An object falls freely from rest under the influence of gravity. If air resistance is negligible, the ratio ofthe distances traveled during each 1-second time interval by the object during the first, second, and third seconds of its fall is
O 1:1:1
O 1:2:3
O 1:2:4
O 1:3:5
O 1:4:9

Answer:

The domain of a function is the set of all possible x values that satisfy the equation. We cannot answer this question without first knowing what the equation for f(x) is.

Step-by-step explanation:

Take for example the function y = f(x) = [tex]x^{2} +3[/tex]. Here, you can plug in literally any value for x and still get our a real number. Thus, the domain of f(x) is (-∞, ∞).

However, if your function is y = f(x) = [tex]\frac{2}{\sqrt{x+3} }[/tex] , not every x value is acceptable. First, we cannot have the denominator (bottom part) of the fraction be zero, because division by zero is undefined. Thus, x = -3 is not an acceptable value for x.

We also cannot take the square root of a negative number. Thus, we have the rule that x + 3 must be greater than or equal to zero.

[tex]x+3 > 0\\\\x > -3\\[/tex]

Normally we would use greater than or equal to zero, but because this is in the denominator, we don't want it to equal zero (and thus x = -3 is not acceptable).

So, the domain of x is (-3, ∞). The parenthesis tell us we do not include the negative three and we do not include infinity. In other words, the domain of x is all numbers greater than -3 but less than infinity.

So, first look at your equation for f(x), then see which values of x don't break the rules of math like division by zero or square roots of negative numbers. Good luck!

Answer:

angles 1 and 6

Step-by-step explanation:

Answer:

C. angle 2 and angle 7

Step-by-step explanation:

hope this helps, have a nice day :)

Answer:

2000 because you got to subtract

Answer:

C

Step-by-step explanation:

it is -25x    X= each time he goes rock climbing

Answer:

Step-by-step explanation:

To solve this problem, isolate the value of x from one side of the equation.

First, switch sides.

-29=x+8

x+8=-29

Then, subtract by 8 from both sides.

x+8-8=-29-8

Solve.

-29-8=-37

x=-37

Therefore, the final answer is x=-37.

Answer:about 5.3

Step-by-step explanation:

Answer:

i believe the answer is D

Step-by-step explanation:

Answer:  4 3/8 yards of wood

Step-by-step explanation:

It would be 5 times the ammount needed for one birdhouse so it would be-

7/8 x 5= 35/8 or 4 3/8

Answer:

147 minutes (2 hours, 27 minutes)

Step-by-step explanation:

Answer:

x = 136, y = 144

Step-by-step explanation:

x+y = 280

y = x +8

use substitution

x + x+8 = 280

2x = 272

x = 136

y= 136+8 = 144

Answer:

the answer is x=136

Step-by-step explanation:

x + y = 280

x + 8 = y (substitute this expression for y)

x + (x + 8) = 280

2x + 8 = 280

2x = 272 -> x = 136

to find y:

x + 8 = y

136 + 8 = y

144 = y

CHECK:

136 + 144 = 280

yes

Answer:

Step-by-step explanation:

x/3 + 6 = 17

Bringing like terms on one side

x/3 = 17 - 6

x/3 = 11

Dividing by 3 on both sides

x = 11/3

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

Answer:

628

Step-by-step explanation:

1) Find the circumference of the wheel (the distance it travels in 1 revolution)

[tex]C=\pi d[/tex] where d is the diameter

Plug in 2 ft as the diameter

[tex]C=(3.14) (2)\\C=6.28[/tex]

Therefore, the circumference of the wheel is 6.28 ft.

2) Multiply the circumference by 100

6.28 × 100

= 628 ft

Therefore, Joe would travel 628 feet if his wheel turns exactly 100 complete revolutions in one direction.

I hope this helps!

Answer:

7

Step-by-step explanation:

Answer:

It will affect the process in the sense that the sample population size will be unknown due to the fact that we don't know the population standard deviation.

Step-by-step explanation:

We are told that you do not know the population standard deviation. Thus, the sample population will not be able to be calculated because this sample standard deviation given will not suffice and we need the population standard deviation to be able to calculate the sample population size.

The absence of population standard deviation will result in performing the one mean t test. The one mean t test gives an insight of the deviation of values from the mean.

For the approval or rejection of the null hypothesis, hypothesis testing has been performed. For performing a test, a hypothesis has been assigned based on the results we wish to obtain. The rejection of null hypothesis leads to acception of the alternate hypothesis, while the approval of the null hypothesis results in the rejection of the alternate hypothesis.

For performing the null hypothesis test, there has been the first step to be the requirement of the hypothesis. The hypothesis has been tested based on the population size. And the test has been performed.

The absence of population standard deviation will result in performing the one mean t test.

The one mean t test gives an insight of the deviation of values from the mean. It has been used for the determination of random data sample, normal distribution, range of sampling.

For more information, refer to the link given below:

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Answer:

27 m

Step-by-step explanation:

The position of a body is given by :

[tex]s=t^3 - 12t^2 + 36t[/tex]

We need to find the total distance traveled by the body from t=0 to t=3.

At t = 0,

[tex]s=0^3 - 12(0)^2 + 36(0)=0\ m[/tex]

At t = 3 s,

[tex]s=(3)^3 - 12(3)^2 + 36(3)\\\\=27\ m[/tex]

So, the total distance from t=0 to t=3 is equal to 27 m.

Answer:

60 pages

Step-by-step explanation:

2pages = 5min

30 x 2 = 60

Therefore, in half an hour Doreen can type 60 pages

Answer:

Chris is correct. All octagons have eight sides and eight angles.

By using the formula for the volume of a cylinder we will see that the approximate radius must be 8.2 inches.

Remember that for a cylinder of radius R and height H the volume is:

[tex]V = 3.14*R^2*H[/tex]

In this case, the height is twice the radius, so we have:

H = 2R

[tex]V = 3.14*R^2*2R = 6.28*R^3[/tex]

And we know that the volume must be 3,500 in^3, now we can replace that and solve for R, we will get:

[tex]3,500 in^3 = 6.28*R^3[/tex]

[tex](3,500 in^3/6.28)^{1/3} = R = 8.2 in[/tex]

The approximate radius of the cylinder must be 8.2 inches.

If you want to learn more about cylinders you can read:

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Answer:

The country's population increased by about 16.73% during this time period.

Step-by-step explanation:

Percent increase:

The percent increase is given by the change multiplied by 100 and divided by the initial value.

In 1990, the population was about 263 million people In 2014, the population was about 307 million people.

Change: 307 - 263 = 44

Initial population: 263

Percentage increase:

44*100/263 = 16.73%

The country's population increased by about 16.73% during this time period.

Answer:

Mark brainliest pls

Step-by-step explanation:

People have given you correct answers but not explained why, perhaps because it seems so obvious.

One of Bayes laws of probability says that if two events e1 and e2 are independent (unrelated), then the probability of both happening together is the product of their individual probabilities.

The die and the coin are independent events. Each is a 50% chance (odd number on a die, heads on a coin). Thus the probability of both happening together is 50% * 50% = 25%.

The probability of obtaining an odd number and a head is 1/4.

Probability deals with the occurrence of a random event. The chance that a given event will occur. It is the measure of the likelihood of an event to occur.The value is expressed from zero to one.

For the given situation,

Let A be Sam rolls a fair dice.

Sample space, s = { [tex]1,2,3,4,5,6[/tex] }

⇒ [tex]n(s)=6[/tex]

An event A is obtaining an odd number, e = { [tex]1,3,5[/tex] }

⇒ [tex]n(e)=3[/tex]

The probability of A is obtaining an odd number,

[tex]P(A)=\frac{n(e)}{n(s)}[/tex]

⇒ [tex]P(A)=\frac{3}{6}[/tex]

⇒ [tex]P(A)=\frac{1}{2}[/tex]

Now, let B be Sam flips a fair coin.

Sample space, s = { [tex]H,T[/tex] }

⇒ [tex]n(s)=2[/tex]

An event B is getting a head, e = { [tex]H[/tex] }

⇒ [tex]n(e)=1[/tex]

The probability of B is getting a head,

[tex]P(B)=\frac{1}{2}[/tex]

Both A and B are independent events.

Thus the probability of obtaining an odd number and a head is

[tex]P(e)= P(A)P(B)[/tex]

⇒ [tex]P(e)=(\frac{1}{2})( \frac{1}{2} )[/tex]

⇒ [tex]P(e)=\frac{1}{4}[/tex]

Hence we can conclude that the probability of obtaining an odd number and a head is 1/4.

Learn more about probability here

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Answer:

15.5t=18(t-0.5) is the correct answer

Step-by-step explanation:

if the first boat travels t time then the second traveld t-0.5 time to take over

The expression on each side of each equation represent the distance travelled. Hence, 15.5t=18(t-0.5) is the correct answer

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that boat left Kyuquot and headed west at 15.5 km/h.

A second boat left Kyuquot half an hour later and headed west at 18 km/h.

Helga’s Equation 15.5t = 18(t + 0.5)

Dora’s Equation 15.5t = 18(t - 0.5)

Therefore, if the first boat travels t time then the second travelled

t-0.5 time to take over

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Answer:

Answer:

I = $ 1,937.50

Step-by-step explanation:

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

I hope this is correct and hope it helps!

Answer:

the probability is 0.0067

Step-by-step explanation:

The computation of the probability of receiving no e-mails during an hour is shown below;

Let us assume x be the number of emails received during an hour

Now the probability of receiving no e-mails is

= e^-5 × 5^0÷ 0!

= e^-5 × 1  ÷ 1

= e^-5

= 0.00674

= 0.0067

Hence, the probability is 0.0067

Answer:

The manager should use a sample size of 12 to determine the average travel expenditure

Step-by-step explanation:

Spent about 20 cents per mile. Distance of 15 miles

We have the mean per a distance, so we use the Poisson distribution. In this distribution, the standard deviation is the square root of the mean. So

[tex]\mu = 20*15 = 300, \sigma = \sqrt{300} = 17.32[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

What sample size should the manger use to determine the average travel expenditure?

This is n for which M = 10. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]10 = 1.96\frac{17.32}{\sqrt{n}}[/tex]

[tex]10\sqrt{n} = 1.96*17.32[/tex]

[tex]\sqrt{n} = \frac{1.96*17.32}{10}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*17.32}{10})^2[/tex]

[tex]n = 11.52[/tex]

Rounding up

The manager should use a sample size of 12 to determine the average travel expenditure

Answer:

dont trust me but i think its subtraction or division

Step-by-step explanation:

Answer:

74 x + 185

Step-by-step explanation:

Step-by-step explanation:

(2x+5)+37 - multiply 37 by 2x and then 37 by 5

which gives you a answer of 74x+185

Answer:

Decreasing because the line is going down meaning it is decreae