Ada' hitory teacher wrote a tet for the cla. The tet i 26 quetion long and i worth 123 point. Ada wrote two equation, where m repreent the number of multiple choice quetion on the tet, and repreent the number of eay quetion on the tet. M=26
3m8=123

The circumference of the circle is given by C = 2 * π * r, where r is the radius. In this case, the circumference of the circle is 2 * π * 14 = 88 cm.

Let's call the linear speed of the object v. Then, in 20 seconds, the object travels a distance of v * 20. This distance is equal to the arc length of the central angle of 1/2 radian:

v * 20 = (1/2) * (C/2π) = (1/2) * (88/2π) = 22/π cm

Solving for v, we get:

v = (22/π) / 20 = 22 / (20π) cm/s

The angular speed ω can be found by dividing the central angle by the time it took to travel that angle:

ω = 1/2 / 20 = 1/40 rad/s

So the linear speed of the object is v = 22 / (20π) cm/s, and the angular speed is ω = 1/40 rad/s.

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The lateral surface area of the frustum with a lower base radius of 6 inches, an upper base radius of 3 inches, and a height of 4 inches is 45π sq. inches is 45π sq. inches

The lateral surface area of the frustum is calculated using the given formula:

Lateral surface area of frustum = π × (sum of the radii) × √(difference of radii²  + height²)

Lower base radius of frustum = 6 inches

Upper base radius of frustum = 3 inches

Height of frustum = 4 inches

Lateral surface area of given frustum = π × (6 + 3) × √[(6 - 3)² + 4²]

                                                              = π × 9 × √[(9 + 16]

                                                              = 9π × 5

                                                              = 45π sq. inches

Hence, the lateral surface area of the given frustum is 45π sq. inches

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Answer: Alan would have to sell less than 540 boxes.

Step-by-step explanation:

The probability that a defective component can be detected by only one inspector is 0.2112. the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

(a) To calculate the probability that a defective component will be detected by only one inspector, we can use the formula for conditional probability: P(detected by first inspector | not detected by second inspector) = P(detected by first inspector and not detected by second inspector) / P(not detected by second inspector).

The probability that a defective component will be detected by the first inspector and not detected by the second inspector can be calculated as follows: P(detected by first inspector and not detected by second inspector) = P(detected by first inspector) * P(not detected by second inspector | detected by first inspector) = 0.88 * (1 - 0.88) = 0.1056.

The probability that a defective component will not be detected by the second inspector is: P(not detected by second inspector) = 1 - P(detected by second inspector) = 1 - 0.88 = 0.12.

The probability that a defective component will be detected by exactly one of the two inspectors can be calculated as follows: P(detected by exactly one inspector) = P(detected by first inspector and not detected by second inspector) + P(detected by second inspector and not detected by first inspector) = 0.1056 + 0.1056 = 0.2112.

(b) To calculate the probability that all three defective components in a batch escape detection by both inspectors, we can use the formula for independent events: P(all three defective components escape detection) = P(first defective component escapes detection) * P(second defective component escapes detection) * P(third defective component escapes detection) = (1 - 0.88)^3 = 0.00178.

So the probability that all three defective components in a batch escape detection by both inspectors is 0.00178.

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Complete question : components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). the first inspector detects 88% of all defectives that are present, and the second inspector does likewise. at least one inspector does not detect a defect on 24% of all defective components. what is the probability that the following occur? (a) A defective component will be detected only by the first inspector? A defective component will be detected by exactly one of the two inspectors? (b) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?

Answer:

x = 1

y = -1

Step-by-step explanation:

y = 3x + 4y

3x + 3y = 0

So, we have 2 equations that are

3x + 3y = 0

x + 2y = -1

Times the second equation by -3

3x + 3y = 0

-3x - 6y = 3

-3y = 3

y = -1

Now put -1 in for y and solve for x

x + 2(-1) = -1

x - 2 = -1

x = 1

Let's check

1 + 2(-1) = -1

1 - 2 = -1

-1 = -1

So, x = 1 and y = -1 is the correct answer.

1862 are the number of wistles that did not pass.

percentage, a relative value indicating hundredth parts of any quantity.

Given that out of 9799 wistles that a company manufactured

19% were rejected for shipment to stores because they did not pass the quality controll standards of the company.

We have to find the number of wistles that did not pass

To find this we have to find 19% of 9799

19/100×9799

0.19×9799

1861.81

Hence, 1862 are the number of wistles that did not pass.

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As per the angle of two arc minutes, the diameter is 16.67 meters.

The term diameter in math is known as a straight line passing through the center of a figure or body

Here we know that a circular object 1000 meters away subtends an angle of two arc minutes.

Here we know that that 1 minutes of arc is 60 seconds in other word it can be written as 1/60 minutes.

So for 2 minutes it can be written as

=> 2 x 1/60 = 1/30

Here we have know that the object is 1000 meters away, then the diameter is calculated as,

=> 1000/2 x 1/30

=> 500/30

=> 16.67

Therefore option (d) is coorect.

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In the right-angled triangle, the value of x is 16.7 degree.

In the given right-angled triangle, the angle x can be determined using the trigonometric function of tangent.  As length of the two legs is 3 feet and 10 feet, and the angle between hypotenuse and the 10 feet leg is x. In a right-angled triangle, the tangent of an angle is the ratio of opposite side to adjacent side. Hence,

Tan Ɵ = Opposite side/Adjacent side

As Ɵ = x, opposite side = 3ft, and adjacent side = 10 ft,

Tan x = 3/10

Tan x = 0.3

x = Tan^(-1) (0.3)

x = 16.7 degree

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The box plot of the  the gender of the pandas in the sample is illustrated below.

The term box plot in math is defined as  a chart tool used to quickly assess distributional properties of a sample and the so-called box-and-whiskers plot shows a clear indication of the quartiles of a sample as well of whether or not there are outliers.

Here we have given that Male pandas weigh, on average, between 80kg and 140kg, and females weigh, on average, between 70kg and 120kg.

The the data for the box plot is written as,

=> 70, 80, 120 and 140.

By using this data we have plotted the box plot for the gender of the pandas in the sample.

And we have predicted the following values through it.

Minimum =70

Q1=75

Median =100

Q3=130

Maximum =140

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Based on the scatter plot below, better prediction for x when y = 42 is 53.

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed. A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events. Scatter plots are used to demonstrate how much one variable affects another by plotting data points on a horizontal and vertical axis. Each row in the data table is represented by a marker, the location of which is determined by the values in the columns.

Here,

The scatter plot below shows that the better estimate for x when y = 42 is 53.

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Jack will require 6 tsp of baking powder if he uses 9 c of flour.

Given: Jack's pancake recipe calls for 3 cups of flour and 2 teaspoons of baking powder.

The amount of baking powder required if Jack uses 9 c of flour is to be determined.

Solution:

For 3 c of flour, 2 tsp of baking powder is required

2/3 tsp of baking powder is required for 1 cup of flour.

We must now determine how much baking powder to use with 9 cups of flour.

2/3X9 tsp of baking powder is required for 9 cups of flour.

= 6 tsp

Jack will therefore require 6 tsp of baking powder if he uses 9 c of flour.

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Answer:

To show that all three medians of a triangle intersect at the same point, we can use the property that the midpoint of each median is the centroid of the triangle.

The centroid of a triangle is a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. This means that the centroid divides each median in a 2:1 ratio, with two thirds of the median length being on one side of the centroid and one third on the other side.

Since the centroid is the same for all three medians, it follows that all three medians must intersect at the same point, which is known as the centroid or the center of gravity of the triangle. This point is denoted by the letter G.

Therefore, we can conclude that all three medians of triangle ABC intersect at point G, which is the centroid of the triangle.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-12x < 36}[/tex]

[tex]\huge\textbf{DIVIDE \boxed{\rm{\bf -12}} to both sides:}[/tex]

[tex]\mathsf{\dfrac{-12}{-12}x < \dfrac{36}{-12}}[/tex]

[tex]\huge\textbf{SIMPLIFY it:}[/tex]

[tex]\mathsf{x < \dfrac{36}{-12}}[/tex]

[tex]\mathsf{x > -3}[/tex]

[tex]\large\text{It is a(n) \boxed{\rm{o p e n e d}} circle SHADED to the RIGHT of your number line}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x > -3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The equivalent fraction is used such that operations like addition and subtraction can be done on fractions that don't have a common denominator.

Equivalent fractions are those fractions that reflect the same value despite having numerators and denominators that differ.

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction.

In their most basic form, all equivalent fractions are reduced to the same fraction. The equivalent fraction is used to enable operations on fractions without a common denominator, such as addition and subtraction.

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If a patient took 400 mg of acetaminophen which has the half life of 4 hour, the amount of acetaminophen that will be in the patient is:

The half-life of acetaminophen is 4 hours, which means that every 4 hours, half of the initial dose of 400 mg will still remain in the patient's body.

At 4 hours after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / 2 = 200 mg

At 2 hours after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / (2^(4/4)) = 200 mg / 2 = 100 mg

At 1 hour after taking the dose, the amount of acetaminophen in the patient's body would be:

400 mg / (2^(4/4)) = 100 mg / 2 = 50 mg

In conclusion, the amount of acetaminophen in the patient's body decreases by half every 4 hours.

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Answer:

f(n) = 32 - 8n

Step-by-step explanation:

24, 16, 8, 0

f(n) = 24 - 8 x (n-1)

f(n) = 32 - 8n

The matrix D is important because it is the diagonal representation of the matrix A, which makes it easier to work with and understand.

When diagonalizing a matrix, the goal is to find a diagonal matrix (D) that is similar to the original matrix (A). This means that the matrix D will have the same eigenvalues as the matrix A and will be represented in a more simplified form.

To find the matrix D, you must first find the eigenvalues of the matrix A. These eigenvalues can be found by solving the characteristic equation, which is found by setting the determinant of the matrix (A - λI) to zero, where λ is the eigenvalue and I is the identity matrix.

Once the eigenvalues are found, you can then find the eigenvectors, which are non-zero vectors that satisfy the equation

=> Av = λv,

where v is the eigenvector.

Once you have both the eigenvalues and eigenvectors, you can then arrange them into the matrix D, where the eigenvalues are on the main diagonal and the eigenvectors are the columns.

To make sure that D is diagonal, you may need to scale the eigenvectors so that the entries are integers. This is called normalizing the eigenvectors.

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Answer:

If Maria uses 2 parts cream and 3 parts milk, then for every 2 parts of cream, she uses 3 parts of milk.

Since she uses 8 liters of cream, we can find the total volume of mixture by finding the equivalent volume of milk that she used.

To find the equivalent volume of milk, we multiply the volume of cream by the ratio of milk to cream:

8 liters * (3 parts milk) / (2 parts cream) = 12 liters

So Maria used 8 liters of cream and 12 liters of milk for a total volume of 20 liters.

The value of a in the equation in the simplest form will be 17 / 6.

We are given an equation:

x³ / x^(1/6) = x^(a)

We need to evaluate the left hand side to find the value of a in the equation in simplest form.

We know that:

x^ (a) / x^ (b) = x^ ( a - b)

Using this, we get that:

x^ (3 - 1/6) = x^ (a)

x^ (17/6) = x^ (a)

By comparing the bases, we get the value of a as:

a = 17 / 6.

Therefore, the value of a in the equation in the simplest form will be 17 / 6.

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The sum of all the elements present in the first six rows of the Pascal's triangle is equal to 63.

Pascal's triangle elements are represented by :

                                                     1

                                             1                1

                                   1                2                 1

                           1              3                 3             1

                      1           4                 6              4             1

               1            5            10               10             5            1

Sum of all the elements of first six rows are:

First row : 1

Second row : 1 + 1 = 2

Third row : 1 + 2 + 1 = 4

Fourth row : 1 + 3 + 3 + 1 = 8

Fifth row : 1 + 4 + 6 + 4 + 1 = 16

Sixth row : 1 + 5 + 10 + 10 + 5 + 1 = 32

Sum of all the six row elements = 1 + 2 + 4 + 8 + 16 + 32

                                                    = 63

Therefore, the sum of all the elements of the first six row of Pascal's triangle is equal to 63.

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Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Maximum Operating Stress, or MOST, is the highest amount of stress to which a structure can be subjected without experiencing permanent deformation.

Maximum Tolerable Moment, or MTM, is the greatest moment that a structure can withstand without breaking. Structural analysis techniques, such as finite element analysis and structural testing, are often used to determine this. When designing and building a structure, MTM must be considered because it is crucial for structural safety. Maximum Operating Stress, or MOST, is the highest stress to which a structure can be subjected without experiencing permanent deformation. This is often decided by running a stress study on the structure and taking into account the materials that were utilised to build it. The building must be able to sustain the anticipated loads throughout its lifespan, which is of utmost importance. Additionally, it is crucial to prevent structural deterioration over time. When designing and building a secure structure, MTM and Most must both be taken into account.

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Answer:

3/2

Step-by-step explanation:

(a) The first three terms, in ascending powers of x, of the binomial expansion of (2 + kx)² are:

(2 + kx)² = 2² = 4

(2 + kx)² = 2 * 2 * kx = 4kx

(2 + kx)² = 2 * k² x² = 4k² x²

(b) If the coefficient of x is 6 times the coefficient of x, then 6 = 4k. Therefore, k = 6/4 = 3/2.

According to trigonometry, the value of sin y cos x.

The term called trigonometry is defined as the type of mathematics that deals with the relationship between the sides and angles of triangles.

Here we know that the function is written as

=> sin x coy y

where r [0, 1/2] [0, 1/2]

Here by Using Fubini’s theorem we can write this as an iterated integral to get,

=> [tex]\int\limits^{1/2}_0\int\limits^{1/2}_0 {sinxcosy} \, da[/tex]

Here the Fubini's theorem states that  the double integral over a region is equal to an iterated integral, which is computed in a similar manner with definite integrals of functions of single variable.

When we integrate the expression, then we get

=> [tex]\int\limits^{1/2}_0 {cos(1+y)sin(1+x)} \, da[/tex]

Again we have to integrate this one, then we get the value as,

=> sin y cos x.

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Step-by-step explanation:

Given eqn

y=1/3x+4

1/3x-y+4=0

eqn of line perpendicular to the given eqn.,

x+1/3y+k=0

since the reqd. line contains the point (2,-3)

2+1/3 (-3)+k=0

2-1+k=0

k=-1

so

x+1/3y-1=0

1/3y=1-x (in slope intercept form)

Answer:

Week 7

Step-by-step explanation:

Connie will have $170 in week 7, because in 3 weeks she will add $30 to her account.

Ling will have $117.5 in week 7, because in 3 weeks he will add $4.50 to his account.

170-117.5=52.5

52.5 is greater than 50, so it satisfies the question.

Five million four thousand three hundred can be written in standard form as 5,004,300.

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Answer:

The number five million four thousand three hundred can be written in standard form as `5,004,300`. In scientific notation, it can be written as `5.0043 x 10^6`.

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The container holds 5 mL of fluid, which is less than 500 mL of fluid.

5 mL is much smaller than 500 mL, so the container holds less than 500 mL of fluid.

The numerator and denominator of a unit conversion factor have the same quantity in different units. Multiplying by a conversion factor has no effect on the number's inherent value because the factor is comparable to multiplying by 1.

The numerator is the intended unit, whereas the denominator is the supplied unit.

The primary guideline is to multiply when converting from a bigger unit to a smaller unit. Divide to convert from a smaller unit to a larger unit. You will reduce the number, and as you are aware, division is all about reducing numbers.

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Answer:  The length of AC is approximately 5.196 units.

Step-by-step explanation:

To find the length of AC, we can use the fact that DE is parallel to AC and AD is parallel to FE, which forms a pair of corresponding angles. Therefore, we can set up a proportion using the fact that corresponding angles are congruent.

DE/AC = AD/FE

We know that DE = 5 and AD = 6, so we can substitute these values into the proportion:

5/AC = 6/FE

We can cross-multiply and solve for AC:

5 * FE = 6 * AC

Next, using the fact that triangle ABC is a triangle, we can use the Pythagorean theorem to find the value of FE.

AB^2 + BC^2 = AC^2

17^2 + BC^2 = (AC)^2

289 + BC^2 = AC^2

Now, substitute the value of FE into the equation we have,

5 * sqrt(AC^2 - 289) = 6 * AC

multiply the both sides of the equation by the reciprocal of 5,

sqrt(AC^2 - 289) = (6/5) * AC

Square both sides of the equation,

AC^2 - 289 = 36/25 * AC^2

subtract the left side from the right side

-289 = -(36/25) * AC^2

divide both sides by -(36/25)

AC = sqrt(289/(1-(36/25)))

AC = sqrt(289/11/25)

AC = sqrt(289/275)

AC = sqrt(289/11)

AC = sqrt(26)

AC = approx 5.196152422706632

Therefore, the length of AC is approximately 5.196 units.

Answer:

Nykai's position in relation to the ocean surface is 13.6 meters. She started 10 meters below the surface, swam down 6.1 meters deeper, and then swam up 2.5 meters. Therefore, her position in relation to the ocean surface is 10 - 6.1 + 2.5 = 13.6 meters.

Step-by-step explanation:

The solution for each right triangle are:

(a) BC = 13.9 units, AB = 11.9 units

(b) XZ = 17.5 units

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

(a) Using trigonometric ratio

sin 31.2° = 7.2/BC   (Sine = opposite/hypotenuse)

BC = 7.2/sin 31.2°

BC = 13.9 units

tan 31.2° = 7.2/AB (Tan = opposite/adjacent)

AB = 7.2/tan 31.2°

AB = 11.9 units

(b) XZ = √(14.4² + 10.0²)     (Pythagoras theorem)

XZ = 17.5 units

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