A sample contains 300 grams of carbon-11, which has a half-life of 20 minutes.
Write a function, A, to represent the amount of carbon-11 remaining in the sample after T minutes.

Answer:

Vertex at (1,-9)

Step-by-step explanation:

Expand the equation by using foil method.

You should get X^2+2x-4x-8

And then add the like terms.

X^2-2x-8

And use this formula to find the vertex.

X=b/2a

plug in the values

X=-2/2(1)

you should get x=1

Thats the one value.

For another one you have to plug in you X= (value which is 1) in the f(x) which now becomes f(1)

the answer is f(1)=-9

answer: the student made an error. The first factor, 9, was distributed to only one of the terms inside the parentheses

Answer:

g

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

616 divided by 11 equals the height

Answer:

Step-by-step explanation:

2*1 /2 = 1*2 / 3 / y

2/2=2/3 / y

1=2/3 x 1/y

1=2/3y

3y=2

y=2/3

Answer:

[10 ft.]

Step-by-step explanation:

It's being given that there is a paralleolgram.

Let the length of its base is x ft.

Therefore, length of height = (x+6) ft.

Also, area of paralleolgram = 160 sq.

ft.

Now, we know that,

Area of paralleolgram = base x height

Therefore, we will get,

=> x(x+6) = 160

=> x² + 6x - 160 = 0

=> x² + 16x - 10x - 160 = 0

=> x(x+16) - 10(x+16)=0

=> (x+16) (x - 10) = 0

=> x +16=0 or X- - 10-0

=> x=-16

or

X = 10

But, we know that, length can't ever be negative.

Therefore, x = 10

Hence, length of base = 10 ft.

Correct question is;

Rosters Chicken advertises "lite" chicken with 30% fewer calories than standard chicken. When the process for "lite" chicken breast production is in control, the average chicken breast contains 450 calories, and the standard deviation in caloric content of the chicken breast population is 20 calories. Rosters wants to design an X-chart to monitor the caloric content of chicken breasts, where 25 chicken breasts would be chosen at random to form each sample. a) What are the lower and upper control limits for this chart if these limits are chosen to be four standard deviations from the target? b) What are the limits with three standard deviations from the target? Upper Control Limit (UCL)calories (enter your response as an integer).

Answer:

A)UCL = 466

LCL = 434

B)UCL = 462

LCL = 438

Step-by-step explanation:

We are given;

Mean;μ = 450

Standard deviation; σ = 20

Sample size; n = 25

A) We are told that these limits are chosen to be four standard deviations from the target.. This means that z-value = 4.

Thus, upper control limit will be the formula;

UCL = μ + 4σ/√n

UCL = 450 + 4(20)/√25

UCL = 450 + 16

UCL = 466

Lower control limit will be;

LCL = μ - 4σ/√n

LCL = 450 - 4(20)/√25

LCL = 450 - 16

LCL = 434

B) We are now told that these limits are chosen to be three standard deviations from the target.

Thus, z = 3

So;

UCL = μ + 3σ/√n

UCL = 450 + 3(20)/√25

UCL = 450 + 12

UCL = 462

Lower control limit will be;

LCL = μ - 3σ/√n

LCL = 450 - 3(20)/√25

LCL = 450 - 12

LCL = 438

The sample mean is an estimate of the population mean.

The sample mean is exactly equal to the population mean

When the population mean is known; the value of the population mean can be used as the sample mean.

This is so because:

The sample mean is an estimate of the population mean.

And it is represented as:

[tex]\bar x = \mu[/tex]

Hence, the true statement is that the sample mean is exactly equal to the population mean

Read more about sample mean at:

https://brainly.com/question/12892403

Answer:

$368.27

Step-by-step explanation:

495.00*0.20=$99

495-99=396

396-35=361

361*1.07=386.27

Answer:

6-13=7 , 7-13=6

6+1=7,7-1=6,

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

Mode is the number that appears the most in the set of data, so we would need to find the number that occurs the most. In this case, it's 52.  

Answer:

Your answer whould be 58

Step-by-step explanation:

exmple 67,67,78,78,67,43,34,12, the mobe is 67

Answer:

56.16 sqm

Step-by-step explanation:

Area of triangle = 0.5 * base * height

= (0.5 * 7 * 7.2) + (0.5 * 8.6 * 7.2)

= (25.2) + (30.96)

= 56.16

Answer:

3x + 1

Step-by-step explanation:

Answer:

I believe it is $1,607 hope it helps

Answer:

8.75

Step-by-step explanation:

Answer:

8 3/4

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

8(-3d + 2) = 88 divide both sides by 8

-3d + 2 = 11 rest 2 on both sides

-3d = 9 divide both sides by -3

d = -3

Answer:

i think D it's 110 cuz : 8×-3d and 8×2 = -24d+2=88 so D=88+24-2=110

Answer:

[tex]\displaystyle y + 2 = 4(x + 1)[/tex]

Step-by-step explanation:

Parallel equations have SIMILAR RATE OF CHANGES [SLOPES], so 4 remains as is as you proceed with plugging the information into the Point-Slope Formula:

[tex]\displaystyle [-1, -2] \\ \\ \boxed{y + 2 = 4(x + 1)}[/tex]

**Remember, all negative symbols give you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so make sure both operation symbols are correct.

I am joyous to assist you at any time.

Multiply the price by the percentage:

3.25 x 142% = 3.25 x 1.42 = 4.62

You pay $4.62

-24.7+30=5.3

his new balance is 5.3

Answer:

$54.70

Step-by-step explanation:

take $24.70 and add $30 to it and $24.70+$30=$54.70

Answer:

hello

[( 2 ² * 6 ⁰ ) / 7 ] ³

=  ( 2 ⁶ * 1 ³) / 7 ³

= ( 64 *1 ) / 343

=   64/343

Step-by-step explanation:

Answer:

The 95% confidence interval   [tex] 81.852  <  \mu <  280.098 [/tex]

Step-by-step explanation:

From the question we are told that

   The  sample mean is  [tex]\= x  =  180.975[/tex]

   The standard deviation is  [tex]\sigma  =  143.042[/tex]

   The sample size is n = 8

Given that the confidence level is  95%  then the level of significance is  

    [tex]\alpha =( 100- 95) \%[/tex]

=>  [tex]\alpha =0.05[/tex]    

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } =  1.96[/tex]

Generally the margin of error is mathematically represented as  

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

=>  [tex]E = 1.96 *  \frac{ 143.042 }{\sqrt{8} }[/tex]

=>  [tex]E = 99.123 [/tex]

Generally 95% confidence interval is mathematically represented as  

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

=>    [tex]180.975 -99.123 <  p <  180.975 +99.123[/tex]

=>    [tex] 81.852  <  \mu <  280.098 [/tex]

Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

The information given is:

We have the standard deviation for the sample, hence, the t-distribution is used.

The interval is given by:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.

Then:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56[/tex]

The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

To learn more about the t-distribution, you can take a look at https://brainly.com/question/25077184

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x^2 + 8x = 0}\\\larg\text{Firstly: FACTOR the LEFT SIDE of the equation}\\\mathsf{\rightarrow x(x + 8) = 0}\\\large\text{Secondly: SET the FACTORS to equal to 0}\\\mathsf{\rightarrow x \approx 0\ or \ x + 8 = 0}\\\large\text{Thirdly: SIMPLIFY}\\\mathsf{\rightarrow x = 0\ or \ x = -8}\\\huge\text{Therefore, your answer is: \boxed{\mathsf{x = 0\ or\ x = -8}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Hello!

Answer:

There are 5500 pounds in 2 3/4 tons

Hope you luck!

Answer:

Step-by-step explanation:

Answer:

Quest 1. is 5.5

Quest 2. is 48

Quest 3. is 7.5

Quest 4. is 6

Quest 5. is 8

Quest 6. is 9

Answer:

x = √80

Step-by-step explanation:

Let's find the hypotenuse of the top side triangle.

Using the Pyth. Theorem:

Let y be the hypotenuse of the top side triangle:

2^2 + 4^2 = y^2

y = √20

Now, the rectangle facing us is formed by two indentical triangles, therefore the bottom side of the triangle is also y = √20 .

Using the Pyth.Theorem again, we can find x:

x^2 + (√20)^2 = 10^2

x = √80 .

Answer:

0.157

Step-by-step explanation:

She can buy 3.4 pounds for $21.58, so we will divide 3.4/21.58 to get 0.157 pounds per dollar.