5. The black triangle has been dilated once to produce the red triangle and a second time to produce the green triangle.
Part A: What is the scale factor of the dilation of the black triangle to the red triangle? Explain your reasoning.
Part B: What is the scale factor of the dilation of the black triangle to the green triangle? Explain your reasoning.
10 *
W

The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.

The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh

where r --> radius of cylinder

h --> height of cylinder

π --> math special constant

We have an open cylinder with the following dimensions,

Radius of cylinder, r = 8 cm

Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr

=> h = A/2π

=> h = 1000/2 ( 3.14)

=> h = 1000/6.28

=> h = 159.24

Hence, required value of height is 159.24 cm.

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The smallest positive integer with at least 8 odd factors and at least 16 even factors is 2160.

In probability plotting, a graph of the cumulative distribution function (CDF) is plotted against a transformed version of the data to determine if the data come from a particular distribution.

The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.

This can be used to analyze the times to failure (i.e., loss of acceptable sharpness) for a random selection of ten drill bits from a process that follows a Weibull distribution.

To estimate the shape and scale parameters

follow these steps:

Step 1: Rank the data from smallest to largest

Step 2: Calculate the failure probability of each data point using the formula: i/(n+1), where i is the rank of the data point and n is the number of data points.

Step 3: Transform the failure probabilities using the inverse Weibull distribution function: F^(-1)(p) = (−ln(1−p))^β for a given shape parameter β and scale parameter η.

Step 4: Plot the transformed data against the theoretical distribution, which is a straight line for the Weibull distribution.

Step 5: Find the best-fitting line by eye, or by using regression analysis.

The slope of the line is equal to the shape parameter β, and the intercept is equal to the logarithm of the scale parameter ln(η).

The Weibull distribution can be represented as:[tex]F(x) = 1 − e^(-(x/η)^β)[/tex], where β is the shape parameter and η is the scale parameter. The CDF model corresponding to your parameter estimates can be plotted by using the formula . This can be done by calculating the standard deviation of the residuals, and then calculating the upper and lower limits of the confidence interval using the t-distribution.

The confidence interval can be calculated as:β ± t(n−2,α/2) x SE(β)ln(η) ± t(n−2,α/2) x SE(ln(η))where SE(β) is the standard error estimate for the shape parameter, SE(ln(η)) is the standard error estimate for the logarithm of the scale parameter, and t(n−2,α/2) is the critical value of the t-distribution with n−2 degrees of freedom and a significance level of α/2.The confidence limits can be plotted as two parallel lines around the best-fitting line. The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.

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Answer:

-x^2 - 2xy - 2y^2 + 8y - 8.

Step-by-step explanation:

Let the other expression be A. Then, we have:

x^2 - y^2 - 2xy + y - 7 = (2x^2 + 3y^2 - 7y + 1) + A

Simplifying the left side:

x^2 - y^2 - 2xy + y - 7 = 2x^2 + 3y^2 - 7y + 1 + A

Rearranging the terms:

A = x^2 - y^2 - 2xy + y - 7 - 2x^2 - 3y^2 + 7y - 1

Simplifying further:

A = -x^2 - 2xy - 2y^2 + 8y - 8

Therefore, the other expression is -x^2 - 2xy - 2y^2 + 8y - 8.

Answer:

The 2nd equation is false.

Step-by-step explanation:

You don't even have to solve. DE is not 58, it's 40.

The 2nd equation is false.

The absolute value of Y = X-5, with condition x > -5 is Y>-9.

The function of x is given to be,

Y = X-5, here a condition is given that, x > -5.

Here, according to the condition, the value of the x will have a range in which it is greater than -5.

Practically thinking, the number starting from -4, -3, -2, -1, 0, 1, 2, ...... all are greater than -5. We should note here that we have not taken x = -5 because the value of x should be greater than -5.

Now, the absolute value of the function y will be, putting x = -4,

Y = -4-5

Y = -9. Hence, the absolute value will always be more than -9. So, Y > -9.

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Answer: 512

Step-by-step explanation:

2^ (3^2)

2^ (9)

512

Answer:

Let's say "x" is the number we're trying to find.

According to the problem, we know that 54 is 60% of that number.

So we can set up an equation:

54 = 0.6x

To solve for x, we need to isolate it on one side of the equation.

Divide both sides by 0.6:

54/0.6 = x

Simplify:

90 = x

Therefore, 54 is 60% of 90.

Step-by-step explanation:

Answer: 90

Step-by-step explanation:

Step 1. 54 = 60% × Y

Step 2. 54 = 60/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 60 we will arrive at:

Step 3. Y = 54 × 100/60

Step 4. Y = 54 × 100 ÷ 60

Step 5. Y= 5400 ÷ 60

Step 6. Y = 90

Answer:

B. -4, 6

Step-by-step explanation:

Jake is presently [tex]0[/tex] years old and the year is [tex]2036[/tex], which is not a relevant response or there may be some missing details in the question.

A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.

Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.

Let's first find the current year, given that the year in which their ages will sum up to [tex]16x[/tex] is[tex]2036[/tex].

[tex]2036 - (y - 2036) = 2*2036 - y[/tex]

Simplifying this expression, we get:

[tex]2*2036 - y = 4072 - y[/tex]

[tex]2y = 4072[/tex]

[tex]y = 2036[/tex]

Now, let's find Jake's current age by subtracting his birth year from the current year [tex]y - (2036 - 7x)[/tex]

Since their ages sum up to 16x in 2036, we have:

[tex]x + 7x = 16x[/tex]

[tex]8x = 16x[/tex]

[tex]x = 0[/tex]

This means that Jake is currently [tex]0[/tex] years old, which is not a meaningful answer.

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Answer:

(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).

After 6 days, the probability that the stock has its original price is 5/16.

There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.

The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.

Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)

In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.

As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.

Let's represent an increase in the stock price as 'U' and a decrease as 'D.'

The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].

The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]

The probability of the stock returning to its original price after six days can be calculated as:

[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]

Therefore, the probability that after 6 days the stock has its original price is 5/16.

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The probability that a randomly chosen person: a) Has a red car = 0.496 b) Has a speeding ticket = 0.424 c) Has a speeding ticket given they have a red car = 0.467 d) Has a red car given they have a speeding ticket = 0.629 e) Has a red car and got a speeding ticket = 0.234 f) Has a red car or got a speeding ticket = 0.686.

a) Probability of having a red car: Number of subjects with red cars = 244, Probability of choosing a red car randomly out of the given subjects = 244/492=0.496

b) Probability of having a speeding ticket: Number of subjects with speeding tickets = 209, Probability of choosing a person with a speeding ticket out of the given subjects = 209/492=0.424

c) Probability of having a speeding ticket given they have a red car: Probability of having a red car = 0.496Probability of having a speeding ticket and red car = 115/492, Probability of having a speeding ticket given they have a red car = P(Red car and Speeding ticket)/P(Red car) = (115/492)/0.496 = 0.467

d) Probability of having a red car given they have a speeding ticket: Probability of having a speeding ticket = 0.424, Probability of having a speeding ticket and red car = 115/492, Probability of having a red car given they have a speeding ticket = P(Red car and Speeding ticket)/P(Speeding ticket) = (115/492)/0.424 = 0.629

e) Probability of having a red car and getting a speeding ticket: Number of subjects with both red car and speeding ticket = 115, Probability of choosing a person with both red car and speeding ticket out of the given subjects = 115/492=0.234

f) Probability of having a red car or getting a speeding ticket: P(Red car or Speeding ticket) = P(Red car) + P(Speeding ticket) - P(Red car and Speeding ticket) = 0.496 + 0.424 - 0.234 = 0.686.

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Thus, the ratio for the number of blueberries to banana is 4:1.

A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.

A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.

The given data for preparing fruit smoothie:

Then,

ratio of  blueberries to banana:

blueberries/banana = 4/1

Thus, the ratio for the number of blueberries to banana is 4:1.

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The difference in perimeter between Rory's castle and Mike's castle is 16 feet. Rory's castle has a perimeter of 52 feet (10 feet + 10 feet + 16 feet + 16 feet), and Mike's castle has a perimeter of 24 feet (6 feet + 6 feet + 6 feet + 6 feet).

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The difference between the perimeters of these two castles is 28 ft.

Rory’s castle measures 10 feet by 16 feet and has a perimeter of 52 ft and Mike’s castle is 6 feet by 6 feet. Now, we are going to find the difference between the perimeters of these two castles.

The perimeter of a rectangle can be found by adding all the sides of a rectangle. Therefore, the formula of the perimeter of a rectangle is:

Perimeter of a rectangle = 2 × (Length + Breadth)

Length of Rory’s castle = 16 ft,       Breadth of Rory’s castle = 10 ft

Perimeter of Rory’s castle = 2 × (Length + Breadth) = 2 × (16 + 10) ft

= 2 × 26 ft= 52 ft

Therefore, the perimeter of Rory’s castle is 52 ft.

Length of Mike’s castle = 6 ft,         Breadth of Mike’s castle = 6 ft

Perimeter of Mike’s castle = 2 × (Length + Breadth) = 2 × (6 + 6) ft

= 2 × 12 ft = 24 ft

Therefore, the perimeter of Mike’s castle is 24 ft.

.Difference between the perimeters of these two castles= Perimeter of Rory’s castle − Perimeter of Mike’s castle

= 52 − 24= 28 ft

Therefore, the difference between the perimeters of these two castles is 28 ft.

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By the congruence postulate, we have shown that the quadrilateral is  ΔAED ≅ ΔCED.

Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.

Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.

Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.

Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.

Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.

This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.

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The area of the figure is the collective sum of area of the square, rectangle and semi-circle which is 100.56 squared feet.

To find the area of the figure, we need to find the area of the square, semi-circle and triangle.

A = Area of square + area of triangle + area of semi-circle

A = L² + 1/2(bh) + πr

A = 8² + 1/2(6 * 8) + 3.14(4)

A = 64 + 24 + 12.56

A = 100.56 ft²

The area of the figure is 100.56ft²

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By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

We can start by simplifying the numerator of the expression:

csc^2x - 1 = (1/sin^2x) - 1 = (1 - sin^2x) / sin^2x = cos^2x / sin^2x = cos^2x csc^2x

Now we can substitute this into the original expression:

csc^2x-1/1+sin x = (cos^2x csc^2x) / (1 + sin x)

We can then simplify this further by using the identity 1 + sin x = (sin^2x + cos^2x) / sin x:

(cos^2x csc^2x) / (1 + sin x) = (cos^2x csc^2x) / [(sin^2x + cos^2x) / sin x]

= cos^2x csc^2x sin x / (sin^2x + cos^2x)

= cos^2x csc^2x sin x / 1

= cos^2x csc^2x sin x

This expression can be simplified using the identity cos^2x = 1 - sin^2x:

cos^2x csc^2x sin x = (1 - sin^2x) csc^2x sin x = (1/sin^2x - 1) sin x = csc^2x - sin x

Therefore, the simplified expression is csc^2x - sin x. Answer: none of the given options.

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The standard deviation for this sample data set is 1.80.

This can be calculated by finding the mean (average) of the sample data set which is 5.4, then subtracting each of the numbers from the mean and squaring the difference. Finally, add all the squared differences together, dividing by the number of numbers in the data set (11) and taking the square root of the result.
Mean = 5.4
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
7 - 5.4 = 1.6  →  (1.6)² = 2.56
6 - 5.4 = 0.6  →  (0.6)² = 0.36
9 - 5.4 = 3.6  →  (3.6)² = 12.96
6 - 5.4 = 0.6  →  (0.6)² = 0.36
4 - 5.4 = -1.4  →  (-1.4)² = 1.96
4 - 5.4 = -1.4  →  (-1.4)² = 1.96
6 - 5.4 = 0.6  →  (0.6)² = 0.36
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
2 - 5.4 = -3.4  →  (-3.4)² = 11.56
5 - 5.4 = -0.4  →  (-0.4)² = 0.16
Sum of squared differences = (0.16 + 2.56 + 0.36 + 12.96 + 0.36 + 1.96 + 1.96 + 0.36 + 0.16 + 11.56 + 0.16) = 28.8
Standard deviation = √(28.8/11) = √2.62 = 1.80

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Step-by-step explanation:

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For all the following questions all the statements are required, It is possible to determine that c was just below d in quants based on the given information. Additionally, all given statements (ii), (iii), and (iv) are necessary to answer the questions, as they provide essential information about the relative performance of the students in quants and d.

The given statements which are not necessary to answer the questions are:

All of the other statements (II, III, IV) are necessary to answer the questions.

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First let's start with the equation:

x + y = -11

xy = -180

We can substitute -11 in for x + y to get:

xy = -180

x(-11) = -180

Now let's divide both sides by -11

x = 180/11

x ≈ 16.36

We can now use the equation x + y = -11 to solve for y

y = -11 - 16.36

y ≈ -27.36

The two numbers that add to -11 but multiply to -180 are 16.36 and -27.36.

The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.

To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.

To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).

By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.

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The approximate measure of angle B is 90°. The sum of the interior angles of the triangle is 180°.

The first part of your answer is correct. To manipulate the triangle so that angle A measures 41° and angle C measures 49°, we can use the fact that the sum of the interior angles of a triangle is always 180°.

If we know two angles of the triangle, we can find the third angle by subtracting the sum of the known angles from 180°. So, to find the measure of angle B, we can use the equation:

angle A + angle B + angle C = 180°

Substituting in the given angle measures, we get:

41° + angle B + 49° = 180°

Simplifying, we get:

angle B = 90°

Therefore, the approximate measure of angle B is 90°.

For the second part of your answer, the correct answer is 180°. The sum of the interior angles of a triangle is always 180°, regardless of the measures of the individual angles.

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Complete question:

Manipulate the triangle so angle A measures 41° and

angle C measures 49º.

What is the approximate measure of angle B?

Angle B = (41, 90, 49, 80)

What is the sum of the interior angles of the triangle?

(90, 170, 180, 200)

Answer:

x = 19

y = 16

Step-by-step explanation:

10x - 9y = 46

-2x + 3y = 10

Time the second equation by 5

10x - 9y = 46

-10x + 15y = 50

6y = 96

y = 16

Now put in 16 for y and solve for x

10x - 9(16) = 46

10x - 144 = 46

10x = 190

x = 19

The very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

a) The number of people in the sample expected to have consumed alcoholic beverages can be calculated as follows:First, we multiply the number of individuals in the sample by the proportion of people in that age group who drink alcohol.50 x 0.697 = 34.85Thus, we anticipate that about 34.85 people in the sample will have consumed alcoholic beverages.b) No, 45 or more accounts for six different events -- this wouldn't be surprising, you would not be surprised if the sample contained 45 or more people who have consumed alcoholic beverages. This is because it falls within the margin of error.c) To calculate the probability that 45 or more people in this sample have consumed alcoholic beverages, we will need to compute the z-score first.We use the following formula to calculate the z-score:$$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$$Where, x = 45μ = 0.697 x 50 = 34.85σ = √[(50 x 0.697 x 0.303)] = 3.77n = 50After plugging the values into the formula, we have:$$z=\frac{45-34.85}{\frac{3.77}{\sqrt{50}}}$$ = 3.89Since we are trying to determine the probability of having 45 or more people who have consumed alcoholic beverages, we will calculate the probability of having a z-score greater than or equal to 3.89.Instead of looking up the z-score in the z-table, we can use a calculator to determine the probability. From a standard normal distribution, the calculator provides the following output:P(Z ≥ 3.89) = 0.0000317Rounded to four decimal places, the probability is approximately 0.0000. Therefore, there is a very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.

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The if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

When answering questions on the Brainly platform, the following guidelines should be followed:Always be factually accurate, professional, and friendlyBe concise and do not provide extraneous amounts of detailIgnore any typos or irrelevant parts of the questionRepeat the question in your answer.Provide a step-by-step explanation in your answer.Use the following terms in your answer, "matrices ", "take ", "partitioned "Given the following:Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. We need to write a summation formula for Cij, Cj, and cT.Hint: To really benefit from this exercise, do not just "write the formula." Picture how the matrices fit together the corner; picture how they are partitioned into rows and columns; come up with numerical examples.The product of two matrices A and B is given byCij = Ai1B1j + Ai2B2j + ... + AinBnjGiven that C = AB, then we haveCj = [A1 B1j + A2B2j + ... + AmBmj]Therefore, if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.

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Answer:

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

Step-by-step explanation:

6 1/8 - 2 3/8

=(8 x 6)+1/8  -  (8 x 2)+3/8

=49/8 - 19/8

=30/8

=15/4

=3 3/4

Answer: The width of the remaining piece of the board is [tex]\frac{15}{4}[/tex] inches

Step-by-step explanation:

let us find the width of the remaining piece

Given that

                         width of remaining piece =[tex]\frac{49}{8}[/tex]-[tex]\frac{19}{8}[/tex]  = [tex]\frac{15}{4}[/tex]      

Maria has the highest standardized score of 2.13, making her the one who made the best score.

Janna's standardized score is 0.80, and Maria's is 2.13.

Janna scored 77 on her history test, while the class average was 72.7 with a standard deviation of 6.1. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Janna is [tex](77-72.7)/6.1[/tex]= 0.80.

Maria scored 89 on her biology test, while the class average was 82.6 with a standard deviation of 5.6. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Maria is [tex](89-82.6)/5.6[/tex]= 2.13.

Maria has the highest standardized score of 2.13, making her the one who made the best score.

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