To find the radius of convergence and interval of convergence of the given power series, we need to determine the values of t or x for which the series converges.
The radius of convergence is the distance from the center of the series to the nearest point where the series diverges.
The interval of convergence is the range of values for which the series converges.
11. For the power series Σ(2η-1)\(t^n\), we need to find the radius of convergence. To do this, we can use the ratio test. Taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms, we get:
lim(n→∞) |(2η – 1)\(t^{n+1}\)/(2η – 1)\(t^n\)|
Simplifying, we have:
|t|
The series converges when |t| < 1. Therefore, the radius of convergence is 1, and the interval of convergence is (-1, 1).
13. For the power series Σ\((n+1)!x^n\), we again use the ratio test. Taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms, we have:
lim(n→∞) \(|(n+1)!x^{n+1}/n!x^n|\)
Simplifying, we get:
lim(n→∞) |(n+1)x|
The series converges when the limit is less than 1, which means |x| < 1. Therefore, the radius of convergence is 1, and the interval of convergence is (-1, 1).
15. For the power series Σn=1 n*4*, we can also use the ratio test. Taking the limit as n approaches infinity of the absolute value of the ratio of consecutive terms, we have:
lim(n→∞) |(n+1)4/n4|
Simplifying, we get:
lim(n→∞) |(n+1)/n|
The series converges when the limit is less than 1, which is always true. Therefore, the radius of convergence is infinity, and the interval of convergence is (-∞, ∞).
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Can someone please give me examples of linear, quadratic, Absolute value, square root, cubic, cube root, exponential, logarithmic, and rational function (parent function) equations to help my friend? Please and thank you. I'll give brainliest to the first person who does all of them and get them right.
Answer:
Step-by-step explanation:
Consider the cube root parent function.
( graph in photo below )
Complete the statements to make them true.
A cube root function will ( 1 ) ________ have an x-intercept and ( 2 ) ________ have a y-intercept.
For the parent cube root function, ( 3 ) ____________ located at .
Answer:
1. always
2. always
3. both intercepts are
the explination photos below
Answer:
I got you
\(f(x)=3x+2\)
\(f(x)=4x^2+3x+7\)
\(f(x)=|x+4|\)
\(f(x)=\sqrt{x+12}\)
\(f(x)=6x^3+4x^2-3x-5\)
\(f(x)=\sqrt[3]{3x-5}\)
\(f(x)=2^x\)
\(f(x)=log_3(x)\)
\(f(x)=\frac{x+5}{x-3}\)
Each function is respective to the order of the list given.
Let me know if you want the graphs
a civil engineer is drawing a plan for the location and length of a new underground sewer pipe on a coordinate grid. the pipe on the plan will run from point n ( a , −2) to point p (1, b ) on the coordinate grid. which expression represents the shortest distance between n and p in units? ( a 2)2 (1 − b )2 (1 − a )2 ( b 2)2
The shortest distance between n and p in units = (1 − a )2+ ( b+ 2)2.
The correct option is B.
Distance between two points:The length of line segment connecting any two points is known as their distance from one another. The length of a line segment connecting the two given coordinates can be used to calculate the distance between the points in coordinate geometry.
What is coordinate geometry used for?The study of geometry utilizing coordinate points is referred to as coordinate geometry (or analytic geometry). The distance between two points can be calculated using coordinate geometry, as can the areas of triangles in the Cartesian plane, the midpoints of lines, and more.
According to the given information:The expression that represents this same shortest distance between P and N in units is found to use the distance between two points to be:
\(d=\sqrt{(1-a)^2+(b+2)^2}\)
The distance between two points, (x1,y1) and (x2,y2), is represented by:
\(d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
the distance between the points N(a, -2) and P(1,b) is:
\(\begin{aligned}&d=\sqrt{(1-a)^2+(b-(-2))^2} \\&d=\sqrt{(1-a)^2+(b+2)^2}\end{aligned}\)
The shortest distance between n and p in units = (1 − a )2+ ( b+ 2)2.
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I understand that the question you are looking for is:
a civil engineer is drawing a plan for the location and length of a new underground sewer pipe on a coordinate grid. the pipe on the plan will run from point n ( a , −2) to point p (1, b ) on the coordinate grid. which expression represents the shortest distance between n and p in units?
A. ( a +2)2+ (1 − b )2
B. (1 − a )2+ ( b+ 2)2
Identify three points that are solutions to
each system.
The solutions for the systems of inequalities are:
a) (0, -100), (0, -150), (0, -1000)
b) (0, 50), (0, 55) , (0, 1,204).
How to identify 3 solutions of each system?When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.
The first one is:
y ≤ x - 8
y < -3x - 9
Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:
-100 ≤ 0 - 8 = -8
-100 < - 3*0 - 9 = -9
Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.
For the second system:
y > 5x + 1
y > 3
Let's do the same thing, x = 0 and y gets really large values, like y = 50
50 > 5*0 + 1 = 1 this is true.
50 > 3 this is true.
so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).
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Determine the intersection, union, and complement sets from the given information.
44. U=(2, 4, 6, 8)
A = (2, 4)
B = (6,8)
a. A ∩ B =
b. AUB=
c. (AUB)' =
The intersection, union, and complement sets based on the universal set U = {2, 4, 6, 8}, are;
a. A ∩ B = {∅}
b. A ∪ B = {2, 4, 6, 8}
c. (A ∪ B)' = {∅}
What is a universal set?The universal set is the set to which the other sets are subsets, and one which contains all the elements.
The Universal set is; U = (2, 4, 6, 8)
The set A = (2, 4)
The set B = (6, 8)
Therefore;
a. The set A ∩ B is the set of elements common to both sets A and B
Therefore no elements common to both sets A and B, therefore;
A ∩ B = {∅}
b. The set A ∪ B is the set that contains elements in set A and elements in set B as well as elements in set A ∩ B
The set A ∪ B = {2, 4, 6, 8}
c. The set of the complement of the union of the set A and B is the set that contains elements that are not in the union of set A and B
A ∪ B = {2, 4, 6, 8} = U,
U' = {∅}
Therefore (A ∪ B)' = {∅}
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after a party , there where 4 1/2 pizzas left over. if they are to be split among 9 people, how much pizza will each person take home?
Using fraction formula,
Each person will receive 1/2 part of left over pizzas .
Fraction : In Mathematics, a fraction defined as the part of the whole thing. For example, a cake is divided into 5 equal pieces, then each piece is denoted by ¼.
We have given that,
After party , 4+1/2 pizzas left over .
number of peoples among spliting of pizza happened = 9
Assume there is x pizzas .
left over part = (4+ 1/2 ) = 9/2
ate by other = 1- 9
9/2 pizzas is divided into 9 people's = 9/2 /9
= 1/2
thus , each person will receive 1/2 of left over pizzas i.e( 4+ 1/2 ).
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a physical education teacher fournd that 62 1/2% of the students exceeded the minimum standards. which represents the part of the students who exceeded the standards?
62.5% or 62.5 out of every 100 students exceeded the minimum standards.
The teacher found that 62 1/2% of the students exceeded the minimum standards. To find the part of the students who exceeded the standards, we need to convert the percentage to a decimal.
To do this, divide 62.5 by 100: 62.5 ÷ 100 = 0.625.
This means that 0.625 represents the decimal form of 62 1/2%.
To find the part of the students who exceeded the standards, multiply 0.625 by the total number of students.
For example, if there are 100 students in total, multiply 0.625 by 100: 0.625 x 100 = 62.5.
Therefore, 62.5 represents the part of the students who exceeded the minimum standards.
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a number, y, is equal to twice the sum of a smaller number and 3. the larger number is also equal to 5 more than 3 times the smaller number. which equations represent the situation? 2 x minus y
The final two equations which represent the given situation are:
2x - y = -6 and 3x - y = -5.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a linear equation of two variables.
Suppose,
The larger number is 'y' and the smaller number is 'x'.
First relation,
'y' is equal to twice the sum of a smaller number (x) and 3. So we represent this as:
y = 2(x+3)
y = 2x + 6
2x - y = -6 ............(1)
Second relation,
The larger number (y) is equal to 5 more than 3 times the smaller number (x). So we represent this as:
y = 5 + 3x
3x - y = -5 .............(2)
Hence, the final two equations which represent the given situation are:
2x - y = -6 and 3x - y = -5.
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dave travels from champaign to chicago often for work. he usually flies from champaign to chicago to save time on busy days. depending on the weather in chicago, the flight might be delayed. suppose that there are 3 possible weather conditions in chicago: sunny, rain, and snow with the corresponding probabilies: 50%, 10%, and 40%. when it is sunny in chicago, the flight will be on time 80% of the time. but in bad weather conditions such as rain, the flight will be delayed 10% of the time. even worse, probability of flights being delayed is 40% when it is snowing in chicago. (assume that weather is the only factor determining whether a flight is on time or delayed.) what is probability a randomly selected flight from chicago to champaign is on time? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 non-zero digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer. symbolic expression if the flight is on time, what is the probability that it is snowing in chicago? you can express your answer as a fraction, decimal, or a percentage. if you asnwer in decimal, include at least 3 non-zero digits after the decimal point. if you answer is a percentage, make sure to include a % sign in your answer.
The probability of a randomly selected flight from Chicago to Champaign being on time is 0.73 or 73% and the probability that it is snowing in Chicago given that the flight is on time is approximately 32.88%..
To calculate the probability of a randomly selected flight from Chicago to Champaign being on time, we need to use the law of total probability by considering the probability of each weather condition in Chicago and its corresponding probability of the flight being on time.
We can calculate the probability of the flight being on time when it is sunny in Chicago as follows:
0.5 (probability of sunny weather) x 0.8 (probability of on-time flight in sunny weather) = 0.4
Similarly, we can calculate the probability of the flight being on time when it is rainy and snowy in Chicago:
0.1 (probability of rainy weather) x 0.9 (probability of delayed flight in rainy weather) = 0.09
0.4 (probability of snowy weather) x 0.6 (probability of delayed flight in snowy weather) = 0.24
Then, we can sum up the probabilities of on-time flights under all weather conditions:
0.4 + 0.09 + 0.24 = 0.73
The symbolic expression for the probability that it is snowing in Chicago given that the flight is on time is P(Snowing|On time). We can use Bayes' theorem to calculate this probability as follows:
P(Snowing|On time) = P(On time|Snowing) x P(Snowing) / P(On time)
We have already calculated P(On time) to be 0.73. The probability of the flight being on time when it is snowing in Chicago is 0.6, and the probability of snowing weather is 0.4. Thus, we can substitute these values into the formula:
P(Snowing|On time) = 0.6 x 0.4 / 0.73 = 0.3288 or 32.88%.
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Determine whether each expression is equivalent or not equivalent to 16^t-0.25?
A) 4^2t/4^0.5
B) 16^t/2^4
C) 16^t/2
The sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be examples abοve are equal tο 16t - 0.25.
What is the expressiοn?Mathematical prοcesses like multiplying, dividing, adding, and nοw even deleting are required. If they were merged, the fοllοwing claim wοuld be made: An equatiοn, sοme statistics, and a mathematical fοrmula Values, cοmpοnents, and mathematical prοcesses like additiοns, subtractiοns, reversals, algebraic fοrmulas, and divisiοns make up a statement οf truth. Wοrds and phrases can be rated and analyzed.
Here,
We pοssess 16t – 0.25.
A) The fοrmula 42t/40.5 equals (22t)² / (20.5) = 24t / (20.5) = 16t / (20.5)4 = 16t / 4 = 4(16t).
Expressiοn A is nοt equal because 4(16t) is nοt the same as 16t - 0.25.
B) \((16)^t/2^4 = (2^4)^t / 2^4\)
=> \(2^{4t} / 2^4 = 2^{(4t-4)} = 16^{(t-1)} (t-1).\)
Expressiοn B is not equivalent because 16(t-1) is nοt equal to 16(t - 0.25).
C) \(16^t/2 = (2^4)^t / 2\)
\(= > 2^{4t} / 2 = 2^{(4t-1)} = 16^t \times 0.5.\)
Expression C is nοt equivalent because 16t * 0.5 does not equal 16t - 0.25.
Hence, As a result, nοne of the examples above are equal to 16t - 0.25.
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Answer:
Step-by-step explanation:
Find The Area of the parallelogram...Explain.
Answer:
8x17=136, so the area is 136 inches squared.
Step-by-step explanation:
find the distance traveled in 15 seconds by an object moving with a velocity of v(t)= 20 + 3t feet per second where t is the time in seconds.
Answer:
4 because you divide 3 and 15 by three which gives you 5 then divide 20 by that gives you 4
Given f(x)=x*-x³-6x², for what values of x will f(x) > 0?
The values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.
To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².
First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).
Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.
Next, we analyze the signs of the factors:
1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.
2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.
3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.
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the dimensions of a closed rectangular box are measured as 70 centimeters, centimeters, and centimeters, respectively, with the error in each measurement at most centimeters. use differentials to estimate the maximum error in calculating the surface area of the box.
The maximum error in calculating the surface area of the box is approximately 0.8 cm^2.
f the box.
We can start by using the formula for the surface area of a rectangular box:
S = 2lw + 2lh + 2wh
where S is the surface area, l is the length, w is the width, and h is the height of the box.
Using the given dimensions, we have:
l = 70 cm
w = x cm
h = y cm
To estimate the maximum error in the surface area calculation, we need to find the partial derivatives of S with respect to l, w, and h:
∂S/∂l = 2w + 2h
∂S/∂w = 2l + 2h
∂S/∂h = 2l + 2w
Then, we can use the differentials to estimate the maximum error in each dimension:
∆l = 0 (since there is no error in the length measurement)
∆w = 0.1 cm (given)
∆h = 0.1 cm (given)
Finally, we can use the total differential formula to estimate the maximum error in the surface area calculation:
∆S ≈ (∂S/∂l) ∆l + (∂S/∂w) ∆w + (∂S/∂h) ∆h
Plugging in the partial derivatives and the estimated errors, we get:
∆S ≈ (2x + 2y) * 0 + (2 * 70 + 2y) * 0.1 + (2 * 70 + 2x) * 0.1
Simplifying, we get:
∆S ≈ 4x + 4y + 140
Note that x and y are unknown, but we can assume that they are close to the measured values, so we can take them to be 70 ± 0.1 cm.
Therefore, the estimated maximum error in the surface area calculation is:
∆S ≈ 4(70 ± 0.1) + 4(70 ± 0.1) + 140
∆S ≈ 560 ± 0.8 cm^2
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Jenny Scored a total of 135 points in 5 games. Each game she scored 2 more points than in the previous game. How many points did she score in the 5th game?
Answer:
135 points = 5 games
1 game = 27 points
2×5=10
135+10= 145
the denominator of a fraction is 4 more than the numerator. on subtracting 1 from each the numerator and the denominator, the fraction becomes 1/2. find the original fraction
Answer:
4/9
Step-by-step explanation:
5-1/5+4 is the right answer so yes
Evaluate and solve for the variable and please show your work.
-2=y+5
x – 7 = 4 + 10
–2x + 3x – 5 = 6 – 21
70 = 7m
4 – 14 = 5x
2y + 3y = 4 – 6 – 13
Answer:
Step-by-step explanation:
-2 = y + 5
- y -2 = 5
- y = 5 + 2
- y = 7
y = -7
-2x + 3x – 5 = 6 – 21
x – 5 = 6 – 21
x – 5 = -15
x = -15 + 5
x = -10
70 = 7m
7m = 70
m = 10
4 – 14 = 5x
-10 = 5x
5x = -10
x = -2
2y + 3y = 4 – 6 – 13
5y = 4 – 6 – 13
5y = -15
y = -3
Answer:
I took I quiz and the answers are correct
Step-by-step explanation:
:) :) :) :) :) :) :)
a. If 4b < a
i. Write the general solution.
ii. Classify the origin.
iii. Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)
i. The general solution to the inequality 4b < a can be written as b < a/4, where "b" represents any real number that is less than "a/4". This solution represents all possible values of "b" that satisfy the inequality.
ii. To classify the origin in this context, we need additional information about the variables involved. Without specific values or constraints on "a" and "b", it is not possible to determine the classification of the origin.
iii. In their relationship, the inequality 4b < a indicates that "b" is strictly less than "a/4". This means that the values of "b" are limited and restricted compared to "a". The inequality suggests that "b" cannot be greater than or equal to "a/4". The relationship between "a" and "b" depends on the specific values assigned to them. Qualitatively different possibilities can arise based on the magnitudes and signs of "a" and "b". Further analysis, such as considering eigenvectors, requires additional information or context specific to the problem.
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To make lemonade , Kate uses 1 cup of lemon juice and 2 cups of sugar. If she makes a larger amount of lemonade with 10 cups of sugar, how many cups of lemon juice does she need?
Answer:
5 cups
Step-by-step explanation:
Answer:
1/2 : 1
2 : 4
3 : 6
Notice that every ratio consists of a number and double the number.
For 1/2 cup lemon juice, use 1 cup sugar.
The amount of sugar is twice the amount of lemon juice.
The ratio is 1:2
Since you are told the ratio is 1:r, that means r is 2.
The unit rate is 2 cups sugar per cup of lemon juice.
Step-by-step explanation:
Can someone please help me i'm running out of time please!!!!
Answer:
10 and 1/2 for the first, and 3 and 3/4 for the second
Step-by-step explanation:
∛ 1
_____
8
plisssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss help
Answer:
1/8
Step-by-step explanation:
The cube root of 1 is just 1.
1/8=1/8.
What number is 10 more than 90?
The answer of 10 more than 90 is 100.
The answer of 10 more than 90 is 100 which can be derived using simple mathematical calculations.
To find 5 more than 5, you can add 5 to the original number 5.
10 + 90 = 100
It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.
An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.
Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.
Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.
Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.
Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.
Therefore, The answer of 10 more than 90 is 100.
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Evaluate the expression for b = 3 and c = 5.
b2c − 11 =
Answer:
34Step-by-step explanation:
b = 3 and c = 5Substitute and evaluate:
b²c - 11 =3²*5 - 11 = 9*5 - 11 =45 - 11 =34Answer:
\(b = 3 \ \: \: : c = 5 \\ \\ b {}^{2} c - 11 = \\ \\ \\ {3}^{2} \times 5 - 11 = \\ \\ 9 \times 5 - 11 = \\ \\ 45 - 11 = \\ \\ = 34\)
What is the equation of the line that passes through the point (-4, -7) and has a
slope of ?
Answer:
the question seems incomplete
the half-life of zn-71 is 2.4 minutes. given you start with 50g of the material, how many minutes will pass before you have 5g left?
Before 5g left, 7.2 minutes had gone by.
How do you define time and distance?Distance, time, and speed are all related to one another in their fundamental concepts. Distance traveled by a body in a given amount of time is its speed. That is Speed = Distance / Time. Normal Speed: Normal Total distance times speed Speed: Speed = Distance x Time Distance = D. (Speed x Time) Distance multiplied by speed equals time. mass This means that it would take 7.2 minutes before you had 5 g left: 0. 502.4. 254.8. 12.57.2. 6.259.6.
Why is it known as a half-life?The amount of time it takes for a radioactive element to decay to half its original value is known as its half life. The time it takes for a source's activity to decrease to half its initial value is implied by this to be the definition of a half life.
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What is the multiple comparisons
problem? What is the family-wise error rate? Use an example to
explain how multiple comparisons leads to an escalation of type 1
error.
Multiple comparisons refer to the testing of multiple hypotheses simultaneously. A family of hypotheses is created when a group of hypotheses is tested simultaneously, each of which is associated with a statistical test.
The multiple comparison problem occurs when numerous hypotheses are evaluated at the same time, leading to an increase in the probability of type 1 errors. Type 1 errors are false positive results that indicate a significant difference between groups when one does not actually exist. It implies that the null hypothesis is rejected when it should not be. Multiple comparison tests evaluate a set of hypotheses as a group instead of individually to reduce type 1 errors.
The significance level of individual hypotheses is reduced, resulting in a lower likelihood of type 1 errors. Family-wise error rate (FWER) is the probability of making at least one type 1 error in a family of hypotheses. It's a commonly used method to control the type 1 error rate in multiple comparisons. The probability of any false positives in a family of hypothesis tests is equal to the FWER. FWER is the probability of making at least one type 1 error in a group of hypotheses.
Bonferroni and Holm's tests are two widely used multiple comparison techniques to control the FWER. Suppose, for example, that researchers want to conduct a study of blood pressure medications and their efficacy on 10 different populations. There are ten null hypotheses in this situation, one for each population. They're all evaluated at a 5% significance level. Each test has a probability of 5% of yielding a type 1 error. As a result, the likelihood of making at least one type 1 error is quite high when all ten hypotheses are tested.
It means that a false-positive conclusion will be drawn for at least one of the populations. This probability of at least one false-positive result is given by the FWER. Bonferroni's correction, which divides the critical significance level by the number of hypotheses being tested, is one method of resolving the issue. Another approach is to use Holm's method, which is similar to Bonferroni's method but takes into account the order of the
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Roma swims at a rate of 54 metre per minute. At this rate how long does she take to swim 270 metre ?
Answer:
Step-by-step explanation:
54 times 270 = 14580
a soccer player took fifteen shots on goal and made two. What percent of his shots resulted in a goal? round to the nearest percent
Answer:
13%
Step-by-step explanation:
2/15 = 0.133333333333333
0.13 = 13%
Answer:
13%
Step-by-step explanation:
If he took 15 shots and made 2, the fraction would be 2/15. 2 divided by 15 is 0.1333…, and that as a percent would be 13.333…%. That rounded to the nearest percent would be 13%.
XYZ is an isosceles triangle in a circle,centre o xy=xz=20and yz=18 calculate to 3 sf b.the diameter of the circle
Answer: 34x+22z-77-99=23c
Step-by-step explanation:
= What is the rational exponent of square root of 15
Answer:
\(\frac{1}{2}\)
Step-by-step explanation:
using the rule of exponents/ radicals
\(\sqrt{x}\) = \(x^{\frac{1}{2} }\) , then
\(\sqrt{15}\) = \(15^{\frac{1}{2} }\)
Please help me!! Will give Brainliest + lots of points!!
Answer:
The correct answer is D.
\(4 \sqrt{3} \)
I 1000000% sure.
Answer:
1. x=16 is the right answer.