The function that represent this exponential decay is given as y = A(0.85)ˣ
What is an exponential function?
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Given that A is the initial value, there is a decay of 15%, hence:
b = 100% - 15% = 0.85
The function that represent this exponential decay is given as y = A(0.85)ˣ
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A different rectangle has a diagonal of 60 yards and a height of 40 yards.find the width of the rectangle rounded to the nearest hundredth
Answer:
2159.6 i think
Step-by-step explanation:
i used a rectangle calculator
please help I'll give brainliest if answer is right
Answer:
The area is about 96.06 or 96.1
Step-by-step explanation:
I tried my best to solve it, I'm sorry if it's wrong.
Find the area of a circle whose radius is 3 1/2(three whole number one over two)
Answer:
38.5 in²
Step-by-step explanation:
Area of circle= πr², where r is the radius
Substitute the value of the radius into the formula above:
Area of circle
= π(3.5)²
= 12.25π
= 38.5 in² (3 s.f.)
Simplify: 5x3+3x2−(−x−6x2)+4x−x2
Answer: 33 plus 3x
Step-by-step explanation: simplified it
Answer:
The answer is 5x3+8x2+5x
Step-by-step explanation:
what type of sequence is 99,33,3,1
Answer:
36 ,36 30,2
Step-by-step explanation:
hope it's okay to you
Which represents the polynomial written in standard form? 4m – 2m4 – 6m2 9 9 4m 2m4 – 6m2 2m4 – 6m2 – 4m 9 9 – 6m2 4m – 2m4 –2m4 – 6m2 4m 9.
The standerd form 4m – 2m^4 – 6m^2 +9.
We have given that the polynomial given below we have to find the standerd form of the polynomial.
What is the standerd form of the polynomial[tex]P(x)=a_nx^n+a_{n-1}x^{n-1}+......+a_1x+a_0[/tex]
n=4
Standard form of the polynomial
[tex]4m - 2m^4 - 6m^2 + 9[/tex]
Rearranginge term we get
[tex]=-2m^4 - 6m^2 + 4m + 9[/tex]
The third term of the given polynomial is 0.
Therefore,the standard form is,
[tex]-2m^4 - 6m^2 + 4m + 9[/tex]
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Use the equation, (1/27)^x=3^(-4x+6), to complete the following problems.
Rewrite the equation using the same base.
Solve for x. Write your answer as a fraction in simplest form.
Please show all work, and refrain from posting links, thank you!
Answer:
Given equation:
[tex]\left(\dfrac{1}{27}\right)^x=3^{(-4x+6)}[/tex]
27 can be written as [tex]3^3[/tex]
Also [tex]\dfrac{1}{a^b}[/tex] can be written as [tex]a^{-b}[/tex]
[tex]\implies \dfrac{1}{27}=\dfrac{1}{3^3}=3^{-3}[/tex]
Therefore, we can rewrite the given equation with base 3:
[tex]\implies (3^{-3})^x=3^{(-4x+6)}[/tex]
To solve, apply the exponent rule [tex](a^b)^c=a^{bc}[/tex]
[tex]\implies 3^{-3 \cdot x}=3^{(-4x+6)}[/tex]
[tex]\implies 3^{(-3x)}=3^{(-4x+6)}[/tex]
[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex]
[tex]\implies -3x=-4x+6[/tex]
Add [tex]4x[/tex] to both sides:
[tex]\implies x=6[/tex]
what is the range of the exponential function y=2^x plus 2?
A. Y<0
B. Y<-1
C. Y<-2
D. Y<-1 (Less than or equal to)
find the value of x when y=14. y= -6x+5
Answer:
x = -3/2
Step-by-step explanation:
To find the unknown value, substitute all known values and solve for the one remaining. After substitution, this becomes a 2-step linear equation, so is solved by the procedure for such equations.
y = -6x +5 . . . . . given
14 = -6x +5 . . . . substitute known value
9 = -6x . . . . . . . subtract 5 (step 1)
9/-6 = x = -3/2 . . . . divide by the coefficient of x (step 2);
Hello!
In order to find the value of x, we should take the value of y and plug it in and then simplify.
[tex]\bold{y=-6x+5}[/tex]
Plug in:
[tex]\bold{14=-6x+5}[/tex]
Switch places:
[tex]\bold{-6x+5=14}[/tex]
Now, subtract 5 from both sides:
[tex]\bold{-6x=14-5}[/tex]
[tex]\bold{-6x=9}[/tex]
Divide both sides by -6 in order to isolate x:
[tex]\bold{x=-\displaystyle\frac{9}{6}}[/tex]
Can this fraction be reduced? Sure, we can divide the numerator (9) and the denominator (6) by 3:
[tex]\bold{-\displaystyle\frac{3}{2}}[/tex]
As a Mixed Fraction:
[tex]\bold{1\displaystyle\frac{1}{2}}[/tex]
Hence, the value of x is:
[tex]\huge\boxed{\boxed{\mathfrak{\star{Answer:{\boxed{-\frac{3}{2} }}}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
#NeverGiveUp
[tex]\rm{A~teen~who~never~gives~up}[/tex]
If X and Y are 2 finite sets such that n() = 9, n( XY) - 4 and n( XY) -15, then n() is
(A) 5
(B) 6
(C) 10
(D) 12
Answer:
I think it's a hope this helps
A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.
How many employees took a break that lasted between 37 and 41 minutes?
Select from the drop-down menu to correctly complete the statement.
Given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.
What is a Box-and-whisker Plot?A box-and-whisker plot is a graphical representation of a data set showing how the data set is distributed into percentiles such as 25%, 50%, and 75%.
The range of the rectangular box covers 50% of the data set.
Thus, 37 - 41 minutes lies between 50% on the box-and-whisker plot, therefore:
50/100 × 360 = 180 employees.
In summary, given the box-and-whisker plot, the number of employees that took a break that lasted between 37 - 41 minutes is: 180.
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Answer:
The answer is 90
Step-by-step explanation:
Its not 180 I take k12 also.
The amount of money you have after investing $400 for 8 years and $600 for 6 years at the same interest rate is represented by 400x^6 + 600x^6. where x is the growth factor. classify the polynomial by the number of terms. what is the degree?
The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.
What is a polynomial?Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.
Polynomials are classified based on degree as linear, cubic, quadratic, etc.
A polynomial with two terms is known as a binomial. Hence:
The polynomial 400x⁶ + 600x⁶ has a degree of 6 and is a binomial.
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What is the slope of the line that passes through (-1, 3) and (-1, 8)?
due today
Answer:
Slope of the line is undefined
Step-by-step explanation:
(x₁, y₁) = (-1 , 3) and (x₂, y₂) = (-1 , 8)
The line is parallel to y-axis. The slope of the line parallel to y-axis is undefined.
Which number is a rational?
Answer:
0/5 = 0
0/200 = 0
0/ (-25) = 0
Step-by-step explanation: I am sure this is it because these are rational numbers
Find the volume of the square pyramid shown below.
PLEASE HELP THANK YOU
Answer:
money left= -50•games played + 47.50
Find the perimeter.
Write your answer as a fraction or as a whole or mixed number.
3
1
4
in
112 in
1
in
12
NA
1
1
in
.
inches
Answer:
7 1/3 inches
Step-by-step explanation:
2 (1 3/4 + 1 11/12)
9+11
3/4+11/12= -------------
12
20/12
=1 2/3+ 2
2(3 2/3)
= 7 1/3
sin 60 =11/x
x=11/sin (60)
Answer:
sixt
Step-by-step explanation:
thats easy the sin should be six
I need this for a geometry assignment........please help
All three are similar
In ∆SUT and ∆VWX
Two sides are similar and one angle is similarSo by SSA they are similar
In ∆PRQ and rest two
All angles are.
80,80,20°So
They are similar by AAA congruence
i need help smh..anyways can someone help me? like asap-
Answer: x<-1
Step-by-step explanation:
The answer is A!
Answer:
See below.
Step-by-step explanation:
Solving the inequality :-
18 < -3(4x - 2)18 < -12x + 612 < -12x-1 > xx < -1Graph A shows the solution to the inequality correctly
HELP ASAPPP
Inga, Kai, and Jason volunteer in the school library. They want to find the average number of pages of a library book. It would be unreasonable to calculate the number of pages in every book to find the average. They decide they need to find a valid sample.
Inga suggests choosing 100 books from the history section to get a sample.
Kai suggests randomly selecting 100 books from the library’s entire catalog.
Jason suggests using 100 books from the teen fiction section to get a sample.
Who suggested the best way to produce a random sample that is not biased?
Answer:
Kai suggested the best way to produce a random sample that is not biased
Step-by-step explanation:
Answer:
The answer is Kai suggested the best way to produce a random sample that is not biased
Step-by-step explanation:
Given cosθ = 3/5, find the five other trigonometric function values. 15
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \impliedby \textit{let's now find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{5^2-3^2}=b\implies \sqrt{25-9}=b\implies \sqrt{16}=b\implies 4=b \\\\[-0.35em] ~\dotfill[/tex]
[tex]sin(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{5}}\qquad \qquad tan(\theta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\qquad \qquad cot=\cfrac{\stackrel{adjacent}{3}}{\underset{opposite}{4}} \\\\\\ sec(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{adjacent}{3}}\qquad \qquad csc(\theta )=\cfrac{\stackrel{hypotenuse}{5}}{\underset{opposite}{4}}[/tex]
The values of the five other trigonometric functions value for the same input θ for which cos(θ) = 3/5 are:
sin(θ) = 4/5tan(θ) = 3/4cot(θ) = 4/3sec(θ) = 5/3csc(θ) = 5/4What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
What is Pythagoras Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
We're given that:
cosθ = 3/5 for some angle θ
Since we've got:
[tex]\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}[/tex]
Therefore, we have:
[tex]\dfrac{3}{5} = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}[/tex]
Let we consider a right angled triangle in which there is hypotenuse of length 5 units and base (from the perspective of one of its non-right angle) of 3 units (as shown in the image attached below).
(we couldve taken 3x and 5x instead of 3 and 5, for any positive real number value of 'x' as when we would take their ratio, that common factor 'x' would get cancelled out. We can think of 3 and 5 as the special case of 3x and 5x when x = 1)
Then, from that perspective, let the perpendicular be of the length 'p' units, then as per the pythagoras theorem, we get:
[tex]p^2 + 3^2 = 5^2\\p = \sqrt{25 - 9} = \sqrt{16} = 4 \: \rm units[/tex]
(took only the positive root to remove the square term because the value of p denotes length, which is a non-negative quantity).
Thus, we have:
From the perspective of the angle θ:
Length of the base = 3 unitsLength of the perpendicular = 4 unitsLength of the hypotenuse = 5 units.Thus, using these values, and the definition of the trigonometric ratios, we get:
sin(θ) = 4/5tan(θ) = 3/4cot(θ) = 4/3sec(θ) = 5/3csc(θ) = 5/4Thus, the values of the five other trigonometric functions value for the same input θ for which cos(θ) = 3/5 are:
sin(θ) = 4/5tan(θ) = 3/4cot(θ) = 4/3sec(θ) = 5/3csc(θ) = 5/4Learn more about Pythagoras theorem here:
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Can someone please help me with this?
Answer:
50
Step-by-step explanation:
If we divide the shape we can get 3 x 10 with equals 30. Then take the remaining which is 2 x 10 and we get 20. Add the two to get 50. The area is 50sq miles.
Hope this helps. pls mark brainliest
How you should answer:
1. Known:
2.Unknown:
3.Rationle:
4.Equation and Solution:
Steps on how to answer:
-State the known
-State the unknown and represent it with a variable
-Provide a rationale for your approach
-Include the equation, exact answer, and decimal approximation
Question 1
Focus on the triangle on the left.
sine is the ratio of opposite over hypotenuse
sin(angle) = opposite/hypotenuse
sin(44) = w/30
w = 30*sin(44)
w = 20.839751 approximately
Now move onto the triangle on the right. We'll use cosine this time.
cos(angle) = adjacent/hypotenuse
cos(x) = w/45
cos(x) = 20.839751/45
cos(x) = 0.463106
x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]
x = 62.412286
Answers:w = 20.839751 approximatelyx = 62.412286 approximately==========================================================
Question 2
Focus on the triangle on the left.
sin(angle) = opposite/hypotenuse
sin(32) = w/5
w = 5*sin(32)
w = 2.649596
Now move to the triangle on the right.
sin(angle) = opposite/hypotenuse
sin(x) = w/5
sin(x) = 2.649596/5
sin(x) = 0.5299192
x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]
x = 31.999996
Answers:w = 2.649596 approximatelyx = 31.999996 approximately==========================================================
Question 3
This time we use the tangent ratio.
Focus on the triangle that has legs of w and 16.
tan(angle) = opposite/adjacent
tan(70) = 16/w
w*tan(70) = 16
w = 16/tan(70)
w = 5.823524
Now let y = x+w and focus on the largest triangle this time.
tan(angle) = opposite/adjacent
tan(41) = 16/y
y = 16/tan(41)
y = 18.405895
This leads to:
y = x+w
x = y-w
x = 18.405895 - 5.823524
x = 12.582371
Answers:w = 5.823524 approximatelyx = 12.582371 approximatelyHello people ~
what's the product of the square root of 3 and the square root of 12
Answer:
6
Step-by-step explanation:
sqrt(3) x sqrt(12) = sqrt(3) x sqrt(4x3) = sqrt(3) x 2sqrt(3)
= 2 ( sqrt(3)² ) = 2 x 3 = 6
Let's see
[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{12}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{3}\times \sqrt{2(2)(3)}[/tex]
[tex]\\ \rm\rightarrowtail \sqrt{3}\times 2\sqrt{3}[/tex]
[tex]\\ \rm\rightarrowtail 2(3)[/tex]
[tex]\\ \rm\rightarrowtail 6[/tex]
Find the volume of a cone with a base diameter of 12 m and a height of 11 m.
Step-by-step explanation:
the volume of a cone is
ground area × height / 3
and the ground area is a circle.
so,
pi×r²×h/3
with r being the radius (half the diameter) and h being the height.
therefore, we get
pi×(12/2)²×11/3 = pi×6²×11/3 = pi×12×11 = 132pi =
= 414.6902303... m³
i need help) Han and Clare go shopping, and they each have a coupon. Answer each question and show your reasoning.
1.Han buys an item with a normal price of $15, and uses a 10% off coupon. How much does he save by using the coupon?
2.Clare buys an item with a normal price of $24, but saves $6 by using a coupon. For what percentage off is this coupon?
The amount of money that Han saves by using a coupon is $1.5%
The percentage off Clare's purchase with the coupon is 25%
How much did Han save?
A coupon reduces the price at which an item is sold
Amount saved = coupon discouunt x normal price
10% x $15
0.1 x $15 = $1.5
What is the percent off Clare's coupon?
Percent off = (6/24 x 100 = 25%
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Select the correct answer.
Which number is an irrational number?
A.
B.
C.
D.
Answer:
its c i just got done doing the same one
Step-by-step explanation:
got it right on my real numbers test and got 100% if you need more help comment under my answer
A box of 100 personalized pencils costs $\$30$. How many dollars does it cost to buy 2500 pencils?
Answer:
$750
Step-by-step explanation:
2500 divided by 100 = 25 and 25 x 30 = 750
Sorry if im wrong
The price for 2500 pencils is $750.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
We have,
A box of 100 personalized pencils costs $30.
So, cost of 1 pencil = $30 / 100 = 3/10
Now, the price to buy the 2500 pencils
= 2500 x 3/10
= 250 x 3
= $750
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Holding a ruler upright at arm’s distance (24 in.), Ronnie aligned the bottom of the ruler with a mark on the utility pole that was about 5 feet above the ground. He saw that the top of the pole aligned with the 6-inch mark on the ruler. Then he took 40 long strides to reach the pole. If each stride was about one yard (3 feet), then the top of the pole is about how many feet high?
Answer:
10 feet
Step-by-step explanation:
Drawing obviously not to scale but... Red segment is the ruler, at least the part between 5 and 6 inches, 1 inch long. Brown segment is the pole, ground to the top. Leftmost point is the eye, green line is the horizontal. The triangles are similar (AAA, the vertical lines are parallel), the ratio of the side is the same as the ratio of the heights. The height of the larger triangle (measured across the green line is
[tex]40 yd \times 3\frac{ft}{yd} \times 12\frac{in}{ft}= 1440''[/tex].
Ratio of the height is then [tex]1440\div24 = 60[/tex].
At this point the height of the pole is 60 times the length of the measure on the ruler, or 60 inches, that is 5 feet. Add the 5 feet the pole was starting from, it's 10 feet.