Scientists use carbon-14 dating to determine the age of a sample of organic material. a. The amount C (in grams) of a 100-gram sample of carbon-14 remaining after t years is represented by the equation C=100(0.99988)t C = 100 ( 0.99988 ) t . Use a calculator to find the amount of carbon-14 remaining after 4 years. Round your answer to the nearest hundredth. The amount of carbon-14 remaining is about grams. b. What percent of the carbon-14 remains after 4 years? Round your answer to the nearest hundredth. The percent of carbon-14 remaining is about %.

Answer:

Amount invested at 4% is $16,000

Amount invested at 9% is  $6,000

Step-by-step explanation:

Let one vestment be x

if total investment is $22,000 then

other investment will  $22,000 - x

simple interest earned in any year is given by

SI = p*r*t/100

where SI is the interest earned

t is the time period of investment

r is the rate of annual interest

_____________________________________

interest on one account 4%

p = x

t = 1 year

SI = x*4*1/100 = 4x/100

_____________________________

interest on one account 9%

p = 22,000 - x

t = 1 year

SI = (22,000 - x)*9*1/100 = (198000 - 9x)/100

_____________________________________

it is given that total interest earned was $1180

thus sum of SI calculated for the 9% and 4% investment will be equal to 1180

4x/100 +  (198000 - 9x)/100 = 1180

=> (4x+198000 - 9x)/100 = 1180

=> 198000 - 5x = 1180*100

=> -5x = 118,000 - 198000

=> -5x = -80,000

=> x = -80,000/-5 = 16,000

Thus,

Amount invested at 4% is $16,000

Amount invested at 9% is $(22,000 - 16,000) = $6,000

Answer:

[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]  

The p value for this case would be given by:

[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Step-by-step explanation:

Information given  

[tex]\bar X=2.8[/tex] represent the sample mean

[tex]s=1.2[/tex] represent the standard deviation

[tex]n=64[/tex] sample size      

[tex]\mu_o =3[/tex] represent the value to verify

[tex]\alpha[/tex] represent the significance level

t would represent the statistic (variable of interest)      

[tex]p_v[/tex] represent the p value

Hypothesis to verify

We want to check if the true mean for this case is less than 3 minutes, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \geq 3[/tex]      

Alternative hypothesis:[tex]\mu < 3[/tex]      

The statistic for this case is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)      

Replacing we got:

[tex]t=\frac{2.8-3}{\frac{1.2}{\sqrt{64}}}=-1.33[/tex]      

The degrees of freedom are given by:

[tex]df=n-1=64-1=63[/tex]  

The p value for this case would be given by:

[tex]p_v =P(t_{63}<-1.33)=0.0942[/tex]  

If we use a significance level lower than 9% we have enough evidence to FAIL to reject the null hypothesis that the true mean is greater or equal than 3 but if we use a significance level higher than 9% the conclusion is oppossite we reject the null hypothesis

Answer:

= 140800 cubic (ft/meters/yards/cm/inches)

Step-by-step explanation:

For Cone

radius (r) = 80

height (h) = 21

Volume Of Cone

= π r² h/3

= 22/7 x 80 x 80 x 21/3

= 22 x 80 x 80

= 22 x 6400

= 11 x 12800

= 140800 cubic (ft/meters/yards/cm/inches)

Answer:

g(x)=3x^2

Step-by-step explanation:

Answer & Step-by-step explanation:

We are given that m∠1 = m∠2. We are to prove that line l is parallel to line m. So, let's make a proof. Your first statement should always be the given statement. You are given the statements. All we have to do is find the reasons for those statements.

Answer:

? = 8.77

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opposite/ hypotenuse

sin 20  = 3/?

? = 3 / sin 20

? =8.7714132

To the nearest hundredth

? = 8.77

We can use the trigonometric function [ sin theta = opposite/hypotenuse ] to solve.

sin(20) = 3/hypotenuse

hypotenuse = 3/sin(20)

hypotenuse = 8.7714...

Round to the nearest hundredth.

8.7714... → 8.77

Therefore, the answer is 8.77

Best of Luck!

Answer:

[tex] \boxed{D. \: 40\degree} [/tex]

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

So,

[tex] = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree [/tex]

Answer:

i) [tex] 3y^2 -4y +1=0[/tex]

We can divide both sides of the equation by 3 and we got:

[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]

Now we can complete the square and we got:

[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]

[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]

We take square root on both sides and we got:

[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]

And the solutions for y are:

[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]

[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]

ii) [tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

And with [tex] a = 3, b=-4 and c =1[/tex] we got:

[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]

And we got:

[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]

Step-by-step explanation:

Part i

For this case we have the following function given:

[tex] 3y^2 -4y +1=0[/tex]

We can divide both sides of the equation by 3 and we got:

[tex] y^2 -\frac{4}{3}y +\frac{1}{3}=0[/tex]

Now we can complete the square and we got:

[tex] (y^2 -\frac{4}{3}y +\frac{4}{9}) +(\frac{1}{3} -\frac{4}{9})=0[/tex]

[tex] (y- \frac{2}{3})^2 =\frac{1}{9}[/tex]

We take square root on both sides and we got:

[tex] y-\frac{2}{3}= \pm \frac{1}{3}[/tex]

And the solutions for y are:

[tex] y_1 = \frac{1}{3} +\frac{2}{3}=1[/tex]

[tex] y_1 = -\frac{1}{3} +\frac{2}{3}=\frac{1}{3}[/tex]

Part ii

We can use the quadratic formula:

[tex] y =\frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

And with [tex] a = 3, b=-4 and c =1[/tex] we got:

[tex] y =\frac{4 \pm \sqrt{(-4)^2 -4(3)(1)}}{2*3}[/tex]

And we got:

[tex] y_1 = 1 , y_2 =\frac{1}{3}[/tex]

Answer:

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 28, \sigma = 5[/tex]

Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

This is the pvalue of Z when X = 32. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{32 - 28}{5}[/tex]

[tex]Z = 0.8[/tex]

[tex]Z = 0.8[/tex] has a pvalue of 0.7881

0.7881 = 78.81% probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Answer:

3 tokens.

Step-by-step explanation:

We need the roulette image, therefore we will suppose one that I will leave as an attached image:

The main thing to keep in mind in this case is that the probabilities are the same, therefore you don't have to take that into account, just operate with the values of each sector, therefore the expected value would be:

expected value = profit - loss

expected value = (5 + 5) - (4 + 3)

expected value = 10 - 7 = 3

This means that the number of tokens waiting for the student to earn for each spin is 3 tokens.

Answer:

8n-25=15+3n

Step-by-step explanation:

We can do this by working backwards and making suitable substitutions.

If n=8

Multiply both sides of the equation by 5

5n=8*5

5n=40

Now, we can rewrite the two sides of the equation as follows

Thus:

5n=40 is equivalent to:

8n-3n=25+15

Add 3n to both sides

8n-3n+3n=25+15+3n

8n=25+15+3n

Subtract 25 from both sides

8n-25=25-25+15+3n

We have:

8n-25=15+3n

Solving this equation will have a solution of n=8.

9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.

To fill the volume with boxes of volume 1 ft³ would require 810 boxes.

Answer:

Find the point on the curve r(t) = (5Sint)i + (5Cost)j +12tk

at a distance 26pi units along the curve from the point (0,5,0) inthe direction of increasing arc length.

(My attempt):

T comes to be 2pi and when the integral is done and solved to givea value of 26pi and the position comes to be (0,5,24pi). However,this calculation and answer though correct (according to the backof the book) does not involve the use of the fact that at time t=0,the particle is at (0,5,0).

What for is that information given then?

Step-by-step explanation:

Consider the curve r(t) = (5Sint)i + (5Cost)j + (12t)k

Need to find the point on the given curve at a distance 26π unit along the curve  from the point (0,5,0) inthe direction of increasing arc length.

Length of a smooth curve is [tex]r(t)=x(t)i+y(t)j+z(t)k, \ \ a\leq t\leq b[/tex] that is traced exactly once as t increase from t = a to t = b, is

[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]

For the given curve

x(t) = 5 sin t

y(t) = 5 cos t

z(t) = 12t

When t = 0

x(0) = 5 sin 0

= 0

y(0) = 5 cos 0

= 0

z(0) = 12(0)

=0

So, the point (0, 5, 0) corresponds to t = 0

So let t = t₀ correspond to any point (x, y, z) on the curve at a distance of 26pi  units from the point t = 0 along the increasing arc length

So, the length of curve from the point t = 0 to  t = t₀ is L = 26pi units

Substitute the known value to the arc length formula

[tex]L=\int\limits^b_a \sqrt{(\frac{dx}{dt} )^2+(\frac{dy}{dt} )^2+(\frac{dz}{dt} )^2dt}[/tex]

[tex]26\pi=\int\limits^{t_0}\sqrt{(5 \cos t)6+(-5 \sin t)^2+(12)^2dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25 \cos ^2t+25 \sin ^2t+144dt} \\\\26\pi=\int\limits^{t_0}_0 \sqrt{25(\cos^2t+ \sin^2t)+144dt}\\\\26\pi=\int\limits^{t_0}_0\sqrt{25(1)+144dt} \\\\26\pi= \int\limits^{t_0}_0\sqrt{169dt} \\\\26\pi= \int\limits^{t_0}_013 dt\\\\26\pi=13\int\limits^{t_0}_0dt\\\\26\pi=13[t]^{t_0}_0\\\\26\pi=13[t_0-0]\\\\26\pi=13t_0\\\\t_0=\frac{26\pi}{13} \\\\t_0=2\pi[/tex]

The point corresponding to [tex]t_0 = 2\pi[/tex]

when t = 0

[tex]x(2\pi)=5 \sin (2\pi)\\\\=0\\\\y(2\pi)=5 \cos (2\pi)\\\\=5(1)=5\\\\z(2\pi)=12(2\pi)\\\\=24\pi[/tex]

Therefore the point corresponding to  [tex]t_0 = 2\pi[/tex] is [tex](0,5,24\pi)[/tex]

Hence, the required point on the given curve at distance 26\pi units along the curve from the point (0,5,0) in  the direction of increasing arc length is [tex](0,5,24\pi)[/tex]

Answer:

The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]

which is the first option in your list of possible answers

Step-by-step explanation:

Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.

Recall that horizontal translations are performed by subtracting from the independent variable  (x) , the number of units you move (in this case 4)

Therefore the new function should look like:

[tex]g(x)=\sqrt[3]{x-4}[/tex]

The answer is A.

did the test

Answer:

  6%

Step-by-step explanation:

Out of 100 rolls, there were 6 instances of 3. The experimental probability of rolling a 3 is ...

  6/100 = 6%

Answer:

40.1% probability that he will miss at least one of them

Step-by-step explanation:

For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

0.95 probaiblity of hitting a target

This means that [tex]p = 0.95[/tex]

10 targets

This means that [tex]n = 10[/tex]

What is the probability that he will miss at least one of them?

Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So

[tex]P(X = 10) + P(X < 10) = 1[/tex]

We want P(X < 10). So

[tex]P(X < 10) = 1 - P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]

[tex]P(X < 10) = 1 - P(X = 10) = 1 - 0.5987 = 0.401[/tex]

40.1% probability that he will miss at least one of them

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

8 units

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

16 = 1/2 (4)*x

16 = 2x

Divide each side by 2

16/2 = 2x/2

8 =x

Answer:

Without any multiple choice options i would have to guess square feet.

Step-by-step explanation:

Answer:

75 dollars

Step-by-step explanation:

You know that 500=100%, so we can set up the following

15%(500/100%) = 75

so the discount 75 dollars

Answer:

Yes

The common difference is .6

Step-by-step explanation:

Take the second term and subtract the first term

-2.2 - (-2.8)

-2.2+ 2.8 = .6

Take the third term and subtract the second

-1.6 - (-2.2)

1.6 +2.2

The common difference is .6

Answer:

Yes

Step-by-step explanation:

-2.8, -2.2, -1.6, -1.0

-2.2-(-2.8)= -1.6 - (-2.2)= -1 - (-1.6)= 0.6

This is AP with first term -2.8 and common difference 0.6

Answer:

[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]

Now if we increase the radius by a factor of 2 the new volume would be:

[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]

And we can find the increase factor for the volume like this:

[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]

Then if we increase the radius by 2 the volume increase by a factor of 4

If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.

On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.

Step-by-step explanation:

For this case we have the following info given:

[tex]r = 5 , h =12[/tex]

and we can find the initial volume:

[tex] V = \frac{1}{3} \pi r^2 h[/tex]

And replacing we got:

[tex] V = \frac{1}{3} \pi (5)^2 (12)= 314.159[/tex]

Now if we increase the radius by a factor of 2 the new volume would be:

[tex] V_f = \frac{1}{3} \pi (2*5)^2 (12)= 1256.637[/tex]

And we can find the increase factor for the volume like this:

[tex] \frac{V_f}{V}= \frac{1256.637}{314.159}= 4[/tex]

Then if we increase the radius by 2 the volume increase by a factor of 4

If we reduce the radius by a factor of 2 then we will have that the volume would be reduced by a factor of 4.

On the figure attached we have an illustration for the cases analyzed we see that when we increase the radius the volume increase and in the other case decrease.

Answer:

the answer is 8x^2+49x+294+1759/x-6

Answer:

30 Nickels and 188 Pennies

Step-by-step explanation:

okay, so to set up the equation first, we have to assign each coin a variable, let's call them p and n:

P= number of pennies

N= number of nickels

the value of a penny is 1 cent, so 1P, and the value of a nickel is 5 cents, so 5N

The problem states that he has 218 coins, meaning that the total number of pennies and nickels adds up to 218:

P + N = 218

the total value of the coins is $3.38, so that would mean that 1P + 5N has to equal $3.38:

1P + 5N = 338

Okay, so now that we have our equations let's solve them using elimination:

we have to get a common coefficient between both equations, so let's multiply our first equation by 5:

P x 5 = 5P

N x 5 = 5N

218 x 5 = 1090

so, now we can solve by elimination:

5P + 5N = 1090

1P + 5N = 338

the N's cancel out:

4P = 752

divide both sides by 4:

P = 188

okay, so if theres a total of 218 coins, subtract 188 from 218:

218 - 188 = 30

so, there are 30 nickels and 188 pennies.

check our work:

5 x 30 = 150

1 × 188 = 188

150 + 188 = 338

338 = 338

I hope this helps! :)

Answer:

B

Step-by-step explanation:

because if you do 40 times 6 and 45 times 6 you get 270 and 240 and you add them up for 510

Answer:

B. -4<x<2

Step-by-step explanation:

The highest x point is -4 and lowest peak is 2

Answer:

B. -4 ≤ x ≤ 2

Step-by-step explanation:

→Basically, the question is asking, "At what point is the line on the graph decreasing?"

→Looking at the graph, you can see that when x = -4, that's when the line on the graph starts to decrease. The line continues to decrease, until it reaches the point where x = 2.

This makes the correct answer "B. -4 ≤ x ≤ 2."

Answer:

82 1/3

Step-by-step explanation:

89 - 6 2/3

Borrow 1 from the 89 in the form of 3/3

88 + 3/3 - 6 2/3

88 3/3 - 6 2/3

Subtract the whole numbers

88-6 =82

Subtract the fractions

3/3 - 2/3 = 1/3

82 1/3