Fossils are remains of organisms found in sedimentary rock. These remains are found in thousands of rock layers around the world and provide evidence for Earth's long history of changing lifeforms. Rock layers that formed more recently A. contain fossils of animals only. B. contain fossils of plants only. C. contain fossils that resemble existing species less closely than do fossils found in older rock layers. D. contain fossils that resemble existing species more closely than do fossils found in older rock layers.

This question falls under the combinatorial mathematics branch. Due to the complex nature of the problem which involves permutations and combinations, it's necessary to use a systematic approach or a computer algorithm to find the total number of scoring sequences that keeps the game 'relatively close'. Hence, the actual numerical answer would require a stronger background in combinatorics.

This question belongs to the subject of combinatorial mathematics, particularly involving permutations and combinations. In this scenario, 'relatively close' is defined as the number of goals scored by the two teams never differing by more than two. The total number of goals scored in the game is twelve.

Let's denote the two teams as Team A and Team B. The game can start in three ways: either Team A scores twice, Team B scores twice, or each team scores once. After that, at any point, the next goal can either maintain the score within the 'relatively close' range of two goals or equalize the score.

Determining the total number of scoring sequences under these conditions requires generating a tree diagram and counting all the possible paths, subject to the condition that the absolute difference between the number of goals for the two teams does not exceed two at any stage. Due to the combinatorial complexity, this task could be difficult without using a systematic approach or computer algorithm.

Therefore, to actually answer this question, one would require a stronger background in combinatorics, and most likely the assistance of programming or mathematics software to execute a brute force count or implement a more advanced mathematical solution.

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Answer:

64

Step-by-step explanation:

took the test

Answer:the volume of cylinder is 785

volume of the sphere is 523.33

the volume of the water that can remain is 261.8

Step-by-step explanation: algebra nation answer

Answer: Its age is expressed as [tex]9.217\times 10^7[/tex]

Step-by-step explanation:

Since we have given that

Age of dinosaur fossil = 92170000 years old

We need to write in scientific notation with the highest level of precision.

Since we know that Scientific notation means put the decimal just after unit digit and for all remaining digit there is to the power of 10.

So, it becomes,

[tex]92170000=9.217\times 10^7[/tex]

Hence, its age is expressed as [tex]9.217\times 10^7[/tex]

The correct answer is £166, £581.

To share £747 in the ratio of 2:7 between Tom and Ben.

Let's define the total parts: 2 + 7 = 9

Tom's share: [tex]\frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]

Ben's share: [tex]\frac{7}{9} \times 747 = \frac{5229}{9} = £581[/tex]

Therefore, the calculation to share £747 in the ratio of 2:7 between Tom and Ben is:

[tex]\text{Tom's share} &= \frac{2}{9} \times 747 = \frac{1494}{9} = £166[/tex]..

[tex]\text{Ben's share} &= \frac{7}{9} \times 747 = \frac{5229}{9} = £581\end{aligned}[/tex]

Where Tom receives £166, and Ben receives £581.

Answer:x+2<1x<1-2x<-1-1 does not satisfy the inequality because though-1 is lesser than 0 but not lesser than

Final answer:

The arc length of a circle with a radius of 10 units and a central angle of 97° is calculated using the formula for arc length, yielding an arc length of approximately 16.975 units.

Explanation:

The question asks us to find the arc length of a circle with a certain radius when a central angle is given. To find the arc length, we use the formula:

Arc length (s) = (θ/360) × 2πr

Where θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14159. Since we know the central angle is 97° and the radius is 10, we can plug these values into the formula:

s = (97/360) × 2×π×10

s ≈ (97/360) × 2× 3.14159 × 10

s ≈ 16.975

Therefore, the arc length is approximately 16.975 units.

Here's what the equation would look like:

30(50) + 0.03(4596)

1500 + 137.88

Paige earned $1637.88.

Answer:

Paige earned $1637.88.

Step-by-step explanation:

i did it enginuity

Answer:

70 is the answer choise I picked it and got it correct

Step-by-step explanation:

Answer:

After 1.25 seconds the twig land on the bush.

Step-by-step explanation:

Given function that shows the height of twig from the ground after t seconds,

[tex]h(t)=-16t^2+30[/tex]

When twig is on the bush,

h(t) = 5 feet   ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )

[tex]\implies -16t^2+30=5[/tex]

[tex]-16t^2=-25[/tex]

[tex]t^2=\frac{25}{16}[/tex]

[tex]\implies t=\pm \frac{5}{4}[/tex]  

Since, time can not be negative,

Hence, t = [tex]\frac{5}{4}[/tex] ≈ 1.25

Therefore, after 1.25 seconds the twig land on the bush.

Answer:

[tex]y= 5x-7[/tex]

Step-by-step explanation:

Using slope-intercept form:

The equation of line is given by:

[tex]y=mx+b[/tex]                    .....[1]

where,

m is the slope of the line

b is the y-intercept.

As per the statement:

The points (3, 8) and (2, 3) fall on a particular line.

Using slope(m) formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points we have;

[tex]m = \frac{3-8}{2-3}=\frac{-5}{-1}=5[/tex]

⇒m = 5

Put m = 5 in [1] we have;

[tex]y=5x+b[/tex]

Substitute the point (3, 8) we have;

8 = 5(3)+b

8 = 15+b

Subtract 15 from both sides we have;

[tex]-7 = b[/tex]

or

b = -7

Then we have;

[tex]y= 5x-7[/tex]

Therefore, the equation of line in slope intercept form is, [tex]y= 5x-7[/tex]

It says that the recipe for 9 servings would require 3/4 cup milk.

He wants to prepare recipe for 6 servings. Let's assume it requires X cups milk.

Now we can use concept of proportions to solve this problem.

The proportion of X cups for 6 servings would be same as 3/4 cup milk for 9 servings. Mathematically, we can write it as follows :-

[tex] \frac{X \;cups \;milk}{6 \;servings} = \frac{\frac{3}{4} \;cups \;milk}{9 \;servings} \\\\
Or\; \frac{X \;cups \;milk}{\frac{3}{4} \;cups \;milk} = \frac{6 \;servings}{9 \;servings} \\\\
\frac{X }{\frac{3}{4} } = \frac{6 }{9 } \\\\
X = \frac{6}{9}*\frac{3}{4} \\\\
X = \frac{6*3}{9*4} \\\\
X = \frac{18}{36} \\\\
X = \frac{1}{2} \;cup \;milk [/tex]

Hence, we require [tex] \frac{1}{2} [/tex] cup milk for 6 servings.

Given is the Rate of each hamburger = 2.10 dollars each.

The number of hamburgers that we sell = 3 hamburgers.

Charges for all 3 hamburgers = 3 x 2.10 = 6.30 dollars.

Tax charged on these 3 hamburgers = 0.38 dollars.

Total Bill = Charges for 3 hamburgers + Tax

Total Bill = 6.30 + 0.38 = 6.68 dollars.

Customer paid = 10 dollars.

The amount to be returned to customer = Bill paid by customer - Total Bill charged = 10 - 6.68 = 3.32 dollars.

Hence, the customer would get a change of 3.32 dollars.

The final algebraic expressions are: [tex]\frac{1}{2} w - \frac{3}{5} x[/tex] and [tex]\frac{1}{30} yz[/tex]

Sure, let's break down each part of your question step-by-step to translate them into algebraic expressions.

Three-fifths x subtracted from 4 times one-eighth w

Let's identify the components first:

Now, write the expression for "three-fifths x subtracted from 4 times one-eighth w":

[tex]\frac{4}{8} w - \frac{3}{5} x[/tex]

Simplifying [tex]\frac{4}{8} w[/tex] to [tex]\frac{1}{2} w[/tex], the algebraic expression becomes:

[tex]\frac{1}{2} w - \frac{3}{5} x[/tex]

60% of the product of one-twelfth y and two-thirds z

Let's identify the components first:

First, calculate the product:

[tex]\frac{1}{12} y \times \frac{2}{3} z = \frac{2}{36} yz = \frac{1}{18} yz[/tex]

Now, we need "60% of that product":

60% can be written as [tex]0.60[/tex], so the expression becomes:

[tex]0.60 \times \frac{1}{18} yz = \frac{3}{90} yz = \frac{1}{30} yz[/tex]

So, the algebraic expression for "60% of the product of one-twelfth y and two-thirds z" is:

[tex]\frac{1}{30} yz[/tex]