I need help with this maths question!

The midterm grades is the grade that is more unusual

for the midterm

the mean = 80 + 78 + 85 + 82 + 79 +79 + 78 + 86 + 80 + 84 / 10

= 81.1

Then the standard deviation is

Variance = [(80-81.1)² + (78-81.1)² + (85-81.1)² + (82-81.1)² + (79-81.1)² + (79-81.1)² + (78-81.1)² + (86-81.1)² + (80-81.1)² + (84-81.1)²] / 10

sd = 2.961

z = 86-81.1/2.961

= 1.66

For the final

Mean = (81 + 88 + 68 + 69 + 69 + 81 + 82 + 86 + 76 + 71) / 10

= 771 / 10

= 77.1

Therefore, the mean of the given numbers is 77.1.

To find the standard deviation, we first need to find the variance. The variance is calculated by finding the average of the squared differences between each number and the mean:

Variance = [(81-77.1)² + (88-77.1)² + (68-77.1)² + (69-77.1)² + (69-77.1)² + (81-77.1)² + (82-77.1)² + (86-77.1)² + (76-77.1)² + (71-77.1)²] / 10

SD = 7.490

z= (86-77.1) / 7.490 = 1.188

Given that 1. 66 is greater that 1.188, we would have to conclude that the midterm is more unusual

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Complete question

The midterm and final exam grades for a statistics course are provided in the data set below. Jaymes, a student in the class, scored 86 on both exams. Treat the given data sets as samples. Jaymes's wants to know which grade is more unusual, the midterm grade or the final exam grade. Use Use a TI-83, TI-83 Plus, or TI-84 calculator to calculate the z-scores corresponding to each grade. Round your answer to three decimal places.

Midterm 80, 78, 85, 82, 79, 79, 78, 86, 80, 84,

final 81, 88, 68, 69, 69, 81, 82, 86, 76, 71

Answer:

-3

Step-by-step explanation:

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3

=

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A

=

−

x

+

13

=

X

=

−

3

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1

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3

The required answer is  sec θ = -√2.

Explanation:-

Part 1: Given cosine of theta is equal to radical 3 over 2 on the domain [0,[infinity]).

To determine three possible angles θ,  the cosine inverse function which is a cos and since cosine function is positive in the first and second quadrant. Therefore  conclude that, cosine function of θ = radical 3 over 2 implies that θ could be 30 degrees or 330 degrees or 390 degrees. So, θ = {30, 330, 390}.Part 2:To convert 495° to radians, multiply by π/180°.495° * π/180° = 11π/4To find sec θ, we use the reciprocal of the cosine function which is sec.

Therefore, sec θ = 1/cos θ.To find cos 11π/4,  the reference angle, which is 3π/4. Cosine is negative in the third quadrant so the final result is sec θ = -√2.

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The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Translating the word problem into an algebraic expression;

\(W = 3 + L\)  ......equation 1

\(H = 4 + L\)  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

\(Volume = length * width * height\)  .....equation 3.

Substituting the values into equation, we have;

\(224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}\)

Rearranging the polynomial, we have;

\(L^{3} + 7L^{2} + 12L - 224 = 0\)

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

\((x - 3) = 0\\x = 3\)

\(P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0\)

We would try with 4;

\(P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0\)

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

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In statistical modeling, a dummy variable is used to represent categorical variables with two or more levels as binary variables (0 or 1).

The presence of a dummy variable in a model does not inherently indicate multicollinearity or singularity of the design matrix. Multicollinearity refers to a situation where two or more predictor variables in a regression model are highly correlated, making it difficult to distinguish their individual effects on the response variable. Multicollinearity can cause instability in the estimation of regression coefficients but is not directly related to the use of dummy variables.

Singularity of the design matrix, also known as perfect collinearity, occurs when one or more columns of the design matrix can be expressed as a linear combination of other columns. This can happen when, for example, a set of dummy variables representing different categories has one category that is completely determined by the others. In such cases, the design matrix becomes singular, and the regression model cannot be estimated.

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Answer:

here..

Step-by-step explanation:

1. LM, MN. and HF in that order.

1 pt2. L, G, N in that order

2. WX, XY, UV, VS in that order

and 2 pt2. W, X, U, V in that order

Answer:

6

Step-by-step explanation:

Perimeter = 2l + 2w

48 = 2(18) + 2(w)

48 = 36 + 2w

12 = 2w

w = 6

Could you please give me brainliest for this? Thank you!

This does not imply that there is a one-to-one correspondence between dorm rooms and students.

A one-to-one correspondence between sets A and B if pairing of each object in A with one and only one object in B, and also another statement is when we counting one- to - one or like counting, one, two, three and so on.

In the question says that : Each and Every student assigned per room then we would be able to guarantee that there is a one-to-one correspondence between dorm rooms and students.

However, the possibility that two students could be assigned per one room, there is no way to imply that there is a guaranteed one-to-one correspondence between dorm rooms and students. It is follows only one student assign one room it is able to guarantee a one-to-one correspondence between dorm rooms and students.

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The solution set of the inequality is represented as [911,∞)

let

x be the number of cans collected by Shane.

Therefore,

Since,  Abha collected 178 more cans than Shane did.

Therefore,

Abha  = 178 + x

Hence,

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

Therefore,

x + 178 + x ≥ 2000

2x + 178 ≥ 2000

2x ≥ 2000 - 178

2x ≥ 1822

x ≥ 1822 / 2

x ≥ 911

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1. True: If Spain has an absolute productivity advantage in producing shoes, then it will have a lower opportunity cost for producing shoes than the rest of the world, allowing them to sell them at a lower price, which would encourage exporting.

2. True: The Ricardian Model explains how nations can gain by specializing in the production of goods that they are relatively more efficient in producing and then trading. It can be used to explain how workers in the same sector can be differently affected due to international trade. 3. Uncertain: The extent to which a specific or mobile factor of production benefits from trade (or trade liberalization) depends on several factors, and cannot be generalized.

4. False: Suppose that Home has a relative abundance of L compared with Foreign, then it means that K is scarce relative to L in Home. Thus, K owners in Home will benefit from free trade policies as it will lead to an increase in the demand for K.

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We can write (15 + 45) as a product of 2 factors using GCF and the distributive property 15(1 + 3).

We are given the following expression-

15 + 45

Now, we can factorize 15 into prime factors as follows -

= 3 × 5 (15 × 1)

Similarly, we can factorize 45 into prime factors as follows -

= 3 × 3 × 5 (15 × 3)

Thus, the greatest common factor of 15 and 45 is 15, so we can

= 15 × 1 = 15 and 15 × 3 is 45

Hence, we can write (15 + 45) as 15(1 + 3).

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Answer:

1. 89 2. 91

Step-by-step explanation:

180-29-62=118-29=89

180--89=91

Answer:

91 and 89 degrees respectively

Step-by-step explanation:

Sooooo, the exterior angle of any angle in a triangle is equal to the sum of the  2 other adjacent interior angles in a triangle. Therefore, we just need to do 29+62, which is 91 degrees, so the Exterior angle is 91 degrees. Next, to find the last unknown angle of a triangle, we can take the sum of the 2 other interior angles and subtract it from 180. Doing this here, we get 180-91, which is 89 degrees.

9.21  is the distance between pοints cοοrdinate plane. Thus, option C is correct.

Cοοrdinate geοmetry (alsο knοwn as analytical geοmetry) is the study οf geοmetry using cοοrdinate pοints. Cοοrdinate geοmetry can be used tο divide lines intο m and determine distances between pοints: n segments, find the midpοint οf a line, figure οut the area οf a triangle in the Cartesian plane, and dο οther things.

pοints (4,7) and (6,-2) οn a cοοrdinate plane.

D = √(x₂ - x₁ )² + (y₂ - y₁)²

    = √(6 - 4)² + (-2 - 7)²

     = √2² + ( -9)²

      = √4 + 81

      = √85

      ≈ 9.21

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All five brothers have a total of $100 combined.

Let's assume Peter's total amount of money is P dollars. We are given that 25% of Peter's money is equal to $5,

so we can set up the equation:

0.25P = 5

To solve for P,

we divide both sides of the equation by 0.25:

P = 5 / 0.25 = 20

Now that we know Peter has $20,

we can find out how much money all five brothers have combined. Since Peter and his four brothers combined their money, the total amount would be:

Total = Peter's money + 4 brothers' money

Total = $20 + 4 x (Peter's money)

Total = $20 + 4 x $20

Total = $20 + $80

Total = $100

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Answer:

6½ gallons

Step-by-step explanation:

Givem the cost of 1gallon of gas = $2.78. . If Cory buys $18 of gas, we are to find the number of gallons did he buy. To do that we will use the equality method as shown;

$2.78 ,= 1gallon

$18 = x gallon

Cross multiply

2.78 × x = 1×18

2.78x = 18

Divide through by 2.78

2.78x/2.78 = 18/2.78

.x = 6.5

Hence Cory buys about 6½ gallons of gas for $18

Answer:

43 m

Step-by-step explanation:

We measure the depth of the dive as the distance beneath the surface of the water.  If Chris goes 30 m below the surface and Michelle 13 m further down, then Michelle's position will be 43 m.

Answer:

\(x = 14.13ft\)

Step-by-step explanation:

Given

See attachment for illustration

Required

Find x

To do this, we apply Pythagoras theorem.

From the attachment, the length of the hypotenuse is 16.7ft

While the length of the opposite/adjacent is 8.9ft

Length x is calculated using:

\(16.7^2 = 8.9^2 + x^2\)

\(x^2 = 16.7^2 - 8.9^2\)

\(x^2 = 199.68\)

Take square roots

\(x = \sqrt{199.68\)

\(x = 14.13ft\)

The distance between the two platforms should be  14.13 ft.

Since the length of the hypotenuse is 16.7ft.

And,  length of the opposite/adjacent is 8.9ft.

Now the distance between should be

\(16.7^2 = 8.9^2 + x^2\\\\x^2 = 16.7^2 - 8.9^2\\\\x^2 = 199.68\\\\x = \sqrt{199.68}\)

= 14.13 ft.

hence, The distance between the two platforms should be  14.13 ft.

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Answer:

\(2 \times { (- 2)}^{n - 1} \)

Answer:

Step-by-step explanation:

The period of the pendulum (t) is approximately 4.77 seconds.

The formula for a basic pendulum's period is

T = 2π√(L/g)

where L is the pendulum's length and g is its gravitational acceleration.

Substituting the given values, we get:

T = 2π√(5.64/9.8)

Simplifying the expression inside the square root, we get:

T = 2π√(0.5755)

Calculating the square root, we get:

T = 2π(0.759)

Multiplying by 2 and π, we get:

T = 4.77 seconds (rounded to two decimal places)

Therefore, the period of the pendulum is approximately 4.77 seconds.

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Answer: the first one is a function. the second one is not.

The value of the transformed function is h ( x ) = f ( x - 6 )² , where the value of c is -6

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) = x²

And , when the function is shifted horizontally by a factor of -6 , we get

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c)

Substituting the values in the equation , we get

h ( x ) = f ( x + c )

when c = -6

h ( x ) = f ( x - 6 )²

Hence , the transformed function is h ( x ) = f ( x - 6 )²

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18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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(a) the present value of $28,500 due 9 periods from now, discounted at 9%, is approximately $14,656.01

(b) the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, is approximately $132,937.51

(a) To calculate the present value of $28,500 due 9 periods from now, discounted at 9%, we can use the present value formula:

Present Value = Future Value / (1 + Interest Rate)^Number of Periods

Plugging in the values, we have:

Present Value = $28,500 / (1 + 0.09)^9

Calculating this expression gives us:

Present Value = $28,500 / 1.9487179487

Present Value ≈ $14,656.01

Therefore, the present value of $28,500 due 9 periods from now, discounted at 9%, is approximately $14,656.01.

(b) To calculate the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, we can use the present value of an annuity formula:

Present Value = Cash Flow * (1 - (1 + Interest Rate)^(-Number of Periods)) / Interest Rate

Plugging in the values, we have:

Present Value = $28,500 * (1 - (1 + 0.09)^(-6)) / 0.09

Calculating this expression gives us:

Present Value ≈ $132,937.51

Therefore, the present value of $28,500 to be received at the end of each of 6 periods, discounted at 9%, is approximately $132,937.51.

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Answer: its 140

Step-by-step explanation:

Answer:

260 Students

Step-by-step explanation:

30% of 400= 140

400-140=260

plz crown

Answer:

A) if and only if a = 0

Step-by-step explanation:

Since Z1 = 12 + 6݅  and Z2 = a + bi , then the product, Z1Z2 = (12 + 6)(a + bi)

Z1Z2 = (12 + 6)(a + bi)

Expanding the brackets, we have

Z1Z2 = 12a + 12bi + 6a + 6bi

Collecting like terms, we have

Z1Z2 = 12a + 6a + 12bi +6bi

Z1Z2 = 12a + 6a + (12b +6b)i

Simplifying, we have

Z1Z2 = 18a + 18bi

For Z1Z2 to be imaginary, then the real part must be zero.

That is 18a = 0 ⇒ a = 0

So, Z1Z2 is imaginary if and only if a = 0

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:

P(X ≥ 2) = \(e^{(-λ2) }= e^{(-1/2.7252)\) ≈ 0.4800

P(X ≤ 3) = 1 - \(e^{(-λ3)} = 1 - e^{(-1/2.7253)\) ≈ 0.6674

P(2 ≤ X ≤ 3) = \(e^{(-λ2)} - e^{(-λ3)} = e^{(-1/2.7252)} - e^{(-1/2.7253)}\) ≈ 0.1474

b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:

P(X > 5.45) =\(e^{(-λ5.45)} = e^{(-1/2.7255.45)}\) ≈ 0.0498

Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.

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Complete Question:

Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.

a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)

b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)