9. One newton equals about 100 g
on Earth. How many newtons
would a football weigh if it had
a mass of 400 g?

The answer is b) n - 1. When constructing a confidence interval for the population mean using the standard deviation of the sample, we use the t-distribution.

The degrees of freedom for the t-distribution is given by n - 1, where n is the sample size. This is because we estimate the population mean using the sample mean, and we lose one degree of freedom in the process. Degrees of freedom refer to the number of independent pieces of information available for estimating a parameter.

Since one piece of information is used to estimate the sample mean, we subtract one from the sample size to get the degrees of freedom for the t-distribution. Therefore, the correct option is b) n - 1.

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Answer:

25%

Step-by-step explanation:

Based on the given conditions, formulate

Calculate the sum or difference:

 Multiply a number to both the numerator and the denominator

: Write as a single fraction: 

Calculate the product or quotient: 

Rewrite a fraction with denominator equals 100 to a percentage: 

Answer:

f(3)=-60

Step-by-step explanation:

f(3)=5*(3^2)-7(4*3 + 3)

f(3)=5*9 - 7*15

f(3)=45-105

f(3)=-60

Answer: -60

Step-by-step explanation:

f(3) means that you replace the input function of x with 3; So, your equation would look something like this:

5(3)^2 - 7(4(3) +3)

= 5(9) - 7(15)

= 45 - 105

= -60

$2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

Let x be the amount invested at 2% and y be the amount invested at 3%. We know that x + y = $5000 and the interest earned is $129. We can use the formula for simple interest, I = Prt, where I is the interest earned, P is the principal (or initial amount invested), r is the interest rate, and t is the time period.

Thus, we have:

0.02x + 0.03y = $129 (1)

x + y = $5000 (2)

We can solve for one of the variables in terms of the other from equation (2), such as y = $5000 - x. Substituting this into equation (1), we get:

0.02x + 0.03($5000 - x) = $129

Simplifying and solving for x, we get:

0.02x + $150 - 0.03x = $129

-0.01x = -$21

x = $2100

Therefore, $2100 was invested at 2% and $2900 ($5000 - $2100) was invested at 3%.

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To find the value of x, we calculate the average of the sample observations. Summing up the observations and dividing by the total number of observations, we get:

x = (125 + 122 + 126 + 100 + 155 + 132 + 121 + 118 + 114 + 125 + 142 + 2 + 130 + 110 + 140 + 129 + 3) / 17 = 114.118 seconds (rounded to three decimal places).b) To find the value of R, we calculate the range of each sample by subtracting the minimum observation from the maximum observation. Then we find the average range across all samples:R = (155 - 100 + 142 - 2 + 140 - 110 + 132 - 114 + 142 - 3) / 5 = 109.2 seconds (rounded to three decimal places).

c) The Upper Control Limit (UCL) and Lower Control Limit (LCL) using 3-sigma can be calculated by adding and subtracting three times the standard deviation from the average:UCL = x + (3 * R / d2) = 114.118 + (3 * 109.2 / 1.693) = 348.351 seconds (rounded to three decimal places).LCL = x - (3 * R / d2) = 114.118 - (3 * 109.2 / 1.693) = -120.115 seconds (rounded to three decimal places).

d) The Upper Control Limit Range (UCLR) and Lower Control Limit Range (LCLR) using 3-sigma can be calculated by multiplying the average range by the appropriate factor:UCLR = R * D4 = 109.2 * 2.115 = 231.108 seconds (rounded to three decimal places).LCLR = R * D3 = 109.2 * 0 = 0 seconds.

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The population of the town in the year 1995 will be 61415.

From the information, the population of a town was 980 in 1970 and the population has been growing at a rate of 18% each year.

Therefore, it should be noted the difference in the number of years will be:

= 1995 - 1970

= 25 years

Therefore, the population of the town in the year 1995 is:

= 980 × (1 + 18%)^25

= 980 × (1.18)^25

= 980 × 66.6686

= 61415

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Answer:

1100 milliliters.

Step-by-step explanation:

First, separate the numbers 275, it will be 200, 70, and 5.

Second, multiply 4x200, it equals 800

Third, multiply 4x70, it equals 280

Fourth, multiply 4x5, it equals 20.

Fifth, add them all together one by one like 280+20=300, then add 280+800 which is 1100.

A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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When a rational number is expressed as a decimal, the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors in the denominator.

For example,

If we consider the fraction 1/7, the decimal representation is 0.142857142857..., and the repeating section has a length of 6 digits. This is because the denominator 7 is a prime number, and there is only one distinct prime factor.

Similarly, for the fraction 1/6, the decimal representation is 0.1666..., and the repeating section has a length of 1 digit. The denominator 6 has two distinct prime factors (2 and 3), but since the prime factor 2 is repeated, it contributes to a repeating section of length 1.

In general, if a rational number can be expressed in the form p/q, where p and q are coprime integers (they have no common factors other than 1), and q has prime factors p1^a1 * p2^a2 * p3^a3 * ..., then the maximum length of the repeating section in the decimal representation is equal to the number of distinct prime factors, which is a1 + a2 + a3 + ...

It's important to note that not all rational numbers have repeating decimal representations. For example, the fraction 1/2 can be expressed as the terminating decimal 0.5.

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Answer:

Take the sum of two to the power three and four away from ten and divide it by one less than three

The probability of any one undergraduate being selected in a random sample of 2550 undergraduates from a population of 25500 can be calculated using the formula:

Probability = Number of individuals in the sample / Total population

In this case, the probability would be:

Probability = 2550 / 25500 = 0.1 or 10%

Therefore, the probability of any one undergraduate being included in the random sample is 10%. This means that for every 10 undergraduates in the population, only one would be included in the sample. It is important to note that this probability assumes a truly random sampling process with no bias or influencing factors affecting the selection of individuals.

In conclusion, the probability of any undergraduate being in a random sample of 2550 undergraduates selected from a population of 25500 is 10%. This information can be useful in determining the representativeness of the sample and making inferences about the larger population based on the characteristics of the sample.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer: C. 15

Step-by-step explanation:

let's firstly convert the mixed fraction to improper fraction.

\(\stackrel{mixed}{2\frac{5}{8}}\implies \cfrac{2\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{21}{8}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} gallons&miles\\ \cline{1-2} \frac{21}{8} & 147\\[1em] 1& m \end{array} \implies \cfrac{\frac{21}{8}}{1}~~=~~\cfrac{147}{m}\implies \cfrac{21}{8}=\cfrac{147}{m} \\\\\\ 21m=(8)(147)\implies m=\cfrac{(8)(147)}{21}\implies m=56\)

Answer:

$25.08

Step-by-step explanation:

48/2= 24(50% of 100% simplifies to 1/2)

24(0.045)=1.08

24 + 1.08 = 25.08

The values are given in the solution.

Given are right triangles we need to find the missing sides of the triangles,

Here in the all the parts we will use the Pythagoras theorem,

Formula =

hypotenuse² = √leg² + leg²

1) 5² = x² + 3²

x = √25-9

x = √16

x = 4

2) x² = 12² + 5²

x = √144+25

x = √169

x = 13

3) 10² = 8² + x²

x = √100-64

x = √36

x = 6

4) 15² = 12² + x²

x = √225-144

x = √81

x = 9

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Answer:

12.

Step-by-step explanation:

That would be sum of wieghts/average weight

= 540 / 45

= 12.

The number of students having an average of 45 kg will be 12.

Average is defined as the ratio of the sum of the number of the data sets to the total number of the data. The average actually determines the middle value of the data.

Given that in a continuous series the average weight of some students Is 45 kg and the sum of their weight is 540 kg.

The average is calculated by the formula below,

Average = (Sum of the data) / Number

Number = ( Sum of the data) / Average

Number = 540 / 45

Number = 12

The total number of students is 12 in number.

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Answer:

9*572=5148

Step-by-step explanation:

Answer:

I believe it is this :

1) C

2) B

((I wasn't paying attention before thanks GuffeyK14))

The Fundamental Theorem of Linear Algebra states that the set of solutions of any system of linear equations can be represented as the sum of an arbitrary solution and the nullspace (subspace) of the homogeneous system corresponding to the given system.

A system of linear equations consists of multiple linear equations with the same variables. The goal is to find a set of values for the variables that satisfy all the equations simultaneously.

The homogeneous system of linear equations is obtained by setting all the right-hand sides of the equations to zero. In other words, the homogeneous system has the same equations as the given system, but without the constant terms.

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Answer: he drives 273 miles for 7 hours

Step-by-step explanation:

Answer:

a: 3°

b: -4°

c: -3°

d: 3°

e: -4°,-3°,0°,3°,3°

f: 7

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

The basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.

A function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented as an equation, a graph, a table of values, or a verbal description. For example, the function f(x) = 2x + 1 represents a relationship between the input x and the output 2x + 1.

To find the maximum height of the basketball, we need to find the vertex of the parabola represented by the function f(x). The vertex of x-coordinate is:

x = -b/2a

The coefficients of the quadratic equation a\(x^2\) + b\(x\) + c are a, b, and c. In this case, a = -4.9 and b = 17, so:

x = -17/(2*(-4.9)) = 1.735 (rounded to 3 decimal places)

Therefore, the basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.

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The conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

Let E be the case where you choose the bogus coin and F be the case where you got heads twice. We wish to calculate P(E|F), which is the likelihood that you chose the fake coin given that you received heads twice.

By Bayes' theorem, we have:

P(E|F) = P(F|E)P(E) / P(F)

We can calculate each term on the right-hand side as follows:

P(F|E) = 1, Because the fake coin contains heads on both sides and always results in two heads when flipped.

P(E) = 1/n, since there is only one fake coin among n coins.

P(F) = P(F|E)P(E) + P(F|not E)P(not E), where not E is the event that you picked a normal coin. We can calculate:

P(F|not E) = (n-1) * (1/2)^2 = (n-1)/4, Because each normal coin has a 50% chance of revealing heads on each given flip and there are n-1 normal coins

P(not E) = (n-1)/n, since there are n-1 normal coins among n coins.

Therefore, we have:

P(F) = 1 * (1/n) + (n-1)/4 * (n-1)/n = (3n-1)/(4n)

Substituting these values into Bayes' theorem, we get:

P(E|F) = 1 * (1/n) / ((3n-1)/(4n)) = 4/(3n-1)

Thus, the conditional probability that you picked the fake coin given that you got heads twice is 4/(3n-1).

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Answer:

$101200

Step-by-step explanation:

A simultaneous equation refers to two or more equations that are solved at the same time.

A simultaneous equation refers to two or more equations that are solved at the same time. Now we shall solve each of the equations;

a. 2x + y = 3 ------(1)

   x - y = 4 ------ (2)

x = 4 + y  ----- (3)

Substituting (3) into (1)

2(4 + y) + y = 3

8 + 2y + y = 3

8 + 3y = 3

3y = 3 - 8

3y = -5

y = -5/3

Hence;

 x - y = 4

x - (-5/3) = 4

x = 4 + 5/3

x = 17/3

b. 2x + 6y =9 -----(1)

x + 3y = 2 ------ (2)

x = 2 - 3y ------ (3)

Substitute (3) into (1)

2( 2 - 3y)  + 6y =9

4 - 6y + 6y = 9 (From this stage we can see that it is not possible to solve the quadratic)

c. 6x - 3y = 12 -----(1)

4x + 2y = 10 ---- (2)

12x - 6y = 24 ---- (3)

12x + 6y = 30 --- (4)

Add (3) to (4)

24x = 54

x= 54/24 = 9/4

Hence;

4(9/4) + 2y = 10

9 + 2y = 10

2y = 10 - 9

y = 1/2

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\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] ~\dotfill\)

\(\cfrac{-3xyz}{-27x^2y^2z^2}\implies \cfrac{-3x^1y^1z^1}{-27x^2y^2z^2}\implies \cfrac{-3}{-27}\cdot \cfrac{1}{x^2x^{-1}y^2y^{-1}z^2z^{-1}} \\\\\\ \cfrac{1}{9}\cdot \cfrac{1}{x^{2-1}y^{2-1}z^{2-1}}\implies \cfrac{1}{9}\cdot \cfrac{1}{x^1y^1z^1}\implies \cfrac{1}{9xyz}\)