help i am struggling
Answer: it's D
Step-by-step explanation:
One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)
The number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
How to find the number of days the penny would stack?Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with
first term a = L and common ratio , r = 2.Since the number of pennies after n days equals N = 2ⁿ
Let
L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSo, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L
Number of days pennies would stack to reach starMaking n subject of the formula, we have
n = ㏒(D/L)/㏒2
Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSubstituting the values of the variables into the equation, we have
n = ㏒(D/L)/㏒2
n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2
n = ㏒(3/1.5 × 10¹⁹)/㏒2
n = ㏒(2 × 10¹⁹)/㏒2
n = ㏒2 + ㏒10¹⁹/㏒2
n = (19㏒10 + ㏒2)/㏒2
n = (19 + 0.3010)/0.3010
n = 19.3010/0.3010
n = 64.1
n ≅ 64 days
So, the number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
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If [tex]\rm \: x = log_{a}(bc)[/tex], [tex]\rm \: y = log_{b}(ca)[/tex], [tex]\rm \: z = log_{c}(ab)[/tex] , the xyz is equal to :
(a) x + y + z
(b) x + y + z + 1
(c) x + y + z + 2
(d) x + y + z + 3
Use the change-of-basis identity,
[tex]\log_x(y) = \dfrac{\ln(y)}{\ln(x)}[/tex]
to write
[tex]xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}[/tex]
Use the product-to-sum identity,
[tex]\log_x(yz) = \log_x(y) + \log_x(z)[/tex]
to write
[tex]xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}[/tex]
Redistribute the factors on the left side as
[tex]xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}[/tex]
and simplify to
[tex]xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)[/tex]
Now expand the right side:
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}[/tex]
Simplify and rewrite using the logarithm properties mentioned earlier.
[tex]xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1[/tex]
[tex]xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}[/tex]
[tex]xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}[/tex]
[tex]xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)[/tex]
[tex]\implies \boxed{xyz = x + y + z + 2}[/tex]
(C)
The correlation in error terms that arises when the error terms at successive points in time are related is termed _____.
Answer:
auto correlation is the answer to the question
Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was
I'M IN LOVE WITH A FAIRYTALE
EVEN THOUGH IT HURTS
CAUSE I DON'T CARE IF I LOOSE MY MIND
I'M ALREADY CURSED
Answer:
888
Step-by-step explanation:
let the number be n then divide by 8 , that is [tex]\frac{n}{8}[/tex]
now add 8 to this
[tex]\frac{n}{8}[/tex] + 8 and finally multiply this by 8 and equate to 952
8([tex]\frac{n}{8}[/tex] + 8) = 952 ( divide both sides by 8 )
[tex]\frac{n}{8}[/tex] + 8 = 119 ( subtract 8 from both sides )
[tex]\frac{n}{8}[/tex] = 111 ( multiply both sides by 8 to clear the fraction )
n = 888
the number chosen was 888
6. Find the distance between points A = (2, 0) and B = (0, 9). Round your answer to the nearest
tenth.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\approx 9.2 \:\: units [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Using distance formula : - } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(x_2 - x_1) {}^{2} + (y_2 - y_1) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(2 - 0) {}^{2} + (0 - 9) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{(2) {}^{2} + (- 9) {}^{2} } [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{ 4 + 81} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{85} \: \: units[/tex]
[tex]\qquad \tt \rightarrow \: \approx 9.2 \: \: units[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The distance between points A and B is 9.2 units.
We have,
To find the distance between two points (a, b) and (c, d) in a coordinate plane, you can use the distance formula:
Distance = √[(c - a)² + (d - b)²]
In this case, point A is (2, 0) and point B is (0, 9).
Now, plug the values into the distance formula:
Distance = √[(0 - 2)² + (9 - 0)²]
Distance = √[(-2)² + 9²]
Distance = √[4 + 81]
Distance = √85
Now, round the answer to the nearest tenth:
Distance ≈ √85 ≈ 9.2 (rounded to the nearest tenth)
Thus,
The distance between points A and B is 9.2 units.
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Find the solution to the system
of equations.
4
y = 2x + 2
3
2
([?], [ ])
-4-3-2/1
1 2 3 4
y=-x-3
-1
-2
3
-4
Answer:
(- 2, - 2 )
Step-by-step explanation:
the solution to the system is at the point of intersection of the 2 lines.
the 2 lines intersect at (- 2, - 2) , then
solution to the system is (2, - 2 )
Which linear function has the steepest slope?
Answer:
[tex]y=-8x+5[/tex]
Slope-intercept form:
[tex]\implies y=mx+b[/tex] [tex](\text{m=slope};\text{b=y-intercept})[/tex]
Using the slope-intercept form, let's identify the other slopes:
Option A:
[tex]y=-8x+5[/tex]
[tex]\text{slope}=-8[/tex]
Option B:
[tex]y-9=-2(x+1)[/tex] (This equation is in point-slope form, the slope it too the left, making it -9)
[tex]\text{slope}=-9[/tex]
Option C:
[tex]y=7x-3[/tex]
[tex]\text{slope}=7[/tex]
Option D:
[tex]y+2=6(x+10)[/tex]
[tex]\text{slope}=2[/tex] (Using point-slope terms, we can find the slope.)
⇒ A 'steep'est slope is closest to almost having a vertical slope or pitch, or relatively high gradient, as a hill, an ascent, stairs, etc.
[tex]\text{This could be a line }[/tex] ⇒ ([tex]\text{positive or negative}[/tex])
Hence, the linear function with the steepest slope is Option A: [tex]y=-8x+5[/tex].
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In the given figure, lines AC and BD intersect each other at point E.
If ∠AEB:∠BEC = 9 : 11, find all the angles.
The value of the angle AED = 99 degree , Angle BEC is 99 degree , angle DEC = 81 degree , angle AEB is 81 degree
What is angle of a Straight Line ?The straight line has an angle of 180 degree.
The two lines AC and BD intersects such that
∠AEB:∠BEC = 9 : 11
Let angle BEC be x
Then
Angle AEB is 9x/11
and angle AEC + BEC = 180 degree
(9x/11) + x = 180
9x +11x = 11 * 180
20x = 11 * 180
x = 99 degree
Angle BEC is 99 degree
and angle AEB is 81 degree
As Angle AED is vertically opposite to angle BEC
Therefore angle AED = 99 degree
As Angle DEC is vertically opposite to angle AEB
Therefore angle DEC = 81 degree.
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b) The height of the control tower. a) The shortest distance between the pilot and the base of the control tower. From a horizontal distance of 10.5km, a pilot observes that the angles of depression of the top and base of a control tower are 36° and 41 degrees respectively. Calculate he following:
From the calculations, the height of the tower is 26.4 Km
What is the angle of depression?If we know that the base of the tower is B and he top of the tower is T then to find the shortest distance between the pilot and the base of the control tower;
Sin 41 = 10.5//BP/
/BP/ = 10.5/Sin 41
/BP/ = 15.9 Km
Now, the height of the control tower is obtained from;
First /AB/ = √(15.9)^2 - (10.5)^2
/AB/ = 11.9 Km
Given that;
Tan 36 = 10.5//BT/
/BT/= 10.5/Tan 36
/BT/= 14.5 Km
Hence the height of the tower is 11.9 Km + 14.5 Km = 26.4 Km
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question below, NEED ASAP!! THANK YOU!!!
Answer:
1
Step-by-step explanation:
[tex] log_{3}(5) \times log_{25}(9) = \frac{ log(5) }{ log(3) } \times \frac{ log(9) }{ log(25) } = \frac{ log(5) }{ log(3) } \times \frac{2 log(3) }{ 2log(5) } = \frac{2}{2} = 1[/tex]
(PLEASE HELP!) Determine the values for the pronumerals that make the following piece-wise functions continuous.
Answer:
a = - 1b = 7Given A piece-wise function, consisting of three lines.
In order to make the function continuous, the first and second pairs of lines should have common points.
Let's find the common points.1. Intersection of the first two lines:
- x = 2 + x -2x = 2x = - 1This determines the value of a:
a = - 12. Intersection of the second two lines:
2 + x = 2x - 52x - x = 2 + 5x = 7This determines the value of b:
b = 7See the graph attached
A store selling school supplies advertises a bundle deal. The consumer can
pick a backpack, a binder, a pack of pencils, and notebook paper for a set
price. There are 6 types of backpacks, 4 types of binders, 5 types of pencils,
and 2 types of notebook paper. How many outcomes are possible in this
bundle?
Using the Fundamental Counting Theorem, it is found that the number of outcomes possible in this scenario is given by:
D. 240.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The number of options for each selection are given as follows:
[tex]n_1 = 6, n_2 = 4, n_3 = 5, n_4 = 2[/tex]
Hence the number of outcomes is given by:
N = 6 x 4 x 5 x 2 = 240.
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Explain what happens when you have an exponent to the power of another exponent.
Answer:
The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 52 raised to the 3rd power is equal to 56.
Step-by-step explanation:
if the first term is -2 and the rule is multiply by 6 and then subtract 13 whats the 3rd term
Answer:
-163
Step-by-step explanation:
-2,-25,-163
-2×6=-12 -12-13=-25
-25×6=-150 -150-13=-163
Answer:
The third term is = -163
Step-by-step explanation:
The first term is = -2
The second term = -2 ×6 = -12 Then - 13 = - 25
The second term = - 25
The third term = -25 × 6 = - 150 Then -13 = -163
The third term is -163
Mark brainliest
4 apples and 3 pears=£2.70 2 apples and 5 pears =£2.40 how much does 1 apple cost and 1 pear
Answer:
The answer is 0.45 pounds for an apple and 0.3 pounds for a pear
Step-by-step explanation:
Answer:
Cost of each apple: [tex]0.45[/tex].
Cost of each pear: [tex]0.30[/tex].
Step-by-step explanation:
Let [tex]x[/tex] denote the cost of each apple. Let [tex]y[/tex] denote the cost of each pear.
The question states that the cost of [tex]4[/tex] apples and [tex]3[/tex] pears is [tex]2.70[/tex]. Thus:
[tex]4\, x + 3\, y = 2.70[/tex].
Likewise, since the cost of [tex]2[/tex] apples and [tex]5[/tex] pears is [tex]2.40[/tex]:
[tex]2\, x + 5\, y = 2.40[/tex].
Solve this system of equations for [tex]x[/tex] and [tex]y[/tex] to find the price of each fruit.
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 2\, x + 5\, y = 2.40\end{aligned}\right.[/tex].
Multiply both sides of the equation [tex]2\, x + 5\, y = 2.40[/tex] by [tex]2[/tex] to match the coefficient of [tex]x[/tex] in the first equation:
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & (2\times 2)\, x + (2 \times 5)\, y = (2 \times 2.40)\end{aligned}\right.[/tex].
[tex]\left\lbrace \begin{aligned} & 4\, x + 3\, y = 2.70 \\ & 4\, x + 10\, y = 4.80 \end{aligned}\right.[/tex].
Substitute the first equation from the new equation to eliminate [tex]x[/tex] and solve for [tex]y[/tex]:
[tex]\begin{aligned}& 4\, x + 10\, y - (4\, x +3\, y) = 4.80 - 2.70\end{aligned}[/tex].
[tex]10\, y - 3\, y = 2.10[/tex].
[tex]7\, y = 2.10[/tex].
[tex]y = 0.30[/tex].
Substitute [tex]y = 0.30[/tex] into an equation from the original system to eliminate [tex]y[/tex] and solve for [tex]x[/tex].
[tex]2\, x + 5\, y = 2.40[/tex].
[tex]2\, x + 5 \times 0.30 = 2.40[/tex].
[tex]2\, x = 0.90[/tex].
[tex]x = 0.45[/tex].
Thus, [tex]x = 0.45[/tex] and [tex]y = 0.30[/tex].
In other words, the price of each apple would be [tex]0.45[/tex]. The price of each pear would be [tex]0.30[/tex].
como faltar a la escuela
Answer:
Como faltar a la escuela. Por favor, ¿cuál es el significado?
there are 2 quarters 1 nickle and 2 dimes in a pocket what is the probility of choosing a coin not returning it too the pocket and then choosing another of greater value
A quadrilateral has three congruent sides. Each of the congruent sides is 5 cm shorter than the forth side. If the quadrilateral has a perimeter of 33 cm, find the length of the longest side
The length of the three congruent sides is 7 cm and the fourth side length is 12cm.
Given quadrilateral has three congruent sides and perimeter of quadrilateral is 33 cm.
A quadrilateral can be expressed as ABCD and three congruent sides are AB, BC, CD and the fourth side is AD.
Let AD=x
then AB=BC=CD=x-5
This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.
So, Perimeter = AB + BC + CD + DA.
Substitute values
(x-5)+(x-5)+(x-5)+x=33
4x-15=33
4x= 48
x=12
Hence the fourth side length is 12cm and the other sides are 7 cm longer.
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The midpoint of AB is M(-2, -1) If the coordinates of AA are (-7, 2) what are the coordinates of B?
Answer:
(3,-4)
Step-by-step explanation:
which number produces a rational number when added to 0.53
Answer:
5/7 or D
Step-by-step explanation:
i just know
Write the sentence as an equation.
253 equals the product of 232 and k
Type a slash ( / ) if you want to use a division sign.
The solution to a given word problem by writing it as an equation is k = 253/232
Expressing word problems in mathematical forms:The process of expressing word problems in mathematical forms takes a logical and chronological approach while taking the variables and arithmetic operations given into consideration.
From the given information, to express the word problem in mathematical form, we have:
253 = 232 × k253 = 232kMaking k the subject of the equation, we have:
k = 253/232
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Which of the following is the solution to the following system of inequalities?
x+2y<4
3x-y >2
The solution will be the point of intersection of the two lines. The solution to the system is (1.1, 1.3)
Inequality graphsInequalities are expression not separated by an equal sign. Given the following inequalities
x+2y<4
3x-y >2
They are both written in standard form. The first line will be a dashed line and shaded below the graph while the second line will be a dashed line and shaded above.
The solution will be the point of intersection of the two lines as attached
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Answer:
Graph D is the correct one.
Step-by-step explanation:
Hey! can someone give me a step-by-step explanation on how to solve this problem correctly? I know for a fact that I did it incorrectly.
Answer:
B. 1:18
Explanation Down Below
Step-by-step explanation:
Hello!
First, let's find the volume of each cylinder by plugging in the given values.
Volume of a Cylinder: [tex]V = \pi r^2h[/tex]
Cylinder ASince the variables are the same as given in the formula, we can just use the formula as the volume.
[tex]\implies{\boxed{{V = \pi r^2h}}[/tex]
Cylinder BWe have to plug in 3r for the radius, and 2h for the height.
[tex]V = \pi r^2 h[/tex][tex]V = \pi (3r)^2(2h)[/tex][tex]V = \pi(9r^2)(2h)[/tex][tex]V = 18\pi r^2h[/tex][tex]\implies \boxed{ V = 18\pi r^2h}[/tex]
RatioWe can see that the Volume of Cylinder B is just 18 times the Volume of Cylinder A, but we can find the same ratio using equations.
[tex]\text{Ratio} = A:B[/tex][tex]\text{Ratio} = \pi r^2h: 18\pi r^2h[/tex][tex]\text{Ratio} = \frac{\pi r^2h}{18\pi r^2h}[/tex][tex]\text{Ratio} = \frac{\not{\pi}\not {r^2}\not{h}}{18\not{\pi}\not{r^2}\not{h}}[/tex][tex]\text{Ratio} = \frac1{18}[/tex][tex]\text{Ratio} =1:18[/tex]The answer is Option B. 1:18.
im really stuck on this one
Answer:
See below
Step-by-step explanation:
The first one IS decay...as 'x' increases the function decreases
the second and third are NOT ...as 'x' increases the value increases
radioactive decay IS decay (obviously)
the one with e^2x is not ....it grows exponentially as x grows
and finally the last one is decay because as x gets larger the value of y gets smaller
pls help asap!!!!
Which number best represents the slope of the graphed line?
Answer:
C: 1/2
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: C. \cfrac{1}{2}[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \textsf{Slope of line - } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{rise}{run} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{0 - ( - 4)}{8 - 0} [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 4}{8 } [/tex]
[tex]\qquad \tt \rightarrow \: m = \cfrac{ 1}{2} [/tex]
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what does a equal if 2÷a=(5/2)÷(5/4)
Question:
2÷a=(5/2)÷(5/4)
Answer:
a = 1
Which graph represents the function r(x) = |x-2| -1
It's whichever graph is an absolute function and is shifted to the right by 2 and is shifted down by 1.
Since I don't have a picture of the graph this is the best I can do to help.
Answer:
see attached
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Given function:
[tex]r(x) = |x - 2| - 1[/tex]
The parent function of the given function is: [tex]f(x) = |x|[/tex]
Translated 2 units to the right: [tex]f(x-2)=|x-2|[/tex]
Translated 1 unit down: [tex]f(x-2)-1=|x-2|-1[/tex]
Graph of Modulus function
Line y = x where x ≥ 0
Line y = -x where x ≤ 0
Vertex at (0, 0)
Therefore, the graph of the given function is the graph of the modulus function translated 2 units to the right and 1 unit down. So, its vertex is at (2, -1).
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Please solve it. It will help me for my exam preparation.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} }{(p - y) {}^{y} } + \cfrac{ - 2p}{(p - y) {}^{y - 1} } + \cfrac{1}{(p - y) {}^{y - 2} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + ( - 2p)(p - y) + 1(p - y) { }^{2} }{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2}- 2p {}^{2} + 2py + p {}^{2} + y{ }^{2} - 2py}{(p - y) {}^{y} } [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ {p}^{2} + {p}^{2} - 2p {}^{2} + 2py - 2py + y{ }^{2} }{(p - y) {}^{y} }[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{ y{ }^{2} }{(p - y) {}^{y} }[/tex]
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10(x + 2) + 10 • 2 for x = 2
Answer:
60
Step-by-step explanation:
10(2 + 2) + 20
=10(4)+20
=40+20
=60
