y= A(0.5)^t/(half-life) What is half-life

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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Answer:

- 1

Step-by-step explanation:

Substitute a = - 1 into the expression, that is

(- 1)³ - 2(- 1)² + 3(- 1) + 5

= - 1 - 2(1) - 3 + 5

= - 1 - 2 - 3 + 5

= - 6 + 5

= - 1

Answer:

=(-1)³-2(-1)²+3(-1)+5

=-1-2(1)+3(-1)+5

=-1-2+3+5

=-3+8

=5

Answer:

hola le noeva si (true) neisa adios

Answer:

41/7

Step-by-step explanation:

You first should multiply the denominator, which is 7, by the whole number part, five, and add the numerator, six, to get the new numerator. Then you place the new number, 41, over the old denominater which leaves you with 41/7.

The mixed fraction 5 6/7 can be converted in to the improper fraction as 41/7.

Given a mixed fraction,

5 6/7

We have to convert this in to improper fraction.

Improper fractions are fractions which contains the numerator which is greater then the denominator.

All improper fractions can be converted in to mixed fraction and vice versa.

Here fraction is 5 6/7.

5 6/7 = 5 + 6/7

Cross multiplying,

5 6/7 = [(5 × 7) + 6] / 7

         = (35 + 6)/7

         = 41/7

Hence the improper fraction is 41/7.

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The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:

\(d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}\)

Given that, the line passes through the points (0,-3) and (7,4).

The equation of the line is given by:

\(y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0\)

Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
\(d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}\)

Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

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Answer:

(3+2)+(4+2)

Step-by-step explanation:

234

Answer:

C.

Step-by-step explanation:

the second answer is correct

Answer:

C. 63 degrees

Step-by-step explanation:

When 2 triangles are congruent, no matter what postulate they are congruent by, all their sides and angles will be congruent.

We know that triangle ABC is congruent to triangle DEF. Their angles and sides are congruent and corresponding.

We know that angle A is 70 degrees, angle B is 47 degrees and angle C is 63 degrees.

Angle C and angle F correspond. Therefore, angle C and angle F are congruent. Angle C is 63 degrees, therefore angle F must be 63 degrees.

C. 63 degrees is the correct answer.

Answer:

-67 I belive

Step-by-step explanation:

Answer:

normally I'd make a joke and say 76 but the answer would be -67 lol

Step-by-step explanation:

Answer:yo

Step-by-step explanation:

Answer:

16,242. 7 cm^3.

Step-by-step explanation:

We need to cut off a square piece at the 4 corners of the cardboard.

Let the length of their edges be x cm.

The volume of the box will be:

V = height * width * length

V = x(100-2x)(40-2x)

V = x(4000 - 200x - 80x + 4x^2)

V = x(4x^2 - 280x + 4000)

V =  4x^3 + - 280x^2 + 4000x

Finding the derivative:

dV / dx =  12x^2 - 560x + 4000  = 0  ( when  V is a maxm or minm.)

4(3x^2 - 140x + 1000) = 0

x =  37.86, 8.80.

Looks like x = 8.80 is the right value but we can check this out be looking at the sign of the second derivative:

V" =  24x - 560, when x = 8.8   V" is negative so this is a Maximum for V.

So the maximum volume of the box is when x = 8.8 so we have

V =  8.8(100-2(8.8)(40 - 2(8.8)

=  16,242. 7 cm^3.

Answer:

0.003 or 3/1000

Step-by-step explanation:

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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a. The probability that difference in sample proportions is more than 6% is 0.1056.

b. There is a 0.2677 probability that the sample proportion from School A is greater than 5% than that from School B.

a. We must first determine the standard error of variation between the two sample proportions in order to determine the probability that the difference in sample proportions is greater than 6:

SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where,

P1 = 57% of students are from school A.

p2 = 61% of students are from school B.

Sample sizes from schools A and B were 75 and 80, respectively.

SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }

= sqrt{ 0.00233 + 0.00240 }

= 0.0803

Now, we can find the Z-score as:

Z = (p1 - p2 - D) / SEp1-p2

where,

D = 6% = 0.06

Z = (0.57 - 0.61 - 0.06) / 0.0803

= -1.248

Using a standard normal distribution table, we can find the probability that Z < -1.248 is 0.1056.

Therefore, the probability that difference in sample proportions is more than 6% is 0.1056.

b. To find the probability that School A sample proportion is more than 5% higher than School B, we need to find the standard error of the difference between the two sample proportions:

SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }

where,

57% of the population in p1 is from school A.

61% of those in p2 are from school B.

75 were included in the sample from school A, while 80 were included in the sample from school B.

SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }

= sqrt{ 0.00233 + 0.00240 }

= 0.0803

Now, we can find the Z-score as:

Z = (p1 - p2 - D) / SEp1-p2

where,

D = 5% = 0.05

Z = (0.57 - 0.61 - 0.05) / 0.0803

= -0.621

We can get the probability that Z -0.621 is 0.2677 by using a standard normal distribution table.

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By evaluating the function, we conclude that f(10) = -7

Here we know that:

g(x) = 2x - 8

And f(x) = 5 - g(x).

Then we can write:

f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13

Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.

f(10) = -2*10 + 13 = -20 + 13 = -7

Then, we conclude that f(10) = 7

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Answer:

\(\mathrm{C.\:}25\)

Step-by-step explanation:

Notice how each congruent square is divided into four equal parts. Since each square has four parts and there are four squares, there are \(16\) of these parts in total. Because each of these parts make up \(\frac{1}{4}\) of each square, all parts are equal. Therefore, you can count the total number of shaded parts to get your percentage.

The top left and bottom right both have one part shaded each for a total of \(2\) parts.

The top right and bottom left have \(0.5\) and \(1.5\) parts shaded, respectively, for a total of \(2\) parts.

Therefore, in total, there are \(2+2=4\) parts shaded out of \(16\) total parts.

Thus, the percentage of the total area that is shaded is:

\(\frac{4}{16}=\frac{1}{4}=\fbox{$25\%$}\).

As a fraction, length of the 15 rods = 8 4/7 feet

As decimal, length = 8.57 feet

initial length pipes = 4 feet

Dividing the length of the pipe into 7:

length of 15 of those rods:

Answer: I think its 2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

volume of the unit cube:

V = 1 * 1 * 1 = 1

volume of the half-cube:

V = 1/2 * 1 * 1 = 1/2

number of half cubs that fit in unit cube:

1/(1/2) = 2

Answer: 2

There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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To calculate the slope between 2 points we use the following equation:

Replacing the points:

In this case, when we find an infinite slope, it means that it is a line parallel to the Y axis. All parallel lines have the same slope.

For the perpendicular case, the slope is equal to:

For the perpendicular case, the slope is zero and would equal one parallel to the X axis.

Answer:

Step-by-step explanation:

The question is asking us to find the slope.

First, we will find the slope of the line that passes through (4,8) and (4,6).

We'll use the slope formula:

\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

Plug in the data :

\(\bf{m=\dfrac{6-8}{4-4}}\)

\(\bf{m=\dfrac{-2}{0}}\)

\(\bf{m=not\:de fined}\)

If a line's slope is not defined, then it's a vertical line:

                                       \(\rule{1}{350}\)

------

Now, what is the slope of a line that's parallel to the one above? Well, since parallel lines have equal slopes, that one will have an undefined slope too.

As for perpendicular lines, they have slopes that are negative reciprocals of each other. We got that the slope is -2/0. The negative reciprocal of that is 0/2, which simplifies to 0.

Alternatively, you could look at it this way: a horizontal line (a line with zero slope) is perpendicular to a vertical line. So the slope of that line is m = 0.

\(\rule{350}{1}\)

Answer:

Move the variables to one side and the constants to the other through subtraction/additions to BOTH SIDES. Then, divide/multiply to get x = some constant.

Step-by-step explanation:

Try Khan Academy.

Answer:

Step-by-step explanation:

First make a ratio,

6:62.64

Now make an equation

6/62.64=4/x

solve for x...

x=41.76

The required plant grew 9 centimeters in the sixth week.

Let x be the number of centimeters the plant grew in the sixth week.
To estimate x, we can use the formula for the mean (average) of a set of numbers:

mean = (sum of numbers) / (number of numbers)

We know the mean for 6 weeks is 9, so we can write:

9 = (13 + 6 + 10 + 5 + 11 + x) / 6

Multiplying both sides by 6, we get:

54 = 45 + x

Subtracting 45 from both sides, we get:

x = 9

Therefore, the plant grew 9 centimeters in the sixth week.

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The elimination method is a method for solving systems of linear equations.

The method of elimination  consists of removing the same variable from two equations and then finding the value of the other variable that is not eliminated after taking the difference between the two equations.

An equation of the form Ax By = C. Here x and y are variables and A, B and C are constants.

To solve the variables of the given equations by elimination method Let's look at a short comprehensible example.

2x + y = 7 ------> (1)

x + y = 5 -------> (2)

To eliminate 'y', subtract (1) - (2),

2x + y - x - y = 7 - 5

x = 2

Substitute x = 2 in equation(1),

2(2) + y = 7

4 + y = 7

y = 3

Therefore, x = 2, y = 3

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Given:

(15x - 5)

To factor a number from another number means to divide both number.

If 5 is factored from both terms, we have:

15x ÷ 5 = 3x remainder 0

5 ÷ 5 = 1 remainder 0

Therefore, we have:

5(3x - 1)

Thus, the number that remains in the second term is .

This is because when 5 divides 5, the remainder is zero.

5 ÷ 5 = 1 remainder 0

ANSWER:

After factoring we have: 5(3x - 1)

The remainder in the second term is 0

Answer:

It is false and true