Suppose a large candy machine has 45% orange candies. Imagine taking an SRS of 25 candies from the machine and observing the sample proportion
pof orange candies. Find the standard deviation of the sampling distribution of
pCheck to see if the 10% condition is met.

Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,

    determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.

The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.

Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9

The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.

When a ball falls from height, it gains potential energy.

Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height

PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules

Initial kinetic energy (KE) = PE of Basketball

KE of Basketball = 18.4 J

Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.

Using the coefficient of restitution (e) we can find the velocity of the balls after collision

   v1 - v2 = -e(u1 - u2)

Initial momentum (P) = Final momentum (P)

before the collision  P = m1u1 + m2u2

after collision  P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P

                           = (0.625 kg * v1) + (0.0585 kg * v2)

        Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)

     Here, m1 = mass of basketball

                     = 0.625 kg,

                m2 = mass of tennis ball

                      = 0.0585 kg,

  u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)

Also given that the time taken by the balls to meet is 0.15 seconds

Let h be the height to which the tennis ball bounces after the collision.

When the tennis ball bounces to height h, it gains potential energy.

KE + PE = Total energy

             = Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h

              = (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²

              = (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²

              = (1/2) * u2² - g * h

Substituting the values of u1, u2, m1, m2, e, t and g, we get:

v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1

   = 1.96 m/sv2

    = (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2

    = 5.5 m/s

Here, u1 = u2 = 0.

Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J

                = -0.286 J - 0.572 h0.572 h

                = -12.83 J / 2h

                = -12.83 J / (2 * 0.572)

                = 11.2 m

Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.

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Answer: 4x(x - 4)

Step-by-step explanation:

4x² - 16x = 4x(x - 4)

Now we can see that the expression inside the parentheses can also be factored:

x - 4 = (x - 4)

So the fully factorized expression is:

4x² - 16x = 4x(x - 4) = 4x(x - 4)

Answer:

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- 4x( x + 4 )

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Step-by-step explanation:

ㅤ

[tex]\large{\pmb{\sf{ - 4x^{2} - 16x}}}[/tex]

ㅤ

[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{4}} \: As \: Common:-}}}}[/tex]

ㅤ

[tex]\large{\pmb{\sf{\leadsto{- 4(x^{2} + 4x)}}}}[/tex]

ㅤ

[tex]\large{\underline{\underline{\sf{Taking \: Out \: {\green{x}} \: As \: Common:-}}}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\pmb{\sf{\leadsto{- 4x(x + 4)}}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━

[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]

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[tex]\large{\dashrightarrow}[/tex] Two positive always makes positive sign when multiplied.

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[tex]\large{\dashrightarrow}[/tex] Two negatives always makes positive sign when multiplied.

ㅤ

[tex]\large{\dashrightarrow}[/tex] A positive and a negative always makes negative sign when multiplied.

ㅤ

[tex]\large{\dashrightarrow}[/tex] The sum of two positives is always positive with a positive sign.

ㅤ

[tex]\large{\dashrightarrow}[/tex] The sum of two negatives is always positive with a negative sign.

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[tex]\large{\dashrightarrow}[/tex] The sum of a positive and a negative is always negative with the sign of whose number is greater.

The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.

In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.

Answer :

1. We are given with a parallelogram whose opposite sides are :-

We know that opposite sides and angles of the parallelogram are equal.

PS = RQ

[tex] \implies \sf \: (-1 + 4x) = (3x + 3) \\ [/tex]

[tex] \implies \sf \: 4x - 3x = 3 + 1\\ [/tex]

[tex] \implies \sf \: x = 4 \\ [/tex]

Length of RQ is (3x + 3)

Substituting value of x = 4 in RQ.

[tex] \implies \sf \: (3x +3) \\ [/tex]

[tex] \implies \sf \: 3(4) + 3 \\ [/tex]

[tex] \implies \sf \: 12 + 3 \\ [/tex]

[tex] \implies \sf \: 15 \\ [/tex]

Therefore, Length of RQ will be 15

2. Find [tex] \sf \angle G [/tex]

We are given with :-

Since, Opposite angles of parallelogram are also equal :

[tex]\angle G = \angle E \\ [/tex]

[tex]\implies \sf \: 5x -9 = 3x + 11 \\ [/tex]

[tex]\implies \sf \: 5x - 3x = 11 +9 \\ [/tex]

[tex] \implies \sf \: 2x = 20 \\ [/tex]

[tex] \implies \sf \: x = \dfrac{20}{10} \\ [/tex]

[tex] \implies \sf \: x = 10 \\ [/tex]

Since [tex] \sf \angle G [/tex] is 5x - 9.

Substituting value of (x = 10) in [tex] \sf \angle G [/tex]

[tex] \implies \sf \: 5(10) - 9 \\ [/tex]

[tex] \implies \sf \: 50 -9 \\ [/tex]

[tex] \implies \sf \: 41 \\ [/tex]

Therefore, [tex] \sf \angle G [/tex] is 41.

Answer:

19. QR = 15 units.

20. m ∡G=41°

Step-by-step explanation:

The properties of a parallelogram are:

Question No. 19.

We know that the opposite side of parallelogram is equal, So

PS=QR

-1+4x=3x+3

First of all we will find the value of x.

-1 + 4x = 3x + 3

Subtracting 3x from both sides, we get:

x - 1 = 3

Adding 1 to both sides, we get:

x = 4

SO, QR=3*4+3=15

Side QR is 15 units.

Question No. 20.

We know that the opposite angle of parallelogram is equal, So

EF=GD

3x+11=5x-9
Subtracting 3x from both sides:

3x + 11 - 3x = 5x - 9 - 3x

11 = 2x - 9

Next, we can add 9 to both sides to isolate the variable term on one side:

11 + 9 = 2x - 9 + 9

20 = 2x

Finally, we can solve for x by dividing both sides by 2:

20/2 = 2x/2

x=10

Now

m ∡G=5x-9=5*10-9=41°

therefore m ∡G=41°

Answer:

We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰

For a pentagon, n=5

so,

[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]

[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]

[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]

[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]

[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]

[tex] \rm \implies \: x + y = 90[/tex]

[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]

There are many formulas related to a pentagon. A few basic ones are given below.

The rounded value of 25.71 to 2 decimal places is 25.71 itself.

To round 25.71 to 2 decimal places, we need to look at the third decimal place, which is 1.

If the third decimal place is 5 or greater, we round up the second decimal place. If the third decimal place is less than 5, we simply drop it and keep the second decimal place as is.

In this case, the third decimal place is 1, which is less than 5, so we simply drop it and keep the second decimal place as is. Therefore, 25.71 rounded to 2 decimal places is:

25.71 ≈ 25.71 (no rounding necessary)

So, the rounded value of 25.71 to 2 decimal places is 25.71 itself.

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1) The area of a circle with a diameter of 1 m is approximately 0.7854 square meters.

2) The area of a circle with a diameter of 100 cm is approximately 7853.98 square centimeters.

3) The area of a circle with a radius of 100 cm is approximately 314159.27 square centimeters.

4) The area of a circle with a radius of 500 mm is approximately 785398.16 square millimeters.

The formula for the area of a circle is A = πr², where A is the area and r is the radius of the circle.

1) If the diameter of the circle is 1 m, then the radius is 0.5 m. Therefore, the area of the circle is:

A = πr² = π(0.5)² = π(0.25) ≈ 0.7854 square meters.

2) If the diameter of the circle is 100 cm, then the radius is 50 cm. Therefore, the area of the circle is:

A = πr² = π(50)² = π(2500) ≈ 7853.98 square centimeters.

3) If the radius of the circle is 100 cm, then the area of the circle is:

A = πr² = π(100)² = π(10000) ≈ 314159.27 square centimeters.

4) If the radius of the circle is 500 mm, then the area of the circle is:

A = πr² = π(500)² = π(250000) ≈ 785398.16 square millimeters.

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Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

Answer: 96

Step-by-step explanation:

M = 180 - 84 = 96

m<k = 96

The total number of pairwise comparisons for k is (k*(k-1))/2.

There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.

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c) The locus of z is a straight line parallel to the y-axis for x = 4.

The locus of a line is the set of all points that satisfy a given geometric condition related to that line. The term "locus" refers to the path or trajectory followed by a point or set of points that satisfy the given condition.

To determine the locus of z in the given equation |z-2| = |z-6|, we can use the definition of the absolute value of a complex number which is

[tex]|x + iy| = \sqrt{(x^2 + y^2)}[/tex]

So, we can square both sides of the given equation to get:

[tex]|z-2|^2 = |z-6|^2[/tex]

put z = (x + iy)

[tex]|x+iy-2|^2 = |x+iy-6|^2\\|(x-2)+iy|^2 = |(x-6)+iy|^2\\[/tex]

[tex][\sqrt{((x-2)^2 + y^2)} ]^{2} = [\sqrt{((x-6)^2 + y^2)} ]^{2}[/tex]

x² + 4 - 4x = x² + 36 - 12x

after simplification, x = 4

Therefore, the locus of z is a straight line parallel to the y-axis passing through the point x = 4.

Hence, the correct option is (c) a straight line parallel to the y-axis.

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Answer: 0000

Step-by-step explanation:

If the volume of a right triangular prism is 72 cubic feet, the area of the base is 2 square feet and the length of DF is approximately 2.83 feet.

To solve the problem, we can use the formula for the volume of a right triangular prism, which is:

Volume = (1/2) x base x height x length

where base is the area of the triangular base, height is the height of the prism, and length is the length of the prism.

We are given that the volume is 72 cubic feet and the height is 9 feet. Therefore, we can write:

72 = (1/2) x base x 9 x length

Simplifying this equation, we get:

base x length = 16

We are also given that the base is an isosceles right triangle. This means that the two legs of the triangle are equal, and the hypotenuse is equal to the length of one leg times the square root of 2.

Let's call the length of one leg of the triangle DF. Then, we can write:

base = (1/2) x DF x DF

Substituting this expression for base into the equation we derived earlier, we get:

(1/2) x DF x DF x length = 16

Simplifying this equation, we get:

DF x DF x length = 32

We know that the hypotenuse of the triangle is DF times the square root of 2. Since the hypotenuse is also one of the edges of the base of the prism, we can set it equal to the length of the prism:

DF x √(2) = length

Substituting this expression for length into the equation we derived earlier, we get:

DF x DF x DF x sqrt(2) = 32

Simplifying this equation, we get:

DF^3 = 16

Taking the cube root of both sides, we get:

DF = 2

Therefore, the area of the base is:

base = (1/2) x DF x DF = 2 square feet

And the length of DF is:

DF x √(2) = 2 x √(2) feet = approximately 2.83 feet.

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Answer:

A survey found that 34% of the students spend time with your family eating dinner. Oh the 500 student surveyed, about how many spend time with their family eating dinner?

Step-by-step explanation:

If 34% of the students surveyed spend time with their family eating dinner, we can find the approximate number of students who do so by multiplying the percentage by the total number of students surveyed:

34% of 500 students = 0.34 x 500 = 170 students

Therefore, about 170 of the 500 students surveyed spend time with their family eating dinner.

If you can, give me brainliest please!

'cell '. The element in the second row and first column of the cell array C is accessed using the phrase c(2,1). The first element in the second row of C is the string "cell," which is that element.

The element in the second row and first column of the cell array C is accessible by the equation c(2,1). The first element in the second row of C is the string "cell," which makes up that element. The string "cell" is the result of c(2,1).

The curly braces in MATLAB are used to retrieve the contents of a cell array. "Access the contents of the cell in the second row and first column of C" is what the phrase C2,1 implies. The string in question is the outcome of the expression since it is present in the relevant cell.

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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.

Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.

Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.

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Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?

Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.

The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.

We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:

We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.

To find out which of these integers meets the other two requirements, we can try each one individually:

x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.

X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.

When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.

x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.

x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.

When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.

x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.

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Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.

Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.

Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.

Thus, Roy bought 5 whole pizzas.

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The definition of vector space that fails is part A and B  because it does not satisfy the any property of vector space.

The following statement can be determined if at-least one part of vector space definition that fails as:

(a) A is not a vector space because it does not contain the zero vector.

The zero vector is the unique vector that satisfies the property that when it is added to any other vector in the space, the result is the original vector.

However, in this case, the [a1, b1] + [a2, b2] = [a1 - a2, b1 - b2] is 0x² + 1, which is not an element of A. Therefore, A fails to satisfy the requirement of having a zero vector, and it is not a vector space.

(b) B is not a vector space because it does not satisfy the distributive property of scalar multiplication over vector addition.

In general, scalar multiplication must distribute over vector addition, meaning that for any scalar a and any vectors u and v in the space, a(u+v) = au + av.

However, in B, the scalar multiplication is defined as usual for R², but the vector addition is defined differently. In particular,[a1, b1] + [a2, b2] = [a1 - a2, b1 - b2].

The vector space definition fails because the vector addition is not associative, and it is also not commutative, which are the first two conditions for vector spaces. Therefore, the first and second conditions of the definition are not met.

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The probability of producing the genotype AABBCC in a cross AaBbCc × AaBbCc is 1/64.

A Punnett square is a grid used to forecast the likelihood of an offspring of a mating between two parents with known genotypes. The grid consists of four boxes or cells with one parent's gamete genotype listed along the top, and the other parent's gamete genotype listed down the side.

To determine what proportion of their offspring will possess a certain genotype or phenotypic characteristic, the gamete genotypes are combined using the grid.

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Answer:

Step-by-step explanation:

1. add 14 to 24

2. ur done!

Probability of the number being part of A∩B= 2/9

The Venn diagram, a style of diagram that illustrates the logical connection between sets, was created by John Venn in the 1880s. The examples are used to illustrate fundamental set connections and introduce basic set theory in the fields of probability, logic, statistics, linguistics, and computer science.

A Venn diagram is a type of visual representation that uses circles to show the relationships between various items or constrained groups of objects. Circles that coincide and those that intersect have certain properties in common. Venn diagrams are helpful for visually illustrating the relationship and differences between two ideas.

The probability of an occurrence is a figure used to indicate the likelihood that the event will occur. It is expressed as a figure between 0 and 1, or between 0% and 100%, when expressed as a percentage. The likelihood that the occurrence will occur increases with the probability.

In this question,

A∩B= 4,9

Probability of the number being part of A∩B= 2/9

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The set [1 0 −3 , −3 1 6 , 1 −1 0] is not a basis for set of real numbers R cubed(ℝ3).

The reason why it is not a basis is because it is not linearly independent. However, the set does span set of real numbers R cubed(ℝ3).To determine if the given set is a basis for set of real numbers R cubed(ℝ3), we need to test for linear independence and for span.Linear independence

The given set is said to be linearly independent if and only if the only solution to the equation a[1 0 −3] + b[−3 1 6] + c[1 −1 0] = [0 0 0] is the trivial solution where a, b and c are constants.If the given set is linearly independent then it is a basis for R3; if it is not linearly independent, it is not a basis for R3.

SpanThe given set is said to span R3 if every vector in R3 can be written as a linear combination of vectors in the given set.

If the given set spans R3, then it can be considered a basis for R3.For us to test if the given set is linearly independent, we can form a matrix by placing the three given vectors into the columns of a 3 x 3 matrix as follows:[1 0 1] [−3 1 −1] [−3 6 0]

By expanding the determinant of the matrix above, we get: det(A) = 0 - 0 - (-3) = 3

Since the determinant is non-zero, we can say that the given set is linearly independent. Since the given set is linearly independent, we can then use it to span R3. Hence the given set does not form a basis for R3 but it is linearly independent and spans R3.

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Answer:3 1 /20

Step-by-step explanation:= 1+3/4+1+3/10

Step-by-step explanation:

4x + y^2 + 2y =  - 5

4x = - y^2 -2y - 5          

4x = - (y^2 + 2y)   - 5      'complete the square' for y

4x = - ( y +1)^2   + 1    - 5

 x = - 1/4 ( y+1)^2  - 1             vertex is at -1, -1

-14x+2y^2-8y -20 = 0

14x = 2y^2 -8y-20

14x = 2 ( y^2 - 4y) - 20     complete the square for y

14x = 2(y-2)^2  -8 - 20

x = 1/7 ( y-2)^2 - 2                Vertex is at   -2 , 2

There are 720 different choices if order matters and there are 120 different choices if order does not matter.

a) If order matters,

The player can choose the first number in 10 ways (any of the digits 0-9), the second number in 9 ways (since one digit has already been chosen), and the third number in 8 ways (since two digits have already been chosen).

So the total number of choices is:

10 x 9 x 8 = 720

Therefore, there are 720 different choices if order matters.

b) If order does not matter,

We need to divide the number of choices by the number of ways the three numbers can be arranged.

Since there are 3 numbers, they can be arranged in 3! = 6 ways.

So the number of choices when order does not matter is:

(10 x 9 x 8) / 6 = 120

Therefore, there are 120 different choices if order does not matter.

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The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.

Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.

Thus, cost of one jacket = 150/50 = $3.

The jacket lasts 5 years thus for 1 year the equivalent cost is:

3/5 = $0.60.

Now, for the other jacket:

Cost per year is = (80/50) / 2 = $0.80 per jacket per year.

Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.

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The area's estimated snapping turtIe popuIation, rounded to the cIosest whoIe number, is 56.

That is correct! As 0 is a whoIe number and aII whoIe numbers were integers, 0 is additionaIIy an integer.

The LincoIn-Petersen index method, which is frequentIy empIoyed to determine the size of a popuIation using a capture-mark-recapture approach, can be utiIized to resoIve this issue.

The estimated popuIation (N) is equaI to (M x C) / R using the foIIowing formuIa:

M is the quantity of peopIe incIuded in the initiaI sampIe (marked turtIes)

C is the second sampIe's size (totaI number of turtIes caught in the second sampIe)

R is the quantity of marked peopIe who were Iocated again in the specimen.

When we enter the specified vaIues into the equation, we obtain:

N = (15 x 15) / 4

N = 56.25

The area's snapping turtIe popuIation is thought to be 56, rounded off to the cIosest whoIe number.

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Using proportions, the real height of the telephone mast is estimated to be 9 meters.

A proportion is a fraction of a total amount, and equations are constructed using these fractions and estimates to find the desired measures in the problem using basic arithmetic operations like multiplication and division. Because the telephone box and the mast are similar figures in this problem, their side lengths are proportional.

The following proportional relationship is established as a result:

x / 1.5 cm = 10.8 cm / 1.8 cm.

The relationship's left side can be simplified as follows:

6 = x / 1.5 cm.

The estimate is then calculated using cross multiplication, as shown below:

6 x 1.5 cm = 9.5 cm².

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The Height of tree is around 8.33 feet tall.

In science, we work out the Height of an item utilizing distance and points. Distance is the even distance between the items, and point is the point over the level of the article's top, which gives the item's level.

We can utilize the rule of comparable triangles.

The hypotenuse of this triangle would be the line associating Jenny's eyes to the highest point of the tree (we should refer to this distance as "h").

We can set up the accompanying extent between the two triangles:

h / 20 = (h + 5) / 8

To solve for "h", we can cross-multiply and simplify:

8h = 20(h + 5)

8h = 20h + 100

12h = 100

h = 8.33 feet

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