Two expressions of the equation

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that [tex]\mu = 14, \sigma = 2[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{14.2 - 14}{0.2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Answer:

espero ayudarte ..............❤❤

Answer:

b

Step-by-step explanation:

Answer:

Sister's house is 7.5 feet high

Step-by-step explanation:

Given :

     My house = 5  feet

     Sisters house = [tex]1\frac{2}{4}[/tex]  [tex]times[/tex]  [tex]my \ house[/tex]

                           = [tex]\frac{6}{4} \times 5[/tex]

                           [tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]

Answer:

Espanol la vecsu

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

The diagonals of a rectangle bisect each other , so

DE = EB , that is

7x - 1 = 2x + 4 ( subtract 2x from both sides )

5x - 1 = 4 ( add 1 to both sides )

5x = 5 ( divide both sides by 5 )

x = 1

Answer:

y = -3x + 13

Step-by-step explanation:

First, find the slope:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]

Finally, find the equation:

[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]

Answer:

3.75cm 44.16cm²

20cm 314cm²

42cm 1384.74cm²

Step-by-step explanation:

Area of a circle = πr²

Where : = π = pi = 3.14

R = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

16. Radius = 7.5 / 2 = 3.75

Area = 3.14 x 3.75² = 44.16

17. Diameter = 10 x 2 = 20

Area = 10² x 3.14 = 314

18. Diameter = 21 x 2 = 42

Area = 21² x 3.14 = 1384.74

Answe

SI Si olla amigo lel just spammin here

Step-by-step explanation:

Answer:

The answer is the square root of 8, or 2root2.

Step-by-step explanation:

Use the distance formula.

d = sqrt((-3-(-5))^2 + (-3-(-1)))

d = sqrt(2^2 + 2^2)

d = sqrt(4 + 4)

d = sqrt8

d = sqrt4 * sqrt2

d = 2 * sqrt2

Answer:

x ≥ 12

Step-by-step explanation:

-3/4x +2 ≤ -7

Subtract 2 from each side

-3/4x +2-2 ≤ -7-2

-3/4x  ≤ -9

Multiply each side by -4/3, remembering to flip the inequality

-3/4x * -4/3 ≥ - 9 *(-4/3)

x ≥ 12

Answer:

x>=12

Step-by-step explanation:

-3/4x + 2<=-7

-3/4x <= -7 -2

-3/4x<=-9

cross multiply

-3x<=-36

dividing throughout by -3

x>=12

Answer:

last step is (2x + 5)(2x + 1)

Step-by-step explanation:

4x^2 + 12x + 5

4x^2 + (10 + 2)x + 5

4x^2 + 10x + 2x + 5

2x(2x + 5) +1(2x + 5)

(2x + 5)(2x + 1)

Answer:

The last one!

Step-by-step explanation:

Answer: B (0,0) r=4

Step-by-step explanation:

Answer:

Correct answers= 18

Incorrect answers=30-18= 12 answers

Step-by-step explanation:

total questions=30

correct answers= x

incorrect answers= 30-x

given: 5 marks for each correct answer

therefore, marks for correct answers = 5*x = 5x

Given: 1 mark deducted for every incorrect answer

therefore, marks deducted = 1(30-x) = 30-x

Total marks scored= 78

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78

5x- (30-x) =78

5x-30+x=78

5x+x=78+30

6x= 108

x=108/6 = 18

Correct answers= 18

Incorrect answers=30-18= 12 answers

(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

x²-3x-10/x²-6x+5 • x-2/x-5

We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)

Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)

Now let's simplify the second fraction:

x-2 / x-5

We can't simplify this fraction any further, so we leave it as is.

Putting it all together, we get:

(x+2) / (x-1) * (x-2) / (x-5)

Multiplying the two fractions, we get:

(x+2)(x-2) / (x-1)(x-5)

This is the simplified form of the expression.

To learn more about fraction from the given link:

https://brainly.com/question/10354322

#SPJ1

Answer:29.16 ml  was left

Step-by-step explanation:

2/3-3/8=

16/23-9/24=

7/24x100/1=

then divide

Explanation:

Perimeter is simply the sum of all the edges. The same way 10 can be made of 4+6 or 3+7, the perimeter can be made by many combinations. if you know the 2 must equal 24cm, then we can create numerous combinations.

A. 13

Explanation= 6 (sons) +6 (daughters) +1 (mother) = 13.

(notes: as a father is not within the problem, there is no reason to be in the answer)

Answer:

B)8

A mother has 6 sons.  If there is only one sister, than each son has a sister.  Don't forget to add the mother.  6 + 1 + 1

Step-by-step explanation:

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]

Step-by-step explanation:

Answer:

153.3852

Step-by-step explanation:

After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2

Answer:

153.385

Step-by-step explanation:

153.38519

153.38519

The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.

153.38519 ≈ 153.385

Hope this helps.

Answer:

[tex]cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Step-by-step explanation:

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Answer:

B. y= ¼

Step-by-step explanation:

3 + ^4√4y = 4

^4√4y =4-3

^4√4y = 1

^4√4y =^4√1

so, 4y = 1

y = ¼

Answer:

No solution is possible from the informatin provided.

Step-by-step explanation:

You didn't include the table,

Answer:

y intercept is found from the pair that has a 0 for the x variable.

Step-by-step explanation:

if a choice was (0,2) this would be the point where the line intercepts the y axis.

x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis

11%

Hope this helps! :)

______________

Answer:

[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]

let the number be b

62.5/100 x b = 25

0.625 x b = 25

b =25/0.625

b=40

half of b= 40/2 = 20