In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 6.7 feet and c = 10 feet, what is b? If necessary, round to the nearest tenth.

The range is 28, the variance of the data is 82.75 and the standard deviation is 9.09.

Data variability is assessed using measures of dispersion. Variance, range, interquartile range, percentiles, and standard deviation are examples of dispersion measurements. Measures of central tendencies, such as mean, mode, and median, are combined with measures of dispersion.

The range is the difference between the largest value and the smallest value. According to the data:

Range = 73 - 45 = 28.

The variance is given as:

V = ∑(x - x')² / n

Where, x is the frequency, x' is the mean and n is the number of elements.

x             d = (x - x')               d²

45               14.25                  203.06    

46               13.25                  175.56

47                12.25                 150.06

56                 3.25                  1.56

59                 0.25                  0.065

59                 0.25                  0.065

60                -1.25                   1.56

62                 -2.25                  5.06

61                   -1.75                   3.06

72                   -12.25               150.06

71                    -11.25                126.56

73                  -13.25                175.56

∑x = 711                                    ∑d² = 992.73

x' = 711 / 12 = 59.25

V = ∑d²/ n

V = 992.73 / 12 = 82.75

The standard deviation is given as:

SD = √V = √82.75 = 9.09

Hence, the range is 28, the variance of the data is 82.75 and the standard deviation is 9.09.

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Answer:

The point (2, - 3) lies in the third quadrant.

Solution

First quadrant     X=positive      and   Y=positive

Second quadrant    X=negative     and   Y=positive

Third quadrant     X=negative      and   Y=negative

Fourth quadrant    X=positive      and   Y=negative

(2,−3) has X=2, positive and Y=−3, negative

The point lies in the fourth quadrant. Hence, the given statement is False.

As a result, the median is 13. The data has a minimum value of 11 and a maximum value of 17.

The median is the value in the center of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, count the number of data points (n) and arrange them in increasing order.

Here,

(a)(i) The median of the data can be found by ordering the data and finding the middle value. In this case, the data has 16 values, so the median is the average of the 8th and 9th values when the data is ordered. The median is therefore 13.

(ii) The minimum value of the data is 11 and the maximum value is 17.

(b) The box-and-whisker diagram is a graphical representation of the distribution of a set of data. It consists of a box, whiskers and dots that show the distribution of the data.

The box represents the interquartile range (IQR), which is the range of the middle 50% of the data. The IQR is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). In this case, the IQR is 15 - 12.5 = 2.5.

The lower edge of the box is Q1 and the upper edge of the box is Q3. The line inside the box is the median.

Whiskers are drawn to the minimum and maximum values, excluding outliers. Outliers are values that are significantly different from the rest of the data. In this case, there are no outliers.

Dots may be used to represent individual data points.

Here's what the box-and-whisker diagram would look like for this data:

| |

| |

|_13|

12.5 15

The median is therefore 13. The minimum value of the data is 11 and the maximum value is 17.

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Explanation:

For any parallelogram, the adjacent angles add to 180.

T+S = 180

(4x+1)+(3x+4) = 180

7x+5 = 180

7x = 180-5

7x = 175

x = 175/7

x = 25

Now we can determine angles T and S.

Notice that they add to 101+79 = 180 to confirm the correct x value, and correct angle measures.

For any parallelogram, the opposite angles are congruent. This allows us to say:

Answer:

LX = WI

I = L

A = G

W = X

I = L

LAX = WIG

Answer:

number 2 or B

Step-by-step explanation:

The value of variables are,

⇒ a = 3100

⇒ b = 0.7

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given that;

Wellington Elementary School bought a printer one year ago for $3,100.

And, Today, the value of the printer has decreased to $2,170 and is expected to continue decreasing each year.

Now, An equation in the required exponential form,

A = A₀(1 - r)ˣ

Substituting the values,

A = 3100(1-r)ˣ.

To find the r:

2170 = 3100(1-r)

r = 0.3

So, The equation is,

Aₙ = 3100(1-0.3)ˣ.

y = 3100(0.7)ˣ.

Therefore, The value of variables are,

⇒ a = 3100

⇒ b = 0.7

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The distance between the ships is increasing at a rate of approximately 98.82 km/h at 4:00 PM.

From the question, we have the following parameters that can be used in our computation:

Distance, D = 170 km

Rates = 40 km/h and 30 km/h

Let t be the time elapsed from noon to 4:00 PM

So, we have

t = 4

The distance between the ships to their east-west and north-south distances is represented as

d^2 = (D + rate 1 * t)^2 + (rate 2 * t)^2

So, we have

d^2 = (170 + 40t)^2 + (30t)^2

d^2 = 170^2 + 13600t + 1600t^2 + 900t^2

Differentiate with respect to time (t)

2D d' = 5000t + 13600

So, we have

D d' = 2500t + 6800

Substitute 4 for t

D d' = 16800

So, we have

d' = 16800/D

This gives

d' = 16800/170

d' = 98.82

So the distance between the ships is increasing at a rate of approximately 98.82 km/h at 4:00 PM.

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Answer:

1/3 or 0.33333

Step-by-step explanation:

To find the product of two fractions, multiply numerators and denominators separately.

You get 2340/7020 which simplifies to 1/3.

Hope that helps.

Answer:

1/3

Step-by-step explanation:

Step 1) 12/13 x 12/15 = 156/195

Step 2) 156/195 x 15/36 = 2340/7020

Step 3) Simplify to get 1/3

Answer:

[tex]\textrm{System A has \boxed{2} real solutions}\\\\\textrm{System B has \boxed{0} real solutions}\\\\\textrm{System C has \boxed{1} real solution}\\[/tex]

Step-by-step explanation:

For a quadratic equation of the form ax² + bx + c = 0

if b² - 4ac > 0 the system will have 2 real roots
if b² -4ac < 0, the system will have 2 imaginary roots(0 real solutions)

if b² -4ac = 0, the system will have exactly one real solution

System A solutions

[tex]x^2 + y^2 = 17\cdots\cdots (1)\\\\y = -\dfrac{1}{2}x\cdots\cdots (2)[/tex]

From equation (2) we get
x = -2y

Substitute this value for x in (1):

(-2y)² + y² = 17

4y² + y² = 17

5y² = 17

y = ±√(17/5)

Both values of y are real, and since x = -2y,x is also real

System B

The equations are:

y = x² - 7x + 10  (1)

y = -6x + 5         (2)

Since left side is y for both:
x² -7x + 10 = -6x + 5

Add 6x to both sides

=> x² -7x + 10 + 6x = -6x + 6x + 5

=> x² -x + 10 = 5

Subtract 5 both sides:
x² - x + 10 - 5 = 0

x² - x + 5 = 0

Comparing to the standard form we get
a = 1, b = -1, c = 5

b²- 4ac = (-1)² - (4 · 1 · 5)

= 1 - 20

= -19

Since b² - 4ac is negative, the system has no real roots

System C

y = -2x² + 9      (1)

8x - y = -17       (2)

In equation(2) isolate y by moving 8x to the right and multiplying by -1

=> -y = -8x - 17

=> y = 8x + 17  (3)

Set right sides of (1) = (3) right side

-2x² + 9 = 8x + 17

Move 8x + 17 to left side

=> -2x² + 9 - (8x + 17) = 0
=> -2x² + 9 - 8x - 17 = 0
=> -2x² - 8x - 8 = 0

we have a = -2, b = -8, c = -8

b² - 4ac = (-8)² - (4)(-2)(-8)

= 64 - (64) = 0

Hence this system has 1 real root

The required radian measure of the central angle theta is  is 0.872 radians or 0.9 radian.

To find the radian measure of the central angle that intercepts an arc of length 10 feet, we can use the formula for the length of an arc:

Arc Length = Central Angle * Radius

where the central angle is measured in radians.

So, we can write:

10 = Theta * 13

Dividing both sides by 13:

10/13 = Theta

Finally, to convert from degrees to radians,

Radian Measure = (Degree Measure) * (Pi / 180)

So, the radian measure of the central angle is:

Theta = (10/13) * (Pi / 180) = 0.872 radians

Thus, required measurement of angle is 0.872 radians or 0.9 radian.

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Answer: You did not include media attachments, there is not enough information to answer this post.

Step-by-step explanation:

Answer: a) The probability of answering "F" to a single true-false question is 1/2. Therefore, the probability of answering "F" to all six questions is (1/2)^6 = 1/64.

b) To find the probability that at least one answer is "T", we can use the complement rule and find the probability that all six answers are "F". The complement rule states that the probability of an event happening is equal to 1 minus the probability of it not happening.

So, the probability that at least one answer is "T" is 1 - (1/64) = 63/64.

Step-by-step explanation:

the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

What is derivative?

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.

dy/dt = 0

-r/k y²+ry-h=0

y = k/2(1±√(1-4h/rk))

Hence the solution of the given derivative will be y = k/2(1±√(1-4h/rk))

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a. An example of a countable collection of disjoint open intervals is the collection of intervals (0, 1/n), where n is a positive integer. This collection of intervals is countable because it can be put in one-to-one correspondence with the positive integers.

In mathematics, a one-to-one correspondence between two sets is a bijective function that maps every element of one set to exactly one element of the other set, and vice versa.

b. An example of an uncountable collection of disjoint open intervals is the collection of intervals (x, x + 1/n), where x is a real number and n is a positive integer. This collection of intervals is uncountable because it can be put in one-to-one correspondence with the real numbers. To see this, note that for any real number x, we can find a positive integer n such that 1/n is smaller than x. Then, the interval (x, x + 1/n) corresponds to x.

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Answer:

Step-by-step explanation:

USE PYTHAGEROMN THEROME a^2+b^2=c^2

9^2+12^2=a^2

81+144=a^2

255=a^2

15=a

The detail that best supports the inference that the auto manufacturing industry supports green solutions is -

"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".

The pyrolysis process is the thermal decomposition of materials at elevated temperatures, often in an inert atmosphere.

Given is that an engineer at an environmentally minded technology company has come up with a process to convert tire waste from the automobile industry into clean energy.

The detail that best supports the inference that the auto manufacturing industry supports green solutions is -

"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".

Therefore, the detail that best supports the inference that the auto manufacturing industry supports green solutions is -

"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".

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Answer:  y=1/2x

Step-by-step explanation:

Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.

To construct a pair of related variables "a" with "b," whereby "b" may also be bigger than zero, apply the straightforward formula "a / b." Two ratios are combined to form one ratio. The ratio would indeed be 1:1 if there were just one guy and three women. In the group, there are fraction 3/4 girls and 1/4 boys. Parts can be a division between two or more items, a number, or a portion of the volume of a component.

Here,

Given :

Ratio  is 1/2

To convert into percentage ,

We multiply it by 100

=> 1/2 * 100

=> 50 %

Thus , percent change is 50%

Therefore , the solution of the given problem of ratio comes out to be percent change is 50% for the 1/2.

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Answer:

y = - [tex]\frac{3}{4}[/tex] x + 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = - [tex]\frac{3}{4}[/tex] , then

y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation

to find c substitute (8, 9 ) into the partial equation

9 = - [tex]\frac{3}{4}[/tex] (8) + c = - 6 + c ( add 6 to both sides )

15 = c

y = - [tex]\frac{3}{4}[/tex] x + 15 ← equation of line

Answer:

Payment Every Month   $151.39

Total of 48 Payments   $7,266.66

Total Interest   $366.66

Step-by-step explanation:

Hope this helps

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It can reject the null hypothesis at a significance level of 0.05 and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.

The formula for the standard error of the mean is:

SE = s / √(n)

where s is the sample standard deviation and n is the sample size.

The null hypothesis for a two-tailed test would be:

H0: The mean sprint speed of the team is equal to 12 seconds.

The alternative hypothesis would be:

Ha: The mean sprint speed of the team is not equal to 12 seconds.

To test this hypothesis, we need to calculate the standard error of the mean for the team.

Using the data provided, we can calculate the sample mean, sample standard deviation, and sample size as follows:

x = (8+12+9+7+8+10+9+11+13.5+8.5+10.5+9.5+11.5+12.5+9.5+10.5) / 16 = 10

s = √(1/(n-1) × ((8-10)² + (12-10)² + ... + (10.5-10)²)) = 1.717

n = 16

Therefore, the standard error of the mean is:

SE = 1.717 / √(16) = 0.429

To test the hypothesis, we can calculate the t-statistic using the formula:

t = (x - μ) / (SE)

where μ is the hypothesized population mean.

Plugging in the values, we get:

t = (10.0625 - 12) / 0.429 = -4.389

Using a t-table with 15 degrees of freedom (n-1), we can find that the probability of obtaining a t-value of -4.389 or more extreme is less than 0.01.

This means that we can reject the null hypothesis at a significance level of 0.05, and conclude that the mean sprint speed of the team is significantly different from the national athletics mean speed of 12 seconds.

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The unknown angle in the hexagon is as follows:

m∠1 = 148 degrees

Erica is making plans to build a fence on her property line. Using the map let's find the angle m∠1 as follows:

Therefore, the angle m∠1 is one of the angle in the hexagon.

Therefore, the sum of angles in a hexagon is as follows:

sum of angles in hexagon = 180(n - 2)

where

sum of angles in hexagon = 180(6 - 2)

sum of angles in hexagon = 720 degrees

Therefore,

180 - 45 - 27 = 108 degrees

180 - 108 = 72 degrees

Hence,

m∠1 = 720 - 142 - 148 - 80 - 72 - 130

m∠1 = 148 degrees

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The minimum number of books she must sell to make a profit is 2.

In mathematics, the gain from any business operation is referred to as the profit. Every time a shopkeeper sells a product, his goal is to make a profit by getting something from the customer. Basically, he sells the item for more money than it costs.

Given that Anna estimates her revenue equation as R = 6.56x

And her cost equation as C = 10.063 + 1.09x.

To get profit revenue is greater than cost, i.e.

R>C

6.56x > 10.063 + 1.09x

subtract 1.09x from both sides

6.56x - 1.09x > 10.063

5.47x > 10.063

divide both sides by 5.47

x > 10.063/ 5.47

x > 1.84

So the minimum number of books she must sell to make a profit is 2.

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The implicit cost of Jack's education is $77,000, which is the amount of foregone income he gave up in order to attend college.

The implicit cost of Jack's education refers to the opportunity cost or the foregone income he gave up in order to attend college. It is a measure of the value of the next best alternative that he had to sacrifice.

First, let's find the total cost of tuition and books. Jack pays $17,000 per year, so the total cost will be 17,000 * 4 = $68,000 over 4 years of college.

Next, let's find the total cost of rent and food. Jack pays $600 per month for rent and $400 per month for food, so the total cost will be 600 + 400 = $1,000 per month. Over 4 years of college, this comes to 1,000 * 12 * 4 = $48,000.

Finally, Jack also pays $125 per month for on-campus parking, so the total cost will be 125 * 12 * 4 = $6,000.

Putting it all together, we can write the equation for the implicit cost of Jack's education as follows:

Implicit Cost = Foregone Income - Total Cost of Tuition, Rent, Food and Parking

Implicit Cost = 45,000 - (68,000 + 48,000 + 6,000)

Implicit Cost = 45,000 - 122,000

Implicit Cost = -77,000

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The table that represents a linear relationship that is also proportional is x-303 and y-202-101-0.

Values are those principles and beliefs that are important to us and guide our actions, decisions, and behaviors. They are our individual and collective sense of purpose and meaning, and they provide us with a sense of direction and purpose. Values become more important when we are faced with difficult choices or decisions, as it helps us determine what is right and wrong. Values can also be seen as a moral compass, as it helps us determine our actions and behaviors. Values can be influenced by our culture, family, and society, but ultimately, they are our own personal beliefs.

This is an example of a direct proportion, where the ratio of the two values remains the same as they increase or decrease. In this table, the ratio of x to y is 3:2, meaning that for every 3 units of x, there are 2 units of y. This ratio remains the same as the values increase or decrease, so this table represents a linear and proportional relationship.

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The dimensions of the packing box are 2 × 3 × 4 feet.

Based on the information provided, we can reasonably infer and logically deduce that the shape of this packing box is a cuboid.

Mathematically, the volume of a cuboid can be calculated by using this following formula:

Volume = L × W × H

Where:

Substituting the given parameters into the volume of a cuboid formula, we have;

24 = L × (1.5L) × 4

24 = 6L²

L² = 24/6

L = √4

Length, L = 2 feet.

Width, = 1.5L = 1.5(2) = 3 feet.

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In the triangle ABC the line segment bisecting AC is the median, i.e. BD.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

The triangle ABC is given.

In Δ ABC, the line segment AC is bisected, so -

AD = CD

The line segment from a vertex to the middle of the other side is what is meant by a median. When the vertex is an angle in an equilateral triangle or the non-congruent angle of an isosceles triangle, it is also an angle bisector.

Since line segment BD bisects AC.

Therefore, the median is BD.

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Since the partnership amount between Bob and Dan is a distinct legal entity, Dan's malpractice claim cannot encumber Bob's assets.

Both Bob and Dan are physicians who work at the same hospital. They established a partnership, which is a distinct legal entity, because they are partners in the company. This indicates that the partnership's assets and liabilities are separate from Bob and Dan's personal assets and liabilities. Therefore, since the action is against the company and not Bob personally, it will not have any effect on Bob's assets if Dan is sued for malpractice. Any obligations resulting from the malpractice lawsuit will be covered by the partnership, and Bob's assets are secure. One of the numerous benefits of creating a partnership is this.

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