x - 6) + 4(x - 6)
⇒ (x - 6)(x - 4)
Hence, rest two factors are (x - 6) & (x - 4)
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Answer:
trinomial that is not a perfect square
Step-by-step explanation:
edgeeeeeeeeeeeeee
please provide the right answer, i am posting this question 3rd
time,...i will not approve until i get the right answer so please
provide a right answer
Exercise 2 (Big O Notation) Determine if $\forall a, b \in \mathbb{N}, f(n)=a^n, g(n)=b^n$, then it follows that $f \in \Theta(g)$
if \($a \neq b$\),\($f(n)$\)and \($g(n)$\) will not have the same growth rate. It is not true that \($\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$\).
To determine whether $f(n) = a^n$ and $g(n) = b^n$ satisfy $f \in \Theta(g)$, we need to evaluate their growth rates and see if there exist constants $c_1$, $c_2$, and $n_0$ such that $c_1 \cdot g(n) \leq f(n) \leq c_2 \cdot g(n)$ for all $n \geq n_0$.
Let's analyze the growth rates of $f(n)$ and $g(n)$ separately:
1. $f(n) = a^n$:
- When $a > 1$, $f(n)$ grows exponentially with $n$. For example, if $a = 2$, $f(n)$ doubles with each increment of $n$.
- When $a = 1$, $f(n)$ is constant and does not grow with $n$.
- When $0 < a < 1$, $f(n)$ converges to 0 as $n$ increases. For example, if $a = 0.5$, $f(n)$ halves with each increment of $n$.
2. $g(n) = b^n$:
- When $b > 1$, $g(n)$ also grows exponentially with $n$.
- When $b = 1$, $g(n)$ is constant.
- When $0 < b < 1$, $g(n)$ converges to 0 as $n$ increases.
In general, if $a \neq b$, $f(n)$ and $g(n)$ will not have the same growth rate. Therefore, we cannot conclude that $f \in \Theta(g)$ for arbitrary $a$ and $b$.
Thus, it is not true that $\forall a, b \in \mathbb{N}, f(n) = a^n, g(n) = b^n$ implies $f \in \Theta(g)$.
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helpppppppppppppppppppp
Answer:
D is right.
it says name the congruent sides. so KR is congruent to SO and OR is congruent to SK
Answer:
D)
Step-by-step explanation:
Sides with the same number of marks are congruent.
The top and bottom sides are congruent. The left and right sides are congruent.
Answer: D)
If the measure of DCE is 28 what is the measure of CED
Answer: Measure of CED is: 212°
Find the length of AN A has coordinates (-4,-7), and N has coordinates (1,5)
The answer is 13 by using Pythagorean theorem.
Sabine rode on a passenger train for 480 miles between 10:30 A.M. and 6:30 P.M. to visit
a friend in a different city.
Part A
Calculate the train's average speed while Sabine was riding.
Answer
miles per hour
Answer:
60
Step-by-step explanation:
630 minus 1030 is 8 hours
480 divided by 8 is 60
Graph The Curve. x = cos(t) + ln(tan(t/2)), y = sin(t), π/4 ≤ t ≤ 3π/4
To graph the curve x = cos(t) + ln(tan(t/2)) and y = sin(t) with the domain π/4 ≤ t ≤ 3π/4, follow these steps: 1. Create a table of values for t within the given domain, such as t = π/4, π/2, and 3π/4. 2. Calculate the corresponding x and y values for each t value using the given equations. 3. Plot the (x, y) coordinates on a Cartesian plane.
To graph the curve, we first need to understand what each term means.
- x = cos(t) + ln(tan(t/2)): This is the equation for the x-coordinate of the curve. It's a combination of the cosine function (cos(t)) and the natural logarithm of the tangent function (ln(tan(t/2))).
- y = sin(t): This is the equation for the y-coordinate of the curve. It's simply the sine function (sin(t)).
Now, let's look at the range of values for t: π/4 ≤ t ≤ 3π/4. This means that t starts at π/4 (45 degrees) and ends at 3π/4 (135 degrees), and it increases in increments of pi/4 (90 degrees).
To graph the curve, we can start by plugging in some values of t to find corresponding (x,y) pairs. Here are a few:
- When t = π/4: x = cos(π/4) + ln(tan(π/8)) ≈ 0.532, y = sin(π/4) ≈ 0.707. So one point on the curve is (0.532, 0.707).
- When t = π/2: x = cos(π/2) + ln(tan(π/4)) = 0 + ln(1) = 0, y = sin(π/2) = 1. Another point on the curve is (0, 1).
- When t = 3π/4: x = cos(3π/4) + ln(tan(3π/8)) ≈ -0.532, y = sin(3π/4) ≈ -0.707. A third point on the curve is (-0.532, -0.707).
We can continue to plug in values of t and plot the corresponding points to create the graph. However, because the equation for x involves the natural logarithm of the tangent function, the curve may not be easy to visualize or sketch by hand.
In general, the curve will have a "wavy" shape due to the combination of the sine and cosine functions. The natural logarithm of the tangent function will also introduce some asymmetry to the curve. To get a more precise sense of the curve's shape, we can use a graphing calculator or software to plot the points and connect them with a smooth curve.
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