What is the median of this set of data?

362, 187, 211, 298, 331, 250, 347, 199

Answer:

12

Step-by-step explanation:

To determine the number of discs, divide the area of the metal sheet by the area of the discs

The metal sheets are in the shape of a rectangle, thus the area of a rectangle would be used to determine the area of the sheet

Area of a rectangle = length x breadth

56 x 33 = 1848 cm^2

The disc is in the shape of a circle.

area of a circle = πr²

π = 3.14

r = radius

3.14 x 7² = 153.86 cm²

Number of discs = 1848 /153.86 = 12

The correct equation for this given condition is;

⇒ s = $56 + $4w

Where, 's' is amount of savings and 'w' is number of weeks.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Francisco is saving money in an account.

The savings amount = $56

And, Put in another $4 per week.

Now,

Let number of weeks = w

And. Total amount in saving amount = s

So, We can formulate;

⇒ s = $56 + $4w

Thus, The correct equation for this given condition is;

⇒ s = $56 + $4w

Where, 's' is amount of savings and 'w' is number of weeks.

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Answer:                             ✭                              ✼                   ❉

The x-intercept is: (-6,0)     ✹                                                    ✶              ✧

That's the point where the graph touches the x-axis.                         ✶             ✲

The y-intercept is: (0,3)        ✦                                       ✦              ✧

That's where the graph touches the y-axis.

Step-by-step explanation:

✶                            ⚙︎                               ✴︎                       ✳︎             ✱              ❊              ✩                        ✧                     ✳︎                 ✴︎                  ❆                                                                     ❄︎                          ✲                            ✱                                               ❆                                   ❁                          ❂                     ❄︎                   ❆                ❅              

Answer:

3

Step-by-step explanation:

log(5) 125 =x

5^x = 125

5^x = 5^3

x=3

Using given area and base length of a rectangle we got that the height of the given rectangle is 6.5 inches.

Rectangle is closed geometric figure that has four perpendicular sides with opposite sides equal.

The formula for the area of the rectangle :

Area of the rectangle = Length × Breadth

Given that the area of a rectangle is 45.5 square inches.

The base of the rectangle is given 7 inches

To find : Height of the rectangle

Let the base length is the length of the rectangle and height is the Breadth of the rectangle.

Then, Area of the rectangle = Length × Breadth

⇒ 45.5 = 7 × Height

⇒ 45.5 /7 = Height

⇒ 6.5 = Height  of the rectangle

Therefore, the height of the rectangle is 6.5 inches.

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10 miles per hour is the average journey speed.

Given that,

Some pupils choose to ride bikes. They move at a 15 mph average speed for the first two hours, and then they stop for lunch for an hour. The pupils ride at a 10 mph speed for an additional hour.

Average speed is ( total distance ) / ( total time )

During the 1st 2 hrs:

distance = speed * time

distance = 15 *2 = 30 miles

During the last hour:

distance = speed * time

distance = 10 *1 = 10 miles

Average speed = 30+10 / 2+1+1 = 40/4 = 10 mil/hr

Therefore, their average speed for the trip is 10 mil/hr

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Answer: C, D, E, F

Step-by-step explanation:

Answer:

1.5 Miles per hour = 2.1999 Feet per second

Step-by-step explanation:

This conversion of 1.5 miles per hour to feet per second has been calculated by multiplying 1.5 miles per hour by 1.4666 and the result is 2.1999 feet per second.

Step-by-step explanation:

 This problem expects us to model the equation for the total cost of the services of the plumber given the conditions stated.

Say the fixed amount charged for coming to your house is $10

say the fix amount charged per is $3

and the time spent to do the job is X

Hence the scenario can be modeled as

\(Y= 3x+10\)

the equation is similar to the equation of a straight line

\(Y= mx+c\)

Answer:

180

Step-by-step explanation:

The simplest form of the rational expression (x² + 4 · x + 4) / (x² + 3 · x + 2) + (x + 8) / (x² - 5 · x - 6) by algebra properties is (x³ - 2 · x² + 5 · x + 20) / (x³ - 4 · x² + x + 6).

In this question we need to simplify a rational expression by means of algebra properties. First, write the entire expression:

(x² + 4 · x + 4) / (x² + 3 · x + 2) + (x + 8) / (x² - 5 · x - 6)

Second, factor all numerators and denominators:

(x + 2)² / [(x + 2) · (x + 1)] + (x + 8) / [(x - 3) · (x - 2)]

Third, simplify each term:

(x + 2) / (x + 1) + (x + 8) / [(x - 3) · (x - 2)]

Fourth, use the properties for the addition of fractions with different denominator:

[(x + 2) · (x - 3) · (x - 2) + (x + 1) · (x + 8)] / [(x + 1) · (x - 3) · (x - 2)]

Fifth, expand and simplify the resulting expression:

[(x² - 4) · (x - 3) + x² + 9 · x + 8] / [(x + 1) · (x² - 5 · x + 6)]

(x³ - 4 · x - 3 · x² + 12 + x² + 9 · x + 8) / (x³ - 5 · x² + 6 · x + x² - 5 · x + 6)

(x³ - 2 · x² + 5 · x + 20) / (x³ - 4 · x² + x + 6)

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Natalie read 4.5 hours each week

In this question,

Natalie reads for 6/8 hour on 6 days each week.

We need to find how many hours Natalie read each week.

Based on the given conditions, formulate: 6/8 × 6

Write as a single fraction:

= (6 × 6)/8

= (3 × 3)/2             .................(Cross out the common factor)

= 9/2

= 4.5 hours

Therefore, Natalie read 4.5 hours each week

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

2 1/3

Step-by-step explanation:

7/3 = 2 1/3

Hope it helps :D

Answer:

x = 1

Step-by-step explanation:

2 + 1 = 3

-3(1)=-3 -3+6=3

3=3

a) 24 b) 10 c) 4

Step-by-step explanation:

a) 4/5 ×30/1 =120/5 simplify then you get 24

b) 2/9 × 45/1 = 90/9 =10

c) 24/1×1/6= 24/6 simplify then you get 4

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

If y varies directly as x and x = 12 when y = 24, what is x when y = 8.?

So, y = c * x

where c is constant

x = 12 when y = 24

so,

24 = c * 12

c = 24/12 = 2

so,

y = 2x

Now, need to find x when y = 8

so,

8 = 2x

x = 8/2 = 4

===============================================================

From the graph:

y-intercept = 3 , it is the value of y when x = 0

the general form of the line: y = mx + b

where b is y-intercept

So, y = mx + 3

to find m, choose point like (2 , 2) and substitute with it

so, y = 2 when x =2

2 = 2m + 3

2m = -1

m = -1/2 = -0.5

so, y = -0.5x + 3

so, to find x-intercept is the value of x when y = 0

so, 0 = -0.5x + 3

0.5x = 3

x = 3/0.5 = 6

m is the slope = -0.5

b is y-intrcept = 3

The constant of proportionality (r) is 0.2.

The constant of proportionality (r) is the value that relates the two proportional quantities x and y. In the equation y = rx, r is the constant of proportionality. To find the constant of proportionality, we can use the given values of x and y and solve for r.

One way to do this is to choose one of the given pairs of x and y values and plug them into the equation y = rx. For example, using the first pair of values, x = 8 and y = 1.6, we get:

1.6 = r(8)

To solve for r, we can divide both sides of the equation by 8:

1.6/8 = r

Simplifying the fraction gives us:

0.2 = r

Therefore, the constant of proportionality is 0.2.

We can check our answer by plugging the value of r back into the equation and seeing if it holds true for the other pairs of x and y values. For example, using the second pair of values, x = 15 and y = 3, we get:

3 = 0.2(15)

Simplifying the right side of the equation gives us:

3 = 3

Since both sides of the equation are equal, our answer is correct. The constant of proportionality is 0.2.

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If the price of the dream car will increase at an annual rate of 1.7 percent, it will cost about $62,232.25 after 7 years.

To find the future cost of the dream car in 7 years, we can use the formula for compound interest.

The formula for compound interest is given:

A = P (1 + r/n)^nt

Where:

A = amount of money after n years

P = principal (initial) amount of money

r = annual interest rate

t = number of years

n = number of times interest is compounded per year

Given that the dream car costs $52,300 today and it will increase at an annual rate of 1.7%, we can find the future cost of the car in 7 years as follows:

P = $52,300r = 1.7% = 0.017t = 7 years

n = 1 (annual compounding)

Using these values in the formula

A = $52,300 (1 + 0.017/1)^(1*7)

A = $52,300 (1.017)^7A ≈ $62,232.25

Therefore, the dream car will cost about $62,232.25 after 7 years.

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The length of the rectangle is represented by the expression x^2 − 6x − 16. (option c)

To find the expression representing the length, we need to use the fact that the area of a rectangle is given by the product of its length and width. In this case, the area of the rectangle is given by the function x^3 − 2x^2 − 40x − 64. Since the width of the rectangle is x + 4, we can write the area as

(x + 4) * L

where L is the length of the rectangle.

To find the expression for L, we can set

x^3 − 2x^2 − 40x − 64 =  (x + 4) * L and solve for L.

First, we distribute the x + 4 on the right side of the equation:

x^3 − 2x^2 − 40x − 64 = x^2 * L + 4L. Then, we compare the coefficients of the x^2 and x terms on both sides of the equation: -2 = L + 4L, which simplifies to -2 = 5L. Finally, we solve for L: L = -2/5.

Thus, the expression representing the length of the rectangle is -2/5.

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Answer:

  B. secondary roads

Step-by-step explanation:

While all of streets, county roads, and secondary roads are generally designed to carry less traffic and/or have lower speed limits than interstate highways, the generic name for such roads is ...

  secondary roads.

Answer:

(a) \(1 > -2\) or \(-2 < 1\)

(b) \(2 > 1\) or \(1 < 2\)

Step-by-step explanation:

Given

\(N = -2F\) --- North Dakota

\(C = 1F\) --- Cheyenne, Wyoming

Solving (a): Inequality to compare both temperatures

From the given temperatures, we can conclude that:

\(C > N\) or \(N < C\)

Because

\(1 > -2\) i.e. 1 is greater than -2

or

\(-2 < 1\) i.e. -2 is less than 1

Solving (b): Inequality to compare the absolute values of the temperatures

We have:

\(N = -2F\)

\(C = 1F\)

The absolute values are:

\(|N| = |-2|\)

\(|N| =2\)

\(|C| = |1|\)

\(|C| = 1\)

By comparison:

\(|N| > |C|\) or \(|C| < |N|\)

Because

\(2 > 1\) i.e. 2 is greater than 1

or

\(1 < 2\) i.e. 1 is less than 2

Answer:38

Step-by-step explanation:

they were born in 1933 and 1971 minus 1933 is 38.

Answer:

$17 per hour

Step-by-step explanation:

Given,

      The amount required to support first-person is $18,946 per year.

      The amount required to support each additional person is $4,437 per year.                                                                                                    

So, The amount required to support 3 additional people = $13,311

Total amount required to support 4 people = $18,946 + $13,311

                                                                         = $ 32,257

Total number of hours Natalia works in a year = 38×50

                                                                             = 1900 hours

The minimum required hourly wage for Natalia =

                  total yearly expenses÷ total working hours in a year

                                       $32,257 ÷ 1900 = $16.97 per hour

                                                                   ≈$17 per hour

Natalia's minimum hourly wage to support her family of 4 is $17.00/hour.

We must first assess the total annual cost of supporting the family in order to determine Natalia's minimum hourly income to support her family of four.

The budget estimator estimates that it will cost $18,946 per year to support the first person and $4,437 per year to sustain each additional person. Natalia has a total of four family members, so her total yearly support expenses would be as follows:

$18,946 + ($4,437 x 3) = $32,257

The annual salary of Natalia must then be determined based on her working hours. She would put in the following number of hours if she worked 38 hours per week for 50 weeks in a year:

38 hours per week x 50 weeks in a year = 1,900 hours.

By dividing the entire annual cost of providing for her family by the number of hours she works per year, we can determine her minimum hourly wage:

1,900 hours / $32,257 = $17.00/hour.

Therefore, Natalia's minimum hourly wage to support her family of 4 is $17.00/hour.

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The population size of the protozoa after seven days, starting with an initial population of five members and a constant relative growth rate of 0.469 per member per day, can be calculated using the formula\(P(t) = 5 * e^{(0.469 * 7)\).

Part 1 of the question establishes that the relative growth rate of the protozoa population is 0.469 per member per day. This information helps us define the differential equation that represents the growth: dP/dt = 0.469P.

Part 2 introduces the exponential growth formula for population growth, which states that \(P(t) = P(0)e^{kt\) where P(t) is the population size at time t, P(0) is the initial population size, k is the growth rate, and e is the base of the natural logarithm.

To find the population size after seven days, we substitute the given values into the formula: \(P(t) = 5 * e^{(0.469 * 7)\). Evaluating this expression yields the final answer, which represents the population size of the protozoa after seven days.

Note: The calculation itself is not included in the answer as the model response is limited to explaining the approach.

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Answer:

A graph increases when the line or bar is goi g up.

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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