The length of each side of an equilateral triangle having an area of square root of 243sq.cm is​

The exact measure of an angle whose measure is 18° in radians is; pi over 10.

Recall, it follows from angle measurements that;

π radians ==== 180°

Hence, it follows from proportion that the measure of 18° in radians, x can be determined as follows;

x = 18 π radians / 180

x = π / 10 radians.

Ultimately, the required measure of 18° in radians as required is; π / 10.

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It will take 5.189 hours to get doubled the size of Sample.

A relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

Growth rate = 5.8%

The continuous exponential growth model for populations is given by:

P(t)= [tex]P_0 e^{rt[/tex]

So, r= 5.8%

r = 0.058

Now, the time taken to double the sample then P(t) = 2P(0).

So, P(t)= [tex]P_0 e^{0.058t[/tex]

2P(0) = [tex]P_0 e^{0.058t[/tex]

[tex]e^{0.058t[/tex] = 2

Taking log on both side

log [tex]e^{0.058t[/tex] = log 2

0.058 t = 0.301

t= 0.301/ 0.058

t = 5.189

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Answer: 0.32 or 32%

Step-by-step explanation: 8/25

Answer:

The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got [tex]0y[/tex]. Instead of subtracting, they should have added it.

Step-by-step explanation:

Given:

[tex]8x+2y=44\\5x+2y=35[/tex]

We can combine the system of equations into a single equation:

[tex]13x+4y=79[/tex]

From this step, we can conclude that the answer for part b is incorrect. The mistake they made was that they subtracted [tex]2y[/tex] from [tex]2y[/tex] and got 0y. Instead of subtracting, they should have added it.

We can continue solving the system of equations by writing y in terms of x.

[tex]8x+2y=44\\2y=44-8x\\y=22-4x[/tex]

now substitute this into the single equation:

[tex]13x+4y=79\\13x+4(22-4x)=79\\13x+88-16x=79\\-3x+88=79\\-3x=-9\\x=3[/tex]

Since we now know that [tex]x=3\\[/tex], we can substitute this into the equation we made for y.

[tex]y=22-4x\\y=22-4(3)\\y=22-12\\y=10[/tex]

The solution for the system of equations is [tex]x=3[/tex] and [tex]y=10\\[/tex].

The order of the numbers from greatest to least are 3.406 > 305 / 100 > 99 × 1/100

Descending order refers to the arrangements of numbers from the greatest to the least.

On the other hand, ascending order is the arrangement of numbers from the least to the greatest.

3.406

305 / 100

= 3.05

99 X 1/100

= 99 × 0.01

= 0.99

Therefore, the arrangements from greatest to least is 3.406, 305 / 100, 99 × 1/100

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Answer:

(C) 29

Step-by-step explanation:

Box plot, because the median can easily be determined from the large set of data.

What exactly is a median?

The median is defined as the value in the centre of a given set of numbers or statistics. There are three main measures in mathematics that are used to calculate the average value for a given group of integers. They are the mean, the median, and the mode. These three indicators are known as central tendency measures. Mean computes the average value of the provided data. A median defines the midway value of the provided data. Mode defines the repeating value of the input data.

Now,

As, A box plot is a very visual means of displaying a concise overview of one or more sets of data. It is especially handy for quickly summarising and comparing several sets of findings from various trials. A box plot, at a glance, gives a graphical representation of the distribution of findings as well as indicators of symmetry within the data.

and it can handle a large set of data.

Hence,

            Box plot, because the median can easily be determined from the large set of data.

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Answer:box plots

Step-by-step explanation:

i did it

The sample space for pulling 2 marbles  to find the probability will be List 3.

Probability conveys how likely an event is to occur. The occurrence of a random event is the focus of this mathematical field of study. The value is in the zero to one range. Mathematicians use probability to predict the likelihood that certain events will take place.

The possibility of something happening is referred to as probability. The probability distribution also utilises this basic concept from probability theory. We must first ascertain the total number of possibilities before calculating the likelihood of a specific event.

The proportion of favourable outcomes to all possible outcomes, or P(E), determines the likelihood that an event will take place.

Now,

Given that Lloyd has a bag of 3 marbles. There is 1 orange marble, 1 green marble, and 1 blue marble.

So no. of ways to pick first ball = 3

as there are three type of balls

and no. of ways to pick second ball= 3 as replacement is allowed.

Therefore total sample space = 3*3=9

Hence,

         The sample space for pulling 2 marbles will be List 3.

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The number of weekly downloads can be modeled using an exponential function h(x) = 548 × 1.04ˣ.

What is exponential function?

An exponential function is a mathematical function in which the value of the output is proportional to the value of a fixed number (known as the base) raised to the power of the input value. The general form of an exponential function is:

                                      y = abˣ

where a and b are constants, x is the input value, and y is the output value. The constant a controls the vertical scaling of the function, while the constant b controls the rate of growth or decay. If b is greater than 1, the function grows rapidly as x increases. If 0 < b < 1, the function decays as x increases. If b is equal to 1, the function is a linear function.

Exponential functions are widely used in many fields, including finance, biology, physics, and engineering, to model growth and decay processes.

The number of weekly downloads can be modeled using an exponential function.

                             h(x) = 548 * 1.04ˣ

where x is the number of weeks after the release date, h(x) is the estimated number of weekly downloads, and 1.04 is the growth factor (1 + the expected weekly increase of 4%).

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Answer:

Step-by-step explanation:

The Rational Zeroes Theorem states that if a polynomial equation has a rational solution (a solution that can be expressed as a fraction of two integers), then that rational solution must be of the form p/q, where p is a factor of the constant term (in this case 36) and q is a factor of the leading coefficient (in this case 4).

Step 1: Find the factors of 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step 2: For each factor of 36, divide it by each factor of 4 to get a list of possible rational solutions.

Step 3: Test each of the possible rational solutions by plugging them into the polynomial equation and seeing if they make the equation equal to zero. If a solution makes the equation equal to zero, it is a root of the polynomial.

Step 4: Once you have found all of the roots of the polynomial, you can use them to write the polynomial in factored form.

Note: This method only works for polynomials with real coefficients and will only give you the real solutions of the equation. If the polynomial has complex solutions, you will need to use a different method to find them.

Answer:

Step-by-step explanation:

The floor-to-ceiling clearance is 7 ft 5 in, which is equal to 7 * 12 + 5 = 89 inches.

We need to construct 8 shelves, each of which is 1 inch thick, so the total thickness of the shelves is 8 * 1 = 8 inches.

We also need to leave an equal space between each shelf and the next, the top shelf and the ceiling, and the bottom shelf and the floor. So, there will be 7 equal spaces in total (6 between shelves and 1 between the bottom shelf and the floor).

Therefore, the space between each shelf and the next will be (89 - 8) / 7 = 11 inches.

Here's a step by step solution:

Calculate the total height of the room in inches: 7 ft 5 in = 7 * 12 + 5 = 89 inches.

Calculate the total thickness of all the shelves: 8 shelves * 1 inch/shelf = 8 inches.

Deduct the thickness of the shelves from the height of the room to find the total space available: 89 inches - 8 inches = 81 inches.

Divide the total space available by the number of spaces (7) to find the space between each shelf and the next: 81 inches / 7 = 11 inches.

The number of positive integers that satisfy the conditions is 4

The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,

To satisfy positive integers that will have sum of four with a 1, a 2 or a 3

The integers are

13

31

112

211

therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3

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The sector angle are 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

A pie chart is a type of graph where a circle is divided into certain sectors where each sector shows a proportion of the whole.

We have to show the given data in a pie chart where each sector represents a proportion of a type of transportation.

39 students uses bus for transportation.

12 students uses bike for transportation.

25 students walk for transportation.

24 students uses car for transportation.

Total number of students = 39 + 12 + 25 + 24 = 100

Total sector angle of a circle = 360°

Sector angle for bus = (39 / 100) × 360 = 140.4°

Sector angle for bike = (12 / 100) × 360 = 43.2°

Sector angle for walk = (25 / 100) × 360 = 90°

Sector angle for car = (24 / 100) × 360 = 86.4°

Hence the sector angle for each mode of transportation is 140.4° for bus, 43.2° for bike, 90° for walk and 86.4° for car.

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The correct equation to find the width, w, of the stone path would be: Option B. (2w+12) (2w+16) = 420

This is because the area of the garden and path is equal to the area of the rectangle with dimensions (12+2w) and (16+2w). Therefore, we can set up the equation:

(12+2w)(16+2w) = 420

Expanding and simplifying, we get:

4w² + 56w - 204 = 0

Dividing by 4, we get:

w² + 14w - 51 = 0

Factoring, we get:

(w+17)(w-3) = 0

Since the width of the path cannot be negative, the only valid solution is w = 3.

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Complete question is in the image attached

Answer:because angles in a triangle add up to 180 degrees.

Step-by-step explanation:

A=40

C=30

So 180-40-30=110

Answer: Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

The accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.

Step-by-step explanation:

To calculate Victor's annual income after 12 years as a teacher, we need to find the future value of his starting salary of $40,000 after 12 years with an average 4 percent raise every year.

Using the formula for the future value of a single amount (FV = PV * (1 + r)^n), where PV is the present value, r is the interest rate, and n is the number of years, we can calculate the future value as follows:

FV = $40,000 * (1 + 0.04)^12 = $47,564

So, Victor's annual income after 12 years as a teacher would be $47,564 if he received an average 4 percent raise every year.

To calculate the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year, we need to use the formula for the future value of a series of equal amounts (FV = A * (1 + r)^n - 1 / r), where A is the annual payment and r is the interest rate.

Plugging in the values, we get:

FV = $3,000 * (1 + 0.05)^12 - 1 / 0.05 = $41,592

So, the accumulated future value of earning $3,000 each year teaching during the summers over 12 years with a 5 percent raise every year would be $41,592.

The two provided payments of $17,000 and $3,300 due in 1 year and 2 years, respectively, would be replaced by two equal payments of $2,287.87 made in 6 months and 5 years.

To solve this problem, we need to find two equal payments that would replace the two given payments, given the time and interest rate. We can use the present value formula to calculate these payments:

PV = C / (1 + r)^n

Where

PV is the present value,  

C is the future value of the payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the first payment of $17,000 due in 1 year, its present value in 6 months can be calculated as:

PV1 = 17,000 / (1 + 0.08/4)^(2*2) = $14,785.28

For the second payment of $3,300 due in 2 years, its present value in 5 years can be calculated as:

PV2 = 3,300 / (1 + 0.08/4)^(4*2) = $2,424.67

To find the equal payments that would replace these two payments, we can use the annuity formula:

PMT = PV / [(1 - (1 + r)^(-n)) / r]

Where

PMT is the equal payment,

PV is the present value,

r is the interest rate per compounding period, and

n is the number of compounding periods.

For the two payments to be made in 6 months and 5 years, respectively, the total number of compounding periods is

4*2.5 = 10.

The equal payment can be calculated as follows:

PMT = (PV1 + PV2) / [(1 - (1 + 0.08/4)^(-10)) / (0.08/4)] = $2,287.87

Therefore, two equal payments of $2,287.87 made in 6 months and 5 years would replace the two given payments of $17,000 and $3,300 due in 1 year and 2 years, respectively.

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Answer:

maybe your friend gets stuck because youre not supposed to divide the denominator, only make a common one by multiplying one or both untill they are the same. Least common multiples

Answer:

Step-by-step explanation:

213232131123123123123123

1. To find the class width, we first need to find the range of the data, which is the difference between the maximum and minimum values: 68 - 10 = 58. Then, we divide the range by the number of classes to get the class width: 58 / 7 = 8.29. However, we will round up to the nearest whole number, so the class width is 9.

2. The lower class limits are 10, 19, 28, 37, 46, 55, and 64, since we add the class width to the lower limit of each previous class to find the lower limit of the next class.

3. The upper class limits are 18, 27, 36, 45, 54, 63, and 68, since we add the class width to the lower limit of each class to find the upper limit of that class.

Answer:

(6, 1)

Step-by-step explanation:

When a point is reflected over the x-axis, its y-coordinate changes sign. When a point is reflected over the y-axis, its x-coordinate changes sign.

So, when point Q, located at (-6,-1), is reflected over the x-axis to create point Q', the new point has the same x-coordinate and a y-coordinate of -1 to 1 = 1. So, Q' is located at (-6, 1).

Next, when Q' is reflected over the y-axis to create Q'', the new point has the same y-coordinate and an x-coordinate of -6 to 6 = 6. So, Q'' is located at (6, 1).

So, the ordered pair that describes the location of Q'' is (6, 1).

Answer:

Step-by-step explanation:

9.

f(x)=x²-10x+3

=x²-10x+25-25+3

=(x-5)²-22

vertex is (5,-22)

it has horizontal tangent at (5,-22)

or

f(x)=x²-10x+3

f'(x)=2x-10

it has horizontal tangent where 2x-10=0 or x=5

f(5)=5²-10(5)+3

=25-50+3

=-22

it has horizontal tangent at (5,-22)

Answer:

151.37

Step-by-step explanation:

Answer:

151.372868 but rounded is 151.37

Step-by-step explanation:

1863.4/12.31=151.372868 rounded is 151.37

The 50% of the data lies above is 49.5. it is called the median.

What is the upper quartile?

Assume that Q₃ represents the upper quartile, which is the median of the data set's upper half. In contrast, Q₁ represents the median and lower quartile of the lower half of the data set. The median is Q₂. Consider a data set that contains n items. The quartiles are then provided by:

Q₁ = [(n+1)/4]

Q₂ = [(n+1)/2]

Q₃ = [3(n+1)/4]

this item

The 50% of the data is median.

The formula of median is

(n+1)/2 th term

The given data is 41, 43, 49.5, 56, and 58.

The number of items is n = 5.

The median of the data is (5+1)/2 the term = 3rd term.

The third term of the data is 49.5.

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The polynomial function of degree 4 is,

⇒ f (x) = 5 (x + 3)² (x - 3)²

Relation between set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable and another variable.

Given that;

Zeroes of function is,

⇒ -3 (multiplicity 2) and 3 (multiplicity 2),

And, It passes through the point (-4,245).

Now, The polynomial function of degree 4 is,

⇒ f (x) = A (x - (- 3))² (x - 3)²

⇒ f (x) = A (x + 3)² (x - 3)²

Since, It passes through the point (-4,245).

Hence, Put x = - 4, y = 245

⇒ 245 = A (- 4 + 3)² (- 4 - 3)²

⇒ 245 = A (- 1)² (- 7)²

⇒ 245 = A × 49

⇒ A = 245/49

⇒ A = 5

Thus, The polynomial is,

⇒ f (x) = A (x + 3)² (x - 3)²

⇒ f (x) = 5 (x + 3)² (x - 3)²

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A customer has 4 x 2 x 3 = 24 different car models to choose from if the customer can choose one type of audio system, one style of roof, and one type of seat cover.

The supportive statement is m∠WKT ≅ m∠TRW.

An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.

A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.

The altitude is the measurement of the angle perpendicular to the parallel sides.

We know a trapezoid is isosceles if the two nonparallel sides are equal.

Therefore, In KWRT, [tex]\overline{WK}[/tex] ≅ [tex]\overline{TR}[/tex] and [tex]\overline{KR} || \overline{TW}[/tex].

The missing statement to support all other statements would be,

m∠WKT ≅ m∠TRW as the angle formed by the pair of the corresponding sides is equal.

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(a) When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

(b) When q = 1, the expected score is 1, which is the maximum possible score.

(c) The optimal value of p also depends on the value of q in this case.

a) The expected score of the meteorologist can be expressed as the weighted average of the two possible scores, where the weights are the probabilities of it raining or not raining:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - q^2)

To maximize the expected score, we need to differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2q(1 - q) = 1 - 2p

Solving for p, we get:

p = (1 - 2q + 2q^2) / 2

So the optimal value of p depends on the value of q. When q = 0 or q = 1, we get p = 0.5, but for other values of q, the optimal value of p is different.

b) If the meteorologist chooses p = q, then the expected score simplifies to:

Expected score = q(1 - (1 - q)^2) + (1 - q)(1 - q^2)

= q^3 + (1 - 2q)q^2 + (1 - q)

To find the maximum expected score, we can take the derivative of this expression with respect to q, set it equal to zero, and solve for q. This gives:

3q^2 - 4q + 1 = 0

This quadratic equation has two roots: q = 1/3 and q = 1. When q = 1, the expected score is 1, which is the maximum possible score. When q = 1/3, the expected score is (8/27), which is the maximum score for any value of q between 0 and 1.

c) If the payoffs are {1 - (1 - p)^2, 1 - 1.1p^2}, then the expected score of the meteorologist is:

Expected score = p(1 - (1 - q)^2) + (1 - p)(1 - 1.1q^2)

To maximize this expected score, we can differentiate it with respect to p, set the derivative equal to zero, and solve for p. This gives:

2.2q^2 - 2q + 1 = 2p

Solving for p, we get:

p = (2.2q^2 - 2q + 1) / 2

So, in this scenario, the value of q also affects the ideal value of p.

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Answer:

132ft

Step-by-step explanation:

The height of the Great Sphinx can be found by using the relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.

Let h1 be the height of the Great Sphinx and h2 be the height of the person. We know that the length of their shadows are 220 ft and 20 ft, respectively.

Since the sun is at the same elevation for both objects, we can set up the following proportion:

h1/220 = h2/20

Cross multiplying, we get:

h1 = (h2 * 220) / 20

Plugging in h2 = 6 ft, we get:

h1 = (6 * 220) / 20 = 132 ft

So, the height of the Great Sphinx is approximately 132 ft.

Thus, the correct answer is 132 ft, which is not in the options provided, but it is a reasonable estimate of the height of the Great Sphinx.

Answer:  I can explain the steps for calculating descriptive statistics for the given data.

For the "number" column:

Mean: To find the mean, add up all the values and divide by the number of values.

Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.

Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.

Maximum: To find the maximum, find the largest value in the list.

Minimum: To find the minimum, find the smallest value in the list.

For the "percent" column:

Mean: To find the mean, add up all the values and divide by the number of values.

Median: To find the median, arrange the values in numerical order and find the middle value. If there is an even number of values, take the average of the two middle values.

Mode: To find the mode, find the value that appears most frequently. If there is no value that appears more than once, then there is no mode.

Maximum: To find the maximum, find the largest value in the list.

Minimum: To find the minimum, find the smallest value in the list.

Regarding the statistics on children whose parents do not have secure employment, it can be determined how each state compares to the surrounding states by comparing the mean, median, and mode of the "number" and "percent" columns. The state with the best or worst data can be determined by comparing the maximum and minimum values in each column. The value that gives a better comparison would depend on the purpose of the analysis. If the goal is to understand the overall number of children affected, then the "number" column would be more appropriate. If the goal is to understand the proportion of children affected in each state, then the "percent" column would be more appropriate.

Step-by-step explanation:

Answer:

76°

Just know that angles on the parallel sides always add up to 180°