Answer:C
Step-by-step explanation:
The constant and the variable relationship is p<9.That means it is "Alva spent less than 9%"
Answer:
it is c
Step-by-step explanation:
Part A
the beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20.
Part B Explain whether the inequality Jack writes is correct or incorrect. In your explanation, include a description of each value in the inequality in terms of what it represents. The beginning of a hiking trail is exactly at sea level. There are three rest stops along the trail. The elevation of the first rest stop is -15 feet. The elevation of the second rest stop is -20 feet. The elevation of the third rest stop is 7 feet. John compares the elevations, in feet, of the first two rest stops by writing the inequality -15 < -20. John states that the inequality he wrote is correct because 15 is less than 20. The change in elevation is greatest between the beginning of the trail and which rest stop? Explain your reasoning.
please help ,need help now
Part A is incorrect because for negative numbers, the greater the magnitude the smaller the number. -2 is smaller than -1, for example, and -20 is smaller than -15.
An elevation of -15ft means 15 ft below sea level, an elevation of -20ft means 20 ft below sea level, and an elevation of (+) 7ft means 7 ft above sea level.
If John started the trail at sea level (0ft elevation), then the greatest change in elevation would be between that and the second rest stop. Take the absolute value of all the numbers and see which one is the largest.
The math problem is 3x - 7 > 5 = 4 so is x greater than 4?
Answer:
yes, x > 4
Step-by-step explanation:
Add 7 to your inequality to get ...
3x > 12
Then divide by 3, and you have ...
x > 4
_____
We're not understanding the meaning of your " = 4" in the problem statement. It appears to have no place, either in the problem or in the solution.
Please help ASAP and help me find what the value of x is
Answer:
x=44
Step-by-step explanation:
33+103+x=180
136+x=180
x=44
The sum of all the angles of a triangle is 180 degrees.
Add all the angles together and set it equal to 180, then solve for x
33 + 103 + x = 180
(136 - 136) + x = 180 - 136
x = 44
Hope this helped!
Charles factors the expression 4/3xy+1/3x using a factor of 1/3x. He writes the factored expression 1/3x(4y+1). Which best describes the accuracy of Charles solution?
A. His solution is accurate
B. His solution is inaccurate. The factor does not divide evenly into both terms.
C. His solution is inaccurate. The factoring of 4/3xy using the given GCF is incorrect.
D. His solution is inaccurate. The factoring of 1/3x using the given GCF is incorrect.
A. His solution is accurate
You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x
Charles' solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]
Taking common as (1/3)x
[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]
The above expression is similar to Charles factor's of expression.
Thus, Charles solution is accurate because expression after factorization is similar to Charles factor's of expression option (A) is correct.
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sin C =
Whats the answer ?!?
The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse
Step-by-step explanation:
The measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse option third is correct.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
We have a right angle triangle with dimensions shown in the picture:
From the sin ratio in the right angle triangle:
sin∠C = 15/17
Thus, the measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse.
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Please respond quickly!!
Answer:
Area of triangle = 6 in^2
Step-by-step explanation:
We need to find the area of triangle. The formula used is:
Area of triangle = 1/2 * b*h
where b=base and h= height
In the given question, b =2 and h= 6
Putting values in the formula:
Area of triangle = 1/2 *2*6
= 12/2
= 6 in^2
Answer:
The area is 6 in^2
Step-by-step explanation:
(a) What is a sequence? A sequence is an unordered list of numbers. A sequence is the sum of an ordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an unordered list of numbers. A sequence is the product of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach 8 as n becomes large. The terms an approach 8 as n becomes small. The terms an approach infinity as n become large. The terms an approach -infinity as 8 approaches n. The terms an approach infinity as 8 approaches n. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes large. The terms an become large as n becomes small. The terms an approach zero as n becomes large. The terms an become small as n becomes small. The terms an become small as n becomes large.
Step-by-step explanation:
A sequence is an ordered list of numbers.
lim n → ∞ an = 8 means that as n approaches infinity (becomes large), an approaches 8.
lim n → ∞ an = ∞ means that as n approaches infinity (becomes large), an approaches infinity (becomes large).
A sequence is an ordered list of numbers, and when lim n → ∞ an = 8, it means the sequence's terms approach 8 as n becomes large. Saying lim n → ∞ an = ∞ indicates that the sequence's terms grow without bound as n increases.
Explanation:Answering your questions on sequences and limits:
(a) What is a sequence?
A sequence is an ordered list of numbers. Unlike a set where the order of elements does not matter, in a sequence, every number has a distinct place. For instance, the sequence of natural numbers is an ordered list starting from 1 and proceeding indefinitely in the order 1, 2, 3, 4, ... etc.
(b) What does it mean to say that lim n → ∞ an = 8?
This statement means that the terms an approach 8 as n becomes large. In other words, as you progress further along in the sequence, the values of the terms get closer and closer to 8, virtually reaching 8 as the sequence goes towards infinity. This is a fundamental concept in understanding sequences' behavior at their extremities.
(c) What does it mean to say that lim n → ∞ an = ∞?
This implies that the terms an become large as n becomes large. As the n value increases, the sequence's terms grow unlimitedly, indicating the sequence's divergence rather than converging to a definite number.
What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?
logarithmic graph passing through point 1, negative 2.
f(x − 2)
f(x + 2)
f(x) − 2
f(x) + 2
Answer: Third option
[tex]f(x) - 2[/tex]
Step-by-step explanation:
The function [tex]y=log_3 (x)[/tex] passes through the point (1,0) since the function [tex]y=log_a (x)[/tex] always cuts the x-axis at [tex]x = 1[/tex].
Then, if the transformed function passes through point (1,-2) then this means that the graph of [tex]y=log_3(x)[/tex] was moved vertically 2 units down.
The transformation that displaces the graphically of a function k units downwards is:
[tex]y = f (x) + k[/tex]
Where k is a negative number. In this case [tex]k = -2[/tex]
Then the transformation is:
[tex]f(x) -2[/tex]
and the transformed function is:
[tex]y = log_3 (x) -2[/tex]
A regular octagon can be concave.
True or False? Please explain.
Thanks!
a regular polygon has all equal angles, interior and exterior, as well as all equal sides.
Check the picture below.
the one on the left is a regular octagon, as well as a convex one.
the one on the right is also an octagon, but is concave, the issue is that, though all sides remain equal, the angles do not, and so is not a regular octagon.
Given: MNOK is a trapezoid, MN=OK, m∠M=60°, NK⊥MN, MK=16cm
Find: The midsegment of MNOK
Answer:
the length of the midsegment is 12 cm
Step-by-step explanation:
ΔMNK is a 30°-60°-90° triangle, so side MK is twice the length of side MN. That makes MN = (16 cm)/2 = 8 cm.
Dropping an altitude from N to intersect MK at X, we have ΔMXN is also a 30°-60°-90° triangle with side MN twice the length of side MX. That makes MX = (8 cm)/2 = 4 cm.
The length of the midsegment of this isosceles trapezoid is the same as the length XK, so is (16 -4) cm = 12 cm.
Answer:
12 cm.
Step-by-step explanation:
1. Consider right triangle MNK. In this triangle, angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is a special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with a measure of 30°. This means that this leg is half of the hypotenuse, MN=8 cm.
2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.
3. Trapezoid MNOK is isosceles because of MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.
4. The midsegment of the trapezoid is:
[tex]\frac{MK+NO}{2}=\frac{16+8}{2}=12cm[/tex]
Jake is eating dinner at a restaurant. The cost of his meal, including sales tax, is m dollars. After leaving an 18% tip, the amount Jake pays at the restaurant is represented by the following expression. In this expression, what does the term 0.18m represent?
For this case we have that variable "m" represents the cost of Jake's food. They tell us that he left an 18% tip. That is to say:
m -------------> 100%
tip ------------> 18%
Where "tip" is the cost of the tip based on the cost of the meal.
[tex]tip = \frac {18 * m} {100}\\tip = 0.18m[/tex]
The amount Jake pays is represented by:
[tex]m + 0.18m[/tex]
Where 0.18m is the tip
ANswer:
Tip
Answer:
the tip amount jake pays
Step-by-step explanation:
ruben is making a display that includes dinosaurs in their habitat. the dinosaurs will need to be decreased in size to fit the display.
What's the question?
Answer:
80%
Step-by-step explanation:
"He will start with the Brachiosaurus which has an estimated height of 15 meters and make the model 3 meters on height. by what percent will Ruben decrease the size of the Brachiosaurus in order to fit it into the display"
The percent decrease is the difference in heights divided by the original height.
(15 - 3) / 15
12/15
0.8
So Ruben will decrease the size by 80%.
A certain game consists of rolling a single fair die. If a four or five comes up, you win 8 dollars; otherwise, you lose 4 dollars. Find the expected winnings for this game
Answer:
3/1
Step-by-step explanation:
Well there's 6 sides on a dice and only 2 winning numbers. 6/2=3/1. You have a good chance of losing lol. Is this what you're looking for?
~Keaura/Cendall.
Follow below steps:
To find the expected winnings for the game described, we need to calculate the expected value of one roll of the die based on the outcomes and their corresponding probabilities and payoffs. This is a classic example of a discrete probability distribution problem where the random variable X represents the winnings from one roll of the die.
There are two winning outcomes, rolling a four and rolling a five, each of which has a probability of 1/6 and a payoff of 8 dollars. There are four losing outcomes, rolling a one, two, three, or six, each with the same probability of 1/6 and a loss of 4 dollars.
Therefore, the expected value E(X) is calculated as follows:
P(rolling a 4 or 5) = 1/6 for each, so 2/6 combined since the die is fair.P(rolling any other number) = 4/6 combined, since there are four other possibilities.E(X) = (2/6) * 8 + (4/6) * (-4) = (16/6) - (16/6) = 0
So the expected winnings for this game are 0 dollars, which means that, on average, a player neither wins nor loses money in the long term.
Which statement about the solution of the inequality k<-3 1/4 is true?
The number 7.1 is not a solution to the inequality because -3 1/4 is located to the right of 7.1 on the number line.
The number 0.9 is not a solution to the inequality because -3 1/4 is located to the right of 0.9 on the number line.
The number –3 is a solution to the inequality because –3 is located to the left of -3 1/4 on the number line.
The number -8.4 is a solution to the inequality because -3/14 is located to the left of -3 1/4 on the number line.
Answer: Last option
The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.
Step-by-step explanation:
Note that: [tex]-3\frac{1}{4} =-3-\frac{1}{4} =-3.25[/tex]
The inequality is:
[tex]k<-3 \frac{1}{4}[/tex]
The inequality is:
This means that the inequality includes all values of the number line that are less than -3.25 or that are to the left of -3.25
__-8.4_________-3.25_-3____0___0.9____________7.1__
Note that the number -8.4 is less than -3.25, because it is to its left on the number line.
Then the correct statement is:
The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.
Answer:
the last option!!!
Step-by-step explanation:
i took the unit test
f(x)=e^2x-4
Determine inverse of given function
Answer:
[tex]f^{-1}(x)=\frac{1}{2}ln(x)+2[/tex]
Step-by-step explanation:
Start by changing the f(x) into a y. Then switch the x and the y. Then solve for the new y. Like this:
[tex]y=e^{2x-4}[/tex] becomes
[tex]x=e^{2y-4}[/tex]
To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides. Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.
[tex]ln(x)=ln(e)^{2y-4}[/tex]
When the ln and the e cancel out we are left with
ln(x) = 2y - 4. Add 4 to both sides to get
ln(x) + 4 = 2y. Divide both sides by 2 to get
[tex]\frac{1}{2}ln(x) + 4 = y[/tex].
Since that is the inverse of y, we can change the y into inverse function notation:
[tex]f^{-1}(x)=\frac{1}{2}ln(x)+4[/tex]
Final answer:
To find the inverse function of f(x) = e²ˣ - 4, you switch x and y, solve for the new y, and arrive at the inverse function f^-1(x) = (1/2) * ln(x + 4).
Explanation:
To find the inverse function of f(x) = e²ˣ - 4, we first need to switch the roles of x and f(x), and then solve for the new x. Here are the steps:
Replace f(x) with y to get y = e²ˣ - 4.Switch x and y to get x = [tex]e^{(2y)} - 4[/tex].Add 4 to both sides to isolate the exponential on one side: x + 4 = [tex]e^{(2y)[/tex].Take the natural logarithm of both sides to get ln(x + 4) = 2y.Divide both sides by 2 to solve for y: y = (1/2) * ln(x + 4).So, the inverse function of f(x) = e²ˣ - 4 is f-1(x) = (1/2) * ln(x + 4).
a 47-foot-long piece of pipe is to be cut into three pieces. The second piece is three times as long as the first piece, and the third piece is two feet more than five times the length of the first piece. What is the length of the longest piece?
A. 5 feet
B. 15 feet
C. 27 feet
D. 32 feet
Answer:
27 ft
Step-by-step explanation:
I hope I helped
Answer:
C
Step-by-step explanation:
We need to write this in an algebraic form.
Let's name x the first piece of pipe. If the second piece is three times as long as the first piece, this would be represented as 3x.The third piece is two feet more than five times the first piece, this would be represented as 5x + 2Lastly, the three pieces sum up 47 foot.Therefore, the equation we would have is: [tex]x+3x+5x+2=47\\9x+2=47\\9x=45\\x=45/9\\x=5[/tex]
Therefore, the first piece is 5 feet long.The second piece is 5(3) = 15 feet long.The third piece is 5(5) + 2 = 27 feet long.Thus, the longest piece is 27 feet long.
Using the distributive property to find the product (y — 4)(y2 + 4y + 16) results in a polynomial of the form y3 + 4y2 + ay – 4y2 – ay – 64. What is the value of a in the polynomial?
Answer:
a=16
Step-by-step explanation:
Given
(y-4)(y^2+4y+16)
To find the value of a in the resulting polynomial we have to solve the given expression
=y(y^2+4y+16)-4(y^2+4y+16)
= y^3+4y^2+16y-4y^2-16y-64
To find the value of a, both the polynomials will be compared
y^3+4y^2+16y-4y^2-16y-64
y^3+4y^2+ay-4y^2-ay-64
Comparing the coefficients of both polynomials gives us that
a=16
So, the value of a is 16 ..
Assume that the price of a combo meal is the same price as purchasing each item separately. Find the price of a pizza, a coke, and a bag of chips.
Answer:
pizza: $4, coke: $3, chips: $2
Step-by-step explanation:
Lets make the price of a pizza=p a coke= k and a bag of chips=c
then we have the following equations
p+k+c=9
p+2k=10
2p+2c=12
Because p is common in all the equations we shall make it the subject of each equation.
p=9-(k+c)...........i
p=10-2k..............ii
p=6-c...................iii
We then equate i and iii
9-(k+c)=6-c
9-k-c=6-c
putting like terms together we get:
9-6=-c+c+k
1 coke, k=$3
replacing this value in equation ii
we get p=10-2(3)
p=10-6= 4
1 pizza, p=$4
replacing this value in equation iii
4=6-c
c=6-4
=2
a bag of chips, c=$2
Thus, a pizza, a coke and a bag of chips= pizza: $4, coke: $3, chips: $2
Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo.
What were the dimensions of the original photo?
11 inches by 11 inches
5 inches by 5 inches
3 + inches by 3 + inches
3 inches by 3 inches
Answer:
11 inches by 11 inches
Step-by-step explanation:
The dimensions of the original photo were 11 inches by 11 inches.
We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.
In order to solve for x, we shall first take square roots on both sides of the equation;
The square root of (x – 3)^2 is simply (x - 3).
The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.
Therefore, we have the following equation;
x - 3 = 8
x = 8 + 3
x = 11
Answer:
Option 1: 11 inches by 11 inches
Step-by-step explanation:
Simplify by using factoring: (2a+6b)(6b−2a)−(2a+6b)^2
Answer:
-8a(a+3b)
Step-by-step explanation:
(2a+6b)(6b−2a)−(2a+6b)^2
(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}
2(a+3b) (6b-2a-2a-6b)
2(a+3b) (-4a)
-2(a+3b) x 4a
-2 x 4a (a+3b)
-8a(a+3b)
The simplified expression is -8a² - 24ab.
Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2
First, let's expand the squared term (2a + 6b)^2:
(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)
Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:
(2a + 6b)[(6b - 2a) - (2a + 6b)]
Now, simplify the expression inside the brackets:
(2a + 6b)[6b - 2a - 2a - 6b]
Combining like terms within the brackets:
(2a + 6b)[-4a]
Now, multiply the remaining terms:
-4a(2a + 6b)
-8a² - 24ab
Therefore, the simplified expression is -8a² - 24ab.
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Please help last question
Answer:
The total is 8.
And the total of not green is 6
so the probability is 6/8 or you can write as
3/4
Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
This problem has been solved!See the answerVerify that the line intergral and the surface integral of Stokes Theorem are equal for the following vector field, surface S and closed curve C. Assume that C has counterclockwise orientation and S has a consistent orientation.F= < x,y,z>; S is the paraboloid z = 13 - x^2 - y^2, for 0 less than or equal z less than or equal 13 and C is the circle x^2 + y^2 = 13 in the xy plane.
Line integral: Parameterize [tex]C[/tex] by
[tex]\vec r(t)=\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle[/tex]
with [tex]0\le t\le2\pi[/tex]. Then
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle\cdot\langle-\sqrt{13}\sin t,\sqrt{13}\cos t,0\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}0\,\mathrm dt=\boxed 0[/tex]
Surface integral: By Stokes' theorem, the line integral of [tex]\vec F[/tex] over [tex]C[/tex] is equivalent to the surface integral of the curl of [tex]\vec F[/tex] over [tex]S[/tex]:
[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]
The curl of [tex]\langle x,y,z\rangle[/tex] is 0, so the value of the surface integral is 0, as expected.
Show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1. This one of the ways to define the memoryless property of the geometric distribution. It states the following: given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.
Since [tex]X\sim\mathrm{Geom}(p)[/tex], [tex]X[/tex] has PMF
[tex]P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\in\{1,2,3,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]
By definition of conditional probability,
[tex]P(X=n+k\mid X>n)=\dfrac{P(X=n+k\text{ and }X>n)}{P(X>n)}[/tex]
[tex]X[/tex] has CDF
[tex]P(X\le x)=\begin{cases}0&\text{for }x<1\\1-(1-p)^x&\text{for }x\ge1\end{cases}[/tex]
which is useful for immediately computing the probability in the denominator:
[tex]P(X>n)=1-P(X\le n)=(1-p)^n[/tex]
Meanwhile, if [tex]X=n+k[/tex] and [tex]k\ge1[/tex], then it's always true that [tex]X>n[/tex], so
[tex]P(X=n+k\text{ and }X>n)=P(X=n+k)=(1-p)^{n+k-1}p[/tex]
Then
[tex]P(X=n+k\mid X>n)=\dfrac{(1-p)^{n+k-1}p}{(1-p)^n}=(1-p)^{k-1}p[/tex]
which is exactly [tex]P(X=k)[/tex] according to the PMF.
The memoryless property states that given there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.
Explanation:To show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1, we use the memoryless property of the geometric distribution. The memoryless property states that given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k. So, we have P(X = n + k|X > n) = P(X = k).
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Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x) = 10/x , a= -2f(x) = \sum_{n=0}^{\infty } ______Find the associated radius of convergence R.R = ______
Rewrite [tex]f[/tex] as
[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]
and recall that for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],
[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]
Then the radius of convergence is 2.
The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.
Explanation:Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.
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Four research teams each used a different method to collect data on how fast a new iron skillet rusts. Assume that they all agree on the sample size and the sample mean (in days). Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.
A. Confidence Level: 99.7%; Confidence Interval: 40 to 40
B. Confidence Level: 95%; Confidence Interval: 40 to 50
C. Confidence Level: 68%; Confidence Interval: 43 to 47
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Answer:
D. Confidence Level: 95%; Confidence Interval: 42 to 48
Step-by-step explanation:
48-42=6
6/2=3
3 is smallest
I tested A and got it incorrect so D is the awnser
Confidence Level: 95%; Confidence Interval: 42 to 48. Then the correct option is D.
How to interpret the confidence interval?Suppose the confidence interval at P% for some parameter's values is given by x ± y.
That means that the parameter's estimated value is P% probable to lie in the interval
[x - y, x + y]
Four research teams each used a different method to collect data on how fast a new iron skillet rusts.
Assume that they all agree on the sample size and the sample mean (in days).
Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.
Then we have
48 - 42 = 6
Then we have
6/2=3
3 is smallest
Then the correct option is D.
Learn more about confidence intervals here:
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"Find four numbers proportional to the numbers 2, 4, 5, and 6 if the difference between the sum of the two last numbers and the sum of the first two numbers is equal to 4.8."
Answer:
1.92, 3.84, 4.8, 5.76
Step-by-step explanation:
In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.
You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.
Then the numbers are ...
0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}
Answer:
[tex]\boxed{\text{1.92, 3.84, 4.80, and 5.76}}[/tex]
Step-by-step explanation:
The numbers must be in the ratio 2:4:5:6.
Let's call them 2x, 4x, 5x, and 6x. Then
5x + 6x = 11x = sum of last two numbers
2x + 4x = 6x = sum of first two numbers
According to the condition,
11x – 6x = 4.8
5x = 4.8
x = 0.96
2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76
The numbers are [tex]\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}[/tex]
Check:
(4.80 + 5.76) – (1.92 + 3.84) = 4.8
10.56 – 5.76 = 4.8
4.8 = 4.8
OK.
Write the equation 8y = x – 0.8 in standard form. Identify A, B, and C.
480x + 5y = –48 where A = 480, B = 5, and C = 96
480x – 1y = –48 where A = 480, B = –5, and C = 96
5x – 480y = 48 where A = 5, B = –480, and C = 96
1x + 96y = 9.6 where A = 1, B = –96, and C = 0.8
Answer:
[tex]5x-40y=4[/tex]
Step-by-step explanation:
we know that
The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers
In this problem we have
[tex]8y=x-0.8[/tex]
Multiply by 5 both sides
[tex]40y=5x-4[/tex]
Adds both sides 4
[tex]40y+4=5x[/tex]
Subtract 40y both sides
[tex]4=5x-40y[/tex]
Rewrite
[tex]5x-40y=4[/tex] ----> equation of the line into standard form
A=5
B=-40
C=4
please help
must show work
number 6
and
number8
Answer:
6 is -3
8 is -5
Step-by-step explanation:
3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. The Radius is 7 inches and the Height is 12.
The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.
Volume of cone = 3.14 x 7^2 x 12/3
Volume of cone = 3.14 x 49 x 4
Volume of cone = 615.44 cubic inches.
The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)
Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)
= 1/2 x 4/3 x 3.14 x 343
= 718.01 cubic inches.
Total volume = 615.44 + 718.01 = 1333.45 cubic inches.
Rounded to the nearest tenth = 1,333.5 cubic inches.
"Solve the problem of exponential growth. According to the U.S. Census Bureau, the population of the United States in 2010 was 308 million. This is a 9.6% increase over the 2000 count. Assuming this continued what would the population be in 2030?"
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million
Answer:
370 million
Step-by-step explanation:
In the 10 years from 2000 to 2010, the population was multiplied by the factor ...
100% + 9.6% = 109.6% = 1.096
In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:
2030 population = (308 million)·(1.096²) ≈ 370 million