The archaeological site of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland. Because of it's archaeological importance, Tara has received extensive study (Reference: Tara: An Archaeological Survey by Conor Newman, Royal Irish Academy, Dublin). Suppose an archaeologist wants to estimate the density of ferromagnetic artifacts in the Tara region. For this purpose, a random sample of 55 plots, each of size 100 square meters, is used. The number of ferromagnetic artifacts for each plot is determined.

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Explanation:

1/6 is the probability of rolling a '3' since there is one side we want out of 6 total.

The probability of getting an ace is 4/52 because there are 4 aces out of 52 cards total.

If that card isn't put back, then we have 52-1 = 51 cards left. That means the probability of drawing a black 2 is 2/51. The numerator 2 has nothing to do with the card value of '2'. It has to do with the fact we have 2 black cards (2 of spades, 2 of clubs) out of 51 left over.

We multiply the fractions to get the final answer

(1/6)*(4/52)*(2/51)

(1*4*2)/(6*52*51)

8/15912

1/1989

When using a calculator, we can see that,

1/1989 = 0.0005 = 0.05%

There is a very small chance of all three events happening at the same time.

Answer:

The graph of function g is the graph of function f shifted 6 units up

Step-by-step explanation:

If you plug in the values, [tex]g(x) = 2^{x} + 6[/tex]. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.

Answer:

The answer is below

Step-by-step explanation:

Given that mean (μ) = $32500, standard deviation (σ) = $2500.

a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For x < 36000:

[tex]z=\frac{36000-32500}{2500}=1.4[/tex]

From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%

b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)

Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)

Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.

Hence 95% of salaries is between $27,500 and $37,500.

c) 95% of salaries is between $27,500 and $37,500.

P(x < 27500) = (100% - 95%) / 2 = 2.5%

d) If the z score is less than -3 or greater than 3, it is considered an outlier.

For x < 42000:

[tex]z=\frac{42000-32500}{2500}=3.8[/tex]

Hence $42000 is an outlier

Answer:

1,94,658km

Step-by-step explanation:

If you are talking about how much distance it has to travel in 1 second then you can simply subtract 1,05,342 from 3,00,000. This process gives total of 1,94,658km remaining for it to travel.

Goodluck

Answer:

3(5x + 4y)

Step-by-step explanation:

Given

15x + 12y ← factor out 3 from each term

= 3(5x + 4y) ← in factored form

Answer:

<W=180 - (30+81)

<W=69°

Using Sine rule to evaluate x

x/sin30 = 19/sin69

x= 19sin30/sin69

x= 10.2m ( Nearest tenth)

Answer:

B

Step-by-step explanation:

Hi there!

TL;DR: Observe the vertices of the shapes inside the circles and their relationship with the circle.

For the first figure, the rectangle has 4 vertices and there are 4 dots on the perimeter of the circle.

For the second figure, the triangle has 3 vertices and there are 3 dots on the perimeter of the circle.

For the third figure, the line has 2 points and there are 2 dots on the perimeter of the circle.

For the fourth figure, there would most likely be only one dot on the perimeter of the circle (4, 3, 2, 1). The only option that shows this is B.

I hope this helps!

Answer:

[tex]P(x \le 3.24) = 0.97725[/tex]

Step-by-step explanation:

Given

[tex]\bar x = 2.5[/tex]

[tex]\sigma = 0.37[/tex]

Required

Percentage that is not more than 3.24

The above implies that:

[tex]x = 3.24[/tex]

Calculate z score

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]

[tex]z = \frac{0.74}{0.37}[/tex]

[tex]z = 2[/tex]

So, the probability is represented s:

[tex]P(x \le 3.24) = P(z \le 2)[/tex]

From z probability

[tex]P(z \le 2) = 0.97725[/tex]

Hence:

[tex]P(x \le 3.24) = 0.97725[/tex]

Answer:

seems to be the same as the other angle

Step-by-step explanation:

i use desmos for these graphs btw

Answer:

22%

Step-by-step explanation:

their is a total of 2392 adults, the number of people, who would be most likely to chose Italian food is 526.

p= 526/ 2392=22%

The probability of choosing Italian food is 21.9%.

"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".

For the given situation,

Total number of adults = 2392

American food = 670

Italian food = 526

Mexican food = 407

Chinese food = 383

Japanese food = 167

Others = 239

The event is the probability of choosing Italian food.

[tex]P(e)=\frac{526}{2392}[/tex]

⇒[tex]P(e)=0.219[/tex]

Rounded to nearest whole percent = [tex]0.219[/tex] × [tex]100[/tex]

⇒[tex]21.9\%[/tex]

Hence we can conclude that the probability of choosing Italian food is 21.9%.

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This question is incomplete, the complete question is;

Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)

[1 0 0 1]

[0 0 1 0]

[0 0 0 0]

(x1, x2, x3, x4) =________

Answer:

the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )

Step-by-step explanation:

Given the data in the question;

coefficient matrix

[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]

Now, from linear system;

[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]

So, with the matrix, the associated equation is;

x₁ + x₄ = 0, x₃ = 0

Number of variables is 4 and ranked of the matrix is 2,

Hence, there are infinite solutions,

There are also two free variables;

from the question,

Let x₄ = t and x₂ = s be the free variables

so

x₁ + x₄ = 0

x₁ + t = 0

x₁ = -t

Therefore, the solution for the given system is;

( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )

Answer:

40

Step-by-step explanation:

The median is the middle number

There are 10 numbers

The middle is between 5th and 6th number

Take the 5th and 6th numbers and average them

(39+41)/2 = 80/2 = 40

The median is 40

Mass of each rock in Nija's collection is 40.

Answer:

The median is the middle number

n=10 numbers

The middle is between 5th and 6th number

Taking the 5th and 6th numbers:

average(39+41)/2 = 80/2 = 40

Answer:

The rate of decrease is: [tex]43.2mm^3/min[/tex]

Step-by-step explanation:

Given

[tex]l = 18mm[/tex]

[tex]\frac{dl}{dt} = -0.8mm/min[/tex] ---- We used minus because the rate is decreasing

Required

Rate of decrease when: [tex]l = 18mm[/tex]

The volume of the cube is:

[tex]V = l^3[/tex]

Differentiate

[tex]\frac{dV}{dl} = 3l^2[/tex]

Make dV the subject

[tex]dV = 3l^2 \cdot dl[/tex]

Divide both sides by dt

[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]

Given that: [tex]l = 18mm[/tex] and [tex]\frac{dl}{dt} = -0.8mm/min[/tex]

[tex]\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)[/tex]

[tex]\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min[/tex]

[tex]\frac{dV}{dt} = -43.2mm^3/min[/tex]

Hence, the rate of decrease is: 43.2mm^3/min

Answer:

A) -8x+2

Step-by-step explanation:

-8x + 7 - 5 - 5x + 5x

-8x -5x + 5x + 7 - 5

- 8x+2

9514 1404 393

Answer:

  the correct answer is marked

Step-by-step explanation:

The circle with center (h, k) and radius r has equation ...

  (x -h)² +(y-k)² = r²

For the given center, that is ...

  (x -1)² +(y +1)² = r²

The value of r² can be found by using the given point for x and y, and seeing what value of r² makes the equation true.

  (5 -1)² +(7 +1)² = 4² +8² = 16 +64 = 80

So, r² = 80 makes the equation true, and that equation is ...

  (x -1)² +(y +1)² = 80

Answer:

F (5,-8)

Step-by-step explanation:

By rearranging,

y= 4x-28

Substitute each of the x values of the answers, eventually you will get to F and discover that when x = 5, y= -8

y= 4(5) - 28

y= -8

So, when x= 5, y= -8,

Point F is  (5,-8)

Answer:

d. employed individuals aged 25-29

Step-by-step explanation:

"Population" in a research study is the comprehensive group that the experimenter or the researcher is interested in.

It is given that US Census Bureau, showed that percentage of the employed individual who are of age group 25 years to 29 years are college educated and is at all time high.

The research study focuses on the specific age group of individuals those who graduated form college or at least have a bachelor degree.

Thus the population of the research study those who studied in each of the four years are the employed individuals aged from 25-29.

Answer:

9.3 hours

Step-by-step explanation:

Given

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

Required

Hours of sunlight on Feb 21, 2013

First, calculate the number of days from Jan 1, 2013 to Feb 21, 2013

[tex]days = 52[/tex]

So:

[tex]x = 52[/tex]

So, we have:

[tex]y = 2.89\sin(0.0145x-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.0145*52-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(0.754-1.40) + 10.99.[/tex]

[tex]y = 2.89\sin(-0.646) + 10.99.[/tex]

[tex]y = 2.89*-0.6020 + 10.99.[/tex]

[tex]y = -1.740 + 10.99.[/tex]

[tex]y = 9.25[/tex]

[tex]y = 9.3[/tex] --- approximated

Answer:

Hello! answer: 20

Step-by-step explanation:

These are vertical angles meaning they will have the same measure so... 20 + 40 = 60 20 × 3 = 60 therefore x = 20 hope that helps!

In the given scenario, the value of x is 20. The correct option is A.

A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and congruent, and opposite angles are congruent as well.

To find the value of x in the given diagram, we need to use the fact that the opposite sides of a parallelogram are equal in length.

Therefore, we can set the expressions for the opposite sides equal to each other and solve for x:

x + 40 = 3x

Simplifying the equation, we get:

40 = 2x

Dividing both sides by 2, we get:

x = 20

Therefore, the value of x is 20.

For more details regarding parallelogram, visit:

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Answer:

a. 81 square inches

b. 108 inches

Step-by-step explanation:

The area of all 5 squares combined is 405 square inches. This is 5 times the area of 1 square. 405/5 = 81. The area of 1 square is 81 square inches.

Since this is a square, the sides are equal. Thankfully the area of 1 square is a perfect square so the length of one side of the square is a full number, which is 9. All of the squares are congruent as shown in the diagram so we simply add every length together (there are 12 sides, each side is 9 inches).

12*9 = 108 and that is the perimeter.

Answer:

area

Step-by-step explanation:

a = 405/5 = 81

a =81 square inches

perimeter

p = √81

= 9

=4×9×5

=180 inches

Answer:

A = $3,101.09

A = P + I where

P (principal) = $2,600.00

I (interest) = $501.09

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.53/100

r = 0.0353 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,600.00(1 + 0.0353/12)(12)(5)

A = 2,600.00(1 + 0.002941667)(60)

A = $3,101.09

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,600.00 at a rate of 3.53% per year compounded 12 times per year over 5 years is $3,101.09.

(a) ft/s

(b) 1ft/s

Given equation;

y = (- 16x² + 50x + 3)ft       -------------(i)

Where;

y is measured in feet(ft)

x is measured in seconds(s).

(a) The rate of change of y with respect to x is found by dividing the total change in y by the total change in x. i.e

Δy / Δx

Where;

Δy = y₂ - y₁  

Δx = x₂ - x₁

∴ Δy / Δx = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]              --------------(ii)

Since y is measured in feet, Δy will also be measured in feet.

Also, since x is measured in seconds, Δx will also be measured in seconds.

Therefore, the rate of change of y with respect to x (Δy / Δx) will be measured in feet per second (ft/s)

(b) The rate of change of y between x  = 0 and x = 2 can be found by using equation (ii)

Where;

y₂ is the value of y at x = 2 found by substituting x = 2 into equation (i)

y₁ is the value of y at x = 0 found by substituting x = 0 into equation (i)

=> y₂ =  - 16(2)² + 50(2) + 3 = 39

=> y₁ =  - 16(1)² + 50(1) + 3 = 37

Now, substitute the values of y₂, y₁, x₂ and x₁  into equation (ii)

Δy / Δx = [tex]\frac{39 - 37}{2 - 0}[/tex]  

Δy / Δx = [tex]\frac{2}{2}[/tex]

Δy / Δx = 1

Therefore, the rate of change of y is 1 ft/s

Answer:

The expected number of hunters who hit the duck they aim at is 3.6

Step-by-step explanation:

Given;

number of hunters, n = 6

the probability of killing a duck, p = 0.6

The expected number of hunters who hit the duck they aim at?

In binomial distribution, the expected value is equal to the product of the number of trials and the probability of success.

The expected number of hunters who hit the duck they aim at is calculated as follows;

E = np

E = 0.6 x 6

E = 3.6

Therefore, the expected number of hunters who hit the duck they aim at is 3.6

Answer:

[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]

Step-by-step explanation:

Given

This question has a missing graph (See online)

Required

[tex]3 * f(-8) - 3 * g(-2)[/tex]

From the graph:

[tex]f(-8) = -2[/tex]

and

[tex]g(-2) = -4[/tex]

So, we have:

[tex]3 * f(-8) - 3 * g(-2) = 3 * -2 -3 * -4[/tex]

[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]

Answer:

Kelvin’s error is that when he got the final result, that was the amount that was marked down. He still needed to find the price after the original price was marked down by that number wich in this case is $18.39. So using one of his steps, 30.65(0.6)=18.39. We can subtract 30.65 (original price) and 18.39 (mark down price). You’d get 11.26 dollars as the final price.

Answer:

y = 5x – ¼

Step-by-step explanation:

The equation for the slope intercept form is given by:

y = mx + c

Where m and c are the slope and intercept on the y-axis respectively.

From the equation i.e y = mx + c, we can see that y is the subject of the equation.

Now, comparing the equation of the slope intercept form (i.e y = mx + c) with those given in the question above, we can see that only the equation:

y = 5x – ¼

has y as the subject of the equation.

Therefore, y = 5x – ¼ gives the correct answer to the question.

Answer:

the answer is 3.5

Step-by-step explanation: