Ask question

Ask question

All categories

1 year ago

6

Insulin is used to regulate sugar in the bloodstream. A dose of 10 units breaks down by about 5% each minute after injection. Ho

w long does it take for the remaining insulin to be half of the original dose? Round to the nearest tenth.

1 answer:

s344n2d4d5 [400]1 year ago

8 0

Answer:

Explanation:

• The initial dose of the Insulin = 10 Units

The insulin breaks down by about 5% each minute, therefore:

• The decay rate, r= 5%

We want to determine the time it will take for the remaining dosage to be half (5 units) of the original dose.

We use the exponential decay function:

$N(t)=N_o(1-r)^t$

Substituting the given values, we have:

$\begin{gathered} 5=10(1-0.05)^t \\ \frac{5}{10}=0.95^t \\ 0.5=0.95^t \end{gathered}$

To solve for t, we change to logarithm form.

You might be interested in

A sample of eight workers in a clothing manufacturing company gave the following figures for the amount of time(in minutes) need

lilavasa [31]

Answer:

$10.108 < \mu < 13.892$

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

We have the following distribution for the random variable:

$X \sim N(\mu , \sigma=0.45)$

And by the central theorem we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12$

The sample deviation calculated $s=2.268$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=8-1=7$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.36$

Now we have everything in order to replace into formula (1):

$12-2.36\frac{2.268}{\sqrt{8}}=10.108$

$12+2.36\frac{2.268}{\sqrt{8}}=13.892$

So on this case the 95% confidence interval would be given by (10.108;13.892)

$10.108 < \mu < 13.892$

7 0

3 years ago

I need help with this

erastovalidia [21]

Answer:

First box:

1/8 of 5, 5 x 1/8, 5 divided by 8

Second Box:

8 divided by 5, 1/5 of 8,

Third Box:

5 x 8

Step-by-step explanation:

8 0

3 years ago

Solve the following linear equation.<br><br> 6(x + 2) = 30 x

DENIUS [597]

Answer:

x=1/2

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Mom baked a Dutch apple pie in a 9-inch pie pan. She cut the pie into 6 equal pies so that

Hatshy [7]

The area and arc length of each piece can be found using the

relationship between a circle and a sector of the circle.

Responses (b, c, and d are approximated):

a. 120°

b. 10.6 square inch

c. 28.3 in.

d. Area: 15.8 in.², Central angle: 89.1°

<h3>How can the pie pieces dimensions be evaluated?</h3>

Given:

Diameter of the pan, d = 9-inch

Number pie pieces cut from the apple pie = 6

The pie pieces are sectors of a circular pie.

a. The central angle of one pie pieces = $\dfrac{360^{\circ}}{6}$ = 60°

Therefore;

The central angle of two pie pieces = 2 × 60° = <u>120°</u>

b. Area of circular pie = π·r²

Where;

$r = \mathbf{\dfrac{d}{2}}$

Therefore;

$r = \dfrac{9}{2} = \mathbf{ 4.5}$

$The \ area \ covered \ by \ each \ pie \ piece = \dfrac{\pi \times 4.5^2}{6} \approx \mathbf{10.6}$

The area covered by each pie piece is approximately <u>10.6 square inch</u>

c. The circumference of a circle = 2·π·r

The circumference of the original pie = 2 × π × 4.5 in. ≈ <u>28.3 in.</u>

d. Let the arc length of the pie piece = 7 inches

$\mathbf{Area} \ of \ the \ \mathbf{pie \ piece}= \dfrac{7}{2 \cdot \pi \cdot 4.5} \times \pi \times 4.5^2 = \dfrac{7}{2 } \times 4.5 = 15.75 \approx 15.8$

The area of the pie piece is approximately <u>15.8 in.²</u>

<u />

<u />

<u /> $The \ central \ angle \ of \ the \ pie \ piece = \dfrac{7}{2 \cdot \pi \cdot 4.5} \times 360^{\circ} \approx \underline{ 89.1^{\circ}}$

Learn more about circumference, area and sector of a circle here:

brainly.com/question/12985985

5 0

2 years ago

PLEASE HELP ASAP!!!!!! What is the surface area of the pyramid?

Virty [35]

48 is the base, the area of each triangle is 44

multiply that by 4 = 176

176+48=224

6 0

3 years ago