Find the mean, median, mode, and range of the data set.
16, 18, 14, 3, 11, 1, 18

Answer:

$6.35

Step-by-step explanation:

10 quarters =

10 × .25 = $2.50

17 dimes =

17 × .10 = $1.70

40 nickels =

40 × .05 = $2.00

15 pennies =

15 × .01 = $0.15

2.50+1.70+2.00+.15

= 6.35

The total is $6.35.

Answer:

3/6+4/6=7/6 (or 1 1/6)

Step-by-step explanation:

Multiply 1/2 by 3, add the top and bottom numbers together

Then I simplified 7/6 to 1 1/6 because 7 goes into 6, 1 time and there is still 1 remaining

Answer:

x=27°

Step-by-step explanation:

180°-54°=126°

180°-126°=54°

54°÷2=27°

Answer:

I never had this question but trying to help according to formula

let b=12

let h=3

According to given formula,

a=bh÷2

a=(12×3)÷2

a=36÷2

a=28in2

Answer:

11

Step-by-step explanation:

AB = 3x + 4 and AC which is twice of AB is equal to 11x - 17

2 (3x + 4) = 11x - 17

6x + 8 = 11x - 17

8 + 17 = 11x - 6x

25 = 5x

5 = x

AC = CD = 11x - 17 ➡ 11×5 - 17 = 38

CD = 38 and DE = 49 - 38 = 11

The probability of choosing a white marble from the box can be determined by dividing the number of white marbles by the total number of marbles.

In this case, the box contains 7 green marbles and 6 white marbles, so the total number of marbles is 13.

To find the probability, we divide the number of white marbles (6) by the total number of marbles (13):

Probability of choosing a white marble = 6 / 13

To express this as a decimal number, we divide 6 by 13:

Probability of choosing a white marble ≈ 0.4615 (rounded to 4 decimal places)

The probability of choosing a white marble from the box is approximately 0.4615.

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Answer:

79

Step-by-step explanation:

Order of operations GERMDAS

Grouping: no grouping

Exponents: 9²=81 so 6÷3+81-4

Radicals: no radicals

Multiplication: no multiplication

Division: 6÷3=2 so 2+81-4

Addition: 2+81=83 so 83-4

Subtraction: 83-4=79

Answer:

79

Step-by-step explanation:

6/3+9^2-4             9^2= 81           6/3+81-4                  6/3 = 2                  2+81-4= 79

Equations, their parts and how to solve them is discussed above.

Given is an equation that models the amount of profit the movie (Mission Impossible III) earned (in millions of dollars) at the Box Office each week.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign.

The steps to solve a basic equation with one variable (linear) are given below:

        with the same exponent) by adding/subtracting them.

Therefore, equations, their parts and how to solve them is discussed above.

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The three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

So, let 7x, 3x, and 2x be the three numbers.

7x+2x = 9x is the product of the lowest and greatest number.

In accordance with:

9x-30=2(3x)

To make the equation easier:

9x-30=6x

30 extra on both sides:

9x=6x+30 or,9x-6x=30

3x=30, x=10,

So, the numbers will be:

7x=7(10) = 70

3x=3(10) = 30

2x=2(10) = 20

Therefore, the three numbers that are in the ratio 7:3:2 are 70, 30, and 20.

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The world record for memorizing and reciting the most digits of pi is held by Rajveer Meena from India. He recited 50,000 decimal places of pi in 2020, which is the current recognized world record.

Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means it cannot be expressed as a finite decimal or a fraction. The decimal representation of pi is non-repeating and goes on indefinitely without a pattern. The value of pi is approximately 3.14159, but it is commonly approximated as 3.14 for simplicity in mathematical calculations. However, the exact value of pi has been calculated to trillions of digits using various computational methods. The quest to calculate more digits of pi continues to this day, and the computation of pi serves as a benchmark for testing the performance of supercomputers and computational algorithms. The current record for calculating the most digits of pi is trillions of digits, achieved through the use of powerful computers and advanced algorithms.

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Answer:17

7, 9, 11, 13, 14, 17,

The model equation for the fish population growth in the lake can be represented by the logistic equation:

d P/dt = r * P * (1 - P/K) - H
where:
- d P/dt represents the rate of change of the fish population over time
- r is the growth rate, which is 0.1 per month
- P is the fish population size in thousands
- K is the carrying capacity, which is 50 thousand
- H is the harvesting rate, which is 0.6 thousand per month

To find the equilibria, we set d P/dt = 0 and solve for P:

0 = r * P * (1 - P/K) - H

Simplifying the equation, we get:

r * P * (1 - P/K) = H

Plugging in the values, we have:

0.1 * P * (1 - P/50) = 0.6

Solving this equation, we find two equilibria:

P = 0 (which is not relevant in this case)

P = 30 thousand

To classify the equilibria as stable or unstable, we need to examine the behavior of the fish population around the equilibrium points. We can do this by considering the sign of dP/dt for values of P greater and smaller than the equilibrium.

For P > 30 thousand, d P/dt is negative, indicating that the population is decreasing. This means that the equilibrium point at P = 30 thousand is stable.

For P < 30 thousand, d P/dt is positive, indicating that the population is increasing. This means that the equilibrium point at P = 30 thousand is unstable.

Therefore, the only relevant equilibrium point is at P = 30 thousand, and it is stable.

Assuming there are plenty of fish in the lake to start with, the long-term fish population will approach the carrying capacity of 50 thousand, as the growth rate slows down and the harvesting rate is constant. Therefore, the long-term fish population will be greater than 0.12 thousand fish.
In conclusion, the model equation for the fish population growth in the lake is

d P/dt = r * P * (1 - P/K) - H.

The equilibria are P = 0 thousand (not relevant) and P = 30 thousand, with the equilibrium at P = 30 thousand being stable. The long-term fish population, assuming plenty of fish initially, will approach the carrying capacity of 50 thousand and be greater than 0.12 thousand fish.  

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Answer:

The foci for the following ellipse are incorrect

Step-by-step explanation:

Given equation: \(7x^2+8y^2=30\)

Divide whole equation by 30

So, \(\frac{x^2}{\frac{30}{7}}+\frac{y^2}{\frac{30}{8}}=1\)

General equation of ellipse: \(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}\)

On comparing\(a =\frac{30}{7}\)

\(b = \frac{30}{8}\\c^2=a^2-b^2\\c=\sqrt{a^2-b^2}\\c=\sqrt{(\frac{30}{7})^2-(\frac{30}{8})^2}\\c=\frac{15\sqrt{15}}{28}\)

So,the foci for the following ellipse are incorrect

Jenna will have total money, y= 166 + 23x.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Jenna had saved $166.

She will earn $23 per day of work

If x represents the number of days she works the she will earn

= 23x

So, She will have total

= 166+ 23x

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Answer:

1. x = 0

12. x = 3

13. x = 0

14.

The population standard deviation for a population of watermelons, with 75.4% of the watermelons having radii between 15.0 cm and 22.0 cm and a known population mean of 18.5 cm, can be determined.

In a normal distribution, the area between two standard deviations from the mean encompasses approximately 68% of the data. Since 75.4% of the watermelons fall within the range of 15.0 cm and 22.0 cm, this range exceeds one standard deviation from the mean. Therefore, we can conclude that the range of 15.0 cm to 22.0 cm represents approximately two standard deviations from the mean.

To find the population standard deviation, we can use the following formula:

Standard Deviation = (Upper Limit - Lower Limit) / (2 * Number of Standard Deviations)

In this case, the upper limit is 22.0 cm, the lower limit is 15.0 cm, the number of standard deviations is 2, and the mean is 18.5 cm. Plugging these values into the formula, we get:

Standard Deviation = (22.0 - 15.0) / (2 * 2) = 7.0 / 4 = 1.75 cm

Rounding the answer to two decimal places, the population standard deviation is approximately 1.75 cm.

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Answer:

the answer is D last option

Step-by-step explanation:

14x12x16

The steps to evaluate an exponential expression include:

First, you need to identify the base which is the number being raised to a power, and the exponent is the power to which the base is being raised. Then replace this base with the value that is needed to be used.

Use this exponent such that you can find out the number of times the base will multiply itself and then do the multiplication and simplify the expression.

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Step-by-step explanation:

3.15m or 3 3/20m

She has a total of 12.6m of ribbbon.

She has to make 4 flowers and each has ribbon.

You take 12.6÷4

Answer:

she would use 3.15 meters on each flower because when you divide 12.6 meters by 4 it equals 3.15 meters.

Answer:

The value of x = 13

The value of KN = 23.5

Step-by-step explanation:

Here are some of the characteristics of a rectangle.

Given the diagonals of a rectangle

KM = 4x-15

KL = 9x-80

We know that the diagonals of a rectangle are equal, so

KL=KM

9x-80=4x-15

9x-4x= -15+80

5x = 65

divide both sides by 5

5x/5 = 65/5

x = 13

Therefore, the value of x = 13

as

KM = 4x-15

so substitute x = 13

KM = 4(13) - 5 = 52 - 5 = 47

From the diagram, it is clear that N is the midpoint of the diagonal KM.

so

KN = 1/2 KM

substitute KM = 47

KN = 1/2 × 47

KN = 23.5

Therefore, the value of KN = 23.5

Summary:

The value of x = 13

The value of KN = 23.5

The correct answer is b) 0.

To evaluate the line integral of h(x, y) over the given circle, we can use the parameterization of the circle in terms of the angle θ, where x = cos θ and y = sin θ. Substituting these values into h(x, y) = yi + xj, we obtain h(θ) = sin θ i + cos θ j. Then, we can compute the line integral using the formula:

∫h(x, y) ds = ∫h(θ) ||r'(θ)|| dθ

where r(θ) = cos θ i + sin θ j is the parameterization of the circle and ||r'(θ)|| = 1 is the magnitude of its derivative. Therefore, the line integral simplifies to:

∫h(x, y) ds = ∫0^2π (sin θ i + cos θ j) dθ

Integrating the x-component and y-component separately, we get:

∫h(x, y) ds = [-cos θ]0^2π + [sin θ]0^2π = 0

Thus, the line integral of h(x, y) over the given circle is 0. This means that the work done by the vector field h(x, y) as it moves along the circle is zero, which indicates that the vector field is conservative. In other words, h(x, y) can be expressed as the gradient of a scalar potential function.

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Answer:

2a(x + 3y)

Step-by-step explanation:

2ax + 6ay

factor out a 2a

2a(x + 3y)

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

The equation of the graph is y = -2x + 1

From the question, we have the following points on the line

(0, 1) and (1, -1)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 1

Using the points, we have

m + 1 = -1

m = -2

So, the equation is y = -2x + 1

In (a), we have

c = 1

This is the y-intercept

For the x intercept, we have

-2x + 1 = 0

This gives

x = 1/2

Parallel lines have equal slopes

This means that the slope must be -1/2

Because the line must go through (0, 0), the equation is y = -1/2x

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Answer:

x=5

Y=0

Hope this helpssssssssssssssss

Answer:

x=1; y=13/5

Step-by-step explanation:

(I'm sure you can do given yourself)

<D=<B                 Def of parallelogram

8x+5=5y              Substitution

<a and <d is         Def of paralleogram

supplementary

3x+10=5y             Substitution

8x+5=5y                 Do system of equations

3x+10=5y                

8x+5=3x+10            they both equal 5y so set both the equations together

5x+5=10                  subtract 3x from both sides

5x=5                       subtract 5 from both sides

x=1                            divide by 5 on both sides

8(1)+5=5y                  plug in x to one of the previous equations

13=5y                         Simiplfiy

y=13/5                        

The probability of a prison sentence greater than 18 years for a person convicted of second-degree murder is 0.1056 or about 10.56%.

We must normalize the variable using the following method in order to determine the likelihood that a person convicted of second-degree murder will serve a jail term longer than 18 years:

\(z = (x - μ) / σ\)

where: mean of the distribution (15 years), delta: standard deviation, and x: value of interest (18 years in this example) (2.4 years).

When we enter the values, we will get that:

z = (18 - 15) / 2.4 = 1.25

Then, we can use a calculator or table of the standard normal distribution to determine the probability associated with this z-score. The likelihood of a sentence longer than 18 years is represented by the region to the right of the value z = 1.25. We determine that the region to the right of 1.25 is roughly 0.1056 using a common normal distribution table.

Hence, the likelihood that a person convicted of second-degree murder will serve a sentence in jail longer than 18 years is 0.1056 or roughly 10.56%.

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