A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?

Answer:

50 years

Step-by-step explanation:

Assuming it doesn't compound, 5,000*3 = 15,000.

5,000 * 6% = 5,000 * 0.06 = 300.

15,000 / 300 = 50 years.

The probability that at least one out of 7 devices of this type will function for at least 44 months is 1 - 0.9779167, or 0.0220833.

The probability density function of X, the lifetime of a certain type of device, is given by [tex]f(x) = 0 if x < 21; 1/x^2 if x > 21.[/tex]To find the probability that X > 48

To find the probability that at least one out of 7 devices of this type will function for at least 44 months

we can use the binomial distribution formula.

The probability is given by [tex]P(X ≥ 1) = 1 - P(X = 0)[/tex]. Using the cumulative distribution function.

The probability that X = 0 is given by [tex]1 - 1/44^2, or 0.9779167.[/tex]

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Step-by-step explanation:

Total price of the 4 toys = 4 x $1.50 = $6.00

  tax is  6% of 6.00

               =   .06 * $ 6.00 =  $ .36    which is added to the purchase price

$ 6.00 + .36 = $ 6.36          change from a $10 will be

$   10.00 - 6.36 = $ 3.64

Answer: $3.64

Step-by-step explanation:

If we're using the formula, tax = % of whole, we will need to fill some values.

The whole is $6, as it's the total money you need to pay before tax

% can be written as 6/100, as we are being charged 6% in tax, and percent is written as 1/100

"of" is just a way to say * in english

So our equation is tax = 6/100 * 6

Which means tax = 36/100

Then, you add the tax to the original value, to get $6 + $0.36 = $6.36

Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.

The lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit.

To convert the temperature of -89.2°C to Fahrenheit, we can use the formula:

[tex]F = (C * 1.8) + 32[/tex]

Substituting:

°F = (-89.2 × 1.8) + 32

°F = -128.56 + 32

°F = -97

Therefore, the lowest temperature ever recorded on earth of -89.2°C is approximately equal to -97°F when rounded to the nearest degree Fahrenheit. It's important to note that this is just an approximation as we rounded the result to the nearest degree. However, it gives us a good idea of how extremely cold the temperature was. It's worth mentioning that at such low temperatures, it's important to take appropriate precautions to avoid any adverse health effects.

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We have that, the correct match of the description with its mathematical expression is provided with the mathematical expression "or".

Correct matching of the description to its mathematical expression is given as follows: The residual of an estimated regression equation is compared to the mathematical expression "or".

Explanation: A residual is the difference between the actual value of a variable and the predicted value of that variable. The residuals are denoted as "or". Therefore, the Residual of an estimated regression equation is compared to the mathematical expression "or".

Other options are incorrect as follows: Oba does not match any description given in the question. Therefore, it is a wrong option. Obo doesn't match any description given in the question. Therefore, it is a wrong option. Oy+ 61 does not match any description given in the question. Therefore, it is a wrong option.

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The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.

A type of motion known as upward motion involves an item moving up against the pull of gravity.

The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.

The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.

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Answer:

[tex]6z \: = 6 + z \: \\ z {}^{6} = z \times z \times z \times z \times z \times z \\ [/tex]

The mathematical statement in the form of expression can be written as 15625z⁶.

An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -

2x + 3y + 5

2z + y

x + 3y

Given is to find the mathematical statement -

"Difference between 6z and z to the power of 6"

We can write the given mathematical statement in the form of expression as -

(6z - z)⁶

(5z)⁶

5⁶ x z⁶

125 x 125 x z⁶

15625z⁶

Therefore, the mathematical statement in the form of expression can be written as 15625z⁶.

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If y is directly proportional to x, when x = 60, y = 6.

Proportional refers to a relationship between two quantities in which one quantity is a constant multiple of the other. In other words, if one quantity increases or decreases by a certain factor, the other quantity will also increase or decrease by the same factor.

Directly proportional is a specific type of proportionality where two quantities increase or decrease by the same factor. In other words, if one quantity doubles, the other quantity also doubles. If one quantity triples, the other quantity also triples, and so on.

In the given question,

If y is directly proportional to x, we can use the formula:

y = kx

where k is the constant of proportionality.

To find the value of k, we can use the given values:

y = kx

50 = k(500)

Solving for k:

k = 50/500

k = 0.1

Now that we know the value of k, we can use the formula to find the value of y when x = 60:

y = kxy = 0.1(60)

y = 6

Therefore, when x = 60, y = 6.

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Answer:

  3x -y = -6

Step-by-step explanation:

You want the equation of the line with intercepts (0, 6) and (-2, 0).

The equation of the line with x-intercept 'a' and y-intercept 'b' is ...

  x/a +y/b = 1

For the given intercepts, the equation is ...

  x/(-2) +y/6 = 1

In standard form, we want the leading coefficient positive and the integer coefficients mutually prime. We can get there by multiplying by -6:

  3x -y = -6

__

Additional comment

You can get slope-intercept form by solving for y, or you can recognize that ...

  slope = rise/run = -(y-intercept)/(x-intercept) = -6/-2 = 3

Since you already know the y-intercept, you can write the slope-intercept equation as ...

  y = 3x +6

There are perhaps a dozen or more forms of the equation for a line. The "intercept form" equation is one of the more useful ones.

The triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

The Angle-Side-Angle (ASA) Congruence Theorem is a postulate in geometry that states that if two triangles have two angles and the included side of one triangle congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

Triangle YXZ is formed from a reflection and then a dilation of the triangle WVZ, then the relations between the angles are given as follows:

The side lengths WV and YZ, which are the side lengths between these two angles, form a proportional relationship, hence the triangles WYC and YXZ are similar by the Angle-Side-Angle Congruence Theorem.

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According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.

Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:

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The probability of a. rolling an even or 3 is 2/3. b. Rolling an even or a number greater than 2 is 5/6. c. Rolling an odd or a number less than 6 is 5/6. d. Rolling a 2 and a 4 is 0.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. A sample space is made up of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail. An experiment is a trial or procedure carried out to generate a result.

Given that, you roll a single fair 6 sided die.

a. Rolling an even or 3:

P(even or 3) = P(even) + P(3) - P(even and 3)

P(even or 3) = 1/2 + 1/6 - 0

P(even or 3) = 2/3

b. Rolling an even or a number greater than 2:

P(even or >2) = P(even) + P(>2) - P(even and >2)

P(even or >2) = 1/2 + 4/6 - 1/3

P(even or >2) = 5/6

c. Rolling an odd or a number less than 6:

P(odd or <6) = P(odd) + P(<6) - P(odd and <6)

P(odd or <6) = 3/6 + 5/6 - 1/3

P(odd or <6) = 5/6

d. Rolling a 2 and a 4:

P(Rolling a 2 and a 4) = 0.

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the unique polynomial we're looking for is: f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).

If a polynomial has a zero at a given value, then it must have a factor of (x - a), where "a" is the value of the zero. Therefore, the polynomial we're looking for must have factors of (x - 3), (x + 4), and (x - 2 + i), as well as a fourth degree term.

We can write the polynomial in factored form as:

f(x) = A(x - 3)(x + 4)(x - 2 + i)(x - 2 - i)

where A is a constant factor that we need to determine.

Expanding this expression, we get:

f(x) = A(x⁴ - 7x³ - 8x² + 106x - 240)

To find A, we can use the fact that f(0) = -180:

f(0) = A(0⁴ - 7(0)³ - 8(0)² + 106(0) - 240) = A(-240) = -180

Solving for A, we get:

A = [tex]\frac{-180}{-240}[/tex] = 3/4

Therefore, the unique polynomial we're looking for is:

f(x) = [tex]\frac{3}{4}[/tex](x - 3)(x + 4)(x - 2 + i)(x - 2 - i).

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Answer: There are 10 students who are in both the hockey and football teams.

Step-by-step explanation: We can use the principle of inclusion-exclusion to find the number of students who are in both the hockey and football teams.

The total number of students in both teams is the sum of the number of students in the hockey team and the number of students in the football team, minus the number of students who are in both teams (to avoid double-counting):

Total = Hockey + Football - Both

Substituting the given values, we get:

100 = 40 + 70 - Both

Simplifying, we get:

Both = 40 + 70 - 100

Both = 10

Therefore, there are 10 students who are in both the hockey and football teams.

The required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

In geometry, corresponding sides and corresponding angles of polygons are compared as part of the tests for congruence and resemblance.

In these tests, the order of adjacency is maintained by pairing each side and each angle of one polygon with a side or angle of the other polygon.

Angles that are equal in size and are found on the same side as the transversal line are called corresponding angles.

Either both are acute or both are obtuse.

By creating an F shape, we can typically identify comparable angles.

So, now after reading the description we know exactly what are corresponding angles.

Now, we can easily tell that the pair of corresponding is:

∠HIK and ∠EFI

Therefore, the required pair of corresponding angles in the given situation is (A) ∠HIK and ∠EFI.

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The answers are:

(A) More compound interest than simple interest after 35 years: $260

(B) More compound interest than simple interest after 45 years: $445

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

The interest you earn on interest is known as compound interest.

Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

You will wind up with $110.25 at the conclusion of the second year.

Now, calculate according to the given graph as follows:

(A) More compound interest than simple interest after 35 years:

870 - 610 = $260

(B) More compound interest than simple interest after 45 years:

1150 - 705 = $445

Therefore, the answers are:

(A) More compound interest than simple interest after 35 years: $260

(B) More compound interest than simple interest after 45 years: $445

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There are 14 elements in both M and N.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines.

An element (or member) of a set is any one of the distinct objects that belong to that set. Writing means that the elements of the set A are the numbers 1, 2, 3 and 4. Sets of elements of A, for example , are subsets of A.

The principle of inclusion and exclusion (PIE) is a counting technique that computes the number of elements that satisfy at least one of several properties while guaranteeing that elements satisfying more than one property are not counted twice.

We can use the inclusion-exclusion principle to find the number of elements in both M and N.

n(MUN) = n(M) + n(N) - n(M∩N)

Substituting the given values, we have:

35 = 31 + 18 - n(M∩N)

Simplifying this equation, we get:

n(M∩N) = 14

Therefore, there are 14 elements in both M and N.

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Answer:

The formula for the nth term of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

In this case, a1 = -8 and r = -2. Therefore, we have:

a2 = a1 * r = (-8) * (-2) = 16

a3 = a2 * r = 16 * (-2) = -32

a4 = a3 * r = (-32) * (-2) = 64

So, the next three terms of the sequence are 16, -32, and 64.

Answer:

a₂ = 16

a₃ = -32

a₄ = 64

Step-by-step explanation:

The general formula for a geometric sequence is:

[tex]a_n=a_1 \cdot r^{n-1}[/tex]

where:

Substitute the given values of a₁ and r into the formula to create an equation for the nth term:

[tex]\implies a_n=(-8) \cdot (-2)^{n-1}[/tex]

To find the values of a₂, a₃ and a₄, substitute n = 2, n = 3 and n = 4 into the equation.

[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{2-1}\\&=(-8) \cdot (-2)^{1}\\&=(-8) \cdot (-2)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3&=(-8) \cdot (-2)^{3-1}\\&=(-8) \cdot (-2)^{2}\\&=(-8) \cdot (4)\\&=-32\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2&=(-8) \cdot (-2)^{4-1}\\&=(-8) \cdot (-2)^{3}\\&=(-8) \cdot (-8)\\&=64\end{aligned}[/tex]

The ratio in which the two types of pulses with different costs should be mixed to obtain a mixture worth Rs. 16.50 per kg is 1:2 or 0.5:1.

Let's start by assigning some variables to the problem. Let x be the ratio of the first type of pulses (costing Rs. 15 per kg) and y be the ratio of the second type of pulses (costing Rs. 20 per kg). We can then write:

x + y = 1 (since the two types of pulses make up 100% of the mixture)

We also know that the cost of the final mixture is Rs. 16.50 per kg. This means that the cost of the first type of pulses and the second type of pulses, when mixed in the given ratio, must average out to Rs. 16.50 per kg. We can express this as:

15x + 20y = 16.50(x + y)

Simplifying this equation, we get:

15x + 20y = 16.50x + 16.50y

3y = 1.5x

y/x = 0.5

This tells us that the ratio of the second type of pulses to the first type of pulses should be 0.5. We can also express this as a ratio of x:y, which would be 1:2. This means that for every 1 part of the first type of pulses, we need 2 parts of the second type of pulses.

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(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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The weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

Building Price per square ft ($) Number of sq. ft Building 1 75 and 125,000, Building 2 85 and 37,000, Building 3 90 and 77,500, Building 4 45 and 35,000, Building 5 50 and 40,000. Now, the formula to calculate weighted average price per square foot is,

Weighted Average Price per square foot = [ (Price per sq. ft of Building 1 * Number of sq. ft of Building 1) + (Price per sq. ft of Building 2 * Number of sq. ft of Building 2) + (Price per sq. ft of Building 3 * Number of sq. ft of Building 3) + (Price per sq. ft of Building 4 * Number of sq. ft of Building 4) + (Price per sq. ft of Building 5 * Number of sq. ft of Building 5) ] / Total sq. ft of all buildings.

Applying the values in the formula,

Weighted Average Price per square foot = [(75 * 125000) + (85 * 37000) + (90 * 77500) + (45 * 35000) + (50 * 40000)] / (125000 + 37000 + 77500 + 35000 + 40000)= [9375000 + 3145000 + 6975000 + 1575000 + 2000000] / 297500= 23092500 / 297500= 77.72

Therefore, the weighted average price per square foot of the five offices owned by Weyland Corp is 77.72.

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The parking lot has a width of around [tex]0.937[/tex] meters.

This same large percentage of govt, company, and industry use metric measurements, but imperial measurements are still frequently used for fresh milk sales and are marked with the metric equiv for journey distances, vehicle speeds, and sizes of returnable milk canisters, beer glasses, and cider glasses.

100 centimeters make up one meter. Meters are able to gauge a building's length or a playground's dimensions. 1000 meters make up one kilometer.

[tex]3760 cm = 37.6 m[/tex]

Solve for the width,

[tex]area = (1/2) * (base1 + base2) * height[/tex]

where,

base1 [tex]= 73.4 m[/tex]

base2 [tex]= 37.6 m[/tex]

area [tex]= 2,930.4[/tex] square meters

Let's solve for the height first,

[tex]height = 2 * area / (base1 + base2)[/tex]

[tex]height = 2 * 2,930.4 / (73.4 + 37.6)[/tex]

[tex]height = 2 * 2,930.4 / 111[/tex]

[tex]height = 56.16 m[/tex]

We nowadays can apply the algorithm to determine the width.

[tex]width = (area * 2) / (base1 + base2) * height[/tex]

[tex]width = (2 * 2,930.4) / (73.4 + 37.6) * 56.16[/tex]

[tex]width = 5856.8 / 111 * 56.16[/tex]

[tex]width = 5856.8 / 6239.76[/tex]

[tex]width = 0.937[/tex]

Therefore, the width of the parking lot is approximately [tex]0.937[/tex] meters.

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Answer:

27+2.25π

Step-by-step explanation:

Cube's volume is 3x3x3 = 27

The radius of the hemisphere is 3/2 = 1.5

Volume of a sphere is 4/3 π r^3

Plug in: 4/3 π 1.5^3 = 4.5π

Divide by 2: 2.25π

Total volume: 27+2.25π

The initial speed of a ball thrown horizontally from the roof of a building at a height of 54 m and hitting the ground at a height of 32 m from the bottom is equal to 9.64 m/sec.

A ball throws horizontally from the roof of a building. This is where we have to take horizontal movement into account.

Height of building = 54 m

Height of ground from base = 32 m Calculates the initial speed of the ball.

Since the ball is thrown horizontally, its initial velocity has no vertical component. When released, the ball is subject to gravity and accelerates downward until it hits the bottom. To determine how long the ball stayed in the air before hitting the ground, use the following formula,

d = 1/2×g×t²

where g --> acceleration due to gravity

t --> time

d --> the distance covered by ball before hitting the ground, g= 9.81 m/s².

So, 54 m = (1/2) × 9,81 m/s² × t²

=> t² = 54/4.90

=> t² = 540/49

=> t² = 11.02 sec²

=> t = 3.31963 ~ 3.32 sec

So the ball will stay in the air for about 3.32 seconds. Let v₀ₓ be the horizontal component of the initial velocity. According to the information of the problem, the ball landed 32 m from the bottom of the building. Let's make the initial position x₀ = 0. Then, the final horizontal displacement of a ball will be equals to 32 metres. Using the distance velocity relation, x = x₀ + v₀ₓt and substituting all known values in it,

=> 32 m = 0 + v₀ₓ × 3.32 sec

=> v₀ₓ = 32/3.32

=> v₀ₓ = 9.6385 ≈ 9.64 m/sec

Hence, required value is 9.64 m/sec.

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Complete question:

A ball is thrown horizontally from the roof of a building 54 m high and hits the ground 32 m from the base. What was the initial speed of the ball?

Answer:

3m

Step-by-step explanation:

red wire = 27

black wire= 12

so, we take HCF (highest common factor)

which would be 3 so all the wires would be cut into 3m long.

I hope it helps.

Answer:2m

Step-by-step explanation:

as the factors of 12 are:1, 2, 3, 4, 6 and 12

and the factors of 26 are:1, 2, 13 and 26

so if you are talking meters 2 would be the longest

i hope you get this right x

The final pyramid has a volume of 16 cubic inches. To find this, first multiply the number of blocks in each row together. 8 blocks in row 1 = 8 x 2 x 2 = 32; 6 blocks in row 2 = 6 x 2 x 2 = 24; 4 blocks in row 3 = 4 x 2 x 2 = 16; and 2 blocks in row 4 = 2 x 2 x 2 = 8. Then add all these numbers together to get 32 + 24 + 16 + 8 = 80. Finally, divide this number by 3 to get the volume, 80/3 = 16.

Answer:

We know that (23x)² + (1y)² = 7133029. From the right hand side of the equation, we can see that the last digit of 7133029 is 9. Using this information, we can deduce that the last digit of (23x)² must be 9, because (1y)² can only end in 1, 4, 5, 6 or 9.

Now we know that the last digit of (23x)² is 9 and the last digit of 23x is 3. Therefore the last digit of x is 3.

So, the last digit of the first number is 3. And the answer is (A) 3

Answer:

[tex]\frac{9}{4}[/tex]

Step-by-step explanation:

Answer:

   [tex]\frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{3}[/tex]

[tex]\frac{3}{4}[/tex] × [tex]\frac{3}{1}[/tex]  = [tex]\frac{9}{4}[/tex] ( to divide we make the other fraction reciprocal)

[tex]\frac{9}{4}[/tex] as mixed fraction= [tex]\frac{1}{4}{2}[/tex]