The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

The mastodon bones are approximately 6764 years old, determined by calculating carbon-14 decay, with 42.1% of the original carbon-14 remaining after losing 57.9%, and using the known half-life of 5750 years.

The procedure to determine the age of the mastodon bones involves the principle of radioactive decay, specifically using carbon dating. Carbon-14, a radioactive isotope of carbon with a half-life of 5750 years, is used to date materials that were once part of a living organism.

Since the mastodon bones have lost 57.9% of their original Carbon-14, less than one half-life has passed. By using the exponential decay formula, we find that the remaining amount of Carbon-14 is 100% - 57.9% = 42.1%. One half-life (5750 years) would result in 50% remaining, and since 42.1% is a bit less than 50%, we need to determine how much less in terms of time. The calculation requires solving the following equation: N/N_0 = (1/2)^(t/T), where N is the remaining amount of Carbon-14, N_0 is the original amount, t is the time passed, and T is the half-life of Carbon-14.

To solve for t, we rearrange the equation to t = T * (log(N/N_0) / log(1/2)). Substituting the known values (T = 5750, N/N_0 = 0.421), we can calculate the time t that has passed since the death of the mastodon. When we perform this calculation, we find the bones to be slightly older than one half-life, equating to approximately 6764 years old.

Answer:

b.

packaging costs

Step-by-step explanation:

Packaging costs are not fixed costs.

Option B is the correct answer.

Fixed costs are expenses that do not vary with changes in the volume of goods or services produced.

They are typically time-related and can be considered "fixed" in the short term.

We have,

(a) Equipment leases are usually fixed costs because they involve a set monthly or annual payment regardless of how much the equipment is used.

(c) Insurance can also be considered a fixed cost because the premium is usually paid regularly, such as monthly or annually, and does not change based on the number of claims made.

(d) Salaries are typically considered fixed costs because they are paid regularly and do not change based on the amount of work done or sales made.

However,

(b) packaging costs are typically variable costs because they are directly related to the number of products produced.

The more products produced, the more packaging materials are needed, resulting in higher packaging costs.

Thus,

Packaging costs are not fixed costs.

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Answer:

452.16 units^2

Step-by-step explanation:

Given

Radius = r= 6 units

The formula for finding the surface area of a sphere is:

[tex]A = 4\pi r^2\\A= 4 * 3.14 * (6)^2\\A=12.56*36\\A = 452.16[/tex]

In the formula, π is taken as 3.14.

So, the surface area of the given sphere is 452.16 units^2 ..

Answer:

452.39 units²

Step-by-step explanation:

To get the surface area of a sphere, all you need is the radius. The formula for the surface area is:

V=4πr²

So all you need to do is plug in the values:

V = 4πr²

V = (4)(π)(6)²

V = 4π36

V = 452.39 units²

BUT WAIT! If your teacher set the value of π to 3.14, the answer would be 452.16 units².

Answer:

13%

Step-by-step explanation:

took all numbers add them together than divided by 3

Answer:

The focus point is (2 , 0) ⇒ answer D

Step-by-step explanation:

* Lets revise the equation of the parabola in standard form

- The standard form is (x - h)² = 4p(y - k)

- The focus is (h, k + p)

- The directrix is y = k - p

- If the parabola is rotated so that its vertex is (h , k) and its axis of

 symmetry is parallel to the x-axis, it has an equation of

 (y - k)² = 4p(x - h)

- The focus is (h + p, k)

- The directrix is x = h - p

* Lets solve the problem

∵ The equation of the parabola is y = 1/8(x² - 4x - 12)

- Lets make x² - 4x completing square

∵ √x² = x  

∴ The 1st term in the bracket is x

∵ 4x ÷ 2 = 2x

∴ The product of the 1st term and the 2nd term is 2x

∵ The 1st term is x

∴ the second term = 2x ÷ x = 2

∴ The bracket is (x - 2)²

∵  (x - 2)² = (x² - 4x + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out  

  the bracket to keep the equation as it

∴ (x² - 4x + 4) - 4 = (x - 2)² - 4

- Lets put the equation after making the completing square

∴ y = 1/8 [(x - 2)² - 4 - 12]

∴ y = 1/8 [(x - 2)² - 16] ⇒ multiply both sides by 8

∴ 8y = (x - 2)² - 16 ⇒ add 16 to both sides

∴ 8y + 16 = (x - 2)² ⇒ take from the left side 8 as a common factor

∴ 8(y + 2) = (x - 2)²

∴ The standard form of the equation of the parabola is

   (x - 2)² = 8(y + 2)

∵ The standard form of the equation is (x - h)² = 4p(y - k)

∴ h = 2 , k = -2 , 4p = 8

∵ The focus is (h , k + p)

∵ h = 2

∵ 4p = 8 ⇒ divide both sides by 4

∴ p = 2

∴ The focus = (2 , -2 + 2) = (2 , 0)

* The focus point is (2 , 0)

Answer:

D 2,0

Step-by-step explanation:

Answer:

  -8

Step-by-step explanation:

x = -2 is in the range -3 ≤ x ≤ -1, so the definition f(x) = 4x applies.

  f(-2) = 4(-2) = -8

Answer:

-8

Step-by-step explanation:

The value of f(-2) is -8.

            -2 if x < -3

f(x) -     4x if -3 < x < -1

            x^2 if x> -1

Answer:

502.7

Step-by-step explanation:

I'm not sure on this! but this is what I think its supposed to be, I'm sorry if that's wrong

Answer:

y = 1/2x +6

Step-by-step explanation:

We have a point and a slope.  Therefore we can use the point slope form to create a line

y-y1 = m(x-x1)

y-5 = 1/2(x--2)

y-5 = 1/2(x+2)

Distribute the 1/2

y-5 = 1/2x +1

Add 5 to each side

y-5+5 = 1/2x +1+5

y = 1/2x +6

This is in slope intercept form

Answer:

The option B

Step-by-step explanation:

The  weak correlation rank is between 0,25 and 0,5

The correlation is 0,26,  which mean that 26 per cent of the variation is caused for set x

Answer:  A. It is a weak negative correlation, and it is not likely causal.

Step-by-step explanation:

Given : The number of times a player has golfed in one’s lifetime is compared to the number of strokes it takes the player to complete 18 holes.

It means there is correlation . But there it is not likely causal because one  thing is not causing other.

The correlation coefficient relating the two variables is -0.26.

We know that when the absolute value of correlation coefficient lies between 0.1 to 0.3, then it indicates that there is weak association.

The absolute value of given correlation coefficient (0.26) lies between 0.1 to 0.3, therefore, it shows weak correlation.

Also, it has negative sign , so it must indicate a weak negative correlation.

Answer: 120

Step-by-step explanation: to get this answer you do 5! (5 factorial), which means you multiply that number by all those which are lower down to one, or 5x4x3x2x1 in this case, which is 120

Answer: 240

Step-by-step explanation: 5 x 4 x 3 x 2 x1 = 240

Answer:

Parameter because the value is a numerical measurement describing a characteristic of a population.

Step-by-step explanation:

A parameter tells you something about the entire population.This means that you will know the "something" after asking every person in that group.In this question, the study was conducted for all 1580 seniors, and it was found that a parameter of 40% own a television.

In the given scenario, the 40% figure is a parameter because it involves a measurement from the entire population of college seniors, not a sample.

The value that 40% of all 1580 seniors at a college own a television represents a parameter because it is a numerical measurement that describes a characteristic of a population. Since the study includes all seniors at the college, it is not a sample but the entire population of interest. Therefore, the 40% figure is a fixed value that characterizes that specific group. Had the percentage come from a study of a subset of the college seniors, it would be considered a statistic, as it would be an estimate derived from a sample used to infer about the larger population.

Let's consider another example to clarify the difference. If the U.S. federal government surveyed all high school seniors in the United States concerning their plans for future education and employment and found that 50% were planning to attend a four-year college, that 50% would be a parameter because it includes the entire population. In contrast, if the government only surveyed a sample, such as seniors from a selection of high schools, the result would be a statistic.

Answer:

  $257.95

Step-by-step explanation:

We have assumed the payment is made at the end of each month, and the last payment will bring the balance to $1 million.

Answer:

  symmetry about the y-axis is shown

Step-by-step explanation:

Points on the right of the line of symmetry (x=0, the y-axis) are the same distance from that line as the corresponding points on the left. (That is what makes it a line of symmetry.)

There is no point of rotation that will map one figure to the other after rotation, hence no point or rotational symmetry.

Answer:

Step-by-step explanation:

The figure on the right is obtained by reflecting the figure on the left across the y-axis.

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

Answer:

Probability of missing two passes in a row is 0.08.

Step-by-step explanation:

Event E = A football player misses twice in a row.

P(E) = ?

Event X = Football player misses the first pass

P(X) = 0.4

Event Y = Football player misses just after he first miss

P(Y) = 0.2

Both the events are exclusive so the probability of occuring of these two events can be calculated by the formula:

P(E) = P(X).P(Y)

P(E) = 0.4*0.2

P(E) = 0.08

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=4000(1-0.10)^t\implies A=4000(0.9)^t \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=100(1-0.08)^t\implies A=100(0.92)^t[/tex]

Answer:

A. Confidence level

Step-by-step explanation:

The illustration showed that​ 26% of applicants said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company.

The margin of error was given as plus or minus 3 percentage points.

The important feature of the poll that was​ omitted was - confidence level.

The percent of all samples that are included in the true population parameter is given by a confidence level.

Confidence interval defines the probability that the given population parameter will fall within a specific range of values.

Mathematically we can express the scenario as :

Sample size is given as 1910​ professionals

Point estimate is 26%

Confidence level is not given.

Confidence interval is plus or minus 3 percent around 26%.

[tex]\bf \textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \boxed{\stackrel{\textit{difference of squares}}{(x^3-y^2)(x^3+y^2)}+2y^4}\implies [(x^3)^2-(y^2)^2]+2y^4 \\\\\\ x^6-y^4+2y^4\implies \boxed{x^6+y^4}[/tex]

Answer:

a) [tex](x^3-y^2)(x^3+y^2)+2y^4=x^6+y^4[/tex] is an identity.

Step-by-step explanation:

Most of the left hand sides are in this form:

[tex](a-b)(a+b)[/tex].

When you multiply conjugates you do not have to use full foil.  You can just multiply the first and multiply the last or just use this as a formula:

[tex](a-b)(a+b)=a^2-b^2[/tex].

Choice a), b), and d). all have the form I mentioned.

So let's look at those choices for now.

a) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]

[tex](x^6-y^4)+2y^4[/tex]  (I used my formula I mentioned above.)

[tex]x^6+y^4[/tex]  

So this is an identity.

b)  [tex](x^3-y^2)(x^3+y^2)[/tex]

[tex]x^6-y^4[/tex] (by use of my formula above)

This is not the right hand side so this equation in b is not an identity.

d) [tex](x^3-y^2)(x^3+y^2)+2y^4[/tex]

[tex](x^6-y^4)+2y^4[/tex]

[tex]x^6+y^4[/tex]

This is not the same thing as the right hand side so this equation in d is not an identity.

Let's look at c now.

c) [tex](x^3+y^2)(x^3+y^2)[/tex]

There is a formula for expanding this so that you could avoid foil. It is

[tex](a+b)(a+b) \text{ or } (a+b)^2=a^2+2ab+b^2[/tex].

Just for fun I'm going to use foil though:

First: x^3(x^3)=x^6

Outer: x^3(y^2)=x^3y^2

Inner: y^2(x^3)=x^3y^2

Last: y^2(y^2)=y^4

---------------------------Add.

[tex]x^6+2x^3y^2+y^4[/tex]

This is not the same thing as the right hand side.

Answer:

D.

Step-by-step explanation:

Just see which point yields the highest value.

f(x,y)=4x-3y

Checking choice A:

(x,y)=(5,0)

f(5,0)=4(5)-3(0)=20-0=20.

Checking choice B:

(x,y)=(4,6)

f(4,6)=4(4)-3(6)=16-18=-2.

Checking choice C:

(x,y)=(7,5)

f(7,5)=4(7)-3(5)=28-15=13.

Checking choice D:

(x,y)=(8,2)

f(8,2)=4(8)-3(2)=32-6=26

Choice D yields the highest value of the points given for our relation f(x,y)=4x-3y.

The correct answer is A

Explanation:

A Venn diagram is a type of diagram used in mathematics and other fields to show sets and their relationship, because of this, Venn diagrams include at least two sets that are presented in two overlapped circles, in this each circle represents the elements that exclusively belong to each set, while the elements that belong two both sets are placed in the overlapped sections and the elements that do not belong to any of the sets are outside the circles. This implies, in the Venn diagram presented the elements that belong to swamp are in section B, the ones that belong to rainforest are in section D, the elements bot sets share are in section C and those that do not belong to any of the sets presented or that are different from the are in section A, as these elements are outside the circles and therefore do not belong to any of the sets that are represented by the circles.

Answer:

The percentage of at least one person of the team advanced is 95%

Step-by-step explanation:

For this exercise is necessary to understand the concept of combination, this is calculate as:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

Where n is the total elements and k is the size of the group that is going to be chosen. This calculation give as the number of ways that is possible to choose a group of k with n elements.

So, the only possibility that there is no one of the same team that advance to the next round is that all of the people chosen were of the other 3 that doesn’t belong to the group mentioned. Then there is only one way to get this case.

On the other hand there are 20 ways to conform a group of 3 from a 6 elements and is calculate as:

[tex]6C3=\frac{6!}{3!(6-3)!}[/tex]

[tex]6C3=20[/tex]

Therefore, the percentage that any of the group mentioned pass to the next round is 1 in 20 or 5%.  

So, the percentage that at least one of the group mentioned pass to the next round is the compliment, that’s mean that it is 95%.

Answer:

The correct option is 1.

Step-by-step explanation:

Rhombus is a special case of parallelogram.

The properties of a parallelogram and rhombus:

1. Opposite sides parallel and equal.

2. Diagonals bisect each other.

3. Opposite angles are congruent.

The consecutive sides of a parallelogram may or may not be equal. But a rhombus has four congruent sides.

If a parallelogram has four congruent sides, then that parallelogram is known as rhombus.

The required statement that describe a parallelogram must be a rhombus is  "parallelogram with four congruent sides ".

Therefore the correct option is 1.

Answer:

This is what i got

Answer:

im not sure I understand the question.

Step-by-step explanation:

Answer:

equidistant from the endpoints of the segment.

Step-by-step explanation:

Answer:

56060550

Step-by-step explanation:

555x101010=56060550

That’s a lot of zombies and I’m scared now.

Answer:

56,060,550

Step-by-step explanation:

Answer:

  7x

Step-by-step explanation:

This illustrates the meaning of a logarithm.

The natural log of 7x is the power to which e must be raised to give 7x. When you raise e to that power, you get 7x.

Answer:

(3)x+(3)

Step-by-step explanation:

Answer:

[tex]\frac{m}{n}[/tex]

Step-by-step explanation:

Setting it up as a fraction will help us see the simplification process a bit easier.

[tex]\frac{am}{an}[/tex]

a/a = 1, so they cancel each other out, leaving us with simply

[tex]\frac{m}{n}[/tex]

Answer:

The ending cash balance is $12,800

Step-by-step explanation:

This is an addition and subtraction problem. We begin with the initial cash balance of $6,800. Next we are "provided" cash from various activities of $37,000. Based on the word used we can tell that this means we have to add this to our initial balance like so,

[tex]6,800 + 37,000 = 43,800[/tex]

Now our balance is $43,000. Next we are told that Net Cash "used" in investing activities is $13,600 and "used" in financing activities is $17,400. Based on this word we can tell that this money is being subtracted from our balance.

[tex]$43,000 - 13,600 - 17,400 = 12,800[/tex]

Finally, we can see that the ending cash balance is $12,800

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The ending cash balance for Stormer Company can be calculated by starting with the beginning cash balance, adding the net cash provided by operating activities, and then subtracting the net cash used in investing and financing activities: $6,800 beginning balance + $37,000 provided - $13,600 invested - $17,400 financed = $12,800 ending cash balance.

To solve this problem, it's crucial to understand that the ending cash balance is calculated by adding or subtracting the net cash provided or used from the beginning balance. In this scenario, the company has reported net cash provided by operating activities, as well as net cash used in investing and financing activities. To find the ending cash balance, you should follow these steps:

So, based on the numbers provided by the Stormer Company, its ending cash balance should be $12,800.

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No, it is not a proportional relationship because the graph does not go through the origin. A proportional relationship is supposed to be a straight line, starting from the origin. It starts on the number 4.

The true statement is (b) No, it is not a proportional relationship because the graph does not go through the origin

Proportional relationships are represented with linear equations that begin from the origin.

From the attached figure, we can see that: the graph begins from (0,4)

For the graph to be proportional it must begin from (0,0) as the origin

This means that, the graph does not represent a proportional relationship.

Hence, the true statement is (b)

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Answer:

so width of border is 10 inches

Step-by-step explanation:

Given data

board size = 12 * 16 inches

border area = 380 square inches

to find out

width of border

solution

let us assume width of border is x

first we find area of board i.e. 12 × 16 = 192 sq inches

and border area is given = 380 square inches

so total area of border and board is 192 + 380 = 572 sq inches

so we can say ( x+ 12 ) (x +16 ) = 572

solve this equation we get

x² +16x + 12x + 192 = 572

x² + 28x + 192 = 572

x² + 28x - 380 = 0

solve this equation and we get two value of x i.e.

x = 10 and x = -38

we will consider positive value here

so width of border is 10 inches

Answer:

The width of the border is 5 inches.

Step-by-step explanation:

Let x be the width of the border,

Given,

The rectangular board has the dimension 12 inches by 16 inches,

Thus, the dimension of the figure by joining the border with the board is,

(12+2x) inches by (16+2x) inches,

= (12+2x)(16+2x)

Hence, the area of the border = area of the figure by joining the border with the board - area of the board

= (12+2x)(16+2x) - 12 × 16

According to the question,

The area of the border = 380 square​ inches,

[tex](12+2x)(16+2x) - 12\times 16=380[/tex]

[tex]192+24x+32x+4x^2-192=380[/tex]

[tex]4x^2+56x-380=0[/tex]

[tex]4x^2+76x-20x-380=0[/tex]

[tex]4x(x+19)-20(x+19)=0[/tex]

[tex](4x-20)(x+19)=0[/tex]

By zero product property,

[tex]x=5\text{ or }x=-19[/tex]

Since, width can not be negative,

Hence, the width of the border is 5 inches.

Answer:

The most appropriate answer option is D) The girls are generally taller than the boys.

Step-by-step explanation:

A) The shortest boy is taller than the shortest girl:

The shortest guy is not taller than the girl so its false.

B) The range for the girls is greater than the range for the boys:

Range for girls = 56 - 44 = 12

Range for boys = 54 - 41 = 13

C) There is an outlier in the data for the boys, but not for the girls:

It is present in both.

D) The girls are generally taller than the boys:

Average height of boys = [tex]\frac{(41)+(44\times3)+(46\times3)+(48\times2)+(50\times3)+(52\times)+(54\times4)}{20}[/tex] = 49.05

Average height of girls = [tex]\frac{(44\times2)+(46\times2)+(48)+(50\times3)+(52\times4)+(54\times3)+(56\times4)}{20}[/tex] = 50.9

Therefore, the correct answer option is D) The girls are generally taller than the boys.

Answer:

D) The girls are generally taller than the boys.

Step-by-step explanation:

The heights of a group of boys and girls at a local middle school are shown on the dot plots. When comparing the shapes of the two sets of data, the girls are generally taller than the boys.