We have the equation:
[tex]W=W_0(\frac{1}{2})^{\frac{n}{100}}[/tex]And we want to find the value n, correspondign to the number of years necessary in order to the substance to decay in half.
Let's say that we have 1 Kg of the substance, this is Wo, the initial weight. Since we want to find the the decay of half the substance we use W = 1/2
And write:
[tex]\frac{1}{2}=1\cdot(\frac{1}{2})^{\frac{n}{100}}[/tex]Now we can use a property of logarithms:
[tex]\ln (a^b)=b\ln (a)[/tex]Thus applying natural log on both sides:
[tex]\ln (\frac{1}{2})=\ln (\frac{1}{2}^{\frac{n}{100}})[/tex]By the property:
[tex]\ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{})[/tex]We can divide on both sides by ln(1/2):
[tex]\begin{gathered} 1=\frac{n}{100} \\ n=100 \end{gathered}[/tex]The number of years for the radioactive substance to decay to half its initial weigh are 100 years.
The step to get rid of the ln(1/2) is:
[tex]\begin{gathered} \ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{}) \\ \frac{\ln (\frac{1}{2})}{\ln (\frac{1}{2})}=\frac{n}{100}\frac{\ln (\frac{1}{2}^{})}{\ln (\frac{1}{2})} \\ 1=\frac{n}{100}\cdot1 \\ 1=\frac{n}{100} \end{gathered}[/tex]
In a forest there are 99,278 trees. Each tree has about 57 branches and each branch has about
1,628 leaves.
Estimate the number of leaves in the forest by giving the answer in billions (for example, 2.12 or
3.56).
Answer:
9.53
Step-by-step explanation:
Estimate of trees: 99,300
Estimate of branches: 60
Estimate of leaves: 1600
All of the numbers multiplied togethered: 99,300 x 60 x 1600 = 9,532,800,000
9,532,800,000 to the billions is 9.53b
Note: i do not know if this will be accepted since you didn't put any answer choices so yeah
Find the minimum, first quartile, median, third quartile, and maximum of the data set below.4.92.76.2.54.75.46.53.812type an integer or decimal
SOLUTION
The Data set given is
4.9,2.7,6.2,5,4.7,5.4,6.5,3.8,12
The minimum of the data set is the lowest data in the distribution
[tex]\text{minimun}=2.7[/tex]The first quartile is given by
[tex]Q_1=(\frac{N}{4}+1)^{th}[/tex]where N=frequency of the data=9
[tex]Q_1=\frac{9}{4}+1=1.25+1=2.25^{th}[/tex]Then the first quartile becomes
[tex]Q_1=4.7[/tex]The median is the middle number after arrangement
[tex]2.7,3.8,4.7,4.9,5.0,5.4,6.2,6.5,12[/tex][tex]undefined[/tex]
You are hiking a trail over multiple days. At the start of your hike, you decide that you need to hike at least 22 miles in the first 3 days, but can't hike more than 34 miles, as you'll pass into swampy terrain where camping won't be possible. You want to hike the same distance each day. Let x represent the number of miles you hike each day.
The number of miles you hike each day is 7.4 miles.
What is the unitary method?The unitary approach, to put it simply, is used to determine the value of a single unit from a specified multiple. How to determine the worth of a single pen, for instance, if 40 pens cost Rs. 400. The unitary approach can be utilized. Additionally, after determining the value of a single unit, we can multiply it to determine the value of the other units. Most ratio and proportion concepts are addressed using this methodology. To compute the value of other units using the unitary approach, the value of a unit quantity must first be determined. This can be varied in two different ways.
Direct VariationInverse Variation3 days = 22 miles
1 day = x
x = 7.4 miles
Still 12 miles are left so I will need half a day more approximately.
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Put the following rational numbers in ascending order. r 0.4, 7/10, 9/10
Answer:
Step-by-step explanation:
Ascending is least to greatest.
We can convert the fractions into decimals.
SO,
7/10 can be 0.7 and 9/10 can be 0.9
In least to greatest order, it would be:
0.4, 0.7, 0.9 ANSWER
I tried doing the method my teacher taught me but i keep getting it wrong
ANSWER
x = 12
EXPLANATION
By the intersecting chords theorem, the product of each segment of one chord equals to the product of each segment of the other chord:
[tex]15\cdot8=10x[/tex]Solving for x:
[tex]\begin{gathered} 120=10x \\ x=\frac{120}{10} \\ x=12 \end{gathered}[/tex]Graph the parabola.
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
The graph of the parabola is added as an attachment
The vertex is (0, 0)The points to the right are (1, 1) and (2, 4)The points to the left are (-1, 1) and (-2, 4)How to graph the parabola?From the complete question (added at the end of the solution), the equation of the parabola is given as
y = x²
When a parabola has the form of y = x², then the vertex of the parabola is
Vertex = (0, 0)
Set x > 0 to determine the points to the right
When x = 1
y = 1² = 1
When x = 2
y = 2² = 4
Set x > 0 to determine the points to the left
When x = -1
y = -1² = 1
When x = -2
y = -2² = 4
So, the points are
(1, 1), (2, 4), (-1, 1) and (-2, 4)
While the vertex is (0, 0)
Next, we plot the graph of the parabola using a graphing calculator
See attachment for the graph
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Complete question
Graph the parabola y = x²
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
Tiana invests $83,927 in a start-up company. She will be repaid at the end of 7 years at 7% interest compounded annually. Find the amount of interest she willearn on this investment.DO NOT ROUND ANY NUMBERS UNTIL YOUR FINAL ANSWER!Round to the nearest dollar.
For a initial amount invested P at a annual interest rate r, the total amount after n years is given by:
[tex]A=P\cdot(1+r)^n[/tex]For P = $83927, r = 0.07 and n = 7, we have:
[tex]\begin{gathered} A=83927\cdot1.07^7 \\ A=\text{ \$134768.422} \end{gathered}[/tex]Then, the amount of interest Tiana will earn on this investment is given by:
[tex]A-P=134768.422-83927=\text{ \$50841}[/tex]Tan theta=10
Find sin(2theta)+cos(2theta)
Answer: B
Step-by-step explanation:
[tex]\tan \theta=10 \implies \sin \theta=\frac{10}{\sqrt{101}}, \cos \theta=\frac{1}{\sqrt{101}}[/tex]
[tex]\sin 2\theta=2\sin \theta \cos \theta=2 \left(\frac{10}{\sqrt{101}} \right)\left(\frac{1}{\sqrt{101}} \right)=\frac{20}{101}[/tex]
[tex]\cos 2\theta=2\cos^2 \theta-1=2 \left(\frac{1}{\sqrt{101}} \right)^2 -1=-\frac{99}{101}[/tex]
[tex]\therefore \sin 2\theta+\cos 2\theta=\frac{20}[101}-\frac{99}{101}=-\frac{79}{101}[/tex]
Name the type of transformation shown. 1. A. 2 IN
It is a transilation transformation.
The coordinate is moved 6 units to the right and 6 unit to down ward direction.
First find the term that should be added so that the expression is a perfect-square trinomial. w² + 7w + ___Then factor the trinomial.(___)²
to do a perfect-square trinomial the third term must be the square of the half of the second term
the sencond term is 7,so
[tex](\frac{7}{2})^2=\frac{49}{4}[/tex]so the expresion is
[tex]w^2+7w+\frac{49}{4}[/tex]and the factor
[tex](w+\frac{7}{2})^2[/tex]An example
[tex]w^2+\frac{8}{5}w+\cdots_{}[/tex]the third term is
[tex]\begin{gathered} (\frac{\frac{8}{5}}{2})^2 \\ \\ (\frac{4}{5})^2 \\ \\ =\frac{16}{25} \end{gathered}[/tex]so the percet-square is
[tex]w^2+\frac{8}{5}w+\frac{16}{25}[/tex]find the value of x.
The value of x = - 12°
Isosceles triangleThe triangle which has two equal sides or two equal sides is called an Isosceles triangle. In a Isosceles triangle the angles made by equal sides with 3rd side will be equal
Here from given question we have,
Measure of ∠2 = x + 85
And the measure of another angle = 73
From given picture,
Two sides of triangle are equal then the given triangle will be an Isosceles triangle
As we know in a Isosceles triangle the angles made by the two equal sides with 3rd side will be equal
=> ∠2 = 73
=> x + 85 = 73
=> x = - 85 +73
=> x = -12°
Therefore,
The value of x = -12°
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Question 1 (1 point)Write the equation in slope intercept form13x – 11y = –12Don’t forget to transpose
Solve for y in the equation in standard form
[tex]\begin{gathered} 13x-11y=-12 \\ -11y=-13x-12 \\ y=\frac{-13x-12}{-11} \\ y=\frac{13}{11}x+\frac{12}{11} \end{gathered}[/tex]You need a common numerator in order to add or subract two fractions.
O True
O False
Answer: False
Step-by-step explanation:
You need a common denominator (the bottom number)
(c) The total amount paid for a banquet, including gratuities of one-twentieth of the price
quoted for the banquet, was $2457. How
much of the amount paid was gratuities?
the amount paid for gatuities which 5 percent of the cost of banquet is
How to work out percentages?A percentage refers to a specific number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%.". The cost of gratuities is 1/20 or 5 percent of the amount paid for banquet. let us assume that x is the amount paid for banquet so
2457 is 120 percent of x
or 2457= [tex]\frac{120}{100}[/tex]×x
which implies x=2457×[tex]\frac{100}{120}[/tex]
x=2047.5$
this is the amount of banquet. to get the cost of gratuities we subtract this amount from the total cost.
amount paid for gratuities is 2457-2047.5=409.5$
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Kimberly wants to invest $3,000 in an account that earns 4% annual interest, and x dollars in an account that earns 7%, so that, on average, she earns 5.5% interest for both accounts. Select the equation to model the situation.A.0.04(3,000) + 0.07x = 0.55xB.0.055(3,000 + x) = 120 + 0.07xC.0.04x + 0.07x = 3,000D.0.055(3,000) = 0.04x + 0.07x
As given by the question
There are given that the total investment money is $3000 and earns 4% annual interest.
Now,
x dollars in an account that earns 7% and that earns 5.5% interest for both accounts.
Then, for the equation
Assuming that the money is invested at simple interest for one year,
We have:
[tex]\begin{gathered} 0.04(3000)+0.07x=0.055(3000+x) \\ 120+0.07x=0.055(3000+x) \end{gathered}[/tex]Hence, the correct option is B
Answer:
B- .0.055(3,000 + x) = 120 + 0.07x
Using the midpoint and distance formulas, calculate the coordinate of the midpoint and the length of the segment.
The midpoint formula [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
What are coordinates?
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.
The x-axis & y-axis are the two axes that make up a coordinate plane (vertical).
The coordinates of the origin, which is the location where the two axes connect, are (0, 0).
The following formula is used to determine the separation between two coordinates :
The midpoint formula [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex] and the length of coordinates can be determined from the formula [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
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please help me i don't even know I'm behind
Answer: 6.33
Step-by-step explanation:
[tex]x^2 =36 \implies x=\pm 6\\\\x^3 =125 \implies x=5\\\\x^2=81 \implies x=\pm 9\\\\x^3 =512 \implies x=8\\\\x^2 =100 \implies x=\pm 10\\\\x^2 =121 \implies x=\pm 11\\\\x^2 =49 \implies x=\pm 7\\\\x^3 =64 \implies x=4\\\\x^3 =8 \implies x=2\\\\[/tex]
So, the correct answers are 5, 10, and 4, and thus the mean is 19/3, or about 6.33.
Hi can you help me with this problem i dont understand itIll do anything if your correct
You can use multiplication to generate an equivalent ratio by multiplying both sides of the ratio by the same factor, this way:
[tex]\begin{gathered} 47\cdot2\colon3\cdot2 \\ 94\colon6 \end{gathered}[/tex]Question 10 of 10 The graph of the absolute value parent function, f(x) = [xl, is stretched horizontally by a factor of 3 to create the graph of g(x). What function is g(x)?
Answer:
[tex]g(x)=|\frac{x}{3}|[/tex]Explanation:
We are given absolute value function:
[tex]f(x)=|x|[/tex]It has been stretched horizontally by a factor of 3, we need to find a new function that shows the stretched functions:
Stretch-Compress-along x:
[tex]\begin{gathered} g(x)=f(cx) \\ \end{gathered}[/tex]Stretch if:
[tex]0Compress if:[tex]c\text{ }>1[/tex]Since our function is Stretched by a factor of 3, therefore our function g(x) is:
[tex]g(x)=f(\frac{x}{3})=|\frac{x}{3}|[/tex]This is a new function.
Answer:
Step-by-step explanation:
g(x) = |1/3x|
Write an equation of a parabola with a vertex at the origin and a diretrix at y=5.
The equation of the parabola with a vertex at the origin and a directrix at; y = 5 as described in the task content is; x² = -20y.
How to write equation of a parabola with a vertex at the origin?It follows from the task content that the vertex of the parabola is at the origin while it's directrix is the line; y = 5.
Therefore, it follows that the focus of the parabola is; f = -5, since; (f - k) = (k - 5) where, k = 0.
Ultimately, a = 1/4(f-k).
a = 1/4(-5-0) = -1/20.
Recall, the vertex form equation of a parabola takes the form;
y = a(x - h)² + k; where (h, k) is the vertex.
Therefore, since the vertex is at the origin; we have;
y = (-1/20) (x -0)² + 0
y = -x²/20
20y = -x²
Ultimately, the required equation of the parabola is;
x² = -20y.
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Answer:
[tex]y = -\frac{1}{20} x^{2}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{4(f-k)}(x - h)^{2} + k[/tex] Use the equation of the parabola. The vertex is at the origin, then (h, k) is (0, 0). Substitute 0 for h and k in the equation.
[tex]y = \frac{1}{4(f-0)} (x-0)^{2} + 0[/tex] Simplify.
[tex]y = \frac{1}{4f} x^{2}[/tex]
The directrix is given [tex]y = 5[/tex]. The distance from the focus to the vertex equals the distance from the vertex to the directrix, so
[tex]f - k = k - 5\\f = -5[/tex] Substitute -5 for f in the equation of the parabola above.
[tex]y = \frac{1}{4 * - 5} x^{2}[/tex] Simplify.
[tex]y = - \frac{1}{20} x^{2}[/tex]
bebe ené’eben’´´enz’bzva
Answer:
What?
Step-by-step explanation:
What?
how many grams are in a Kilogram?1,0000.0010.01100
Ok, so
The answer is that there's 1,000 grams in a Kilogram. That's the equivalence.
What is the product of 3x^2 and 2x^3y+5xy^4 ?
The product of two expressions can be calculated using distributive property as,
[tex](2x^3y+5xy^4)(3x^2)=2x^3y\times3x^2+5xy^4\times3x^2[/tex](Distributive property (A+B)C=AC+BC) )
[tex]\begin{gathered} (2x^3y+5xy^4)(3x^2)=6x^{3+2}y+15x^{1+2}y^4 \\ =6x^5y+15x^3y^4 \end{gathered}[/tex]Therefore, the product of the expressions is,
[tex]6x^5y+15x^3y^4[/tex]According to the graph, what is the temperature at the beginning of the year85 degrees60 degrees38 degrees0 degrees
From the graph
the curve start from a point close to 40
Hence at the beginning of the year January, the teperature was 38 degree
hello can you help me to understand this. 4 (18) it's 2 dots (19) 3 dots (20) 6 dots (21) 4 dots (22) 1 dots (23) 1 dot (24) ??? I don't get it
Explanation
to plot this, you need to count the numbers of weigth for that number, for example
for 18
count in the table all the 18
you will get 18 is 2 times in the table (2)
now, for 19
count the number of 19's in the table 3
and so on
Step 1
then, for 24
total = 0
so, as we have not 24 as a data, there is not need to plot it
I hope this helps you
3 11 / 16 simplified
Multiply the full number by the denominator to convert a mixed number to an improper fraction. If the value be 3 11 / 16 then simplifying the value 59 / 16.
How to convert mixed numbers to improper fraction?Multiply the full number by the denominator to convert a mixed number to an improper fraction. Include it in the numerator. Add that total to the denominator from the beginning.
To make a mixed number from an improper fraction, divide the numerator by the denominator. After division, the mixed number is produced in such a way that the obtained quotient becomes the entire number, the remainder becomes the new numerator, and the denominator remains constant.
Let the value be 3 11 / 16
Convert mixed numbers to improper fraction: [tex]$a \frac{b}{c}=\frac{a \cdot c+b}{c}$[/tex]
[tex]$&3 \frac{11}{16}=\frac{3 \cdot 16+11}{16}=\frac{59}{16} \\[/tex]
= 59 / 16
Therefore, the correct answer is 59 / 16.
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3. Which statement is true? B a.
The true statement is b.
Use the figure to answer exercises 6-7. 8 ft 5 ft 6. Frank drew a square pyramid and its net to represent a fort. Complete the net by filling in the missing measure. Choose the correct answer below. OA. ОВ. OC. OD. 1.25ft 42.5ft 18 ft 5 ft 0 LA CA 5ft 1.25ft 8 ft 2.5ft
Answer:
6. C
7. 105 ft²
Explanation:
The square pyramid has a square base with a side's length equal to 5 ft and a slant height equal to 8 ft.
Now, the only option that shows a square with a side length equal to 5 is C. So, the right net is C.
Then, the amount of fabric depends on the area of the net. The area of the net is equal to the area of the square added to the area of the triangles.
The area of the square is:
Area = side x side = 5 x 5 = 25 ft²
The area of the triangles is:
Area = 1/2 x base x height = 1/2 x 5 x 8 = 20 ft²
Then, the total area of the net is:
Total Area = 25 ft² + 4( 20 ft²)
Total Area = 25 ft² + 80 ft²
Total Area = 105 ft²
So, Frank needs 105 ft² of fabric to make the fort.
defines substitution
In this case, the answer is very simple.
Defines substitution.
The answer is:
The substitution method for solving systems of linear equations, consists of solving or isolating one of the unknowns (for example, x) and substitute its expression in the other equation.
In this way, we will obtain a first degree equation with the other unknown (y), and once solved ''y'', we calculate the value of ''x'' substituting the value of ''y'', that we already know.
Find the greatest common factor of the terms of the polynomial.
15z4 -30z³ +6z²