Archeologists have studied sizes of Egyptian skulls in an attempt to determine whether breeding occurred between different cultures. Listed below are the
widths (mm) of skulls from 150 A.D. Construct a 99% confidence interval estimate of the mean skull width.
128.1 138.2 125.7 132.3 143.2 134.7 138.8 129.3
mm< (Round to two decimal places as needed.)

We need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.

We need to determine the dimensions of the footings. Since the footings are 8 inches thick, we can convert this to feet by dividing by 12:

8 inches / 12 inches/foot = 0.67 feet

The dimensions of the footings will depend on the size of the building, but let's assume for this example that the footings are 2 feet wide and 30 feet long.

Volume = length x width x thickness

= 30 ft x 2 ft x 0.67 ft

= 40.2 cubic feet

Convert the volume to cubic yards.

Since there are 27 cubic feet in a cubic yard, we can divide the volume by 27:

40.2 cubic feet / 27 cubic feet/cubic yard = 1.49 cubic yards

Adding 10% as instructed, we get:

1.49 cubic yards + 0.149 cubic yards = 1.639 cubic yards

Therefore, we need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.

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We can use the recursive formula to find the values of the sequence:

g3 = 3·g2 + g1 = 3·5 + 3 = 18

g4 = 4·g3 + g2 = 4·18 + 5 = 77

g5 = 5·g4 + g3 = 5·77 + 18 = 395

g6 = 6·g5 + g4 = 6·395 + 77 = 2457

g7 = 7·g6 + g5 = 7·2457 + 395 = 17276

Therefore, the 7th term of the sequence is g7 = 17276.

The probability that the individual is employed full-time, given that he or she is between 18 and 49 years of age is 0.403.

We have,

From the table,

Total number of individuals.

= 2740

And,

The total number of individuals employed full-time, given that he or she is between 18 and 49 years of age.

= 175 + 348 + 581

= 1104

Now,

The probability that the individual is employed full-time, given that he or she is between 18 and 49 years of age.

= 1104/2740

= 0.403

Thus,

The probability that the individual is employed full-time, given that he or she is between 18 and 49 years of age is 0.403.

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Answer:

3 coins each row

Step-by-step explanation:

if you put 3 coins in 4 rows it we'll be equivalent to 12

The first three terms of the given sequence is 7, 21 and 63. Therefore, option D is the correct answer.

Given that, the sequence can be generated using aₙ=3aₙ₋₁ and a₁=7.

Here, n is a whole number greater than 1.

So, a₂=3a₂₋₁

a₂=3a₁

a₂=3×7

a₂=21

a₃=3a₂

a₃=3×21

a₃=63

So, the first three terms are 7, 21, 63

Therefore, option D is the correct answer.

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Answer:

If Marco completely filled a box with 36 unit cubes with no gaps or overlap, then the box must have a volume of 36 cubic units.

The box could have different dimensions depending on how the cubes are arranged. For example, the box could be a cube with side length 3 units, since 3 x 3 x 3 = 27. Then, Marco could add another layer of 3 x 3 cubes on top of the first layer, giving a total of 3 x 3 x 4 = 36 cubes.

Alternatively, the box could have dimensions 6 x 1 x 6, since 6 x 1 x 6 = 36. This box would have two layers of 6 x 6 cubes stacked on top of each other.

There are many other possible dimensions for the box, but all of them must have a volume of 36 cubic units to accommodate the 36 unit cubes with no gaps or overlap.

[tex]1/2 * 2 * 1 = 1[/tex] square unit.

Step-by-step explanation:

To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.

The solution is:

Break-even point in units= 1,000 units

Here, we have,

Explanation:

Giving the following information:

The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45.

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 20,000 / (45 - 25)

Break-even point in units= 1,000 units

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complete question:

The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45, how many units must the company sell to break?

A)  The equation of the line of the best fit is y = -1.5x + 3024.3

B)  The number of turtles to be hatched in 2011 = 8

Let us assume that x represents the years since 2003 and y represents the  number of turtles hatched each year.

From the table of data values we draw a scatter plot.

The scatter plot for the data of  the number of turtles hatched each year since 2003 is shown below.

From the scatter plot, the equation of the line of the best fit is:

y = -1.5x + 3024.3

Now we need to find the number of turtles to be hatched in 2011.

i.e., we find the value of y for x = 2011

y = -1.5x + 3024.3

y = -1.5(2011) + 3024.3

y = 7.8

y ≈ 8

Thus, the number of turtles to be hatched in 2011 = 8

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We can use the box plots to make inferences about plant heights at the two nurseries because; "The random samples are likely to be 4) representative of the population of plants at each nursery." (Option C)

A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles.

The box plot is useful for examining the range and distribution of numerical data sets. The box plot is useful for organizing vast volumes of data and seeing outlier values.

Disadvantages: Because it deals with a summary of the data distribution, the box plot is ineffective for thorough data analysis.

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The y-intercept represents the base price of $200 for airfare from NYC.

The slope represent a cost of $0.30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided about this trip, a linear equation that models the situation is given by;

y = mx + c

y = 0.30x + 200

When x = 2000, the price of airfare (y) is given by;

y = 0.30(2000) + 200 = $800.

When y = 500, the distance traveled (x) is given by;

500 = 0.30x + 200

300 = 0.30x

x = 1000 miles.

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The future value of the investment is equals to $[tex]32,582.78[/tex].

The number of monthly payments over 4 years is:

= 4 years x 12 months/year

= 48 months.

We will use future value of an annuity formulae to solve which is FV = PMT x [(1 + r)^n - 1] / r

Plugging in the values, we get:

FV = 650 * [(1 + 0.022/12)^48 - 1] / (0.022/12)

FV = 650 * (0.09190014604/0.00183333333)

FV = 650 * 50.1273524766

FV = 32582.7791098

FV = $32,582.78.

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If person deposits $300 monthly in an account earning 7% interest compounded monthly, the results will be as follows:

a) The amount (future value) in the account in 25 years = $243,021.51

b) Total deposits or payments into the account = $90,000.00

c) The total interest earned = $153,021.51

The future value, total deposits, and the total interest can be computed using an online finance calculator as follows:

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 7%

PV (Present Value) = $0

PMT (Periodic Payment) = $300

Results:

Future Value (FV) = $243,021.51

The sum of all periodic payments = $90,000 ($300 x 25 x 12)

Total Interest = $153,021.51

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a) How much will you have in the account in 25 years?

b) How much total money will you put into the account?

c) How much total interest will you earn?

Answer:

13/38

Step-by-step explanation:

To find the odds in favor of selecting a comedy, we divide the number of comedies by the total number of plays. In this case, there are 13 comedies out of a total of 38 plays  Therefore, the odds in favor of selecting a comedy are 13/38. I hope that helps!

The diameter of the circle, given the radius of 8 m, can be found to be 16 m.

One can discover the diameter of a circle, based on its radius, by multiplying the radius value with 2 since the length of the diameter is twice that of the former.

Comparatively, another segment of equal distance measured between the central position of the same given circle to only one point found within the border outline is called the radius. Henceforth, simply duplicating the established radius equivalent will provide conclusive knowledge of its corresponding diameter measure.

The diameter is therefore :

= 8 x 2

= 16 meters

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The value of probability of getting a bowl of chicken soup is,

⇒ 52.1%

Given that;

Two way frequency table is shown.

Hence, We get;

The value of probability of getting a bowl of chicken soup is,

⇒ 642/1233

⇒ 0.5206 x 100%

⇒ 52.1 %

Thus, The value of probability of getting a bowl of chicken soup is,

⇒ 52.1%

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Answer: 62 words/ 1 minute

Step-by-step explanation:

186 words/3 minutes is basically 186 divided by 3. So divide the numerator by the denominator.

Example: $35 for 5lbs of flour. 35/5 in the simplest form is 7/1; therefore it is the unit rate.

Answer:  

Worth in 2019 is $12423.75

Explanation:

Current worth is C=$28000

Depreciation rate is D=15%

Time in years is T=19

Worth (W) 2019: W=C(1−D100)T=2800⋅(1−15100)19=$12423.75 [Ans]

Answer:

To calculate how much Joe would earn for working a 35-hour week, you need to multiply his hourly wage by the number of hours he worked123. For example, if Joe is paid $19.26 per hour, then his weekly pay is:

$19.26 x 35 = $673.10

This is his gross pay, which means it does not include any deductions for taxes or other benefits. His net pay, or take-home pay, may be lower depending on his filing status, allowances, withholding information and voluntary deductions1. You can use an hourly paycheck calculator to estimate his net pay1.

I hope this helps you understand how to calculate hourly pay. If you have any other questions, please let me know.

Answer:

So the bearing from C to A is approximately 87° to the nearest degree.

Step-by-step explanation:

(a) To find the distance from C to A, we can use the cosine rule. Let's call the distance from A to B "d1" and the distance from B to C "d2". Then:

d1² = (600 km/h * 1 hour)² = 360,000 km²

d2² = (400 km/h * 1 hour)² = 160,000 km²

Now, let's find the angle between d1 and d2. We know that the angle between the two bearings is 130° - 35° = 95°. We also know that the angle between d1 and d2 is 180° - 95° = 85° (because the three angles in a triangle add up to 180°).

Using the cosine rule:

d² = d1² + d2² - 2d1d2cos(85°)

d² = 360,000 + 160,000 - 2(600)(400)cos(85°)

d ≈ 1,013 km

So the distance from C to A is approximately 1,013 km to the nearest kilometre.

(b) To find the bearings from C to A, we can use trigonometry. Let's call the bearing from C to A "x". Then:

cos(x) = (d2/d)

cos(x) = 160,000/1,013,000

x ≈ 87°

So the bearing from C to A is approximately 87° to the nearest degree.

A cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.

Given that, an object will weigh 1/6 of its weight on moon of earth,

So, a cat having a weight of 10 4/5 pound will weight =

10 4/5 × 1/6

= 54/6 × 1/6

= 54 / 36
= 9/6

= 3/2

= 1 1/2

Hence a cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.

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Answer:

He made 7 black-and-white drawings and 2 color drawing

Step-by-step explanation:

10x+25y=120

x+y=9

Multiply bottom by ten,

10x+25y=120

10x+10y=90

--------------------

15y=30

y=2

Now find x

x+2=9

x=7

Answer:  7 black and white, 2 color

Step-by-step explanation:

Let b= black and white drawings 10 min

Let c= color 25 min

She make 9 total drawings

b+c=9

She takes 2 hrs  = 120 min

10b + 25c =120

Now you have 2 equations.  Solve the system of equations.  They want you to use elimination.  Take the 1st equation multiply both sides by -10 so when you add it to next it will eliminate b

-10(b+c=9)                 multiply -10 to both sides

-10b-10c=-90             add to other equation

-10b-10c=-90

10b+25c=120

        15c=30

c=2                  >substitute back into an original equation

b+c=9    c=2    >substitute

b+2=9              > subtract 2 from both sides

b=7

The angle between the ladder and the ground is increasing at a rate of 0.217 radians per second when the bottom of the ladder is 8 ft from the wall.

We have,

Let's call the distance from the wall to the bottom of the ladder x, and the angle between the ladder and the ground θ.

We want to find dθ/dt when x = 8 ft and the ladder is 10 ft long.

From trigonometry, we know that sin(θ) = x/10.

Differentiating both sides with respect to time (t), we get:

cos(θ) x dθ/dt = 1/10 x dx/dt

We are given that dx/dt = 1.3 ft/s, and we can find cos(θ) using the Pythagorean theorem:

cos(θ) = √(1 - sin²(θ)) = √(1 - x²/100) = √(1 - 16/25) = 3/5

Now we can substitute in the values and solve for dθ/dt:

(3/5) x dθ/dt = 1/10 x 1.3

dθ/dt = (1/10 x 1.3) / (3/5)

dθ/dt = 0.217 rad/s (rounded to two decimal places)

Therefore,

The angle between the ladder and the ground is increasing at a rate of 0.217 radians per second when the bottom of the ladder is 8 ft from the wall.

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Answer:

Each package will contain 1/2 pound of meat.

Step-by-step explanation:

To divide 8 1/2 pounds of hamburger meat into 17 equal packages using fractions, you need to divide the total weight by the number of packages:

First, convert the mixed number 8 1/2 to an improper fraction:

(8 * 2) + 1 = 16 + 1 = 17

So, 8 1/2 = 17/2

Now, divide 17/2 pounds by 17 packages. Since division is the same as multiplying by the reciprocal, we'll multiply by the reciprocal of 17, which is 1/17:

(17/2) * (1/17)

Multiply the numerators together (17 * 1 = 17) and the denominators together (2 * 17 = 34):

17/34

Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (17):

17 ÷ 17 = 1

34 ÷ 17 = 2

So, the simplified fraction is 1/2.

Answer:

24%

Step-by-step explanation:

Answer:

  decreasing 0.5 m/s

Step-by-step explanation:

You want the rate at which the height of a shadow on a wall is decreasing as a 2 m tall man walks at 1.3 m/s toward the wall. The shadow is cast by a light 12 m from the wall, and the man is 4 m from the wall at the time of interest.

In the attached diagram, triangles ABC and LMA are similar. This lets us write the proportion ...

  y/x = 2/(12 -x)

  y = 2x/(12 -x) . . . . . . multiply by x to get expression for y

Taking the derivative with respect to time gives ...

  y' = (2/(12 -x) +2x/(12-x)²)x'

At x = 4, this is ...

  y' = (2/8 +8/8²)x' = (3/8)x'

When x' = -1.3 m/s, the rate of change of the shadow height is ...

  y' = (3/8)(-1.3 m/s) = -0.4875 m/s

The length of the shadow is decreasing at about 0.5 m/s.

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The statement which is true include the following: A. (0, 0) is the x- and y-intercept of the function.

In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept and y-intercept are located at the origin (0, 0).

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Answer:

Step-by-step explanation:

You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse   ⇒   r = 15·sin(72°) ≈ 14.3

  Cos = Adjacent/Hypotenuse   ⇒   s = 15·cos(72°) ≈ 4.6

The acute angles in a right triangle are complementary, so ...

  S = 90° -R = 90° -72° = 18°

The given triangle can be proven to be a right triangle thanks to the Pythagorean Theorem.

The Pythagorean Theorem is a significant principle in mathematics that concerns the trio of sides in a right triangle. Specifically, it declares that the square of the hypotenuse's length--the side opposite to the 90-degree angle--is identical to the total sum of the squares of both legs' lengths within the same right triangle.

This means that the above would be a right triangle if:

a ² + b ² = c ²

9 ² + 12 ² = 15 ²

81 + 144 = 225

225 = 225

This is therefore a right triangle.

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