The amount of a sample remaining after t days is given by the equation P(t)=A(1/2)^t/h where A is the initial amount of the sample and h is half-life, in days, of the substance.
Answers
Answer:
2.5 mg
Step-by-step explanation:
Substitute the givens into the equation. A is the initial amount, 16 mg. H is the halflife, 8 days. T is the time in days that has passed, 16 days. So we get P(t)= 10(1/2)^(16/2). This ends up being 10(1/2)^2. 1/2^2 is 1/4. 10(1/4)=2.5 mg
To understand how to use the equation P(t) = A(1/2)^(t/h), let's break down each part of the formula and see how it applies to a real-world situation.
P(t): This represents the remaining amount of the substance at time t, where t is measured in days.
A: This is the initial amount of the substance before any decay has started.
(1/2): This factor represents the principle of half-life, which, in this context, means that the substance is reduced to half its previous amount after each half-life period passes.
t: This is the time that has passed, measured in days.
h: This is the half-life of the substance, which is the amount of time it takes for half of the substance to decay.
The half-life formula can be used to calculate the amount of substance that will remain after a certain amount of time has passed. Here is how you use it:
1. Start by determining the initial amount A of the substance. This is how much of the substance you begin with.
2. Determine the half-life h of the substance, which is usually provided by scientific data or an experiment.
3. Choose the time period t that you are interested in. This is how many days from the start time you want to know the remaining amount of the substance for.
4. Plug the values of A, h, and t into the formula P(t) = A(1/2)^(t/h).
5. Calculate (1/2)^(t/h). This requires you to raise (1/2) to the power of the fraction t/h. This fraction is the number of half-lives that have passed in the time period t.
6. Multiply the initial amount A by the result from step 5 to get P(t), the amount of the substance that remains after t days.
Let's go through an example to make it clear:
Example:
If the initial amount A is 100 grams and the half-life h is 10 days, how much of the substance will remain after 20 days?
Using the formula:
1. A = 100 grams (initial amount)
2. h = 10 days (half-life)
3. t = 20 days (time passed)
Plug the values into the formula:
P(t) = A(1/2)^(t/h)
P(20) = 100(1/2)^(20/10)
Calculate the exponent:
(1/2)^(20/10) = (1/2)^2 = 1/4
Multiply the initial amount by the result of the exponent:
P(20) = 100 * 1/4
P(20) = 25 grams
So after 20 days, 25 grams of the substance would remain.
Related Questions
The decimal form of 43% is
Answers
Answer:
.43
Step-by-step explanation:
If I see % in a number I like to think of it as times 1/100 or divided by 100 (those are the same thing).
So we are doing 43 divided by 100 (or 43/100) which gives you .43 .
Anytime you divide by 100 you have to move the decimal left twice. (43 is 43. so 43. divided by 100 is .43)
Example
23.5%=.235
Why?
23.5 divided by 100 is .235
Another example
4%=.04
Why?
4. divided by 100 is .04
The annual 2-mile fun-run is a traditional fund-raising event to support local arts and sciences activities. It is known that the mean and the standard deviation of finish times for this event are respectively \mu μ = 30 and \sigma σ = 5.5 minutes. Suppose the distribution of finish times is approximately bell-shaped and symmetric. Find the approximate proportion of runners who finish in under 19 minutes.
Answers
Answer: 0.0228
Step-by-step explanation:
Given : The mean and the standard deviation of finish times (in minutes) for this event are respectively as :-
[tex]\mu=30\\\\\sigma=5.5[/tex]
If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.
Let X be the random variable that represents the finish times for this event.
z score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{19-30}{5.5}=-2[/tex]
Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-
[tex]P(X<19)=P(z<-2)=0.0227501\approx0.0228[/tex]
Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228
Final answer:
To find the proportion of runners finishing a 2-mile fun-run in under 19 minutes, we calculate the z-score for a finish time of 19 minutes given the mean of 30 and standard deviation of 5.5. The calculated z-score of -2 corresponds to about 2.28% of runners according to the standard normal distribution.
Explanation:
To find the approximate proportion of runners who finish in under 19 minutes, we will use the properties of the normal distribution because the distribution of finish times is approximately bell-shaped and symmetric. Given that the mean finish time (μ) is 30 minutes and the standard deviation (σ) is 5.5 minutes, we can calculate the z-score for a finish time of 19 minutes.
The z-score is calculated by the formula:
z = (X - μ) / σ
Where X is the finish time of interest (19 minutes), μ is the mean (30 minutes), and σ is the standard deviation (5.5 minutes).
Plugging in our values we get:
z = (19 - 30) / 5.5 = -11 / 5.5 = -2
Using a standard normal distribution table or calculator, we can find the area to the left of z = -2, which corresponds to the proportion of runners finishing in under 19 minutes. This value is approximately 0.0228 or 2.28% of the runners.
Find the value of x if m arc ADC = (4x + 4)° and m angle ABC = 150°.
Answers
Answer:
The measure of angle x is 74°
Step-by-step explanation:
we know that
The inscribed angle measures half of the arc that comprises
so
∠ABC=(1/2)[arc ADC]
substitute the given values
150°=(1/2)[4x+4]
300°=[4x+4]
4x=300-4
4x=296
x=74°
I am having a hard time with this proof of vertical angles. The choices for them are at the bottom.
Answers
Answer:
Angles 1 and 3 are verical: Given
Angles 1 and 3 are formed by ntersecting lines:
Definition of vertical angles.
Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:
Definition of linear pair.
1 and 2 are supplementary, and 2 and 3 are supplementary:
Linear Pair Theorem
Angles 1 and 3 are congruent:
Congruent Supplement Theorem
Step-by-step explanation:
The first is given because it tells you it is given.
The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.
The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.
The fourth statement comes from the theorem of linear pairs. Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.
The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.
The value of an antique plate after x years can be modeled by f(x) = 18(1.05)x. Which graph can be used to approximate the number of years it will take for the plate’s value to be $30?
Answers
Answer:
The approximate number of years is 10
The graph in the attached figure
Step-by-step explanation:
Let
f(x) the value of an antique plate
x is the number of yeras
we know that
The system of equations that represented the problem is equal to
[tex]f(x)=18(1.05)^{x}[/tex] ----> equation A
[tex]f(x)=30[/tex] ----> equation B
Solve the system by graphing
The solution of the system of equations is the intersection point both graphs
using a graphing tool
The solution is the point (10.47,30)
see the attached figure
therefore
The approximate number of years is 10
Answer:
1st graph
Step-by-step explanation:
just did it in edge
If two lines l and m are parallel, then a reflection along the line l followed by a reflection along the line m is the same as a
A. translation.
B. reflection.
C. rotation.
D. composition of rotations.
Answers
If two lines l and m are parallel, then a reflection along line l followed by a reflection along line m is the same as a translation. Therefore, the correct answer is: A. translation.
If two lines l and m are parallel, a reflection along l followed by a reflection along m is equivalent to a translation. This can be understood geometrically: when a figure is reflected across parallel lines, it undergoes a displacement without changing its orientation.
The sequence of two reflections results in the figure being shifted along a path parallel to the original lines, akin to a translation. While reflections change orientation and translations shift position, the combination of two reflections across parallel lines maintains the figure's orientation while relocating it.
Explain whether the fractions 3/6 and 7/14 are equivalent. Explain.
**I know it's equivalent but I don't understand how.
Answers
7/14 divided by 7/7 equals 1/2
The fractions 3/6 and 7/14 are equivalent because they both can be simplified to 1/2.
*You just have to find the simplified versions of the fractions*
Hope this helps!
3/6 and 7/14 can both be reduced to 1/2
Lets start with 3/6
3 divided by 3 1
-- ----
6 divided by 3 2
now, 7/14
7 divided by 7 1
-- ----
14 divided by 7 2
Whatever you do to the numerator (top number) you have to do to the denominator (bottom number)
Line C: y = x + 12 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why? (A) (4, 14), because one of the lines passes through this point.(B) (4, 14), because the point lies between the two axes(C) (5, 17), because both lines pass through this point(D) (5, 17), because the point does not lie on any axis
Answers
Answer:
C)
Step-by-step explanation:
We are given with a pair of linear equations,
y=x+12
y=3x+2
Let us solve them for x and y
In order to solve them we subtract first equation from the second ,
0=2x-10
Adding 2x on both sides we get
2x=10
Dividing both sides by 2 we get
x=5
Now replacing this value of x in first equation
y=5+12=17
Hence the solution of the two equations is (5,12)
And by solution of a linear pair of equations, we mean that both the lines passes through that point.
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
Answers
Answer:y = 18(1.15)^x
Step-by-step explanation:
g o o g ; e
Answer:
The required equation is [tex]y = 18(1.15)^x[/tex].
Step-by-step explanation:
Consider the provided information.
The Initial value of poster = $ 18
After 1 year amount of increase = $ 20.70
With the rate of 15% = 0.15
Let future value is y and the number of years be x.
[tex]y = 18(1.15)^x[/tex]
Now verify this by substituting x=1 in above equation.
[tex]y = 18(1.15)^1=20.7[/tex]
Which is true.
Hence, the required equation is [tex]y = 18(1.15)^x[/tex].
I need help pretty please!
Answers
Answer:
cos(z) = .3846153846 and angle z = 67.38°
Step-by-step explanation:
Side UV is corresponding to side YX. Side VW is corresponding to side YZ. Side UW is corresponding to side XZ.
Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that. So side YX is
[tex]\frac{3}{5}*36=21.6[/tex]
We are next told that side VW is 39, so side YZ is
[tex]\frac{3}{5}*39=23.4[/tex]
In order to find the cos of angle z, we need the adjacent side, which is side XZ. Side XZ is 3/5 of side UW. Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:
[tex]39^2-36^2=UW^2[/tex] and
[tex]UW^2=225[/tex] so
UW = 15
Now we can say that side XZ is
[tex]\frac{3}{5}*15=9[/tex]
The cos of an angle is the side adjacent to the angle (9) over the hypotenuse of the triangle (23.4) so our ratio is:
[tex]cos(z)=\frac{9}{23.4}[/tex]
which divides to
cos(z) = .3846153846
If you need the value of the angle, use the inverse cosine function on your calculator in degree mode to find that
angle z = 67.38°
In step one do you found the volume (in cubic feet) of the main tank(359,006.67). The maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed on the main show tank at any given time? I must explain your answer using words and you must show all working calculations to receive credit
Answers
Answer:
4 killer whales
Step-by-step explanation:
The dimensional analysis is ...
(whales/ft³)(ft³/tank) = whales/tank
Putting the numbers with the units, we get ...
(1.1142·10^-5 whales/ft³)(3.5900667·10^5 ft³/tank) = 4.00005... whales/tank
The maximum number of killer whales allowed in the main show tank is 4.
Simplify. –2.2 – 3.1 A. 0.9 B. 5.3 C. –5.3 D. –0.9
Answers
Answer:
C. -5.3
Step-by-step explanation:
Simply add the negatives straight across to arrive at your answer.
I am joyous to assist you anytime.
Answer: C.-5.3
Step-by-step explanation: I could be wrong
Is the pythagorean theorem only for right triangles
Answers
Yes, the Pythagorean Theorem only works with right triangles.
You can use it to solve for the hypotenuse, or either one of the sides depending on the information you are provided with.
Answer:
yes
Step-by-step explanation:
PLEASE HELP ME WITH THIS MATH QUESTION
Answers
Answer:
The measure of arc EF = 146°
Step-by-step explanation:
From the figure we can see two circles with same center.
From the figure itself we get measure of arc AB is same as measure of arc EF, measure of arc Ac is same as measure of arc ED and measure of arc BC is same as arc FD.
The measure of arc AB = 146°
Therefore the measure of arc EF = 146°
URGENT PLEASE HELP ME WITH THIS MATH QUESTION Should
Answers
Answer:
A composition of transformations is a combination of two or more transformations.A composition of reflections over parallel lines has the same effect as a translation (twice the distance between the parallel lines.
Step-by-step explanation:
a baseball is thrown into the air with an upward velocity of 30 ft/s. its initial height was 6 ft, and its maximum height is 20.06 ft. how long will it take the ball to reach its maximum height? round to the nearest hundredth.
i've been stuck on this question for almost an hour so if anyone can help that would be greatly appreciated
Answers
Check the picture below.
where is the -16t² coming from? that's Earth's gravity pull in feet.
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{30}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{6}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\\\ h(t)=-16t^2+30t+6 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+30}t\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\bf \left(-\cfrac{30}{2(-16)}~~,~~6-\cfrac{30^2}{4(-16)} \right)\implies \left( \cfrac{30}{32}~,~6+\cfrac{225}{16} \right)\implies \left(\cfrac{15}{16}~,~\cfrac{321}{16} \right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (\stackrel{\stackrel{\textit{how many}}{\textit{seconds it took}}}{0.9375}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{up it went}}}{20.0625})~\hfill[/tex]
Answer:
Step-by-step explanation:
I'm not sure if this question is coming from a physics class or an algebra 2 or higher math class, but either way, the behavior of a parabola is the same in both subjects. If a parabola crosses the x axis, those 2 x values are called zeros of the polynomial. Those zeros translate to the time an object was initially launched and when it landed. The midpoint is dead center of where those x values are located. For example, if an object is launched at 0 seconds and lands on the ground 3 seconds later, it reached its max height at 2 seconds. So what we need to do is find the zeros of this particular quadratic, and the midpoint of those 2 values is where the object was at a max height of 20.06.
I used the physics equation representing parabolic motion for this, since it has an easier explanation. This equation is
[tex]x-x_{0}=v_{0}+\frac{1}{2}at^2[/tex]
where x is the max height, x₀ is the initial height, v₀ is the initial upwards velocity, t is time (our unknown as of right now), and a is the acceleration due to gravity (here, -32 ft/sec^2). Filling in our values gives us this quadratic equation:
[tex]20.06-6=30(t)+\frac{1}{2}(-32)t^2[/tex]
Simplifying that a bit gives us
[tex]14.06=30t-16t^2[/tex]
Rearranging into standard form looks like this:
[tex]0=-16t^2+30t-14.06[/tex]
If we factor that using the quadratic formula we find that the 2 times where the ball was launched and then where it came back down are
t = .925 and .95 (the ball wasn't in the air for very long!)
The midpoint occurs between those 2 t values, so we find the midpoint of those 2 values by adding them and dividing the sum in half:
[tex]\frac{.925+.95}{2}=.9375[/tex]
Therefore, the coordinates of the vertex (the max height) of this parabola are (.94, 20.06). That translates to: at a time of .94 seconds, the ball was at its max height of 20.06 feet
From a bowl containing five red, three white, and seven blue chips, select four at random and without replacement. Compute the conditional probability of one red, zero white, and three blue chips, given that there are at least three blue chips in this sample of four chips.
Answers
Answer:
The probability is [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Let A be the event of one red, zero white, and three blue chips,
And, B is the event of at least three blue chips,
Since, A ∩ B = A (because If A happens that it is obvious that B will happen )
Thus, the conditional probability of A if B is given,
[tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}[/tex]
Now, red chips = 5,
White chips = 3,
Blue chips = 7,
Total chips = 5 + 3 + 7 = 15
Since, the probability of one red, zero white, and three blue chips, when four chips are chosen,
[tex]P(A)=\frac{^5C_1\times ^3C_0\times ^7C_3}{^{15}C_4}[/tex]
[tex]=\frac{5\times 35}{1365}[/tex]
[tex]=\frac{175}{1365}[/tex]
[tex]=\frac{5}{39}[/tex]
While, the probability that of at least three blue chips,
[tex]P(B)=\frac{^8C_1\times ^7C_3+^8C_0\times ^7C_4}{^{15}C_4}[/tex]
[tex]=\frac{8\times 35+35}{1365}[/tex]
[tex]=\frac{315}{1365}[/tex]
[tex]=\frac{3}{13}[/tex]
Hence, the required conditional probability would be,
[tex]P(\frac{A}{B})=\frac{5/39}{3/13}[/tex]
[tex]=\frac{65}{117}[/tex]
[tex]=\frac{5}{9}[/tex]
Find the value of x, if m arc FN = 5x – 10 and m= arc UN = 3x + 30.
Answers
Answer:
x=20
Step-by-step explanation:
we know that
Triangles YNF and YUN are congruent by SSS
Because
YN=YF=YU=r -----> the radius of the circle
FN=NU ----> given problem
therefore
∠FYN=∠NYU
and
arc FN=∠FYN -----> by central angle
arc NU=∠NYU -----> by central angle
so
arc FN=arc NU
substitute the given values
5x-10=3x+30
solve for x
5x-3x=30+10
2x=40
x=20
Can someone help me please?
A rectangle with a perimeter of 92 inches has a length of 14 inches longer than its width. What is its width in inches.
Please explain step by step thank you.
Answers
Answer:
16 inches
Step-by-step explanation:
w = width of the rectangle
l = length of the rectangle
The perimeter of a rectangle is the length around it:
P = 2w + 2l
Given:
P = 92
l = w + 14
Substituting:
92 = 2w + 2(w + 14)
92 = 2w + 2w + 28
64 = 4w
w = 16
The width of the rectangle is 16 inches.
Final answer:
The width of the rectangle is 16 inches, deduced by using the perimeter formula for a rectangle and solving for width with given conditions.
Explanation:
To find the width of the rectangle given its perimeter and the fact that its length is 14 inches longer than its width, we start by listing what we know:
The perimeter of the rectangle is 92 inches.
The length (L) is 14 inches longer than the width (W).
Remember, the perimeter (P) of a rectangle is given by P = 2L + 2W. We can substitute L with W + 14, since the length is 14 inches more than the width. This gives us:
P = 2(W + 14) + 2W
Now we can plug in the value for P:
92 = 2(W + 14) + 2W
Then, distribute:
92 = 2W + 28 + 2W
Combine like terms:
92 = 4W + 28
Now, subtract 28 from both sides:
64 = 4W
Lastly, divide by 4 to solve for W:
16 = W
So, the width of the rectangle is 16 inches.
What is the first step in simplifying the expression
Answers
For this case we have the following expression:
[tex]\frac {11x-2-3 (1-7x) ^ 2} {(x + 1)}[/tex]
We must indicate the first step that allows to start the simplification of the expression.
It is observed that the first step to follow is to solve the square of the binomial that is in the numerator of the expression.
[tex](1-7x) ^ 2[/tex]
Answer:
Option A
Answer:
0
Step-by-step explanation:
11x-2-3(1-7x)^2/(1x+1)
11x-2-3-21x/1+1
-32x-2-3-1
-32x-1+1
-32=0
/-32 /-32
x=0
Solving Quadratic Equations posttest
A.
B.
C.
D.
Answers
Answer:
D. [tex] x = 3 \pm \sqrt{10} [/tex]
Step-by-step explanation:
[tex] x^2 - 6x - 1 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
a = 1; b = -6; c = -1
[tex] x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]
[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]
[tex] x = 3 \pm \sqrt{10} [/tex]
HELP ASAP Solve log7 b > 2. Question 18 options: b > 7 b > 49 b > 2–7 b > 14
Answers
Answer: Second Option
[tex]b > 49[/tex]
Step-by-step explanation:
We have the following expression:
[tex]log_7(b) > 2[/tex]
We have the following expression:
To solve the expression, apply the inverse of [tex]log_7[/tex] on both sides of the equality.
Remember that:[tex]b ^ {log_b (x)} = x[/tex]
So we have to:
[tex]7^{log_7(b)} > 7^2[/tex]
[tex]b > 7^2[/tex]
[tex]b > 49[/tex]
The answer is the second option
HELP!
Select the correct answer.
Two equal spheres with the maximum possible radius are carved out of a right cylinder.
Find the ratio of the volume of one sphere to the volume of the right cylinder.
A.
1 : 1
B.
1 : 3
C.
2 : 3
D.
3 : 1
Answers
Answer:
The ratio of the volume of one sphere to the volume of the right cylinder is 1 : 3 ⇒ answer B
Step-by-step explanation:
* Lets explain how to solve the problem
- The spheres touch the two bases of the cylinder
∴ The height of the cylinder = the diameters of the two spheres
∵ The diameter of the sphere = twice its radius
∴ The diameter of the sphere = 2r, where r is the radius of the sphere
∵ The height of the cylinder = 2 × diameter of the sphere
∴ The height of the cylinder = 2 × 2r = 4r
- The spheres touch the curved surface of the cylinder, that means
the diameter of the sphere equal the diameter of the cylinder
∴ The maximum possible radius of the sphere is the radius of the
cylinder
∵ The radius of the sphere is r
∴ The radius of the cylinder is r
- The volume of the cylinder is πr²h and the volume of the sphere is
4/3 πr³
∵ The height of the cylinder = 4r ⇒ proved up
∵ The radius of the cylinder = r
∵ The volume of the cylinder = πr²h
∴ The volume of the cylinder = πr²(4r) = 4πr³
∵ The radius of the sphere = r
∵ The volume of the sphere = 4/3 πr³
∴ The ratio of the volume of one sphere to the volume of the right
cylinder = 4/3 πr³ : 4 πr³
- Divide both terms of the ratio by 4 πr³
∴ The ratio = 1/3 : 1
- Multiply both terms of the ratio by 3
∴ The ratio = 1 : 3
∴ The ratio of the volume of one sphere to the volume of the right
cylinder is 1 : 3
Find the angle between the given vectors to the nearest tenth of a degree. u = <6, 4>, v = <7, 5>
Answers
Answer: 1.8°
Step-by-step explanation:
To calculate the angle between the vectors u and v we use the formula of the dot product.
The dot product between two vecotores is:
[tex]u\ *\ v = |u||v|*cosx[/tex]
Where x is the angle between the vectors
As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors
[tex]u=6i + 4j\\v=7i +5j[/tex]
Then:
[tex]u\ *\ v = 6*7 + 4*5[/tex]
[tex]u\ *\ v = 42 + 20[/tex]
[tex]u\ *\ v =62[/tex]
Now we calculate the magnitudes of both vectors
[tex]|u|=\sqrt{6^2 + 4^2}\\\\|u|=2\sqrt{13}[/tex]
[tex]|v|=\sqrt{7^2 +5^2}\\\\|v|=\sqrt{74}[/tex]
Then:
[tex]62 = 2\sqrt{13}*\sqrt{74}*cosx[/tex]
Now we solve the equation for x
[tex]62 = [tex]cosx=\frac{62}{2\sqrt{13}*\sqrt{74}}\\\\x=arcos(\frac{62}{2\sqrt{13}*\sqrt{74}})\\\\x=1.8\°[/tex]
Determine if a triangle with side lengths 8, 14, and 15 is acute, right, or obtuse
Answers
Answer:
Acute
Step-by-step explanation:
The Converse of the Pythagorean Theorem states that:
If [tex]a^2+b^2 > c^2[/tex] then the triangle is acute.If [tex]a^2+b^2 < c^2[/tex] then the triangle is obtuse.If [tex]a^2+b^2 = c^2[/tex] then the triangle is right.The side lengths 8, 14, and 15 are given. We can assume the hypotenuse (or c) is the longest side length, so it is 15.
c = 15It doesn't matter which order of the numbers are plugged in for a and b, so a and b will be 8 and 14.
a = 8b = 14Now we have to add [tex]a^2[/tex] and [tex]b^2[/tex] to see if the sum is greater than, less than, or equal to 15 (c).
[tex]a^2 + b^2[/tex][tex]8^2 + 14^2[/tex]Calculate the rest of the problem.
[tex]8^2=64 \newline 14^2=196[/tex][tex]64+196=260[/tex]We have to find what [tex]15^2[/tex] is before we can make a decision using the Converse of the Pythagorean Theorem.
[tex]15^2=225[/tex]260 ([tex]a^2+b^2[/tex]) is greater than 225 ([tex]c^2[/tex]). This means that the triangle is acute because [tex]a^2+b^2>c^2[/tex].
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation? Y = 1,000(1.15)6 2,313 bacteria y = 1,000(1.15)7 y = 1,000(1.5)5 y = 1,000(1.5)6 11,391 bacteria
Answers
Answer:
The correct option is Y = 1,000(1.15)6 2,313 bacteria
Step-by-step explanation:
According to the given statement a growth medium is inoculated with 1,000 bacteria.
Bacteria grow at a rate of = 15% = 0.15
Add 1 to make it easier = 0.15+1 = 1.15
We have to find the population of the culture 6 days after inoculation.
= 1000(1.15)^6
=1000(2.313)
= 2313 bacteria
The population of the culture 6 days after inoculation = 2313 bacteria
Therefore the correct option is Y = 1,000(1.15)6 2,313 bacteria....
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Jane and Lee had dinner at The Palace The bill totaled $20 30 with tax The service
was good, so they decided to leave a 15% tip. What is 15% of $20 30. to the
nearest cent?
Answers
Answer:
$3.45
Step-by-step explanation:
$20.30 / 10 = $2.30 = 10%
$2.30 / 2 = $1.15 = 5%
$2.30 + $1.15 = $3.45 = 15%
If f(x) = -2x - 5 and g(x) = x^4 what is (gºf)(-4)
Answers
Answer:
81
Step-by-step explanation:
(g∘f)(-4) is another way of writing g(f(-4)).
First, find f(-4):
f(-4) = -2(-4) − 5
f(-4) = 3
Now plug into g(x):
g(f(-4)) = g(3)
g(f(-4)) = 3^4
g(f(-4)) = 81
NEED HELP FAST!!!!!!!!!!!
John the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did Plan A and 5 who did Plan B. On Saturday there were 9 clients who did Plan A and 7 who did Plan B. John trained his Friday clients for a total of 6 hours and his Saturday clients for a total of 12hours. How long does each of the workout plans last?
Answers
Answer:
45 minutes each
Step-by-step explanation:
Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.
3x+5y=6
9x+7y=12
Now solve using substitution or elimination. I will use elimination.
-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.
9x+7y=12, add the equations
-8y=-6 solve for y
y= 3/4 of an hour or 45 minutes
Next plug y into either equation
3x+5(3/4)=6 Solve for x.
3x+15/4=6
3x=2.25
x=0.75, also 45 minutes
To check plug in each variable value to each equation to see if they work if you need to.
Can someone please help me with this transformation question
Answers
Answer:
x+(-2), y+(-3)
Step-by-step explanation:
Trapezoid ABCD has vertices A(-5,2), B(-3,4), C(-2,4) and D(-1,2).
The reflection across the y-axis has the rule
(x,y)→(-x,y),
so
A(-5,2)→A'(5,2)B(-3,4)→B'(3,4)C(-2,4)→C'(2,4)D(-1,2)→D'(1,2)The translation that maps points A', B', C' and D' to E, H, G, F is
A'(5,2)→E(3,-1)B'(3,4)→H(1,1)C'(2,4)→G(0,1)D'(1,2)→F(-1,-1)and has a rule
(x,y)→(x-2,y-3)