Certain Drugs Are Eliminated From The Bloodstream At An Exponential Rate (for Example, 10% Of A Drug (2024)

We need to find the expected gain or loss for the store.

This corresponds to the expected value of the variable x with the following possible values and probabilities:

x 1600 800 0

p(x) 20% 75% 5%

We know that the expected value is the sum of the products xp(x), for all possible values of x.

Thus, we obtain:

[tex]\begin{gathered} 1600\cdot20\%+800\cdot75\%+0\cdot5\% \\ \\ =1600\cdot\frac{20}{100}+800\cdot\frac{75}{100}+0 \\ \\ =16\cdot20+8\cdot75 \\ \\ =320+600 \\ \\ =920 \end{gathered}[/tex]

Answer

The expected gain for the store is $920.

5)ABCD is a rhombus with non-perpendicular adjacent sides.

1) Let's apply a graphical approach to this question by plotting the points on a Cartesian plane.

2)

Instead of using the distance formula, let's count on the graph the measurements of all legs, and use the Pythagorean relation.

[tex]AB\Rightarrow a^2=b^2+c^2\Rightarrow a^2=1^2+2^2\Rightarrow a^2=5\Rightarrow a=\sqrt{5}[/tex]

Note that we counted the "rise" vertical displacement and the "run" horizontal displacement the hypotenuse is the length

Therefore, we can conclude that all sides have the same measurement.

AB=BC =CD= DA

3) So now, let's examine the options, since a Rhombus and a Square have congruent sides, we can keep with them. There is not much information to state that this is a square. Thus, the answer is:

5) ABCD is a rhombus with non-perpendicular adjacent sides.

A. Since the soccer team won 16 times out of 25 games this season, then the team's frequency of winning is 16.

B. The team's relative frequency of winning is the ratio between 16 and 25.

[tex]16:25=\frac{16}{25}=16\div25=0.64[/tex]

Therefore, the team's relative frequency of winning is 0.64.

Part C:

Frequency is the exact number of times an event (winning) occurred while the relative frequency indicates how often or the chance of an event occurring within the possible total observations.

Answer:

y-intercept = (0, 0)

Domain = x > 0 (positive real numbers)

Axis of symmetry: y = 0

Explanations:

The equation of the parabola given is:

[tex]y^2\text{ = 8x}[/tex]

The general equation of a parabola when the directrix is parallel to the y-axis is:

[tex]y^2\text{ = 4ax}[/tex]

Comparing the two equations:

4a = 8

a = 8/4

a = 2

To find the y -intercept, let x = 0

[tex]\begin{gathered} y^2\text{ = 8(0)} \\ y^2\text{ = 0} \\ y\text{ = 0} \end{gathered}[/tex]

y intercept = (0, 0)

The domain is the set of all real numbers greater than 0, because y will be finite for all values of x greater than 0

To perform the symmetry test:

The axis of symmetry is the line that passes through the vertex and focus, which is y=0

Explanation

[tex](x+5)^2=4[/tex]

Step 1

Square both sides of the equation.

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To find:

The mode of the given data set.

Solution:

The given data set is 76,89,72,99,85,68,92,87,91.

There is no mode for the given set of data because every number appears only once.

Thus, there is no mode of the data set.

SOLUTION

Write out the function foir the height

[tex]h(t)=-16t^2+40t+6[/tex]

The speed of an object is the rate of change of distance with time. Since rate of change is also differentiation, hence we diferentiate the function above

Applying the rule of differentiation, we have

Recall the rule for diffentiation

[tex]\begin{gathered} \text{If } \\ y=x^n \\ \text{Then} \\ \frac{dy}{dx}=ny^{n-1} \end{gathered}[/tex]

hence, we have

[tex]\begin{gathered} \frac{dh}{dt}=-16\times2t^{2-1}+40\times1t^{1-1} \\ \\ \frac{dh}{dt}=-32t+40 \end{gathered}[/tex]

Then the speed of the ball is goven by the function

[tex]V=\frac{dh}{dt}=-32t+40[/tex]

At t= 1, we substitute into the function we obtained for speed

Hence, we have

[tex]\begin{gathered} V=-32(1)+40 \\ Where\text{ t=1} \\ V=-32+40 \\ V=8\text{fts}^{-1} \end{gathered}[/tex]

hence

The speed of the ball at t=1s is 8ft/s

To put the number in the standard for letting it lies between 1 and 10 and multiplies it by 10 to the power of the number of decimal places

[tex]1,431,281,810,739,360\text{ = }1.431281810739360\times10^{15}[/tex]

We moved from right to left 15 decimal places, so the power of 10 is 15

if we round it to 2 decimal places the answer will be

[tex]1.43\times10^{15}[/tex]

The circumference of a circle is given by the formula:

[tex]C\text{ = }\pi\cdot\text{ D}[/tex]

That is the number pi (3.141592....) times the diameter. Then, we have (for pi = 3.14):

[tex]C\text{ = 3.14 }\cdot\text{ 12 ft = 37.68 ft}[/tex]

The circumference is 37.68ft.

a)

For the first line of the table, we have the value of y and we want to find the value of x when y is equal to 5, our equal is

[tex]4x-2y=8[/tex]

Let's put y equal to zero and solve it for x

[tex]\begin{gathered} 4x-2\cdot0=8 \\ \\ 4x=8 \\ \\ x=\frac{8}{4}=2 \end{gathered}[/tex]

Then when y = 0 we have x = 2.

Now let's solve it for x equal to zero

[tex]\begin{gathered} 4x-2y=8 \\ \\ 4\cdot0-2y=8 \\ \\ -2y=8 \\ \\ y=\frac{-8}{2}=-4 \end{gathered}[/tex]

When when x = 0 we have y = -4. Now we can complete the table!

And the points on the graph will be

SOLUTION

Given the question on the question tab;

[tex]\begin{gathered} 2^8=256 \\ \end{gathered}[/tex]

The following statements are true about 2^8;

Final answer:

Given the equation

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

the solution can be found with the quadratic formula, as follows:

[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{3\pm\sqrt[]{(-3)^2-4\cdot2\cdot1}}{2\cdot2} \\ x_{1,2}=\frac{3\pm\sqrt[]{9^{}-8}}{4} \\ x_{1,2}=\frac{3\pm1}{4} \\ x_1=\frac{3+1}{4}=1 \\ x_2=\frac{3-1}{4}=\frac{1}{2} \end{gathered}[/tex]

The solution set is {1/2, 1}

We are given the expression 10-4x and we are asked to evaluate the expression when x=1 and x=2.

To do this we would substitute the value of x= 1 and also do that for x=2.

STEP 1

When we substitute x= 1, we have

[tex]\begin{gathered} 10-4x \\ =10-4(1) \\ =10-4 \\ =6 \end{gathered}[/tex]

Therefore, for x=1, the answer gives 6

STEP 2

When we substitute x = 2, we have

[tex]\begin{gathered} 10-4x \\ =10-4(2) \\ =10-8 \\ =2 \end{gathered}[/tex]

Therefore for x=2, the answer gives 2

Since 6 is greater than 2, x = 1 will give you the larger value of 6.

ANSWER: OPTION 2

In this case the answer is very simple. .

We'll have to carry out several steps to find the solution.

Step 01:

Data

x = y eq. 1

x + y = 4 eq.2

Step 02:

part a. graph .

The point where the lines intersect is the solution.

Therefore, analyzing the graph the solution would be.

x = 2

y = 2

Step 03:

part b. substitution.

eq.1 x = y we substitute in equation 2

eq. 2 y + y = 4

2 y = 4

y = 4/2

y = 2

And since x = y, then, x = 2

The answer is:

x = 2

y = 2

Given:

The temperature at an altitude of A feet above the ground is found from an expression,

[tex]T=66-\frac{A}{300}[/tex]

The temperature at 18000 feet is,

[tex]\begin{gathered} T=66-\frac{18000}{300} \\ T=66-60 \\ T=6^{\circ}F \end{gathered}[/tex]

Answer: The temperature at 18000 feet is 6 degrees Fahrenheit.

The set builder notation represents the solution as an inequality that has the values of the solution.

The values of x that are greater than or equal to 0 and less than or equal to 5 are represented in inequality form by 0 <= x <= 5.

Therefore the set builder notation is given by:

[tex]\lbrace x|0\leq x\leq5\rbrace[/tex]

So the correct option is the fourth one.

Domain:

The domain of a function f(x) are all possible values that x can assume.

Sometimes, such in fractions or in square roots, x has constraints. In other cases, x has no constrains, so the domain is all real numbers.

In this exercise:

F(x) = 5

This means that for each value of x, y = 5.

In the function, there are no fractions or roots, so the domain is all real numbers.

The correct answer is:

B. all real numbers

ANSWER

n + 6.2 (Option A)

By definition 1 liter consists of 1000ml then,

[tex]1L\Rightarrow1000mL[/tex]

Using the conversion factor,

[tex]7600mL\ast\frac{1L}{1000mL}=7.6L[/tex]

Answer:

7600 mL is the same as 7.6L.

}

The lengths 13,80 and 81 cannot form a right triangle.

Can the lengths form a right triangle?

A right triangle is polygon with three sides and an angle that measures 90 degrees. In a right triangle, the sum of the square of the two shorter sides is equal to the square of the longest side.

13² + 80² ≠ 81²

169 + 6400 = 6561

6569 ≠ 6561

Because the sum of the squares of the two shorter sides (13 and 80) is not equal to 81, the lengths cannot form a right triangle.

To learn more about right triangles, please check: https://brainly.com/question/4364353

#SPJ1

Problem

The coordinates of the image of line segment RT are R'(-2,-4) and T'(4,4). The image was produced by a dilation with a scale factor of 42 centered at the origin. What are the coordinates of the endpoints of the pre-image?​

Solution

Since the scale factor for the image is 1/2 then the scale factor for the preimage would be: 2

And then the original coordinates are:

R = (-4, -8)

T= (8,8)

[tex]x=\frac{130\cdot38}{100}=\frac{4940}{100}=49.4[/tex]

sample size=130

[tex]\text{proportion(p)=}\frac{49.4}{130}=0.38^{}[/tex]

q=1-p=1-0.38=0.62

z=1.96 from 95%

Therefore

[tex]ME=1.96\cdot\sqrt[]{\frac{0.38\cdot0.62}{130}}=0.083[/tex]

The domain is the set of all possible x-values that the function can assume.

Given the function:

[tex]g(x)=\frac{2}{x}[/tex]

To find the domain, we have to look for restrictions for x-values.

It is known that the denominator of a fraction can not be zero.

Then, x ≠ 0.

So, the domain is of g(x) is (-∞,0) U (0, ∞).

To know the better deal, we would have to get the chage per hour:

Margaret: $30 per hour

[tex]\frac{60}{2}=\text{ 30 per hour}[/tex]

Lindsay:

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In order to calculate the compound amount, we can use the formula below:

[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]

Where A is the amount after t years, P is the principal (initial amount), r is the interest rate and n is how many times the interest is compounded in a year.

So, for P = 25000, r = 0.06, t = 10 and n = 2, we have:

[tex]\begin{gathered} A=25000\cdot(1+\frac{0.06}{2})^{2\cdot10} \\ A=25000(1.03)^{20} \\ A=45152.78 \end{gathered}[/tex]

Therefore the amount after 10 years is $45152.78.

We will ahve the following:

Rolling a singe die 19 times and keeping track of the numers that are rolled does not result in a binomial distribution.

The reason is that in a die there are multiple numbers, more than two; and a binomial distribution requires to data exit points, but there can be more than two in this case.

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1) In this system, let's solve it with the Elimination Method. We can begin by getting rid of the y-variables by adding those equations simultaneously:

[tex]\begin{gathered} \begin{matrix}27x-y=9\end{matrix} \\ -23x+y=3 \\ ---------- \\ 4x=12 \\ \frac{4x}{4}=\frac{12}{4} \\ x=3 \\ \\ \end{gathered}[/tex]

2) Now, let's find the x variable by plugging into any of those equations the quantity of x:

[tex]undefined[/tex]

explicit formula:

[tex]a_n=-5x+3\mleft(n-1\mright)​[/tex]

First a1

[tex]\begin{gathered} a_1=-5x+3(1-1) \\ a_1=-5x \end{gathered}[/tex]

Now, for an

[tex]a_n=a_{n-1}+3[/tex]

Answer:

The amount that was left is;

[tex]\text{ \$307.20}[/tex]

Explanation:

Given that;

Brianna worked 48 hours at $8 a hour.

The total earnings for the eek is;

[tex]\begin{gathered} T=\text{time }\times rate=48\times\text{ \$8} \\ T=\text{ \$384} \end{gathered}[/tex]

Since taxes were 20%, the amount on taxes is;

[tex]\text{taxes}=20\text{\% of T}=\frac{20}{100}\times\text{ \$384}=\text{ \$76.8}[/tex]

The amount that would be left after taxes is;

[tex]\begin{gathered} \text{ \$384}-\text{ \$76.8} \\ =\text{ \$307.20} \end{gathered}[/tex]

Therefore, the amount that was left is;

[tex]\text{ \$307.20}[/tex]