Exponential decay function is a form of an exponential function
What are exponential decay function?These are exponential functions that reduce in value as the input value increases.
This in other words, means that the rate of an exponential decay function is less than 1.
An exponential function is represented as:
[tex]y = ab^x[/tex]
Where b is the rate.
When b < 1, the function is an exponential decay function
For instance:
[tex]y = 3(0.9)^x[/tex] is an exponential decay function
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A bowl contains 28 black, 21 red, 23 blue, and 10 green balls
A ball is drawn at random. P (blue).
Answer:
P (blue) = 23 / 82
Step-by-step explanation:
There are 23 blue out of 82 (28 + 21 + 23 + 10 = 82) balls
or,
23 / 82
So, the probability of a blue ball being chosen is 23/82
(or a 28% chance [rounded])
Help please I’ll make it brainliest!!!!!
Step-by-step explanation:
it is very simple, once you remember that "kilo" means 1000, "mili" means 1/1000, and "centi" means 1/100.
and therefore 1 cg = 10 mg, or 1 cm = 10 mm.
"deci" means 1/10.
and therefore 1 dm = 100 mm, 1dg = 100 mg.
1.
9.32 kg = 9.32×1000 = 9320 g
2.
1.429 g = 1.429/1000 = 0.001429 kg
3.
287 g = 287/1000 = 0.287 kg
4.
4.6 L = 4.6×1000 = 4600 mL
5.
0.119 L = 0.119×1000 = 119 mL
6.
9936 mL = 9936/1000 = 9.936 L
7.
26793 mL = 26793/1000 = 26.793 L
8.
0.06 L = 0.06×1000 = 60 mL
9.
170 cg = 170×10 = 1700 mg
10.
2674 cm = 2674/100 = 26.74 m
11.
9.05 mm = 9.05/100 = 0.0905 dm
12.
2 L = 2×1000 = 2000 mL
13.
62.4 L = 62.4×1000 = 62400 mL
14.
99.9 mm = 99.9/1000 = 0.0999 m
15.
4.34 g = 4.34×100 = 434 cg
16.
10 km = 10×1000 m = 10×1000×1000 = 10000000 mm
17.
65 cL = 65/100 = 0.65 L
18.
105 mL = 105/1000 = 0.105 L
19.
0.27 g = 0.27×100 = 27 cg
20.
7777 m = 7777/1000 = 7.777 km
Part 1: Given cosine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).
Part 2: Given θ = 495°, convert the value of θ to radians and find sec θ.
The cosine ratio is given as:
[tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex]
See attachment for the graph of [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] under the domain of [0,∞)
From the graph, we can see that some values of [tex]\theta[/tex] when [tex]\cos(\theta) = \frac{\sqrt 3}{2}[/tex] are:
[tex]\theta = \frac{\pi}{6}[/tex] [tex]\theta = \frac{11\pi}{6}[/tex] and [tex]\theta = \frac{13\pi}{6}[/tex]
The value of sec θWe have:
θ = 495°
Convert to radians
[tex]\theta = 495 * \frac{\pi}{180}[/tex]
Evaluate
[tex]\theta = \frac{11\pi}{4}[/tex]
The value of sec θ is then calculated as:
[tex]\sec(\theta) = \sec(\frac{11\pi}{4})[/tex]
Using a calculator, we have:
[tex]\sec(\theta) = -1.414[/tex]
Hence, the value of [tex]\sec(\theta)[/tex] is -1.414
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The surface area of a right cone which has a base diameter of 6 units and a height of 8 units is:
75 units squared.
108 units squared.
151 units squared.
188 units squared.
The area of a 2D form is the amount of space within its perimeter. The surface area of the cone is 108.79967 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Given the diameter of the cone is 6 units, therefore, the radius of the cone is 3 units, and the height of the cone is 8 units. Thus, the surface area of the right cone is,
A=πr [r+√(h²+r²)]
A = 108.79967 units²
Hence, the surface area of the cone is 108.79967 units².
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Find the area of the sector in terms of pi. 170 6 Area = [?] T
Answer:
see the attachment photo!
Factoriser: X=a^ 2 b^ 2 +2a\%+a^ 4 7/2
The factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)
How to factorize the expression?The expression is given as:
x = a²b² + 2a + a⁴
Factor out a from the expression
x = a(ab² + 2 + a³)
The above expression cannot be further factorized.
Hence, the factorized expression of x = a²b² + 2a + a⁴ is x = a(ab² + 2 + a³)
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please answer this question
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-• [tex]\sf{ Polynomial :- ax^{2} + bx + c }[/tex]
• The zeroes of the given polynomial are α and β .
Let's Begin :-Here, we have polynomial
[tex]\sf{ = ax^{2} + bx + c }[/tex]
We know that,
Sum of the zeroes of the quadratic polynomial
[tex]\sf{ {\alpha} + {\beta} = {\dfrac{-b}{a}}}[/tex]
And
Product of zeroes
[tex]\sf{ {\alpha}{\beta} = {\dfrac{c}{a}}}[/tex]
Now, we have to find the polynomials having zeroes :-
[tex]\sf{ {\dfrac{{\alpha} + 1 }{{\beta}}} ,{\dfrac{{\beta} + 1 }{{\alpha}}}}[/tex]
Therefore ,
Sum of the zeroes
[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} )+( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{ ( {\alpha} + {\beta}) + ( {\dfrac{1}{{\beta}}} +{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{{\alpha}+{\beta}}{{\alpha}{\beta}}}}[/tex]
[tex]\sf{( {\dfrac{ -b}{a}} ) + {\dfrac{-b/a}{c/a}}}[/tex]
[tex]\sf{ {\dfrac{ -b}{a}} + {\dfrac{-b}{c}}}[/tex]
[tex]\bold{{\dfrac{ -bc - ab}{ac}}}[/tex]
Thus, The sum of the zeroes of the quadratic polynomial are -bc - ab/ac
Now,Product of zeroes
[tex]\sf{ ( {\alpha} + {\dfrac{1 }{{\beta}}} ){\times}( {\beta}+{\dfrac{1 }{{\alpha}}})}[/tex]
[tex]\sf{ {\alpha}{\beta} + 1 + 1 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]
[tex]\sf{ {\alpha}{\beta} + 2 + {\dfrac{1}{{\alpha}{\beta}}}}[/tex]
[tex]\bold{ {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]
Hence, The product of the zeroes are c/a + a/c + 2 .
We know that,
For any quadratic equation
[tex]\sf{ x^{2} + ( sum\: of \:zeroes )x + product\:of\: zeroes }[/tex]
[tex]\bold{ x^{2} + ( {\dfrac{ -bc - ab}{ac}} )x + {\dfrac{c}{a}} + 2 + {\dfrac{ a}{c}}}[/tex]
Hence, The polynomial is x² + (-bc-ab/c)x + c/a + a/c + 2 .
Some basic information :-• Polynomial is algebraic expression which contains coffiecients are variables.
• There are different types of polynomial like linear polynomial , quadratic polynomial , cubic polynomial etc.
• Quadratic polynomials are those polynomials which having highest power of degree as 2 .
• The general form of quadratic equation is ax² + bx + c.
• The quadratic equation can be solved by factorization method, quadratic formula or completing square method.
Which choice describes the value of m when –5(m + 1) ≤ 23?
A 28
5
m
B 28
5
m
C 18
5
m
D 18
5
The first step to solving almost any problem is to determine what the question is asking and what is given to us to help solve that problem. Looking at the problem statement, they are asking for us to determine which option best describes the value of m in the expression provided. The only thing that we are provided with is an expression which we need to solve for m.
Let's begin to solve the expression for m by first dividing both sides by -5. However, since we are dividing by a negative, that means that we must flip the sign.
Divide both sides by -5
[tex]-5(m + 1) \le 23[/tex][tex]\frac{-5(m + 1)}{-5} \le \frac{23}{-5}[/tex][tex]m + 1 \ge -\frac{23}{5}[/tex]The next step that we must take is to subtract 1 from both sides but before that let's convert it into an improper fraction with a denominator of 5 so we can easily deal with it with the other fraction.
Subtract both sides by 1
[tex]m + \frac{5}{5} - \frac{5}{5} \ge -\frac{23}{5} - \frac{5}{5}[/tex][tex]m \ge -\frac{23}{5} - \frac{5}{5}[/tex][tex]m \ge \frac{-23 - 5}{5}[/tex][tex]m \ge \frac{-28}{5}[/tex]We have finally came up to our final answer which would state that m is greater than or equal to negative 28 over 5. The options that you have provided seem like the formatting has messed up but I'm sure that on your side you can see the correct answer.
anyone who can solve this problem
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if p(a)=a^3-6a^2+11a-9 and p(a)=-3,find the value of a?
If the perimeter of an equilateral triangle is 30cm, find its area.
Answer:
A ≈ 43.3 cm²
Step-by-step explanation:
the area (A) of an equilateral triangle is calculated as
A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is a side of the triangle )
given perimeter = 30 cm , then
s = 30 cm ÷ 3 = 10 cm
then
A = [tex]\frac{10^2\sqrt{3} }{4}[/tex] = [tex]\frac{100\sqrt{3} }{4}[/tex] = 25[tex]\sqrt{3}[/tex] ≈ 43.3 cm² ( to the nearest tenth )
Which of the following polygons is a quadrilateral
Answer:
C
Step-by-step explanation:
A quadrilateral is a shape with 4 sides.
A is a triangle, 3 sides
B is a pentagon, 5 sides
D is a hexagon, 6 sides
C is a quadrilateral, 4 sides
Answer:
Step-by-step explanation:
c
a quadrillateral quadrilateral has four sides
A large construction company wants to review the ages of its sales representatives. A sampling of the ages of 25 sales reps are given:
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45
The following histogram is a representation of the data.
A histogram has ages on the x-axis, and frequency on the y-axis. Ages 20 to 24 has a frequency of 2, 25 to 29 is 2, 30 to 34 is 5, 35 to 39 is 4, 40 to 44 is 5, 45 to 49 is 5, 50 to 54 is 1, 55 to 59 is 1.
Calculate the mean and median ages.
a.
The mean age is 38.28. The median age is 38.
b.
The mean age is 38. The median age is 38.28.
c.
The mean age is 37.08. The median age is 38.
d.
The mean age is 36.88. The median age is 37.08.
Please select the best answer from the choices provided
A
B
C
D
The mean and median of the given set of data are respectively; The mean age is 38.28. The median age is 38.
How to find the mean and median of a set of data?The mean simply means the average of the set of data. Thus;
Mean = ∑x/n
∑x = 22 + 24 + 28 + 28 + 30 + 31 + 31 + 32 + 32 + 35 + 36 + 37 + 38 + 41 + 42 + 42 + 44 + 44 + 45 + 46 + 46 + 47 + 47 + 49 + 50
∑x = 957
Mean = 957/25
Mean ≈ 38.28
B) Median is the midterm when arranged in ascending order. When we arrange in ascending order, we get;
22, 24, 28, 28, 30, 31, 31, 32, 32, 35, 36, 37, 38, 41, 42, 42, 44, 44, 45, 46, 46, 47, 47, 49, 50
Thus, the median is 38.
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A ray extends forever in one direction. True or False
Answer:
True
Step-by-step explanation:
Rays have one endpoint and one arrow, which means that they extend forever in one direction.
In a shipment of 20 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested? (1/1140)
Please help me to answer this question. This question is under of topic basic and rule probability. I hope one of you guys can come up with a complete answer.
Answer:
a. 1/760
b.1/1140
c.27/8000
d.3/5000
I chose D, is this correct
Step-by-step explanation:
When Jessie goes to the mall, she alwavs makes sure to have $10 for lunch at the food court. At the tood court, her favorite restaurant is Wings I Stuff. Each bone-in wing costs $0.35 each and each boneless wing costs 50.45 each. What is the greatest number of each wing that she can purchase with her money?
The computation shows that the greatest number of each wing that she can purchase with her money will be 28 wings.
How to calculate the value?From the information, Jessie goes to the mall, she alwavs makes sure to have $10 for lunch at the food.
In this case, he cannot be able to buy boneless wings a it cost $50.45. Therefore, the number of bone in wing that can be bought will be:
= 10/0.35
= 28
Therefore, the computation shows that the greatest number of each wing that she can purchase with her money will be 28 wings.
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John Pelson's weekly net pay is $972.11. His weekly deductions are $185.00 for FIT; 5% of gross for SIT; 2% of gross for CIT; Social Security and Medicare; $64.00 for health insurance; and $25.00 for charity? Find the weekly gross pay
Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.
How to calculate gross pay?Let G represents weekly gross pay. The gross pay can now be calculated as follows:
Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)
Substitute all the relevant values into the equation (1) and solve as follows:
$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00
$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G
$1,246.11 = (1 – 0.05 – 0.02)G
$1,246.11 = 0.93G
G = $1,246.11 / 0.93
G = $1,339.90
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Determine u-x and o-x from the given parameters of the population and the sample.size. round the answer to the nearest thousandth where appropriate u=27 o=5 n=14
The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.
How to calculate the values?From the information given about the population and sample mean, the values include:
u=27 o=5 n=14
The standard deviation will be:
= 5/✓14
= 5/3.74
= 1.34
Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.
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Which of these show the correct shape after the translation?
I CAN’T SHOW ALL OF THE ANSWER CHOICES BUT CAN SOMEONE TELL ME IF I CHOSE THE RIGHT ANSWER?
The option that depicts a translation is option B. See the attached image and the explanation for this answer below.
What is Translation in Mathematics?Translation in Math refers to the movement of a shape vertically or horizontally along the x or y-axis without altering its original dimensions.
Going by the above definition, it is clear that Option B is the translated image (assuming that the original image is as given in the image attached.
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write each equation in slope intercept form x+7y=48
Answer:
y=-1/7+48/7
Step-by-step explanation:
You want to isolate the Y so you subtract the x to the other side.
Next you divide both numbers on the right hand side by 7 and that gives you
y=-1/7+48/7
Helppp what’s the answer
Answer:
players on both teams are about the same height on average
Step-by-step explanation:
because both are same
is the U.S. ever on sale to canadians?
Answer:
No because Us is powerful country canada is also powerful but U S ever sale to candians
The parabola y=x^2y=x
2
y, equals, x, squared is shifted up by 777 units and to the left by 111 unit.
What is the equation of the new parabola?
y=y=y, equals
Answer:
Step-by-step explanation:
The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.
Answer:
y=(x+1)^2 +7
When the parabola y=x² is shifted up by 7 units and to the left by 1 unit then the equation of the new parabola is y = (x-1)² + 7.
When a parabola is shifted vertically or horizontally, its equation changes accordingly.
In this case, the parabola y = x² is shifted up by 7 units and to the left by 1 unit.
Adding a constant value to the function shifts the graph vertically.
In this case, adding 7 to the original function y = x² will shift it up by 7 units:
y = x² + 7
Subtracting a constant value from the input of the function shifts the graph horizontally.
In this case, subtracting 1 from the x-values of the function y = x² + 7 will shift it to the left by 1 unit:
y = (x-1)² + 7
Hence, the equation of the new parabola after both shifts is y = (x-1)² + 7.
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Grades 3, 4, and 5 have their annual field day together. Each grade is given 15 gallons of water. If there are a total of 370 students, will there be enough water for each student to have 2 cups? First, solve for how many cups the students have.
Using proportions, it is found that the number of cups per student is of 1.97. hence there will not be enough for each student to have 2 cups.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each gallon is worth 16 cups, hence, since each grade is given 15 gallons of water, and the trip consists of three grades, the number of cups is given by:
C = 3 x 15 x 16 = 720.
There is a total of 370 students, hence the number of cups per student is given by:
n = 720/370 = 1.97.
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Select ALL the correct answers. Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000. Which statements are true for the given function? When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155." The independent variable is t. The dependent variable is f(t). The independent variable is f(t). The dependent variable is t. When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced." When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced." Reset Next
Using function concepts, it is found that the correct statements are given by:
The independent variable is t. The dependent variable is f(t).When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced." When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."What does the function f(t) represents?It gives the amount of garbage, in tons, produced by a city in t years after 2000.
The amount depends on the number of years, hence:
t is the independent variable.f(t) is the dependent variable.Hence, the correct statements are given by:
The independent variable is t. The dependent variable is f(t).When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced." When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."More can be learned about functions at https://brainly.com/question/25537936
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MATH
•••••••••
AGAIN DON'T DELETE THIS QUESTION!
••••••••••••
PLEASE ANSWER THIS CORRECTLY
(NEED SOLUTIONS)
•••••••••••••••
Step-by-step explanation:
See the attached pics it explains everything
Answer:
Corresponding Angles Theorem
When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).
Alternate Exterior Angles Theorem
When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Part AQ1. As s ║ c we can apply the Corresponding Angles Theorem:
⇒ 11x - 5 = 116
⇒ 11x - 5 + 5 = 116 + 5
⇒ 11x = 121
⇒ 11x ÷ 11 = 121 ÷ 11
⇒ x = 11
Q2. As s ║ c we can apply the Alternative Exterior Angles Theorem:
⇒ 12x - 4 = 148
⇒ 12x - 4 + 4 = 148 + 4
⇒ 12x = 152
⇒ 12x ÷ 12 = 152 ÷ 12
⇒ x = 38/3 = 12.7 (nearest tenth)
Part BQ1. As j ⊥ r then the sum of the angles is 90°
⇒ 4x + 6x + 10 = 90
⇒ 10x + 10 - 10 = 90 - 10
⇒ 10x = 80
⇒ 10x ÷ 10 = 80 ÷ 10
⇒ x = 8
Q2. As j ⊥ r we can apply the Vertical Angles Theorem:
⇒ 5x - 10 = x + 70
⇒ 5x - 10 + 10 = x + 70 + 10
⇒ 5x = x + 80
⇒ 5x - x = x + 80 - x
⇒ 4x = 80
⇒ 4x ÷ 4 = 80 ÷ 4
⇒ x = 20
The first four terms of a sequence are shown on the graph below. On a coordinate plane, points are at (1, negative 1), (2, 8), (3, negative 16), (4, 32). What can be concluded about the sequence? The common ratio of the sequence is 2. The common difference of the sequence is 2. The next term of the sequence is represented by the point (5, 64). The next term of the sequence is represented by the point (5, –64).
Answer:
The next term of the sequence is represented by the point (5, –64)Step-by-step explanation:
Note: The first point should be (1, - 4)
According to the points, the sequence is:
t₁ = - 4, t₂ = 8, t₃ = - 16, t₄ = 32or
- 4, 8, - 16, 32, ...We can observe it is a geometric sequence with common ratio of - 2, as:
r = 32/ - 16 = - 16/8 = 8/ - 4 = - 2The following term is:
t₅ = t₄*r = 32*(- 2) = - 64The coordinates of same term are:
(5, - 64)As we see the correct answer choice is D.
Above is a table that gives the interest per every $100 financed. Use the table to determine the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed.
a.
13%
c.
15%
b.
14%
d.
16%
The annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.
How to determine Annual Percentage Rate?From the table, the APR for 35 months loan that charges $22.38 per every $100 financed is seen to be 14%.
Thus, we can conclude that the annual percentage rate for a 35 month loan that charges $22.38 per every $100 financed is seen from the table to be 14%.
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Answer:
a. 13%
Step-by-step explanation:
E2020!
HELP ASAP!!!!!!!!!!!
Answer:
a) ΔCED ~ ΔCAB
b) 157.5 m
Step-by-step explanation:
The similarity statement for geometric figures lists the corresponding vertices in the same order. Corresponding sides of similar figures are proportional. That fact can be used to find the missing side length.
__
a)The right angles are corresponding. Angle C corresponds to itself, so the similarity statement can be written ...
ΔCED ~ ΔCAB
__
b)Corresponding sides are proportional, so we can write ...
AB/AC = ED/EC
AB/(50+160) = 120/160 . . . . . using the numerical values
AB = 210 × 120/160 = 157.5 . . . meters
The length of the lake is 157.5 meters.
For what value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution
The value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2
System of equationFor a system of equation to have no solution, the expression on both sides must be different.
Given the system of equation
6x-5y=3 and
3x+ay=1
For the equations to have no solution, the a1/a2= b1/b2
Substitute
6/3 = -5/a
Cross multiply
2 = -5/a
a= -5/2
Hence the value of the constant a will the system of linear equations 6x-5y=3 and 3x+ay=1 have no solution is -5/2
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