The percentage change of the given exponential function f(x) = 400(0.85)^(x) is; 15%
How to Interpret Exponential decay function?
The general form of an exponential decay function is:
y = a(1 – b)^(x)
where:
y is the final amount that remains after a period of time decayed
a is the initial amount
x is the time
Decay factor = (1 – b).
where;
b is the percent change written in decimal form.
We are given the exponential function as;
f(x) = 400(0.85)^(x)
Now, from the general form of an exponential decay function, we can say that;
1 - b = 0.85
b = 1 - 0.85
b = 0.15 or 15%
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I Need help QUICK!
Which graph represents the solution set for p + 3.6 > −5.8? number line with open circle on point negative 9.4 and arrow shaded to the left number line with open circle on point negative 9.4 and arrow shaded to the right number line with open circle on point negative 2.2 and arrow shaded to the left number line with open circle on point negative 2.2 and arrow shaded to the right
Answer: c
Step-by-step explanation:
The solution set for the inequality is p > -9.4. See attachment below for the graph.
How to Graph the Solution Set for an Inequality?An open circle is used when the inequality sign involved is ">" or "<". That is, it is used for numbers that are less than or greater than.
An arrow shaded to the right means the solution set is greater than a given value, while an arrow shaded to the left means the solution set includes all values that are less than a given value.
Given the inequality, p + 3.6 > −5.8, solve for p:
p + 3.6 > −5.8
Subtract 3.6 from both sides
p + 3.6 - 3.6 > -5.8 - 3.6
p > -9.4
Thus, the solution set would be all the values that are greater than -9.4. The graph is shown below.
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2) What is the equation for the below function? Show your work!
The equation for the given function passing through (0,5) and (4,0) is equal to y = (-5 /4)x +5.
As given in the question,
As shown in the graph drawn we have
( x₁ , y₁ )=(0, 5)
( x₂ , y₂ )=( 4, 0)
Equation for the given function passing through ( x₁ , y₁ ) = (0, 5) and
( x₂ , y₂ )=( 4, 0) is given by :
( y - y₁ )/ (x -x₁ )=( y₂ - y₁ )/( x₂ - x₁ )
⇒( y -5) / (x -0)=( 0 -5)/( 4 -0)
⇒( y - 5) /x=-5/4
⇒y -5=(-5/4)x
⇒y=(-5/4)x + 5
Therefore, the equation for the given function passing through (0,5) and (4,0) is equal to y=(-5 /4)x +5.
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a farmer is building a fence to enclose a rectangular area consisting of 2 separate regions. the 4 walls and one additional vertical segment to separate the regions are made up of fencing. if the farmer has 648 feet of fencing what are the dimensions of the region which enclose the maximum area?
The dimensions of the region which enclose the maximum area is a side of 162 feet and vertical segment of 108 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the side parallel to the vertical segment and y represent the other side. If the farmer has 648 feet of fencing, hence:
x + x + y + y + x = 648
3x + 2y = 648
y = 324 - 1.5x
Area (A) = xy
A = xy
A = x(324 - 1.5x)
A = 324x - 1.5x²
The maximum area is at A' = 0, hence:
A' = 324 - 3x
324 - 3x = 0
3x = 324
x = 108 feet
y = 324 - 1.5(108) = 162 feet
x = 108 feet, y = 162 feet
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Which term of the arithmetic sequence 7, 3, -1, -5, ... is -385?
99th term of the given arithmetic sequence 7, 3, -1, -5, ... is -385.
We are provided with the arithmetic sequence mentioned below;
7, 3, -1, -5, ................. -385
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n−1)d
where [tex]a_{1}[/tex] is the first term, [tex]a_{n}[/tex] is the nth term and d is the difference between a term and its previous term.
With the help of provided arithmetic sequence we can write;
[tex]a_{n}[/tex] = -385
[tex]a_{1}[/tex] = 7
d = difference between a term and its previous term = 3 - 7 = -4
Put these values in equation 1 , we will get
-385 = 7 + (n-1) (-4)
392 = 4n -4
4n = 396
n = 99
So we can conclude that the 99th term of the arithmetic sequence 7, 3, -1, -5, ... is -385.
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can someone tell me how to solve this
Answer:
See below
Step-by-step explanation:
If there are no other forces on the body. the NET force is the result of the two forces acting to the left and total 5 N Left
Answer: The correct answer is Net Force = 5, Direction = N
Step-by-step explanation: Net force in the same direction is cumulative and simply added together, where opposing forces are subtracted. In this case, they are in the same direction or to the left.
Lea
owhs 800 shares of ABC, Incorporated. On April 6, the corporation Instituted a 5-for-2 stock split. Before the split, each share was worth $42.60.
a. How many shares did Lea hold after the split?
b. What was the post-split price per share?
c. Show that the split was a monetary non-event for Lea. Pre-split and post-split market values=
Answer:
2000
Step-by-step explanation:
Number of shares after split is 5/2 times the pre split value =800*5/2 = 2000
Select the correct answer.
Which inequality is represented by the number line?
Answer:
I think C. Correct me if I am wrong.
Step-by-step explanation:
Hope it helps! =D
Answer: The answer is C.
Step-by-step explanation: Because I use a graphing calculator
What is the slope-intercept form of the equation of the line that contains the points (1, 4)and (0, 1)?
Answer:
3
Step-by-step explanation:
m=y2-y1÷x2-x1
4-1÷1-0=3÷1=3
Part 1 pls help with this
Answer:
Below.
Step-by-step explanation:
1) Alternate exterior angles
2) Alternate interior angles
3) Alternate exterior angles
4) Alternate exterior angles
5) Alternate interior angles
6) Corresponding angles
7)Alternate exterior angles
8) Alternate interior angles
9) Corresponding angles
10) Corresponding angles
When two parallel lines are intersected by a transversal 8 angles are formed.
Alternate exterior angles: These angles are located outside the parallel lines but on the opposite side of the transversal.
Alternate interior angles:
These angles are located inside the parallel lines but on the opposite side of the transversal.
Corresponding angles: These angles are located at the same relative position on the same side of the transversal.
use the given domain to find the range of function. help please
The range for the given domain D = {2, -3, 0} of the function f(x) = 2x² + 7 is; R = {7, 15, 25}
What is the Range of the Function?We are given the function as;
f(x) = 2x² + 7
We are given the domain set as;
D = {2, -3, 0}
Now, the range will simply be gotten by plugging in each domain value into the given function to get the output. Thus;
Range when x = 0 is;
y = 2(0)² + 7
y = 7
Range when x = 2 is;
y = 2(2)² + 7
y = 15
Range when x = -3 is;
y = 2(-3)² + 7
y = 25
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Which transformation
of y = f(x) moves the graph
7 units to the left and 3 units down?
1) y=(x+7)-3
2) y=f(x+7)+3
3) y=f(x-7)-3
4) y=f(x-7)+3
find the domain of each function
f(x)=(x+5)/x
FOR THE GIVEN FUNCTION WE WILL HAVE TO CHECK DENOMINATOR PART BECAUSE IT IS THE ONE WITH THE GREATER EFFECT ON MAKING THE FUNCTION UNDEFINED.
THE FUNCTION WILL BE UNDEFINED ONLY IF x=0
THIS BRINGS US TO A CONCLUSION OF SAYING THE DOMAIN IS ALL REAL NUMBERS BUT X IS NOT EQUAL TO 0
Ben can type 25 words in half a minute. At this rate, how many words can he type in 5 minutes?
250 word in 5 minutea
Step-by-step explanation:
1. 25×2 (Because 25 is half of a minute so I need to multiplie by two)
2. It gives you 50 u multiplie by 5 because u need to find the answer for 5 minutes
3. 50×5= 250!!
Answer:
250
Step-by-step explanation:
25x2 (wpm) * 5 (minutes) = 250
words per minute means words typed every minute. if ben types 50 words per minute, this means he can type 250 words in 5 minutes.
(sorry for edit, i misread words in half minute as words per minute, credit to lina6561 for making me realize)
Name the property used in the given expression −33/ 57 × −7/ 28 = −7/ 28 × −33/ 57 . With steps and solution pls
Step-by-step explanation:
as the other answer said, if is the commutative property of multiplication (the same as for addition, as multiplication is just a shortcut form of special additions) :
a × b = b × a
you need a solution ? you mean, you need this multiplication done and simplified, right ?
you know that
a/b × c/d = (a×c)/(b×d)
so,
-33/57 × -7/28 = -33/57 × -7/(4×7) =
= -33/57 × -1/4 = (-33×-1)/(57×4) =
= 33/228
City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour for a special install of 1,920 squares free how much will they charge
Total charge for 1,920 squares feet is $160.
What is basic algebra ?The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in all areas of mathematics, including trigonometry, calculus, and coordinate geometry. 2x + 4 = 8 is a straightforward algebraic expression.In algebra, symbols are used, and operators are used to connect the symbols to one another. It is more than just a mathematical idea; it is a skill that we all utilize on a regular basis without even being aware of it.
Given that :City carpet advertises that they can instal 1,200 square feet of carpet in 2 1/2 hours They charge $40 per hour.
City carpet can install 1,200 square feet of carpet in 2.5 hours
In 1 hour they can install [tex]\frac{1200}{2.5} =480 squares feet[/tex]
In 4 hour they can install 1920 squares feet carpet
They charge $40 per hour
So total charges for 1920 square feet will be 4 ×40
= $160
Total charge for 1,920 squares feet is $160.
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given a normal distribution with mean 100 and standard deviation 10, find the number of standard deviations the measurement is from the mean. express the answer as a positive number. 87
The measurement deviates from the mean by more than 100 standard deviations.
What does simple math standard deviation mean?It's a way to gauge how widely apart each data point is from the mean. The standard deviation formula comes in two different forms: Standard deviation for the population When you can measure the entire population or the entire collection of data, you use the population version of the formula. Experts in statistics have determined that measurements that fall within a 2 SD range of the true value are more accurate than those that do not..
based on the facts provided;
the average population, =100
The standard deviation for the population
σ=10
Z score:
Z=X−μσ
X:The measurement.
The number of standard deviations the measurement is from the mean:
We are not given the measurement. So, assuming the measurement is equal to 139.
When
X=139
Z=139−100/10
=3.9
It implies that the measurement of
139 is 3.9
standard deviation above the mean of 100;
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whats the first answer
a.
[tex] {3}^{2} \times {3}^{x} = {3}^{7 \\ } \\ \\ {3}^{2 + x} = {3}^{7} \\ 2 + x = 7 \\ x = 7 - 2 \\ x = 5[/tex]
b.
[tex] {7}^{8} \div {7}^{y} = {7}^{6} \\ {7}^{8 - y} = {7}^{6} \\ 8 - y = 6 \\ y = 8 - 6 \\ y = 2[/tex]
c.
[tex]( {q}^{4} )^{z} = q ^{12} \\ q^{4 \times z} = q^{12} \\4 z = 12 \\ \frac{4z}{4} = \frac{12}{4} \\ z = 3[/tex]
I used the laws of exponents.
i need your helppppppp
The result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5
n(-2) = 4/3
n(0) = 2/3
n(5) = -1
The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex]
The function is an equation which expression the relationship between one variable and another variable. If one variable is independent variable then another variable will be dependent variable.
The function is n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x= -2,0 and 5
Here we have to substitute the value of x in the given function
n(-2) = -1-(1/3)(-2)+5/3
= -1+(2/3)+5/3
= 4/3
n(0) = -1-(1/3)(0)+5/3
= -1+(5/3)
= 2/3
n(5) = -1-(1/3)(5)+5/3
= -1-(5/3)+(5/3)
= -1
Hence, the result of the function n(x)= [tex]-1-\frac{1}{3}x+1\frac{2}{3}[/tex] when x = -2,0 and 5
n(-2) = 4/3
n(0) = 2/3
n(5) = -1
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Please help me my mom is very upset and I’m grounded
look and solve this:
a) fractions; 15.3/3
b) yes, it is a rational number
Work out the values of a, b, c and d.
Justify each of your answers.
W
Z
33%
aº
16°
45°
d°
80°
22%
X
Y
Not drawn accurately
Answer69
Step-by-step explanation:
solution to this inequality 15+x<24
Answer: x < 9
Step-by-step explanation:
Move all terms not containing x to the right side of the inequality.
f (x) = 2x-1 and g (x) = x+2. Find f(g(x))
Answer:2x^2+3x-2
Step-by-step explanation:
2x-1*x+2=2x^2+3x-2
Answer:
2x+3
Step-by-step explanation:
so first you plug in g(x) in for x in f(x). this is how it will look like
2(x+2)-1
then you distribute the 2 in both terms in the parenthesis.
2(x)+2(2)-1
after that, you multiply them and you will get this
2x+4-1
subtract 4 and 1 and this is your answer
2x+3
Grayce has three diamonds that weigh 0.275 g each. Morgan has two diamonds that weigh 0.412 g each. Who has more grams of diamonds?
Grayce has 0.825 g of diamonds and Morgan has 0.824 g of diamonds. Grayce has more grams of diamonds
Calculating weightsFrom the question, we are to determine the person that has more grams of diamonds
From the given information,
"Grayce has three diamonds that weigh 0.275 g each"
and
"Morgan has two diamonds that weigh 0.412 g each"
Thus,
The total mass of Grayce's diamonds is 3 × 0.275 g
3 × 0.275 g = 0.825 g
Also,
The total mass of Morgan's diamonds is 2 × 0.412 g
2 × 0.412 g = 0.824 g
Since 0.825 is greater than 0.824,
Then,
Grayce has more grams of diamonds.
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The integer 6 makes which of the following equations false?
−6(t − 8) = 12
5m + 3 = 3m
t + 5 = 11
9 = 2x − 3
Answer:
5m+3 =3m
Step-by-step explanation:
−6(t − 8) = 12
-6((6) -8) =12
5m+3=3m
5m-3m=3
2m=3
2(6)≠3
t + 5 = 11
(6) + 5 = 11
9 = 2x − 3
2x = 9+3
2(6) = 12
Show your work. Please help I really need!
a. Expression for length L in terms of x is L = 1040 - 2x
b. Expression for the area of the pasture in terms of L and x, A = Lx
c. Expression for the area of the pasture in terms of x only = x (1040 - 2x)
d. The area of the pasture will enclose greater than or equal to 60 square feet
How to find the area in terms of the given dimensionsGiven data
length of fence = 1040 ft
length if the pasture = L
width of the pasture = x
Expression for length L in terms of x
from the figure we can see that the fenced part is 3 sides which include 2 widths and 1 length. So we represent this with the expression below
L + x + x = 1040
L + 2x = 1040
L = 1040 - 2x
Expression for the area of the pasture in terms of L and x
Area of the pasture, A = L * x
A = Lx
Expression for the area of the pasture in terms of x only
= L * x
and L = 1040 - 2x
= x (1040 - 2x)
A sentence that makes the area to enclose at least 60 000 square feet.
from A = Lx
we have
A = Lx ≥ 60
The area of the pasture will enclose greater than or equal to 60 square feet
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Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
The minimum number of sets of knives Kaj should buy if the restaurant needs at least 736 knives is 48. 4 sets of knives
How to find the minimum number of sets of knives Kaj should buy?Number of knives needed by the restaurant = at least 736 knivesNumber of knives currently available at the restaurant = 155 knivesEach set of knives = 12Number of sets of knives needed to buy = x155 + 12x ≥ 736
substract 155 from both sides12x ≥ 736 - 155
12x ≥ 581
divide both sides by 12x ≥ 581 / 12
x ≥ 48.41666666666666
Approximately,
x ≥ 48. 4 sets of knives
In conclusion, the sets of knives kaj needs to buy more is 48. 4 sets of knives
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b) A different pattern is made using 20 straight lines
and 14 arcs.
The straight lines and arcs are made from metal.
20 straight lines cost £12
cost of one straight line: cost of one arc = 2:3
Work out the total cost of metal in the pattern.
26.4
total cost of metal in the pattern is £24.6
What is ratio and proportion ?To compare two values is to use a ratio. A proportion is formed when two ratios have the same value. Choose whether the ratio is part-to-part or part-to-whole before you write it.
Calculation20 straight line cost £12
12 ÷ 20 = 0.6 per straight line
straight line : cost of one arc = 2:3
arc = 0.6 x (3/2) = 0.9
total = 12 + 14 x 0.9
= 12 + 12.6
= 24.6
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y’all pls help smakhwhwhdhdj
Answer:
x = 22° (alternate angles, M//N)
Cual es elvalor absoluto del opuesto de 2,5 ?
Answer:|2.5|
Step-by-step explanation:
En este caso el valor absoluto de 0 a |2.5| es 2.5. Esto se debe a que ya sea que cambies la ecuación o no para que sea igual a otro número, la respuesta SIEMPRE será 2.5. ¡Espero que esto haya ayudado! :D