A coroner arrives at a murder scene at 11p.m. She finds the temperature of the body to be 85.7 degrees F. She waits one hour, takes the temperature again, and finds it to be 81.2 degrees F. She notes that the room temperature is 70 degrees F. Assuming that the temperature of the body was 98.6 degrees F when the murder occurred, when was the murder committed?

The required container of fries costs $1.20, as er the given condition

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let's call the cost of a container of fries "x".

We know that 4 burgers cost 4 * $3.20 = $12.80.

So the total cost of burgers and fries is $12.80 + 3x = $16.40.

Subtracting the cost of the burgers from both sides:

3x = $16.40 - $12.80 = $3.60

Dividing both sides by 3:

x = $3.60 / 3 = $1.20

So each container of fries costs $1.20.

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Step-by-step explanation:

Inequality Interval Notation Graph

Sajan Rai

Solve the inequalities below. Write the solution set in interval notation and graph the solution.

8x−12>158x-12>15

Solution:

Interval notation for the solution:

(-∞,5/8) U (5/8, ∞)

To graph the solution, we need to find the points that make the inequality true and shade the region that corresponds to these points. On the number line, we can start by finding x values that make the inequality equal to zero:

8x - 12 = 0

x = 12/8 = 3/2

and

15 - 8x = 0

x = 15/8 = 9/4

Next, we need to test values that are less than 3/2 and greater than 9/4 to determine the direction of the inequality. If the inequality is true for values less than 3/2, then we shade the region to the left of 3/2. If the inequality is true for values greater than 9/4, then we shade the region to the right of 9/4. In this case, since the inequality is "greater than," the shading goes to the right of 9/4 and to the left of 3/2.

Answer: 3(1p)

Step-by-step explanation:

Answer: 3+3p or 3p+3

Step-by-step explanation:First write the information given. You will need to multiply the quantity 3 by each of the terms one and p. It should look something like this 3(1+p). Multiply three to both quantities and the answer yields 3+3p or 3p+3.

Answer: 15 students per teacher

Step-by-step explanation:

825 students/55 teachers=15

Answer:

15

Step-by-step explanation:

825 divided by 55 = 15

Answer:

2,810 feet

Step-by-step explanation:

Take a look at the diagram

There are two triangles formed with a common side AB

AB represents the vertical height of the plane = 5150 feet

AC represents the distance of car 1 from O

In ΔABC, m∠A = 90°, m∠ABC = 38°

Since the three angles of triangle must add up to 180°
90 + 38 +m∠C = 180

128 + m∠C = 180°

m∠C = 180 - 128 = 52°

In a right angle triangle where one side is the angle ∅, the ratio of the side opposite this angle to the side adjacent to the angle is tan∅

Using the values provided we get
tan(52°) = 5150/AC

AC= 5150/tan(52) = 4,023.62 feet ≈ 4024 feet

This is the horizontal distance of the first  car from the plane

Similarly for ΔABD

m∠D = 180 - (90 + 53) = 37°
tan(37) = 5150/AD

AD= 5150/tan(53) = 6,834.28 feet ≈ 6834 feet

This is the horizontal distance of the second car from the plane

The distance between the two cars = 6,834 - 4,024

= 2,810 feet

Answer:

[tex]\frac{7}{5}[/tex]

Step-by-step explanation:

Slope of a line =  Gradient

                        [tex]= \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]

Based on the two points provided in the question:

[tex]x_{1} = -8[/tex]

[tex]y_{1} = -3[/tex]

[tex]x_{2} = -3[/tex]

[tex]y_{2} = 4[/tex]

Slope = [tex]\frac{4 - (-3)}{-3 - (-8)}[/tex]

         = [tex]\frac{4 + 3}{-3 + 8}[/tex]

         = [tex]\frac{7}{5}[/tex]

It falls between: The population mean is 13. 8. The population variance is 192. The population's standard deviation is 13.856.

A key measure of dispersion in statistics is population standard deviation. additional reading Statisticians compute variance to determine how various values inside a data collection interact to one another. While calculating the population variance, one may also compute the dispersion in relation to the population means.

The range: 15 - 2 = 13

The population mean is:

Mean = ( 2 + 10 + 15 + 2 + 12 + 13 + 7 + 3 + 8  ) / 9 = 8

The population variance ( S² or Sigma² ):

S ² = 1/9 · ( ( 2 - 8 )² + ( 10- 8 )² + ( 15 - 8 )² + ( 2 - 8 )² + ( 12 - 8 )² + ( 13 - 8 )² + ( 7 - 8 )² + ( 3 - 8 )² + ( 8 - 8 )²  )

S ² = 192

The population standard deviation:

S = √(S²) = √192 = 13.856

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Answer:

He would be 15 years old.

Step-by-step explanation:

If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.

The statement that is true based on the data set is B. There is one outlier that indicates an unusually small number of assignments required in that class.

The given data set is

22, 23, 23, 21, 18, 4, 17, 15, 23, 20, 24, 15, 25, 16

Arrange the data is ascending order.

4, 15, 15, 16, 17, 18, 20, 21, 22, 23, 23, 23, 24, 25

Divide the data in 4 equal parts.

(4, 15, 15), 16, (17, 18, 20), (21, 22, 23), 23, (23, 24, 25)

Now, we can say that

Q1= 16

Q3= 23

The interquartile range of the data set is 23- 16 = 7

If the data lie in the interval [Q1-1.5(IQR), Q3 + 1.5 (IQR)], then the data set has no outliers.

All the data lie in the interval [5.5,33.5] except 4. So, 4 is an outlier of the given data.

There is one outlier that indicates an unusually small number of assignments required in that class. Therefore the correct option is option B

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Which of the following statements is true based on the data set?

There is one outlier that indicates an unusually large number of assignments required in that class.

There is one outlier that indicates an unusually small number of assignments required in that class.

There are two outliers that indicate an unusually large number of assignments required in those two classes.

There are two outliers that indicate an unusually small number of assignments required in those two classes.

The mean of the probability distribution is 3.188, the sampling distribution is 2.25 and x is an unbiased estimator.

a. To find the mean (u) of a probability distribution, we calculate the expected value as follows:

u = ∑x * p(x) = (0.5 * 0.0625) + (2.5 * 0.125) + (0.25 * 0.25) + (0.25 * 0.25) + (0.25 * 0.25) = 2.25

To find the variance (o^2) of the distribution, we calculate it as follows:

o^2 = ∑(x - u)^2 * p(x) = (0.5 - 2.25)^2 * 0.0625 + (2.5 - 2.25)^2 * 0.125 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 = 0.5625

So, o = √0.5625 = 3.188

b. The sampling distribution of the sample mean x for a random sample of n=2 measurements from this distribution is given by:

x = (x1 + x2) / n = (2.25 + 2.25) / 2 = 2.25

As n approaches infinity, the sample mean x approaches the population mean u, and the distribution of x becomes more and more concentrated around u.

c. Yes, x is an unbiased estimator of u because its expected value is equal to the population mean: E(x) = u.

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The area covered by the circular spotlight is given as follows:

C. 153.86 square feet.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

π can be rounded to 3.14, hence the equation for the area is given as follows:

A = 3.14r².

The radius is of 7 feet, hence the area is given as follows:

A = 3.14 x 7²

A = 153.86 square feet.

Meaning that option C is the correct option for this problem.

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The number of seventh grade winners is 25.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: total swimmers is 80 and the ratio of seventh to all swimmers is 5:16

According to the proportion in the question we get

5/16=s/80

s=5/16 × 80

s=25

The number of seventh grade winners is 25.

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Answer:

Zeroes & Multiplicity:

x = 0        :   Multiplicity = 2

x = -6/5   :   Multiplicity = 9

x = 8        :   Multiplicity = 2

Step-by-step explanation:

The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]

We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.

This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.

So this gives us the following equations:

[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]

Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.

The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.

Maddie wrote six different equations based on the triangle below.Four of the six equations that Maddie wrote are correct which are options A, D , E and F.

This is referred to as a polygon with three edges and three vertices.

Triangle ABC was given in the picture.

∠A = 60° and ∠B = 90° which is given in the figure

sin 60° = perpendiculer /hypotenuse

√3/2 = BC/10

BC = √3/2 × 10

BC = 5√3

tan 60° = perpendiculer /base

√3 =  5√3/AB

AB = 5√3/√3

AB = 5

sin 60° = 5√3/10 = √3/2

cos 60° = base / hypotenuse

cos 60° = 5/10 = 1/2

tan 60° = perpendicular /base

tan 60° = 5√3/5 = √3

cot 60° = 1 /√3

Therefore the equations which are correct are sin 60° =√3/2, cos 60° = 1/2, tan 60° = √3, and cot 60° = 1 /√3.

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The population of Indiana residents aged 5 years and older is around 5.7 million.

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

322000 people lacked basic math skills

5.6% of the population of Indiana residents aged 5 years and older

Let's call the population of Indiana residents aged 5 years and older "x".

The equation to estimate the population is:

322000  =  x*5.6/100

322000 = x * 0.056

Dividing both sides by 0.056:

322,000 / 0.056 = x

x = 5750000

So, the population of Indiana residents aged 5 years and older is approximately 5.7 million.

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First find the actual difference:

   82 - 67 = 15

Now divide that difference by the starting value (82 in this case):

    15 / 82 ≈ 0.182927

Convert that to a percent:

   0.182927 = 18.2927%

That's the percent change, a decrease of about 18.2927%

You would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle. Pythagorean triples are another name for the right triangle's sides. Here, examples are used to explain the theorem's formulation and proof.

The Pythagorean theorem is mostly used to determine a triangle's angle and the length of an ambiguous side. The base, perpendicular, and hypotenuse formulas can all be derived using this theorem.

Given that, park is in the shape of a rectangle 8 miles long and 6 miles wide.

The diagonal of the park is calculated using the Pythagoras theorem.

The Pythagoras theorem is given as:

c² = a² +b²

c² = 8² + 6²

c² = 64 + 36

c² = 100

c = 10

If you walk along the diagonal you need to walk 10 miles.

If you walk along the two sides the distance is:

d = 8 + 6 = 14 miles

Hence, the difference between the distance is:

14 - 10 = 4 miles.

Hence, you would need to walk 4 miles less if you walk along the diagonal rather than the two sides.

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The common ratio is approximately -0.6.

Let the first term in the geometric series be "a" and the common ratio be "r". Then, the formula for the sum to infinity of a geometric series is:

S = a / (1 - r)

And the formula for the sum of the first n terms of a geometric series is:

Sn = a * (1 - r^n) / (1 - r)

So, using the information given:

18 = a / (1 - r)

And:

130/9 = a * (1 - r^4) / (1 - r)

Solving for "r" using these two equations:

18 = a / (1 - r) ==> a = 18 * (1 - r)

130/9 = a * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r) * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r^4)

Dividing both sides by 18:

7/5 = (1 - r^4)

So:

r^4 = 1 - 7/5 = -2/5

Taking the fourth root of both sides:

r = (-2/5)^(1/4)

So, the common ratio is approximately -0.6.

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The mean is 14.7, the median is 16, and the mode is 16.

To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.

The sum of the data values is:

14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043

The number of observations is:

14 + 11 + 23 + 10 + 13 = 71

The mean is calculated as follows,

1043 / 71 = 14.7 (rounded to one decimal place)

The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.

14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18

The median is 16.

The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).

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Answer:

To write 31415/10000 as a decimal you have to divide numerator by the denominator of the fraction.

We divide now 31415 by 10000 what we write down as 31415/10000 and we get 3.1415

The dimensions for the block can be 3 x 4 x 5.

Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

Given:

We have wire of length 60 m.

Now, to find the length, width and height of block we have to factorize 60.

60 = 3 x 4 x 5

So, the measurement of the block can be length x width x height can be

3 x 4 x 5.

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Method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

A relation is a function if it has only One y-value for each x-value.

One method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

To do this, you can start by selecting a set of corresponding terms from each sequence and attempt to express the relationship between them using mathematical operations.

It's important to note that finding a mathematical relationship between two sequences can sometimes be difficult, and in some cases may not be possible.

In such cases, it may be helpful to analyze the sequences using other methods, such as graphical representation or statistical analysis, to gain insight into their behavior.

Hence, method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.

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Reliability refers to the consistency of measures, whereas validity refers to the truthfulness of a measurement.

The size, capacity, or amount of something determined by measurement. Use equal amounts of ingredients. Something used for measurement (such as a ruler or cup). A unit used to measure. A foot is a measure of length. 

Statistics is a science concerned with developing and studying methods for  measure, collecting, analyzing, interpreting, and presenting empirical data. 

Statistics is the branch of mathematics for collecting, analyzing and interpreting data. Statistics can be used to predict the future, determine the likelihood of certain events occurring, and answer research questions. 

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The variables of the equation systems are those x values where f(x) & g(x) are of identical value, as displayed in the table.

The definition of just an equation in algebra is a scientific statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The intersection spots of the functions that comprise up an equation system are where it has solutions when it is plotted on a graph.

The intersection points, when the units have the same numerical value, are where the solution to the equation may be found on a table.

The following are the solutions from the table provided by the picture at the conclusion of the response:

f(x) and g(x) both have a specific number of 14 with x = 1, indicating that x = 1.

f(x) and g(x) both have a numerical value of such 6 at x = 9, indicating that x = 9.

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The length and width of the rectangle are 11 and 78 respectively.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, the length of a rectangle is 4 inches more than its width.

let x be the width of a rectangle.

thus, length = 4 + width

From the general formula of area and perimeter:

Area of rectangle = length*width

Perimeter of rectangle = 2(length + width)

In our case,

Area = x * (4 + x)

Area = x² + 4x

Perimeter = 2( 4 +x+ x)

Perimeter = 8 + 4x

Since the area of the rectangle is equal 5 inches more than 2 times the perimeter.

Thus,

x² + 4x = 5 + 2(8 + 4x)

x² + 4x = 5 + 16 + 8x

x² + 4x = 21 + 8x

x² + 4x -8x -21 = 0

x² - 4x -21 = 0

x = 7 and -3

Thus,

the width of the rectangle = 7

and the length of the rectangle = 11

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Complete question:

length of a rectangle is 4 inches more than its width. the area of the rectangle is equal 5 inches more than 2 times the perimeter. find the length and width.

the confidence intervals for the situation is 46%

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

the particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion.

Let's calculate the percentage or proportion of patients that were dogs:

p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46

Hence the confidence intervals for the situation is 46%

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If the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.

What is the circumference of the circle?

The Circumference of a circle is basically the perimeter of the circle. It is given as (2×π×r) or (π×d).

The hand on a circular clock moves along the circumference of the circle, and the length of the circumference of a circle is given by the formula:

C = 2 * π * r

where C is the circumference, π is Pi (approximately equal to 3.14), and r is the radius of the circle.

In this case, the radius of the circle is half the length of the hand, or 12cm / 2 = 6cm.

So the circumference of the circle is:

C = 2 * π * 6 = 12 * π

Since the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled an angle of 5 * (360/12) = 150 degrees.

To find the distance traveled along the circumference, we need to multiply the circumference by the fraction of the circle traveled, which is equal to the angle in radians divided by 2π.

To convert from degrees to radians, we can use the formula:

radians = degrees * (π / 180)

So, the distance traveled by the hand is:

distance = C * (150 * (π / 180)) / (2 * π) = 12 * (150 * (π / 180)) / 2 = 9.5 cm (rounded to the nearest cm)

hence, if the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.

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The probability of guessing the top 3 horses in order in a field of 20 horses in the Kentucky derby is, Very low value approximately 0.000145

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

There are total 20 horses,

The probability of guessing the top 3 horses in order = ?

The probability of guessing the top 3 horses in order in a field of 20 horses in the Kentucky Derby would be 1 in 20 x 19 x 18 = 6840.

This means that the probability of guessing the top 3 horses correctly would be 1/6840 or approximately 0.000145.

It is a very low probability and requires a lot of knowledge, research, and luck to correctly guess the top 3 horses in order.

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