The amount of​ carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27​% of its​ carbon-14. How old are the​ paintings?

Answer:

Option (B)

Step-by-step explanation:

If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.

Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]

a + c = 172°

Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.

Therefore, a = c

⇒ a = c = 86°

Therefore, a = 86°

Option (B) will be the answer.

Answer:

The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.

Step-by-step explanation:

There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.

Answer:

The histogram for the data is attached below.

Step-by-step explanation:

Arrange the data in ascending order as follows:

S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}

Compute the range:

[tex]Range=Max.-Min.\\=514-291\\=223[/tex]

Compute the class width:

[tex]Class\ Width =\frac{Range}{No.\ of\ classes}=\frac{223}{8}=27.875\approx 28[/tex]

The classes are as follows:

290 - 318

319 - 347

348 - 376

377 - 405

406 - 434

435 - 463

464 - 492

493 - 521

Compute the frequency distribution as follows:

Class Interval         Frequency

 290 - 318                     5

 319 - 347                      3

 348 - 376                     3                  

 377 - 405                     5

 406 - 434                     7

 435 - 463                     4

 464 - 492                     1

 493 - 521                      2

The histogram for the data is attached below.

Answer:

It is a well formed formula

Step-by-step explanation:

1 - p,q,r are well formed formulas.

2 - [tex]p \ \lor \ q[/tex]  is a well formed formula as well.

3 - [tex]\neg r[/tex] is a well formula as well

4 - [tex](\ p \ \lor \ q) \ \land \ \neg r[/tex] is a well formula as well.

Step-by-step explanation:

Hello there!!

no need to be panic we will help you, alright.

look solution in picture ok...

sorry for cutting in middle.

Hope it helps...

Answer:

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Step-by-step explanation:

In this question, we are to determine the t critical value that will capture the t-curve area in the cases below;

We can use the t-table for this by using the appropriate confidence interval with the corresponding degree of freedom.

The following are the answers obtained from the table;

a) Central area = 0.95, df = 10 t = (-2.228, 2.228)

(b) Central area = 0.95, df = 20 t= (-2.086, 2.086)

(c) Central area = 0.99, df = 20 t= ( -2.845, 2.845)

(d) Central area = 0.99, df = 60 t= (-2.660, 2.660)

(e) Upper-tail area = 0.01, df = 30 t= 2.457

(f) Lower-tail area = 0.025, df = 5 t= -2.571

Answer:

acute isosceles triangle

vertex angle, y =  44.0 degrees. (smallest angle)

Step-by-step explanation:

If the sides are in the ratio 4:4:3,

two of the sides have equal lengths, so it is an isosceles triangle.

Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.

To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.

The base angle x is given by the ratio

cos(x) = 1.5/4 = 3/8

Consequently the base angle is  arccos(3/8) = 68.0 degrees.

The vertex angle equals twice the complement of 68.0

vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)

Answer:  D. y = (x - 3)² + 2

Step-by-step explanation:

Inverse is when you swap the x's and y's and solve for y.

               y = [tex]\sqrt{x-2}[/tex] + 3

Swap:      x = [tex]\sqrt{y-2}[/tex] + 3

Solve:  x - 3 = [tex]\sqrt{y-2}[/tex]

           (x - 3)² = [tex](\sqrt{y-2})^2[/tex]

           (x - 3)² = y - 2

    (x - 3)² + 2 = y

Answer:

3x

Step-by-step explanation:

39*x / 13

39/13 * x

3*x

3x

Answer:

3x

Step-by-step explanation:

We are given the expression:

39*x /13

We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.

(39*x /13) / (13/13)

(39x/13) / 1

3x / 1

When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.

3x

The expression 39*x/13 can be simplified to 3x

Answer:

Hey there!

Jimmy has 15-7, or 8 apples left.

Hope this helps :)

Answer:

Step-by-step explanation:

When the input is 4, the output of f(x) = x + 21 is f(4).

Substitute x = 4 to f(x):

f(4) = 4 + 21 = 25

Answer:

25

Step-by-step explanation:

We can find the output by plugging in 4 as x into the function:

f(x) = x + 21

f(4) = 4 + 21

f(4) = 25

Answer:

1024

Step-by-step explanation:

4 * 4 * 4 * 4 * 4

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

Answer:

AC2  =  AB2 + BC2     --->     AC2  =  122 + 52     --->   AC  =  13

AD / AB  =  AB / AC     --->     AD / 12  =  12 / 13     --->     AD  =  144/13

DC  =  AC - AD     --->   DC  =  13 - 144/13     --->     DC  =  25/13

AD / DB  =  DB / DC     --->   DB2  =  AD · DC     --->     DB2  =  (144/13) · (25/13)  --->     DB  =  60/13

DB is the geometric mean of AD and DC.

Step-by-step explanation:

Answer:

The stone would take approximately 10.107 seconds to fall 500 meters.

Step-by-step explanation:

According to the statement of the problem, the following relationship of direct proportionality is built:

[tex]t \propto y^{1/2}[/tex]

[tex]t = k\cdot t^{1/2}[/tex]

Where:

[tex]t[/tex] - Time spent by the stone, measured in seconds.

[tex]y[/tex] - Height change experimented by the stone, measured in meters.

[tex]k[/tex] - Proportionality constant, measured in [tex]\frac{s}{m^{1/2}}[/tex].

First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

[tex]k = \frac{t}{y^{1/2}}[/tex]

If [tex]t = 4\,s[/tex] and [tex]y=78.4\,m[/tex], then:

[tex]k = \frac{4\,s}{(78.4\,m)^{1/2}}[/tex]

[tex]k \approx 0.452\,\frac{s}{m^{1/2}}[/tex]

Then, the expression is [tex]t = 0.452\cdot y^{1/2}[/tex]. Finally, if [tex]y = 500\,m[/tex], then the time is:

[tex]t = 0.452\cdot (500\,m)^{1/2}[/tex]

[tex]t \approx 10.107\,s[/tex]

The stone would take approximately 10.107 seconds to fall 500 meters.

Answer:

[tex] -3n - 7 [/tex]

Step-by-step explanation:

Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.

Using the slope-intercept formula, y = mx + b, let's find the equation.

Where,

m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]

[tex] m = \frac{-13 + 10}{1} [/tex]

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

[tex] m = -3 [/tex]

Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept

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

[tex] -10 = -3(1) + b [/tex]

[tex] -10 = -3 + b [/tex]

Add 3 to both sides:

[tex] -10 + 3 = -3 + b + 3 [/tex]

[tex] -7 = b [/tex]

[tex] b = -7 [/tex]

The equation of the given linear function can be written as:

[tex] y = -3x - 7 [/tex]

Or

[tex] f(x) = -3x - 7 [/tex]

Therefore, if the input is n, the output would be:

[tex] f(n) = -3n - 7 [/tex]

Answer:

Step-by-step explanation:

Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.

Volume of a cone V = πr²h/3

If the diameter and the height are equal, then r = h

V = πh²h/3

V = πh³/3

If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min

Using chain rule to get the expression for dV/dt;

dV/dt = dV/dh * dh/dt

From the formula above, dV/dh = 3πh²/3

dV/dh =  πh²

dV/dt = πh²dh/dt

20 = πh²dh/dt

To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.

20 = π(11)²dh/dt

20 = 121πdh/dt

dh/dt = 20/121π

dh/dt = 20/380.133

dh/dt = 0.0526ft/min

This means that the height of the pile is increasing at  0.0526ft/min

Answer:

x = 3/2

y = 2

z = 3/2

Step-by-step explanation:

There are multiple methods to solve these. Message me for the method you need to see step by step.

Answer:

The sample size is 30.

Step-by-step explanation:

The sample size of a histogram can be calculated by summing up all the frequencies of all the occurrences in the data set

From the question the frequency is given as

Frequency = 2 4 6 8 10

The sample size n =

2 + 4 + 6 + 8 + 10

= 30

Therefore the sample size n of the data set = 30

Answer:

The  90%  confidence interval for population mean is   [tex]14.7 < \mu < 19.1[/tex]

Step-by-step explanation:

From the question we are told that

   The sample mean is  [tex]\= x = 16.9[/tex]

    The confidence level is  [tex]C = 0.90[/tex]

     The sample size is  [tex]n = 45[/tex]

     The standard deviation

Now given that the confidence level is  0.90 the  level of significance is mathematically evaluated as

       [tex]\alpha = 1-0.90[/tex]

       [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex]  from the standardized normal distribution table. The values is  [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The  reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex]  instead of  that of  [tex]\alpha[/tex]  is because [tex]\alpha[/tex]  represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%)  did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex]  is just considering the area of one tail which is what we required calculate the margin of error

  Generally the margin of error is mathematically evaluated as

        [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

         [tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]

         [tex]MOE = 2.207[/tex]

The  90%  confidence level interval is mathematically represented as

      [tex]\= x - MOE < \mu < \= x + MOE[/tex]

substituting values

     [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

    [tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]

     [tex]14.7 < \mu < 19.1[/tex]

Answer:

It takes the crew 12 days to clear the bush.

Step-by-step explanation:

Given clears 2/3 acres / 2 days, or 1/3 acre per day

Time to clear 4 acres

= 4 / (1/3)

= 4 * (3/1)

= 12 days

Answer:

[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]

[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]

[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]

And the variance for this case would be:

[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]

And the standard deviation is:

[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]

Step-by-step explanation:

For this case we have the following probability density function

[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]

And for this case we can find the expected value with this formula:

[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]

[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]

[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]

And the variance for this case would be:

[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]

And the standard deviation is:

[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]

Answer:

( x+2) ^2 = 11

x =1.32,-5.32

Step-by-step explanation:

x^2 + 4x -7 = 0

Add the constant to each side

x^2 + 4x -7+7 = 0+7

x^2 + 4x = 7

Take the coefficient of the x term

4

Divide by 2

4/2 =2

Square it

2^2 = 4

Add this to each side

x^2 + 4x +4 = 7+4

Take the 4/2 as the term inside the parentheses

( x+2) ^2 = 11

Take the square root of each side

sqrt( ( x+2) ^2)  =±sqrt( 11)

x+2 = ±sqrt( 11)

Subtract 2 from each side

x = -2 ±sqrt( 11)

To the nearest hundredth

x =1.32

x=-5.32

Answer:

[tex](x+2)^2=11[/tex]

[tex]x=-2 \pm \sqrt{11}[/tex]

Step-by-step explanation:

[tex]x^2+4x-7=0[/tex]

[tex]x^2+4x=7[/tex]

[tex]x^2+4x+4=7+4[/tex]

[tex](x+2)^2=11[/tex]

[tex]x+2=\pm\sqrt{11}[/tex]

[tex]x=-2 \pm \sqrt{11}[/tex]

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.

Answer:

The person above me is correct ( :

Step-by-step explanation:

B

Answer:

AC (b)

Step-by-step explanation:

Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)

Answer:

[tex]\boxed{\sf C}[/tex]

Step-by-step explanation:

The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.

[tex]75\%*\sqrt{20} = 3.354102[/tex]

[tex]\sqrt{10}= 3.162278[/tex]

AC is almost half of AE.

[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]

[tex]\sqrt{10} = 3.16227766017[/tex]

It isn’t close to the option C.

Answer:

3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

Had it on Khan

Answer:

  (T, C, J) = (in dollars)

     (10000, 10000, 0),

     (15000, 4915.97, 84.03),

     (18181.82, 1680.67, 137.51)

Step-by-step explanation:

There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.

__

For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...

  proportion at I1 = (I2 -I)/(I2 -I1)

Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:

  proportion at I2 = (I -I1)/(I2 -I1)

__

We want an overall interest rate of $2000/$20000 = 10%.

Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.

If we use only the options for 9% and 11% (no junk bonds), then we can compute ...

  proportion at 9% = (11 -10)/(11 -9) = 1/2

  proportion at 11% = (10 -9)/(11 -9) = 1/2

1st Option:

  $10,000 in treasury bills; $10,000 in corporate bonds

__

Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:

  proportion at 9% = (13 -10)/(13 -9) = 3/4

Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:

  proportion at 11% = (130 -13)/(130 -11) = 117/119

  proportion at 130% = (13 -11)/(130 -11) = 2/119

2nd option:

  $20,000 × 3/4 = $15,000 in treasury bills

  $5000 × 117/119 = $4,915.97 in corporate bonds

  The remaining amount, $84.03 in junk bonds

__

Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...

  proportion at 9% = (20 -10)/(20 -9) = 10/11

And the proportion at 11% will be ...

  proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)

3rd option:

  $20,000 × 10/11 = $18,181.82 in treasury bills

  $1,818.18 × 110/119 = $1,680.67 in corporate bonds

  The remaining amount, $137.51 in junk bonds

_____

Additional comment

The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)

Answer:

speed=3.33m/s

Step-by-step explanation:

speed= distance÷time

3.33 m/s

length = ?

Answer:

Length  : 50m

Speed   : 5 m  /  s

im sorry if im too late :'(

Answer:

Bigger size   / smaller size = 40

Step-by-step explanation:

Notice that we      

36 / (9/10)    =    30 / (3/4)   = 40

Therefore the proportion model would be

Bigger size   / smaller size = 40

Answer:

hope you get it....sorry for any mistake calculations