1.02 1.05 1.08 1.00 1.00 1.06 1.08 1.01 1.04 1.07 1,00 kg Does this support the hypothesis, at 5%, that the mean weight for the whole batch is over 1.00 kg? 7.4 The expected lifetime of electric bulbs produced by a given process was 1500 hours. To test a new batch a sample of 10 was taken. This showed a mean lifetime of 1455 hours. The standard deviation of the production is known to still be 90 hours. Test the hypothesis, at 1% significance, that the mean lifetime of the electric light bulbs has not changed. 7.5 A sleeping drug and a neutral control were tested in turn on a random sample of 10 patients in a hospital. The data below represent the differences between the number of hours sleep under the drug and the neutral control for each patient: 2.0 0.2 -0.4 0.3 0.7 1.2 0.6 1.8 -0.2 1.0 hours Test, at 5%, the hypothesis that the drug would give more hours sleep on average than the control for all the patients in the hospital. 7.6 A coin is suspected of being biased. It is tossed 200 times and 114 heads occur. Carry out a hypothesis test to see whether the coin is indeed biased at 1% significance for anle of sight employees both?

By using trigonometric relations, we will see that x = 9.97°.

First, we need to find the bottom cathetus of the smaller triangle, we will use the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus).

Where:

Replacing that we get:

Tan(26°) = 50ft/k

Solving this for k, we get:

k = 55ft/tan(26°) = 112.8 ft

Now, we can see that the longer triangle adds 200ft to this cathetus, so now we will have:

Then we have:

Tan(x) = (55ft/312.8ft)

Using the inverse tangent function in both sides, we get:

x = Atan(55ft/312.8ft) = 9.97°

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Answer:

Standard form is Ax + By = C

Step-by-step explanation:

Answer:

The standard form is Ax + Bx = C

Answer:

1) \(y=\frac{3}{2}x+8\)

2)\(y=\frac{13}{11}x +\frac{12}{11}\)

3)\(y=\frac{9}{7}x+1\)

4)\(y=\frac{1}{3}x-2\)

5)\(y=-\frac{6}{5}x-3\)

6)\(y=4x-1\)

7)\(y=\frac{11}{4}x-8\)

8)\(y=\frac{11}{8}x+6\)

Answer:

\(\sf 1) 3x-2y=-16\)

subtract both sides by 3x:

\(\sf -2y=-16-3x\)

\(\sf \cfrac{-2y}{-2} =\cfrac{3x-16}{-2}\)

\(\boxed {\sf y=\frac{3}{2}x +8}\)

________________

\(\sf 2) 13x-11y=-12\)

Subtract 13x from both sides:

\(\sf 13x+11y-13x=-12-13x\)

\(\sf \cfrac{-11y}{-11} =\cfrac{-12-13x}{-11-11}\)

\(\boxed {\sf y=\cfrac{13}{11} \:x+\cfrac{12}{11} }\)

___________________

\(\sf 3) 9x-7y=-7\)

Subtract 9x from both sides:

\(\sf \cfrac{-7y}{-7} =\cfrac{9x-7}{-7}\)

\(\boxed {\sf y=\cfrac{9}{7} \:x+1}\)

___________________

\(\sf 4)x-3y=6\)

Add 3y from both sides:

\(\sf x-3y+3y=6+3y\)

\(\sf x=6+3y\)

Subtract 6 from both sides:

\(\sf x-6=3y\)

Divide both sides by 3:

\(\sf \cfrac{x}{3}-\cfrac{6}{3} =\cfrac{3y}{3}\)

\(\sf \cfrac{1}{3} \:x-2=y\)

\(\boxed {\sf y=\cfrac{1}{3} \:x-2}\)

____________________

\(\sf 5) 6x+5y=-15\)

Subtract 6x from both sides:

\(\sf \cfrac{5y}{5}=\cfrac{-6x-15}{5}\)

\(\boxed {\sf y=-\cfrac{6}{5} \:x-3 }\)

_____________________

\(\sf 6) 4x-y=1\)

Subtract 4x from both sides:

\(\sf \cfrac{-y}{-1} =\cfrac{-4x+1}{-1}\)

\(\boxed {\sf y=4x-1}\)

_______________________

\(\sf 7)11x-4y=32\)

Subtract 11x from both sides:

\(\sf \cfrac{-4y}{4} =\cfrac{-11x+32}{-4}\)

\(\boxed {\sf y=\frac{11}{4} \:x-8}\)

_______________________

\(\sf 8) 11x-8y=-48\)

Subtract 11x from both sides:

\(\sf \cfrac{-8y}{-8} =\cfrac{11-48}{-8}\)

\(\boxed {\sf y=\frac{11}{8} \:x+6}\)

________________________________

Answer:

74 in²

Step-by-step explanation:

Area painted by Micah = 96 ft²

Area painted by Noah = 13750 in²

Converting both area to the same unit :

1 ft² = 144 in²

Therefore, Area painted by Micah :

96 * 144 = 13824 in²

13824 in² > 13750 in² ; hence, Micah painted more ;

To obtain how much more area Micah painted than Noah :

Area painted by Micah - Area painted by Noah

13824 in² - 13750 in²

= 74 in²

The sum of the perimeters of the squares with areas 252 cm², 175 cm², and 112 cm² is __ cm (in radical form).
We get the sum of perimeter in radical form is 158.72 cm.

To find the perimeters of the squares, we need to determine the length of their sides. Since the area of a square is equal to the square of its side length, we can find the side lengths of the squares by taking the square root of their respective areas.

For the square with an area of 252 cm², the side length is √252 cm. Similarly, the side lengths of the squares with areas 175 cm² and 112 cm² are √175 cm and √112 cm, respectively.

The perimeter of a square is four times its side length, so the perimeters of the squares are 4√252 cm, 4√175 cm, and 4√112 cm.

we multiply the side length by 4 for each square and add them up: (4 * 15.87) + (4 * 13.23) + (4 * 10.58) = 63.48 + 52.92 + 42.32 = 158.72 cm.



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Answer:

y= -x+2, f(x) = -x+2

Step-by-step explanation:

the slope-intercept form is

y= mx+b where mis the slope and b is the y-intercept

here b=2 because is where the line intersects the y-axis

slope m= rise/run = -1/1 = -1

y= -x+2

in standard form is

f(x) = -x+2

Answer:

13.5

Step-by-step explanation:

the answer is 13.5, because you do the proportionate equations of 6/4 = x/9, and then you cross multiply to get 4x=54, and then you isolate x, so the answer is 13.5

Answer:

guess

Step-by-step explanation:

The equation of the ellipse with a major axis 24 units long parallel to the x-axis, a minor axis 22 units long, and a center at (6,1) can be written in the standard form.

The standard form of an ellipse with a major axis parallel to the x-axis is given by: ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1. where (h, k) represents the center of the ellipse, and a and b represent half the lengths of the major and minor axes, respectively. In this case, the center is (6, 1), so h = 6 and k = 1. The major axis has a length of 24 units, so a = 24 / 2 = 12. The minor axis has a length of 22 units, so b = 22 / 2 = 11. Substituting these values into the standard form equation, we get: ((x - 6)^2 / 12^2) + ((y - 1)^2 / 11^2) = 1.

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The molar solubility of lead fluoride in a 0.159 M lead nitrate solution is approximately 6.44 x 10⁻⁴ M.

The molar solubility of lead fluoride in a 0.159 M lead nitrate solution can be determined using the solubility product constant (Ksp) for lead fluoride. The solubility product constant represents the equilibrium constant for the dissolution of a sparingly soluble salt.

In this case, the solubility product constant (Ksp) for lead fluoride is given as 3.7 x 10⁻⁹. To find the molar solubility of lead fluoride, we need to consider the stoichiometry of the dissolution reaction.

The balanced equation for the dissolution of lead fluoride (PbF₂) is:

PbF₂(s) ⇌ Pb²⁺(aq) + 2F⁻(aq)

From the equation, we can see that one mole of lead fluoride produces one mole of lead ions (Pb²⁺) and two moles of fluoride ions (F⁻). Therefore, if the molar solubility of lead fluoride is represented by "x" moles per liter, the concentration of lead ions (Pb²⁺) will also be "x" M, and the concentration of fluoride ions (F⁻) will be "2x" M.

Since we are given that the concentration of lead nitrate (Pb(NO₃)₂) is 0.159 M, we can assume that the concentration of lead ions (Pb²⁺) is equal to the initial concentration of lead nitrate.

Using the solubility product constant (Ksp) expression, we can write:

Ksp = [Pb²⁺][F⁻]²

Substituting the concentrations in terms of "x" and "2x", we get:

3.7 x 10⁻⁹ = (x)(2x)²
3.7 x 10⁻⁹ = 4x³

Now, solve for "x" by taking the cube root of both sides:

x = (3.7 x 10⁻⁹)^(1/3)
x ≈ 6.44 x 10⁻⁴ M

Therefore, the molar solubility of lead fluoride is approximately 6.44 x 10⁻⁴ M.

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Answer:

Step-by-step explanation:

Time in travel:

Average speed is 5 mph

Distance travelled:

Correct choice is A

Total time taken

Distance

Option A

Answer:

8=73 degrees

5=107 degrees

Step-by-step explanation:

Please mark me brainliest :D

Answer:

Angle 5 is 107 degrees

Angle 8 is 7s degrees

Step-by-step explanation:

First find angle 5. Since the lines are parallel and cut by a transversal, we can say that Angle 3 and Angle 5 are congruent (same measure) since they are alternate interior angles.

Since Angle 3 is 107 degrees, Angle 5 would also be 107 degrees.

Angle 8 is supplementary to Angle 5.

Angle 5 + Angle 8 = 180

Since we know Angle 5 is 107: 107 + Angle 8 = 180

Angle 8 would then be 73 degrees.

Answer:

Collect, analyze, interpret and present quantitative data

Answer: Collect, analyze, interpret and present quantitative data

Yes, The matrix does indeed have an inverse.

A rectangular or square array of figures, characters, or expressions arranged in rows and columns is known as a matrix. In many different disciplines, including computer science, engineering, physics, and mathematics, matrices are frequently employed and Matrix representations of physical phenomena, such as the wave functions in quantum mechanics, are common in physics. To represent and simulate complicated systems, like circuits and control systems, engineers employ matrices. Matrix-based techniques are utilised in a variety of computer science applications, including image processing, computer graphics, and machine learning.

The elements of a matrix, which are often written with a rectangular bracket, can be used to symbolise it.

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Yes, the inverse of a matrix exists if the determinant of the matrix is -13.

What is a matrix?

Linear equations are expressed using matrices, which are ordered rectangular arrays of numbers. Columns and rows make up a matrix. Mathematical operations like addition, subtraction, and matrix multiplication can also be done on matrices. If there are m rows and n columns, the matrix is represented as m × n matrix. The inverse of a matrix is available only for square matrices.

Now the determinant is a value that is associated with a square matrix.

The product of all the elements in any row or column and their corresponding co-factors is the determinant of a matrix.

For an inverse matrix to exist, the determinant of the matrix should not be zero. This is because the determinant of the inverse matrix is the inverse of the determinant of the original matrix.

If the determinant is zero, then the determinant of the inverse matrix will be 1/0, which is undefined.

So, as long as the determinant is not equal to zero, the inverse matrix exists.

Therefore the inverse of a matrix exists if the determinant of the matrix is -13.

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The correct statement about the congruent figures is,

⇒ a reflection across the x-axis, followed by a translation 3 units to the right.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Three congruent figures are shown in the coordinate plane.

Now, From figure A and figure B,

Figure B is reflection across the x-axis, followed by a translation 3 units to the right across the figure A.

Thus, The correct statement about the congruent figures is,

⇒ a reflection across the x-axis, followed by a translation 3 units to the right.

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Roman has a certain amount of money. if he spends 15, then he has 14 of the original amount left. Roman had originally 20.

To find out how much money Roman had originally, you can follow these steps:
Step 1: Let the original amount of money be "x".
Step 2: According to the problem, if Roman spends $15, he has 1/4 of the original amount left.

So, after spending 15, he has (1/4)x left.
Step 3: Since he spent $15, we can write the equation as: x - 15 = (1/4)x.
Step 4: To solve for x, first multiply both sides of the equation by 4 to get rid of the fraction:

4(x - 15) = 4(1/4)x => 4x - 60 = x.
Step 5: Subtract "x" from both sides:

4x - x - 60 = 0 => 3x - 60 = 0.
Step 6: Add 60 to both sides:

3x = 60.
Step 7: Divide both sides by 3 to find the value of x:

x = 60 / 3 => x = 20.

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The optimal product mix was found to be to produce 600 units of x₁ and 400 units of x₂, yielding a total revenue of Php 22,000.

The mathematical model for the given problem is as follows:Maximize Z = 20x₁ + 25x₂

where x1 is the quantity of x₁and x₂is the quantity of x₂ produced subject to the following constraints

x₁ + 2x₂≤ 1500 (machine A constraint)

x₁ +x₂ ≤ 1300 (machine B constraint)

x₂≤ 500 (machine C constraint)x1 ≥ 0, x2 ≥ 0 (non-negativity constraint)

The mathematical model was solved using MS Excel Solver to obtain an optimal solution.

The optimal solution was found to be x1 = 600 and x2 = 400, which yields a total revenue of Php 22,000.

Therefore, the optimal product mix is to produce 600 units of X1 and 400 units of X2.

A screenshot of the MS Excel Solver solution is attached below.

:The optimal product mix was found to be to produce 600 units of X1 and 400 units of X2, yielding a total revenue of Php 22,000.

The mathematical model was formulated using the given data and solved using MS Excel Solver. The screenshot of the solution using MS Excel Solver has been attached above.

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Answer:The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Step-by-step explanation:

The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

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Answer:

y + 1 = 6(x - 4)

Answer: y + 1 = 6(x - 4)

Answer:

1 out of 13

Step-by-step explanation:

Answer:l=17, w=5

Step-by-step explanation:

Answer: -40t+200

Step-by-step explanation:

The equation for D, in terms of t, represents Angel's distance from City A tt hours after leaving his house is D = 40t.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

Angel is going to drive from his house to City A without stopping. Angel's house is 200 miles from City A.

After driving for 4 hours, he will be 40 miles away from City A.

From the data given in the question:

200 - 40 = 160

160/4 = 40 km/h

D = 40t

Thus, the equation for D, in terms of t, represents Angel's distance from City A tt hours after leaving his house is D = 40t.

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Using sinusoidal function concepts, it is found that the values are A = 2 and D = 2.

The cosine function, with standard period, is represented by:

\(y = A\cos{x} + D\)

In which:

In this problem, the amplitude is of 4 - 0 = 4, hence:

\(2A = 4\)

\(A = \frac{4}{2}\)

\(A = 2\)

The standard function has range between -2 and 2, in this problem it is between 0 and 4, hence the vertical shift up is of 2 units, that is, D = 2.

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Answer:

- 1

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 6, 6 ]

From the graph

f(b) = f(6) = - 2

f(a) = f(- 6) = 10 , thus

average rate of change = \(\frac{-2-10}{6-(-6)}\) = \(\frac{-12}{12}\) = - 1

step by step explanation:

I don't know

sorry really wanna help

A 6-ounce serving of salmon has 2 grams of saturated fat. To determine the percentage of saturated fat in the serving of salmon, we divide the amount of saturated fat by the total amount of fat and multiply by 100.

The total amount of fat in the serving is 7 grams. So:2g / 7g × 100% = 28.57%Therefore, 28.57% of the 6-ounce serving of salmon is saturated fat. This information can be helpful for individuals who are monitoring their saturated fat intake due to health concerns such as high cholesterol or heart disease.

Saturated fat is a type of fat that is solid at room temperature and is typically found in animal products such as meat and dairy. Consuming too much saturated fat can contribute to high cholesterol levels and increase the risk of heart disease. It is important to consume a balanced diet and limit intake of saturated and trans fats.

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This can be calculated by dividing the initial reserves of 300 million tonsThe year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

a) If the extraction of minerals is kept constant at 50 million tons per year, the reserves will be exhausted in 6 years. This can be calculated by dividing the initial reserves of 300 million tons by the annual extraction rate of 50 million tons.

b) If the extraction of minerals declines by 15 percent each year due to increasing extraction costs, we need to determine how long the mineral reserves will last.

To do this, we can calculate the cumulative extraction each year until it reaches or exceeds the initial reserves of 300 million tons. Assuming the extraction declines by 15 percent each year, we can calculate the extraction in each subsequent year and add it to the cumulative extraction from previous years. The year when the cumulative extraction reaches or exceeds 300 million tons will be the time when the mineral reserves are exhausted.

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The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

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