a sample of 800 computer chips revealed that 60% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 57% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.02 level to support the company's claim? state the null and alternative hypotheses for the above scenario.

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]

[tex]\mu=e^{\int p(t)dt}[/tex]

[tex]\mu=e^{\frac{t}{400}}[/tex]

So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]

S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]

Now solving the bracket

S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)

At S(0) = 100

100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C

100 = 4000 + [tex]e^{0}[/tex] C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

Answer:

A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."

Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."

Step-by-step explanation:

An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

Now, According to the question:

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 28in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (28) = JG

14 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

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The surface area of the pyramid is 5,685 ft².

To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:

length, l = 25 ft

width,w = 22 ft

Area = l x w

Area = 25 ft x 22 ft

Area = 550 ft².

To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of

Net dimensions of the pyramid:

length, l = 74.8 ft

width, w = 70.4 ft

h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]

h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]

h = 102.7 ft.

Now, we can use the formula for the area of a triangle:

Area = (1/2) x base x height,

where,

base,b = the length of the rectangular base (25 ft)

height = the slant height (102.7  ft).

So, the area of each triangular face is:

A = (1/2) x 25 ft x 102.7  ft

A = 1283.75 ft².

Since there are four triangular faces, the total area of all the triangular faces is:

A= 4 x 1283.75 ft²

A = 5,135 ft².

To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:

SA= 550 ft² +  5,135 ft² = 5,685 ft².

Hence, the surface area of the pyramid is 5,685 ft².

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Answer: 50g steel, 30g gold and 70g brass

Step-by-step explanation:

     This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.

           5 + 3 + 7 = 15

     Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.

           150g / 15g = 10g

     Next, we will multiply each amount of metal in one ratio by 10.

5g * 10 = 50g steel

3g * 10 = 30g gold

7g * 10 = 70g brass

Answer:

Step-by-step explanation

                                          to get 50g of steel.

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Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Curran:

-4(x-6)< 22

Used the distributive property a(b+c)=ab+ac

-4x+24<22

Then subtracted 24 from bot the sides

-4x<22-24

-4x< -2

Divide both sides by -4 ( inequality changes because of dividing by negative number)

x>1/2

Anjani:

-4(x-6)< 22

Divide both sides by -4

x-6> -22/4

add 6 on both sides

x> -22/4 + 6

x> -11/2 + 6

x> 1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

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The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.

Submarine's descent can be represented by the equation, y = -3100 x

where,  

y is elevation

x is time in hours

We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.

Since the submarine to make the descent to the seafloor 2,100 feet below the surface

So, y = - 2100

y = - 3100x gives

- 2100 = - -3100 x

Divide both sides by -3100,

x = 2100/3100 = 0.677 hours

As a result, the submarine will need 0.677 hours to complete the descent.

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Marlon's height is 42.52 inches.

Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.

z = (x - mean) / standard deviation

where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.

We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.

A z-score of 0.84 corresponds to a cumulative probability of 0.70.

So we can substitute this value into the z-score formula:

0.84 = (x - 40) / 3

Solving for x, we get:

x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches

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Answer: -15x - 9

Step-by-step explanation:

(2x ×2 −6x−5)+(−9x ×2 +5x−4)

(4x-6x-5)+(-18x+5x-4)

(-2x-5)+(-13x-4)

-2x-5-13x-4

-15x -

The value of the given equation is −7x2−x−9.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

The equation (2x 2 −6x−5)+(−9x 2 +5x−4)

Now,

We need to add the two polynomials by combining like terms. Like terms are terms that have the same variable and exponent. For example, 2x2 and −9x2 are like terms because they both have x2

To add like terms, we just add their coefficients. For example, 2x2+(−9x2)=(−7x2)

We can apply this rule to each pair of like terms in the problem and get:

(2x2−6x−5)+(−9x2+5x−4)

=(2x2+(−9x2))+(−6x+5x)+(−5+(−4))

=(−7x2)+(−x)+(−9)

=−7x2−x−9

Therefore, by algebra the answer will be −7x2−x−9.

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The person being called is a function of the phone number, as for each phone number, there is only one person associated with the number.

A relation represents a function when each input value is mapped to a single output value.

The input and output variables for this problem are given as follows:

Each phone number is mapped to a single person, meaning that the relation is in fact a function.

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Answer:

cotθ=√21/2

Step-by-step explanation:

we have,

sinθ= 2/5= perpendicular/hypotenuse

here,

perpendicular=2

hypotenuse = 5

Now using Pythagorean theorem,

h^2 = p^2+ b^2

(5)^2 = 2^2 +b^2

b= √21

so,

cotθ= base/perpendicular = √21 /2

Hope you like the explanation.

The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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Answer: i think y =  x + 5

Step-by-step explanation:

The number of days before she mows the lawn and washes her window on the same day is 60 days.

The day she would mow the lawn and wash her window on the same day would be the least common multiple of 12 and 20.

A multiple of a number is the product of an integer and that number. A common multiple is a multiple that two or more numbers share. The least common multiple is the smallest multiple that two or more numbers share.

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120

Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200

Least common multiple = 60

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The three (3) true statements about the quadratic function, f(x) = x^2 – 5x + 12 and its graph include the following:

A. The value of f(–10) = 82

B. The graph of the function is a parabola.

D. The graph contains the point (20, –8).

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the other true statements about the graph of this quadratic function:

At data point (-10, 82), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(-10) = -10²/5 – 5(-10) + 12

Quadratic function, f(-10) = 82

At data point (20, -8), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(20) = 20²/5 – 5(20) + 12

Quadratic function, f(20) = -8

In conclusion, the graph of this quadratic function, f(x) = x^2 – 5x + 12 does not contain the data point (0, 0) as shown in the image attached below.

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The triangle types is impossible to draw is

A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degrees. The sides that include the right angle are perpendicular and the base of the triangle.

Given:

First, a scalene with right-angled triangle is possible to make.

Now, an isosceles with acute-angled triangle is possible to make such triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement.

Now, an isosceles with obtuse-angled triangle is not possible to make because if two angles are greater than 90 then sum of angles exceed 180.

and, an equilateral with right-angled triangle is not possible to make because in Equilateral triangle are angles are of equal measurement 60.

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Based on the information, it can be concluded Isabella bought  2 paintbrushes and 3 jars of paint.

The average of buying a product is 0.97, which means Isabella can buy a total of 5 items (0.97 x 5 = 4.85)

Based on this different combinations of products are possible, for example, 1 paintbrush and 4 jars or 3 jars and 2 paintbrushes. However, the one that fits the final price is:

2 paintbrushes x 0.95 = $1.9

3 jars of paint x 0.99 = $2.97

$2.97 + 1.9 = $4.87

Note: This question is incomplete, here is the missing information

The paintbrushes cost $0.95 and the jar of paint cost $.099

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Some of the other types of the separation process are used in every house and company. The process of segregating undesirable particles from necessary components is the essence of the separation method. We will study in-depth information about several physical separation techniques in this particular article. The discussion's conclusion would allow students to recognize various techniques and their importance.

The blind man could use one hand to separate the pills by color, for example by holding one group of pills in one hand and the other group of pills in the other hand. Then, he could reach into one hand and take one pill, and reach into the other hand and take one pill, ensuring that he has taken one red pill and one blue pill. Another way could be to put each color pill in a different pocket, so he can feel the different pockets and take one pill of each color.

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Answer:

3 x (5 + 2)

Step-by-step explanation:

Just use the distributive property, it's very simple.

The ball has both kinetic energy and potential energy.

The values of each type of energy the object has are KE = 37.5 J and GPE = 2205 J

Energy is the ability to do work. It can take many forms, such as kinetic energy (energy of motion), potential energy (stored energy) etc.

If a  3-kg bowling ball rolls at a speed of 5 m/s on the roof of the building that is 75 m tall.

Then ball has kinetic energy due to his motion and also has potential energy due to his height.

Thus, M = 3-kg, h = 75 m and V = 5 m/s

KE = 1/2(M)(V)² = 1/2 × 3 × 5² = 37.5 J

GPE = mgh = 3 × 9.8 × 75 = 2205 J

KE + PE = 37.5 + 2205 = 2242.5 J

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The lateral area for the prism is equal to 54 square inches. (Correct choice: B)

Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:

Rectangle

A = w · l

Where:

Finally, we proceed to determine the lateral area of the prism:

A = 3 · (3 in) · (6 in)

A = 54 in²

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The value of the missing angle x of the triangle is; x = 18.67°

The sum of angles on a straight line is 180 degrees. Thus, the supplementary angle to 130 degrees is;

180 - 130 = 50°

Now, the alternate angle to 80 degrees which will be located inside the triangle is 80°.

The sum of angles in a triangle is 180 degrees. Thus;

3x - 6 + 80 + 50 = 180

3x + 124 = 180

3x = 180 - 124

3x = 56

x = 56/3

x = 18.67°

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Answer:

is try ur hardest

Step-by-step explanation:

The measurement of indicated angle is 20 degree.

Here opposite angles are congruent .

Therefore the indicated angle is 20 degree.

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Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".

We know that:

quotient = (3x)/5

quotient + 4 <= 34

We can simplify the first equation:

(3x)/5 + 4 <= 34

We can then solve this inequality for x:

(3x)/5 + 4 <= 34

3x/5 <= 30

3x <= 150

x <= 50

So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9x9=81

Answer:

Step-by-step explanation:

So the rectangle is 9 units wide.

becuase given that the area of the rectangle is 81m'n' square units and the length of the rectangle is 9mn', we can set up the equation as:

81 = 9 x width

To solve for width, we can divide both sides of the equation by 9:

width = 81/9

width = 9

People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

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A. We can see that the intersection made by lines C and D classifies ∠7 and ∠8 as vertically opposite angles.

B. The special angles created by intersection of lines C and D can be used to solve for y by equating the expressions, 5y-29 and  3y+19 as they are vertically opposite angles.

C. Solving for y, we have: y = -5

Intersection, in mathematics, refers to the common elements or overlap between two sets. For example, if set A contains the elements 1, 2, and 3, and set B contains the elements 2, 3, and 4, then the intersection of set A and set B would be the set containing the element 2 and 3. In general, intersection is represented by the symbol ∩. Lines can also intersect to form angles.

Vertically opposite angles are actually known to be equal. It then means that:

∠7 = ∠8 (Vertically opposite angles)

Also, 5y-29 = 3y+19 (Vertically opposite angles)

Thus, solving for y, we have:

5y-29 = 3y+19

5y - 29 -29 = 3y + 19 - 29

5y -3y = - 10

2y = -10

y = -10/2 = -5

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