use the limit comparison test to determine the convergence or divergence of the series. [infinity] 1 n n4 7 n = 1
Answers
The limit is a finite positive number, and the series ∑ (1/n^3) is a convergent p-series (p = 3 > 1), by the limit comparison test, the original series ∑ (n/(n^4+7)) also converges.
How to tell if a series is diverging or convergent:
∑ \((n/(n^4+7))\), from 1 to infinity, n
With the series, we'll apply the limit comparison test.
∑ \((1/n^3)\), from 1 to infinity, n
Considering the ratio of the two series at their limit as n approaches infinity:
lim n→∞ \((n/(n^4+7))/(1/n^3)\)
= lim n→∞ \(n^4/(n^4+7)\)
= 1
Since the series and the limit are both finite positive numbers, ∑ \((1/n^3)\) is a convergent p-series (p = 3 > 1), and according to the limit comparison test, the initial series ∑ \((n/(n^4+7))\) also comes together.
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Related Questions
Ahab pays 1.15 x 10^3 dollars for one year's tuition ay naylor's university his sister attends north central university and pays 2.8 x 10^3 dollars in tuition for her first year what is the difference in tuition paid by ahab and his sister? answer in scientific notation without units the coefficient may be exact or rounded to 2 decimal places
Answers
Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Review the following subtraction rules and properties:
The subtraction identity property (also known as the zero subtraction rule): Any number minus zero is equal to itself. \((2-0=2)\)The rule of subtraction by one: any number minus one will decrease that number by one. \((5- 1 = 4)\)Rule of subtraction number minus itself: any number minus itself is equal to zero. \((2 - 2 = 0)\)Number minus the number immediately before the Subtraction rule: any number minus the number immediately before it is equal to one. \((3 -2 = 1)\)Inverse operation: reverses the effect of another operation. Subtraction reverses addition. (Because \(3 + 2 = 5\), then \(5 - 2 = 3\) and \(5 - 3 = 2\))Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year
To find: Difference in tuition fees paid by Ahab and his sister?
Solution:
To find the difference in their fees we have to perform simply normal subtraction
Subtract the fees of his sister from Ahab's fees which is as follows:
\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)
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Construct a 90% confidence interval for the population mean you. Assume the population has a normal distribution a sample of 15 randomly selected math majors had mean grade point average 2.86 with a standard deviation of 0.78
Answers
The 90% confidence interval is: (2.51, 3.22)
Confidence interval :It is a boundary of values which is eventually to comprise a population value with a certain degree of confidence. It is usually shown as a percentage whereby a population means lies within the upper and lower limit of the provided confidence interval.
We have the following information :
Number of students randomly selected, n = 15.Sample mean, x(bar) = 2.86Sample standard deviation, s = 0.78Degree of confidence, c = 90% or 0.90The level of significance is calculated as:
\(\alpha =1-c\\\\\alpha =1-0.90\\\\\alpha =0.10\)
The degrees of freedom for the case is:
df = n - 1
df = 15 - 1
df = 14
The 90% confidence interval is calculated as:
=x(bar) ±\(t_\frac{\alpha }{2}\), df \(\frac{s}{\sqrt{n} }\)
= 2.86 ±\(t_\frac{0.10 }{2}\), 14 \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 1.761 × \(\frac{0.78}{\sqrt{15} }\)
= 2.86 ± 0.3547
= (2.51, 3.22)
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Consider the system of linear equations. =9.0 x y=9.0 0.50 0.20=3.00 0.50x 0.20y=3.00 find the values of x and y
Answers
The values of x and y in the given system of equations are x = 4.00 and y = 5.00. These values are obtained by solving the system using the method of substitution.
The given system of linear equations is:
0.50x + 0.20y = 3.00 ...(Equation 1)
x + y = 9.00 ...(Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution:
From Equation 2, we can express x in terms of y:
x = 9.00 - y
Substituting this expression for x in Equation 1, we have:
0.50(9.00 - y) + 0.20y = 3.00
Expanding and simplifying:
4.50 - 0.50y + 0.20y = 3.00
-0.30y = -1.50
Dividing both sides by -0.30:
y = -1.50 / -0.30
y = 5.00
Now, substitute this value of y back into Equation 2 to find x:
x + 5.00 = 9.00
x = 9.00 - 5.00
x = 4.00
Therefore, the values of x and y in the given system of equations are x = 4.00 and y = 5.00.
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Suppose that there are 2n + 1 airports where n is a positive integer. The distances between any two airports are all different. For each airport, there is exactly one airplane departing from it, and heading towards the closest airport. Prove by induction that there is an airport which none of the airplanes are heading towards.
Answers
The method of induction is a mathematical proof technique that involves showing that a statement holds for a base case, and then showing that if it holds for n, it also holds for n+1. This process is repeated until the statement is shown to hold for all positive integers.
This statement can be proven by induction.
Base Case:
For n = 1, there are 3 airports. Let the 3 airports be A, B, and C. If an airplane from airport A is heading towards airport B, then the airplane from airport B must be heading towards airport C, and the airplane from airport C must be heading towards airport A. Hence, there is no airport that none of the airplanes are heading towards.
Inductive Step:
Assume that the statement holds for n = k, where k is a positive integer.
We need to prove that the statement holds for n = k + 1, where there are 2(k + 1) + 1 = 2k + 3 airports.
Let the 2k + 3 airports be A1, A2, ..., A2k + 3. Without loss of generality, let the airplane from airport A1 be heading toward airport A2.
Since the distances between any two airports are all different, we have two cases to consider:
If there exists an airport Ai, such that Ai is the closest airport to A1, then airplanes from Ai must be heading towards A1.
If there is no airport Ai that is closest to A1, then there must be the closest pair of airports, say Ai and Aj, such that Ai is the closest to A1 and Aj is the closest to Ai.
In the first case, none of the airplanes are heading towards Ai, and in the second case, neither Ai nor Aj is the closest airport to any other airport. Hence, in both cases, there is an airport that none of the airplanes are heading towards.
By induction, the statement holds for all positive integers n.
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(Note that most of the answers are algebraic expressions involving t) A car starts on a trip and travels at a speed of 55 mph. Two hours later, a second later starts on the same trip and travels at a speed of 55 mph. When the second car has been on the road trip for t hours, the first car has traveled _____ miles and the second car has traveled ______ miles.
Answers
Let t represent the time that the second car has been on the road. If it started 2 hours after the first car started, it means that the time that the first car has been on the road is
(t + 2) hours
Recall,
Distance = speed x time
From the information given,
speed of first car = 55
Thus,
distance travelled by first car = 55(t + 2)
speed of second car = 65
Distance travelled by second = 65t
Thus,
The first car has traveled 55(t + 2) miles and the second car has traveled 65t miles
(4, -3); slope = -1
Answers
Answer:
y + 3 = - x + 4 or y = - x + 1Step-by-step explanation:
Assume you are looking for an equation of the line passing through (4, -3) and having a slope - 1.
Use point-slope form:
y - y₁ = m(x - x₁)y - (-3) = - 1(x - 4)y + 3 = - x + 4or
y = - x + 1Equation in point slope form
y-y1=m(x-x1)y+3=-1(x-4)y+3=4-xy=-x+1If 70 % of A is 3.15 then what is the value of A
Answers
Answer:
4.5
Step-by-step explanation:
the study would use a . the study would use simple random sampling because it would be easy to randomly select of . b. the study would use a . the study would use cluster sampling because the of fall into naturally occurring subgroups. c. the study would use a . the study would use stratified sampling because it would be important to have members from each segment of the population. d. the study is a , because the population is for it to be practical to record all of the responses.
Answers
The study would use a simple random sampling because it would be easy to randomly select. The study would use cluster sampling because the of fall into naturally occurring subgroups. The study would use stratified sampling because it would be important to have members from each segment of the population.
The study is a sample survey, because the population is for it to be practical to record all of the responses.
a. The study would use a simple random sampling because it would be easy to randomly select members of the population. Simple random sampling is a type of probability sampling that is used when the population is homogenous and every member has an equal chance of being selected for the sample.
b. The study would use cluster sampling because the members of the population fall into naturally occurring subgroups. Cluster sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into naturally occurring subgroups.
c. The study would use stratified sampling because it would be important to have members from each segment of the population. Stratified sampling is a type of probability sampling that is used when the population is heterogeneous and can be divided into segments or strata based on certain characteristics.
d. The study is a sample survey, because the population is too large for it to be practical to record all of the responses. Sample survey is a type of survey that collects data from a sample of the population, rather than the entire population. This is often done when the population is too large or when it is not practical to survey the entire population.
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12 cm
8 cm
12 cm
8 cm
h
12 cm
12 cm
Find the
perimeter.
USE A
Answers
Step-by-step explanation:
Just add all of the numbers in the diagram = 64 cm
Solve for x :-
\( \: \)
\({ \large{ \rm{ \frac{7x + 14}{3} - \frac{17 - 3x}{5} = 6x - \frac{4x + 2}{3} - 5 }}}\)
\( \rule{200pt}{5pt}\)
Answers
We need to find value of x from the equation, so let write the equation first;
\({:\implies \quad \sf \dfrac{7x+14}{3}-\dfrac{17-3x}{5}=6x-\dfrac{4x+2}{3}-5}\)
Taking LCM both sides ;
\({:\implies \quad \sf \dfrac{35x+70-(51-9x)}{15}=\dfrac{18x-(4x+2)-15}{3}}\)
Multiplying both sides by 15 and simplifying ;
\({:\implies \quad \sf 35x+70-51+9x=5(18x-4x-2-15)}\)
\({:\implies \quad \sf 44x+19=5(14x-17)}\)
\({:\implies \quad \sf 44x+19=70x-85}\)
\({:\implies \quad \sf 70x-44x=19+85}\)
\({:\implies \quad \sf 26x=104}\)
\({:\implies \quad \sf x=\dfrac{104}{26}=\boxed{\bf 4}}\)
Hence, The required answer is 4
Given: {(7x + 14)/3} - {(17 - 3x)/5} = 6x - {(4x + 2)/3} - 5
Asked: Find the value of x = ?
Explanation: Given equation is {(7x + 14)/3} - {(17 - 3x)/5} = 6x - {(4x + 2)/3} - 5
⇛{(7x + 14)/3} - {(17 - 3x)/5} = {(6x)/1} - {(4x + 2)/3} - (5/1)
⇛{(7x*5 + 14*5 - 17*3 + 3x*3)/15} = {(6x*3 - 4x*1 - 2*1 - 5*3)/3}
⇛{(35x + 70 - 51 + 9x)/15} = {(18x - 4x - 2 - 15)/3}
⇛{(35x + 9x + 70 - 51)/15} = {(18x - 4x - 2 - 15)/3}
⇛{(44x + 19)/15} = {(14x - 17)/3}
⇛[{1/15}(44x + 19)] = [{1/3}(14x - 17)}]
⇛{(44x + 19)/15} = {(14x - 17)/3}
Since (a/b) = (c/d) ⇛a(d) = b(c) ⇛ad = bc
Where, a = 44x + 19, b = 15
c = 14x - 17 and d = 3
On applying cross multiplication then
⇛3(44x + 19) = 15(14x - 17)
Multiply the numbers outside of the bracket with numbers in the bracket.
⇛132x + 57 = 210x - 255
Shift the variable value on LHS and constant value on RHS.
⇛132x - 210x = -255 - 57
Subtract the values on LHS and RHS.
⇛(-78x) = (-312)
Shift the number (-78) from LHS to RHS.
⇛x = {(-312)/(-78)
Simplify the RHS fraction to get the final value of x.
⇛x = 4/1
Therefore, x = 4
Answer: Hence, the value of x for the given problem is 4.
EXPLORE MORE:
Verification:
Check whether the value of x for the given problem is true or false.
If x = 4 then LHS of the equation is
{(7x + 14)/3} - {(17 - 3x)/5}
= [{7(4) + 14}/3] - [{17 - 3(4)}/5]
= {(7*4 + 14)/3} - {(17 - 3*4)/5}
= {(28 + 14))3} - {(17 - 12)/5}
= (42/3) - (5/5)
= (42/3) - 1
= (42/3) - (1/1)
= {(42 - 1*3)/3
= {(42 - 3)/3}
= (39/3)
= 13/1
= 13
And RHS = 6x - {(4x + 2)/3} - 5
= 6(4) - [{4(4) + 2}/3] - 5
= 24 - {(16 + 2)/3} - 5
= 24 - (18/3) - 5
= 24 - (6/1) - 5
= (24/1) - (6/1) - (5/1)
= (24*1 - 6*1 - 5*1)/1
= (24 - 6 - 5)/1
= (24 -11)/1
= 13/1
= 13
On comparing with both the sides, we notice that LHS = RHS is true for x = 4
Hence, verified.
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Solve the equation: 5(3p - 5) + 4p = 5p - 6( p + 4)....
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 4 large boxes and 8 small boxes has a total weight of 125 kilograms. A delivery of 2 large boxes and 3 small boxes has a total weight of 57 kilograms. How much does each type of box weigh?
Answers
Answer:
weight of large box = x kg=18.25kg
weight of small box =y kg=15.5kg
Step-by-step explanation:
weight of large box = x kg
weight of small box =y kg
2 large boxes and 3 small boxes has a total weight of 83 kilograms.
2x+3y=83--------- eq 1
4 large boxes and 8 small boxes has a total weight of 197 kilograms.
4x+8y =197 -------eq 2
multiply eq 1 with -2
-4x-6y =-166
now add both equations
-4x-6y=-166
4x+8y=197
______________________
2y= 31
y=15.5
substitute value of y=17 in eq 1
2x+3y=83
2x+3(15.5)=83
2x+46.5=83
2x =36.5
x=18.25
weight of large box = x kg=18.25kg
weight of small box =y kg=15.5kg
hope this helps :)
At the bank teller's window, arrivals and service times are randomly distributed (Poisson and exponential distributions, respectively). There is only one teller at the window. If the arrival rate is 8 customers per hour, and the service rate is 15 customers per hour, what is the utilization of the teller, as a percentage? (It is a single channel, single server, single phase, unlimited waiting space model). (calculate answer to two decimal places)
Answers
The utilization of the teller is approximately 53.33%.
To calculate the utilization of the teller, we need to compare the arrival rate and the service rate. The utilization represents the fraction of time the server (teller) is busy serving customers.
The arrival rate is given as 8 customers per hour, which means that, on average, 8 customers arrive at the teller's window in one hour. This follows a Poisson distribution.
The service rate is given as 15 customers per hour, indicating that, on average, the teller is able to serve 15 customers in one hour. The service times follow an exponential distribution.
Utilization is calculated as the ratio of the arrival rate to the service rate. In other words:
Utilization = Arrival rate / Service rate
Substituting the given values:
Utilization = 8 / 15 ≈ 0.5333
To express this as a percentage, we multiply the result by 100:
Utilization = 0.5333 * 100 ≈ 53.33%
Therefore, the utilization of the teller in this scenario is approximately 53.33%. This means that, on average, the teller is occupied serving customers about 53.33% of the time, and the remaining time is idle or available for serving new customers.
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a study measuring the effects of a new diuretic medication records hourly urine output of subjects. this measure represents which level of measurement? group of answer choices ratio interval nominal ordinal
Answers
When measuring the effects of a new diuretic medication, hourly urine output represents the ratio level of measurement.
What is ratio level of measurement?
Ratio level of measurement is a type of measurement that features a true zero point, meaning that the value 0 represents the absence of the characteristic being measured.
Some examples of ratio level measurements include weight, height, length, distance, speed, and many others. In this case, the hourly urine output of subjects is measured to determine the effects of a new diuretic medication.
The hourly urine output is a ratio measurement because it has a true zero point, which is the absence of urine output. In other words, if there is no urine output, the value would be 0, which represents the absence of the characteristic being measured.
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If x/y + y/x = -1 , find the value of x^3 - y^3
Answers
Answer:
0
Step-by-step explanation:
Multiplying the first equation by xy, we have ...
x^2 +y^2 = -xy
Factoring the expression of interest, we have ...
x^3 -y^3 = (x -y)(x^2 +xy +y^2)
Substituting for xy using the first expression we found, this is ...
x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0
The value of x^3 -y^3 is 0.
"pioneer logs" is a brand of children's toy which is sold in large cylindrical container.
diameter = 29.5cm
height= 27.5cm
what is the surface area of the lateral side ( the curved part)?
Answers
Answer:
πd X 27.5
π X 29.5 X 27.5= 2548.61704
2548.62cm
Can you please help ASAP. It is very easy
Answers
Hello!
Let the number be x.
We multiply it by 5:
5x
Subtract 3:
5x-3
Hope it helps. Ask me if you have any query.
~An excited gal
\(MagicalNature\) here to help
Alright I've tried everything to try and do this but I'm still struggling. Help. Find the value of x (32 points clear explanation, please)
Answers
Answer:
C. 37.5
Step-by-step explanation:
From inspection of the given triangle, we can see that the straight line that divides the triangle into two smaller triangles is an angle bisector since it divides the angle into two congruent angles.
Angle Bisector Theorem
An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.
\(\implies x:15=40:16\)
Solve for x:
\(\implies \dfrac{x}{15}=\dfrac{40}{16}\)
\(\implies \dfrac{x}{15}=2.5\)
\(\implies x=2.5\times 15\)
\(\implies x=37.5\)
A person invests 8000 dollars in a bank. The bank pays 7% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 15600 dollars?
nt
A=P(1+
)
п
Answers
Answer:
The person must leave the money for around 9.9 years.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Compounded Interest Rate Formula: \(\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg)^{nt}\)
P is principle amount (initial amount)r is interest raten is compounded ratet is time (in years)Algebra II
Logarithms
Logarithmic Property [Exponential]: \(\displaystyle \log (a^b) = b \cdot \log (a)\)Step-by-step explanation:
Step 1: Define
Identify variables.
A = $15600
P = $8000
r = 0.07
n = 1
Step 2: Find Time Elapsed
Substitute in variables [Compounded Interest Rate Formula]: \(\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{1(t)}\)[Exponents] Simplify: \(\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{t}\)(Parenthesis) Simplify: \(\displaystyle 15600 = 8000(1.07)^{t}\)[Division Property of Equality] Divide 8000 on both sides: \(\displaystyle \frac{39}{20} = (1.07)^{t}\)[Equality Property] Log both sides: \(\displaystyle \log \frac{39}{20} = \log (1.07)^{t}\)Simplify [Logarithm Property - Exponential]: \(\displaystyle \log \frac{39}{20} = t \log (1.07)\)[Division Property of Equality] Isolate t: \(\displaystyle t = \frac{\log \frac{39}{20}}{\log 1.07}\)Evaluate: \(\displaystyle t = 9.87057\)Round: \(\displaystyle t \approx 9.9\)∴ it will take the person approximately 9.9 years investing $8,000 with a 7% interest rate compounded annually for them to obtain $15,600.
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Topic: Algebra II
Why derivative of COSX is?
Answers
Answer:
-SINX
Step-by-step explanation:
Determine the number that will complete the square to solve each equation after the constant term has been written on the right side. Do not actually solve. 3 w^{2}-w-24=03w 2 −w−24=0
Answers
The number that will complete the square to solve equation is 1/36.
What is completing the square?
For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form
ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Consider, the given polynomial
3w^2 - w - 24 = 0
Rewrite the polynomial in the form ax^2 + bx = c
Add 24 on both sides,
3w^2 - w - 24 + 24 = 24
⇒ 3w^2 - w = 24
Divide both sides by 3,
\(w^2-\frac{1}{3}w = 8\)
To complete the square x^2 + bx, we add \((\frac{b}{2} )^2\)
Here, b = -1/3
So, \((\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}\)
Adding to both sides of the equation, we have
\(w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}\)
Hence, the number that will complete the square to solve an equation is 1/36.
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In both the Vendor Compliance at Geoffrey Ryans (A) and
Operational Execution at Arrows Electronics there are problems and
challenges. Integrate the problems and challenges from both
cases.
Answers
In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.
One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.
Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.
Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.
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Rút gọn biểu thức √81a^6b^2
Answers
Answer:
English.........plzpzl
measure of angle A = 5 X, measure of angle B = 2X, measure of angle C = 110 degrees
i need help finding x (its a triangle btw)
Answers
7x=70
x=10
Answer:
A = 50
B = 20
C = 110
Step-by-step explanation:
A triangle is equal to 180°
In order to find the measure of each angle, add angle A, B, and C to get 180°
If angle A = 5x, angle B = 2x and angle C = 110 then 5x + 2x + 110 = 180°
To find each angle, first solve for x:
5x + 2x + 110 = 180° start by adding like terms
7x + 110 = 180° now subtract 110 from 180
7x = 70 finally divide 7 from 70
x = 10
To find each individual angle, substitute x with 10. For example:
A = 5x
A = 5(10)
A = 50
B = 2x
B = 20
C = 110
If you were to add A, B, and C it should equal 180°
110 + 20 + 50 = 110
Which picture does not belong? Explain.
Answers
Answer:
D
Step-by-step explanation:
D because the exterior angle in a triangle must equal the two opposite interior angles not one
v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answers
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
severe difficulty in making mathematical calculations as a result of a brain disorder
Answers
Dyscalculia is a learning disorder that affects a person’s ability to do the math.
A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.
The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.
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Polling agency is investigating the voter support for_ regions have equal number of voters ballot measure in an upcoming city election The City is divided in two in them: The agency will select _ random regions Region A and region B. Both population proportion of voters who would sample of 500 voters from one region, Region A of the city Assume that support the ballot measure in Region A is 0. 47. The What is the probability that the proportion of voters in the sample of Region who support the ballot measure greater than 0. 50 ? The polling agency will take another sample from different region, Region B, of the city: The the population proportion of voters who would agency plans to select random sample of 400 voters. Assume that support the ballot measure in Region B is 0. 51 What is the probability that , measure might pass?
Answers
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is approximately 0.1736 or 17.36%. The probability that the ballot measure might pass in Region B can be calculated using a confidence interval approach.
The confidence interval for the population proportion of voters who support the ballot measure in Region B:
CI = p ± z × SE
where p is the sample proportion, z is the critical value for the desired confidence level (e.g., z=1.96 for 95% confidence), and SE is the standard error of the sample proportion.
the standard error of the sample proportion:
SE = \(sqrt [p ×\frac{(1-p)}{n} ]\) = \(sqrt[0.51 ×\frac{(1-0.51)}{400} ]\) = 0.025
where p is the sample proportion and n is the sample size.
the confidence interval using a 95% confidence level:
CI = 0.51 ± 1.96 0.025 = (0.46, 0.56)
Therefore, we can be 95% confident that the true population proportion of voters who support the ballot measure in Region B falls within the range of 0.46 to 0.56. Since the lower bound of the confidence interval is above 0.50, there is a possibility that the ballot measure might pass in Region B. However, the exact probability would depend on the actual population proportion and the sample size.
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How do I divide decimals?
Answers
Answer: move the point or decimal
Step-by-step explanation: you just remove the decimal that means the point the devide and put it back
40 points, pls help!
Answers
Answer:
A=22a
B=5
C=3x
D=2y
Step-by-step explanation:
11a/6x^2y - 5x/12y^2 +3y/4 = (Ay-Bx^3+(Cy)^2y)/3(Dx)^2
22ay/12x^2y^2 - 5x^3/12x^2y^2 + 9x^2y^3/12x^2y^2=(Ay-Bx^3+(Cy)^2y)/3(Dx)^2
(22ay-5x^3+9x^2y^3)/12x^2y^2=(Ay-Bx^3+(Cy)^2y)/3(Dx)^2
(22ay-5x^3+(3xy)^2y)/3(4x^2y^2)=(Ay-Bx^3+(Cy)^2y)/3(Dx)^2
(22ay-5x^3+(3xy)^2y)/3(2yx)^2=(Ay-Bx^3+(Cy)^2y)/3(Dx)^2
Answers:
A=22a
B=5
C=3x
D=2y
A model boat i 15 inche long if the boat i bulit to a cale of 1 : 250 inche how long i the real boat
define a variable
write a porortion
olve the porportion
anwer with word
Answers
If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.
What does a scale look like in math?The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.
Briefing:The scale of drawing the horse = 1 inch :
Therefore in scale
Horse height in drawing equals one inch
The height of the horse = 250 inche
The original height of the horse = 15 inche
The height in the picture = x inches
To find the height the horse in the picture, we have to use proportion
1 inch : 250 inche = x inches : 15 inche
1 / 250 = x / 15
1 × 15= 250x
250x = 15
x = 15/250
x = 0.06 inches
Therefore, the height of the horse in drawing is 0.06 inches
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