A bone that originally contained
150 mg of carbon-14 now contains
100 mg of the isotope. If the half-life
of carbon-14 is 5730 years, how old is
the bone?

Answer:

1.07913403584

Step-by-step explanation:

hope it helps you!!

branliest plssssss

Answer:

641,894,091

Step-by-step explanation:

Answer:

.4

Step-by-step explanation:

Sample proportion of 90% confidence interval for a proportion (0.37, 0.43) is 0.40 .

Thus option C is correct.

Given, A 90% confidence interval for a proportion is found to be (0.37, 0.43) .

Sample proportion - margin of error = 0.37

Sample proportion + margin of error = 0.43

Therefore, the sample proportion will.be the average of the values given above and this will be:

= (0.37 + 0.43)/2

= 0.80/2

= 0.40

Therefore option C is correct.

Know more about sample proportions,

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Answer:

See Below.

Step-by-step explanation:

We want to prove the trigonometric identity:

[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\frac{\sin(\theta)}{1-\sin^2(\theta)}[/tex]

To start, let's simplify the right side. Recall the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

Therefore:

[tex]\cos^2(\theta)=1-\sin^2(\theta)[/tex]

Substitute:

[tex]\displaystyle \frac{\sin(\theta)}{1-\sin^2(\theta)}=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]

Split:

[tex]\displaystyle =\frac{\sin(\theta)}{\cos(\theta)}\left(\frac{1}{\cos(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Therefore, our equation becomes:

[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]

From the Pythagorean Identity, we can divide both sides by cos²(θ). This yields:

[tex]\displaystyle \tan^2(\theta)+1=\sec^2(\theta)[/tex]

So:

[tex]\tan^2(\theta)=\sec^2(\theta)-1[/tex]

Substitute:

[tex]\displaystyle \frac{\tan^2(\theta)}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]

Rewrite:

[tex]\displaystyle (\tan(\theta))^2\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Recall that tan(θ) = sin(θ)/cos(θ). So:

[tex]\displaystyle \frac{\sin^2(\theta)}{\cos^2(\theta)}\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Simplify:

[tex]\displaystyle \frac{\sin(\theta)}{\cos^2(\theta)}=\tan(\theta)\sec(\theta)[/tex]

Simplify:

[tex]\tan(\theta)\sec(\theta)=\tan(\theta)\sec(\theta)}[/tex]

Hence proven.  

Answer:

638 in.²

Step-by-step explanation:

Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.

SA = PH + 2LW

where

P = perimeter of base = 2(L + W),

H = height of prism

L = length of base

W = width of base

SA = 2(16 + 7)(9) + 2(16)(7)

SA = 638

Answer:

1/6

Step-by-step explanation:

1/3 x 1/2 = 1/6

Incomplete question. However, I answered from a general research perspective.

Explanation:

Note, the term sample used in statistical research refers to subjects or persons carefully selected (using a particular sampling method/type ) to represent the target population.

A randomly selected sample could be done as either:

Using any of the above sampling methods could result in 70% of the population being from low-income families as this is a matter of chance. Hence, we can agree with the research results.

Using the z-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.

At the null hypothesis, we test if they were really randomly selected, that is, the proportion is of 80%:

[tex]H_0: p = 0.8[/tex]

At the alternative hypothesis, we test if they were not randomly selected, that is, the proportion is of less than 80%.

[tex]H_1: p < 0.8[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.8, n = 150, \overline{p} = 0.7[/tex]

Then, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.7 - 0.8}{\sqrt{\frac{0.8(0.2)}{150}}}[/tex]

[tex]z = -3.06[/tex]

The critical value for a left-tailed test, as we are testing if the proportion is less than a value, with a significance level of 0.05, is of [tex]z^{\ast} = -1.645[/tex].

Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.

A similar problem is given at https://brainly.com/question/24166849

Answer:

Surface area of cube = 6a²

Side of cube = 5/2

Surface area of cube = 6 (5/2)² = 6 (25/4)

= 37.5 unit²

Answer:

x ≈ − 1.25593754, 1.70270637

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

A) First, find the volume of each cube:

V = s³

  = (1/2)³

  = 1/8 ft³

We have a total of 64 cubes, therefore the maximum volume will be:

Vmax = 64 · (1/8) = 8 ft³

B) The volume of a rectangular prism is given by:

V = w × l × h

Therefore any combination of w × l × h = Vmax = 8 will be fine.

Examples:

2 × 2 × 2

4 × 2 × 1

Answer:

[tex] \frac{4}{5} [/tex]

Answer:

1738.28

Step-by-step explanation:

Given that

The number is 1738.279

We need to round off to 2 decimal places

Now as we know that

If the rounded number would be followed by 0, 1, 2, 3 or 4, so the number would be down

Let us suppose the number is 32 so it would be 30

If the rounded number would be followed by 5,6,7,8 or 9 so the number would be up

Let us suppose the number be 37 so it would be 40

Now as per the given case, the number is 1738.279

So after rounding to 2 decimal places, the number is 1738.28

Answer:

False

Step-by-step explanation:

The definition described is Perimeter

Area is found by multiplying the base by the height or the length by the width

Answer:

Not sure of what your asking....

Step-by-step explanation:

equivalent to: 2(4x+5y)

Answer:

2(4x+5y)

Step-by-step explanation:

the sum of 8x+10y is 8x+10y

i guess you could make it even more complicated if you want

ln(8x)=ln(1/(10y))

ln(8x/(1/(10y)))

or you can just keep it simple

8x+10y = 2(4x+5y)

Sorry, I won't understand

Answer:

c

Step-by-step explanation:

The limit exists because it's continuous since they equal each other

when x approaches zero.

Substitute both expressions with x=0 and both of them will equal 2, so the limit should be 2.

Answer:

The answer is A

Step-by-step explanation:

I got it wrong and it showed that it’s A

Answer:

20°

Step-by-step explanation:

Congruent Triangles:

If two triangles are congruent, their angles have the same measure.

Angle P corresponds to Angle J

Angle J measures 20º, so angle P will also measure 20º

Answer:

The answer is B 100 in^2

Step-by-step explanation:

add 15+11+24 = 50 X 2 = 100

so yeah

good luck :D

Step-by-step explanation:

Original price- $250

Discount 20% x   20

                       -----------

                        5000

Equals amount taken off $5000

Subtract original price        -250

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

                 Sale Price          4750

Hope this helps! If this is not the answer please tell me!

Answer:

A (g(x) = }(x-2)5.1).

Step-by-step explanation:

The function which results after the sequence of transformations given is B. g(x) = 1/2 (x + 2)⁵ - 1.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given function is,

f(x) = x⁵

When a function is compressed vertically, then new function formed will be of the form, k f(x), where k is the factor that is compressed.

After compress vertically by 1/2,

f(x) changes to 1/2 f(x) = 1/2 x⁵

After the horizontal translation of 2 units to the left,

1/2 f(x) changes to 1/2 f(x + 2) = 1/2 (x + 2)⁵.

After vertical translation of 1 unit to the down,

1/2 f(x + 2) changes to 1/2 f(x + 2) - 1 = 1/2 (x + 2)⁵ - 1

Hence the correct option is B . g(x) = 1/2 (x + 2)⁵ - 1.

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Answer:

Step-by-step explanation:

i don't know  sorry

Answer:

5 feet of wall should be on each side of the painting.

Step-by-step explanation:

Given that a 3 foot wide painting should be centered on 13 foot wide wall, to determine how many feet should be on each side of the painting, the following calculations must be performed:

(13 - 3) / 2 = X

10/2 = X

5 = X

Therefore, 5 feet of wall should be on each side of the painting.

Answer:

There are many answers

Step-by-step explanation:

So, since we are finding the equivalent fraction there can be many answers

Here are 5 answers that can help you

• -8/14

• -12/21

• -16/28

• -40/70

• -24/42

Para calcular el volumen  de un prisma rectangular, multiplica sus 3 dimensiones: longitud x ancho x altura.

Answer:

I = p× r× t

300×8×4

pinicipal × rate × time

That is the formula

the answer is 300×8×4= 9600

Answer:

[tex]13[/tex]

Step-by-step explanation:

let the unknown number be x

[tex]x + ( - 9) = 4 \\ x - 9 = 4 \\ x = 4 + 9 \\ x = 13[/tex]

hope this helps you.

Can I have the brainliest please?

Have a nice day!

Answer:

Step-by-step explanation:

30

Answer:

A. H0:μ≥29;HA:μ<29

Pvalue < 0.01

D. Reject H0; the hourly wage is less than $29

Step-by-step explanation:

The null hypothesis will negate the claim which will be the hypothesis to be tested. Therefore, since the claim is to test if hourly wage is less Than 29 ; then the null will be that hourly wage is equal to or greater than 29

H0:μ≥29;HA:μ<29

The Pvalue measure the probability that the extremity of our finding against a certain α level. The Pvalue obtained using the Excel function should be 0.00058

When Pvalue is < α ; We reject the null hypothesis

Hence, Reject H0; the hourly wage is less than $29 and conclude that hourly wage is less Than $29