Drag the tiles to the boxes to form correct pairs. Not all tiles will be used
Match each situation to its corresponding expression.
Answers
Reading from top to bottom. Answers are as follows:
1. 7(2)^t
2. 3000(0.93)^t
3. 300(1.015)^t
4. 300(0.985)^t
We know that the exponential function is given by:
[tex]f(x)=ab^x[/tex]
where a is the initial amount.
and b is the change in the amount and is given by:
[tex]b=1+r[/tex] if the function is increasing by a rate of r
and [tex]b=1-r[/tex] if the function is decreasing by a rate of r.
a)
The initial amount of fish in the trout are: 7
i.e. a=7
Also, the population doubles every year.
This means that that b=2
Hence, the population after t years is given by the function P(t) as:
[tex]P(t)=7(2)^t[/tex]
b)
The original amount of the machine is: $ 3,000
i.e. a=3,000
Also, the value of machine decreases by a rate of 7%
i.e.
[tex]r=7\%\\\\i.e.\\\\r=0.07[/tex]
Hence, we have:
[tex]b=1-r\\\\i.e\\\\b=1-0.07\\\\i.e.\\\\b=0.93[/tex]
Hence, the function which represent the price of the machine after t years i.e. P(t) is given by:
[tex]P(t)=3000(0.93)^t[/tex]
c)
The initial population of colony of ants i.e. a=300.
The number of ants increases at a rate of 1.5% every month.
i.e. [tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]
i.e.
[tex]b=1+r\\\\i.e.\\\\b=1+0.015\\\\i.e.\\\\b=1.015[/tex]
Hence, the function P(t) which represents the population of ants after t months is given by:
[tex]P(t)=300(1.015)^t[/tex]
d)
The initial infected cells i.e. a=300
The infected cells are decaying at a rate of 1.5% per minute.
i.e.
[tex]r=1.5%\\\\i.e.\\\\r=0.015[/tex]
Since, there is a decay hence,
[tex]b=1-r\\\\i.e.\\\\b=1-0.015\\\\i.e.\\\\b=0.985[/tex]
Hence, the function P(t) which represents the number of infected cells after t minutes is given by:
[tex]P(t)=300(0.985)^t[/tex]
Related Questions
If a(x)=3x+1 and b(x)=square root x-4, what is the domain of (b o a)(x)?
answers choices are:
-infinity, infinity
0, infinity
1, infinity
4, infinity
Answers
ANSWER
[tex][1, \infty ][/tex]
EXPLANATION
The given functions are:
[tex]a(x) = 3x + 1[/tex]
[tex]b(x) = \sqrt{x - 4} [/tex]
We want to find the domain of the composite function;
[tex](b \circ \: a)(x) = b(a(x))[/tex]
[tex](b \circ \: a)(x) = b(3x + 1)[/tex]
[tex](b \circ \: a)(x) = \sqrt{3x + 1 - 4} [/tex]
This simplifies to,
[tex](b \circ \: a)(x) = \sqrt{3x - 3} [/tex]
This function is defined for
[tex]3x - 3 \geqslant 0[/tex]
[tex]3x \geqslant 3[/tex]
[tex]x \geqslant 1[/tex]
This can be rewritten as,
[tex][1, \infty ][/tex]
Can someone pleaseeee hellpp??
Answers
Answer:
5.8
Step-by-step explanation:
To get the mean, add up all the numbers
9+4+8+3+5 = 29
Then divide by how many numbers there are (5)
29/5 =5.8
The mean is 5.8
I need to know how to do it and get the answer
Answers
y-6=-4x-4
y=-4x-4+6
y=-4x+2
The answer is B.
Which exponential function is represented by the graph?
Answers
Answer:
see explanation
Step-by-step explanation:
The exponential function is in the form
y = a [tex](b)^{x}[/tex]
Use points on the graph to find a and b
Using (0, 3), then
3 = a [tex](b)^{0}[/tex] ⇒ a = 3
Using (1, 6), then
6 = 3 [tex](b)^{1}[/tex] ⇒ b = 6 ÷ 3 = 2
The equation is y = 3 [tex](2)^{x}[/tex]
Answer:
y = [tex]3*2^{x}[/tex]
Step-by-step explanation:
The general form for an exponential function is :
y = [tex]ab^{x}[/tex]
We need to find out what a and b are using the values given in the graph.
we can see that (x=0, y = 3) and (x=1, y = 6) are points on the curve. Substitute these into the general equation
for (x=0, y = 3),
3 = [tex]ab^{0}[/tex]
3 = a (1) or a = 3
for (x=1, y = 6),
6 = [tex]ab^{1}[/tex]
6 = ab (substitute a=3 from previous calculation)
6 = 3b
b = 2
Hence the equation is:
y = [tex]3*2^{x}[/tex]
Edit reason: typo in the final answer
the area of this circle is 84π m^2 what is the area of a 30 sector of this circle?
Answers
ANSWER
[tex]7 {m}^{2} [/tex]
EXPLANATION
If the area of the circle is 84π m² , then the area of a 30° sector is just a proportion of the full circle.
The area of the 30° sector is
[tex] \frac{30}{360} \times 84\pi \: {m}^{2} [/tex]
[tex] = \frac{1}{12} \times 84 {m}^{2} [/tex]
[tex] = 7 {m}^{2} [/tex]
Hence the area of the 30° sector of this circle is
[tex]7 {m}^{2} [/tex]
Please help me I AM STUCK, and please explain how you get the answer.
Answers
Answer:
x= -10
Step-by-step explanation:
(3)8+ [tex]\frac{\sqrt{2x+29} }{3}[/tex]= 9(3) (multiply both sides by 3)
24+ [tex]\sqrt{2x+29}[/tex]= 27 (move the 24 to the right)
[tex]\sqrt{2x+29}[/tex]=27-24 (subtract)
([tex]\sqrt{2x+29}[/tex])²= 3² (square both sides)
2x+29=9 (move the 29 to the other side)
2x=9-29 (subtract)
2x= -20 (divide both sides by 2)
x= -10
hope this helps and good luck! :)
Sherri rolls a dice, numbered 1 to 6, 64 times. How many times can she expect to roll an odd number?
Answers
Answer:
32
Step-by-step explanation:
Possible outcomes in a fair sided die 1,2,3,4,5,6 = 6 possible outcomes
Odd numbers = 1,3,5 = 3 odd numbers
Probability of rolling an odd number = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]
Total number of rolls = 64
expected number of odd number rolls in 64 roll,
= [tex]\frac{1}{2}[/tex] x 64 = 32
Which of the following is an arithmetic sequence?
A. 1,2,4,8,16,32,...
B. 100,50,25,12.5,...
C. 1,3,5,7,9 ,11,...
D. 1,2,4,7,11,...
Answers
20 POINTS! EMERGENCY!
Answers
Hello There!
The answer is that the Y intercept is 4.
The y intercept is where the graph crosses the y axis. It goes vertical
Answer: the y intercept is 4.
Step-by-step explanation:
In the graph, if the savings account would’ve started with $8, the y intercept would be 8.
We don’t know what the graph is talking about so it’s not the last option.
The line crossed the x intercept at 8 so it’s not B.
What is the solution to the equation 6y –2(y + 1) = 3(y – 2) + 6?
Answers
Answer: y=2
Step-by-step explanation:
Distribute the numbers -2 and 3...
6y-2y-2=3y-6+6
The -6 and 6 cancel each other out...
6y-2y-2=3y
Combine like terms....
4y-2=3y
Move 4y over....
-2=-y
Multiply both sides by -1.....
2=y
That’s your solution! Hope this helps!
Write the expression in complete factored form 3c(p-6)+4(p-6)
Answers
Answer:
(p-6)(3c + 4)
Step-by-step explanation:
Note that (p-6) is a factor of both terms. Factoring out (p-6), we get:
(p-6)(3c + 4).
Solve the equation.
1-3x + 1 + 10x = y + 4
Answers
x= y/7 + 2/7
I think thats right
Use the points (1,-3) and (5,9) to determine the slope between the two points using the slope formula
Answers
[tex]\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{9-(-3)}{5-1}\implies \cfrac{9+3}{4}\implies \cfrac{12}{4}\implies 3[/tex]
Lines m and n are perpendicular if the slope of m is zero then the slope of n is
A.) zero
B.)undefined
C.)negative
Answers
Answer:
undefined
Step-by-step explanation:
A line with a slope of zero is a horizontal line parallel to the x- axis
Thus, a line perpendicular to it is a vertical line parallel to the y- axis, with an undefined slope.
Which equation is represented by the table ?
Answers
Answer:
The correct answer is B. b=3a + 2
Step-by-step explanation:
Plug in the values from column A into each equation and find which one works. In this case, the only option that works is B.
I don’t get this can someone help pls
Answers
So the total you spent on your shirts is 26.24 time 3
So it would look like 3(26.24).
So A and D are wrong
So now looking at the equality signs
< is less than
> greater then
You want to spend less then 100
So the answer is B. Hoped I helped
Given: x
- 4x > 0, then the solution set in interval notation is: (-2, 0)
True
O
False
Answers
Answer:
Second option: False.
Step-by-step explanation:
Given the inequality [tex]- 4x > 0[/tex], you need to solve for the variable "x".
To solve for the variable "x" you can divide both sides of the inequality by -4 (Notice that the direction of the symbol of the inequality changes), then:
[tex]- 4x > 0\\\\\frac{- 4x}{-4} > \frac{0}{-4}\\\\x<0[/tex]
Therefore, the solution set in interval notation is:
[tex](-\infty,0)[/tex]
Then the answer is: False.
APY means ________________.
Answers
Answer:
annual percentage yield
Step-by-step explanation:
APY means annual percentage yield
Write in Expanded form
(-3x)^4
Use parenthesis to indicate multiplication
Answers
Factor the polynomial: -2x3 - 4x2 - 6x
Answers
The polynomial -2x³ - 4x² - 6x is factored by first factoring out the common term -2x, resulting in -2x(x² + 2x + 3). The quadratic x² + 2x + 3 cannot be further factored over the real numbers, giving the final factored form of -2x(x² + 2x + 3).
To factor the polynomial -2x³ - 4x² - 6x, we first look for any common factors in each term of the polynomial. In this case, we can see that each term includes a factor of -2x. Factoring this out, we get:
-2x(x² + 2x + 3)
However, the quadratic x² + 2x + 3 cannot be factored further over the real numbers because it does not have real roots (its discriminant 22 - 4(1)(3) = 4 - 12 = -8 is negative). Therefore, the fully factored form of the polynomial over the real numbers is:
-2x(x² + 2x + 3)
Which table represents a direct variation function?
a.
Input (x)23456
Output (y)7891011
b.
Input (x)246810
Output (y)-3-5-6-7-8
c.
Input (x)-5-4-3-2-1
Output (y)108642
d.
Input (x)-21012
Output (y)-3-3-3-3-3
is it a?
Answers
Answer:
Option C is correct.
Step-by-step explanation:
A direct variation function is
y/x = k
i.e. we can say that the ratio of y and x is equal to a constant value k.
We will check for each Option given.
Option A
7/2 = 7/2
8/3 = 8/3
9/4 = 9/4
10/5 = 2
11/6 = 11/6
Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant
Option B
-3/2 = -3/2
-5/4 = -5/4
-6/6 = -1
-7/8 = -7/8
-8/10 = -4/5
Option B is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant
Option C
10/-5 = -2
8/-4 = -2
6/-3 = -2
4/-2 = -2
2/-1 = -2
Option C is correct as y/x = k as ratio of y/x for each value in table c is equal to constant value -2
Option D
-3/-2 = 3/2
-3/1 = -3
-3/0 = 0
-3/1 = -3
-3/2 = -3/2
Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant .
SO, Option C is correct.
Answer: OPTION C
Step-by-step explanation:
The function of direct variation has this form:
[tex]y=kx[/tex]
Where k is the constant of variation.
Let's check if there is a constant of variation on the Options "a" and "b":
On Option A:
[tex]\frac{7}{2}=3.5\\\\\frac{8}{2}=4[/tex]
On Option B:
[tex]\frac{-3}{2}=-1.5\\\\\frac{-5}{4}=-1.25[/tex]
There is no constant of variation, then these tables do no represent a direct variation.
On the table shown in Option "d" you can observe that "y" does not change when "x" changes. Then it does not represent a direct variation.
Since on the table shown in Option "c":
[tex]k=-2[/tex]
This table represents a direct variation.
scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100% of people who write this exam obtain scores between 425 and 575
Answers
We have
[tex] \mu = 500[/tex]
[tex] \sigma = 100 [/tex]
425 corresponds to a z of
[tex]z_1 = \dfrac{425 - 500}{100} = -\dfrac 3 4[/tex]
575 corresponds to
[tex]z_2 = \dfrac{575 - 500}{100} = \dfrac 3 4[/tex]
So we want the area of the standard Gaussian between -3/4 and 3/4.
We look up z in the standard normal table, the one that starts with 0 at z=0 and increases. That's the integral from 0 to z of the standard Gaussian.
For z=0.75 we get p=0.2734. So the probability, which is the integral from -3/4 to 3/4, is double that, 0.5468.
Answer: 55%
Name the most appropriate metric unit for each measurement like the mass of cow
Answers
Answer:
Kilograms
Step-by-step explanation:
The surface area of square pyramid is 1,089 in^2.
If the dimensions are multiplied by 1/3, what will
be the new surface area?
Answers
The new surface area of a square pyramid when its dimensions are multiplied by 1/3 is calculated by squaring the scale factor (1/3) and multiplying it with the original surface area. In this case, the new surface area is 121 in².
Explanation:When the dimensions of a square pyramid are multiplied by 1/3, each linear dimension of the pyramid becomes one-third of its original size. Since surface area is a two-dimensional measure (length × width), when you scale down each dimension by a factor of 1/3, the new surface area will be the square of that scale factor times the original area. The surface area is proportional to the square of the scaling factor because area is calculated using two dimensions.
The original surface area is 1,089 in². To find the new surface area, we use the scale factor squared: (1/3) ² = 1/9. We then multiply the original surface area by this factor:
New Surface Area = Original Surface Area × (Scale Factor)²
New Surface Area = 1,089 in² × 1/9
New Surface Area = 1,089 in² / 9
New Surface Area = 121 in²
Therefore, the new surface area of the square pyramid when the dimensions are multiplied by 1/3 will be 121 in².
Select the correct answer.
What is the domain of the function f(x) = x^2 + 3x + 5?
A.
all whole numbers
B.
all positive real numbers
all integers
D.
all real numbers
Answers
Answer:
All real numbers
Step-by-step explanation:
f(x) is a polynomial and is well defined for all real values of x
Domain is x ∈ R
The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers
Domain of functionThe domain of a function exists as the set of all possible inputs for the function.A function with a fraction with a variable in the denominator. To discover the domain of this kind of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign.It is provided that,
[tex]$$f(x)=x^{2}+3 x+5$$[/tex]
This exists as the equation of a vertical parabola opens upward.
The vertex exists at a minimum
utilizing a graphing tool
The vertex is the point (-1.5,2.75)
The range is the interval -------> [2.75.∞)
[tex]y \geq 2.75[/tex] ------->All real numbers greater than or equal to 2.75
The domain is the interval -------> (-∞,∞) -----> All real numbers
Hence, The domain of the function[tex]$$f(x)=x^{2}+3 x+5$$[/tex] is (D). All real numbers.
To learn more about the Domain of function refer to:
https://brainly.com/question/13856645
#SPJ2
help me..it has to be rounded to the tenths
Answers
Answer:
10.2 cm²
Step-by-step explanation:
The area (A) of a regular hexagon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
Perimeter = 6 × 2 = 12 cm ( hexagon has 6 sides ), hence
A = 0.5 × 12 × 1.7 = 6 × 1.7 = 10.2 cm²
Answer:
10.2cm^2
Step-by-step explanation:
An automobile dealer has 10 Fords, 7 Buick’s, and 5 Plymouth’s in her used-car lot. If a person purchases a used car, find the probability that it is a Ford or Buick.
Answers
Answer:
The probability is [tex]0.7727[/tex] or [tex]77.27\%[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem we have
[tex]x=10+7=17[/tex]
[tex]y=10+7+5=22[/tex]
substitute
[tex]P=\frac{17}{22}=0.7727[/tex]
Convert to percentage
[tex]0.7727*100=77.27\%[/tex]
Some months have 30 days, some months have 31 days; how many have 28?
Answers
All of the months have 28 days. Although some may have more then 28 days they always have AT LEAST 28 days
Hope this helped!
~Just a girl in love with Shawn Mendes
which statement justifies why angle EBC measures 90?
Answers
Answer:
The sum of the measures of two complementary angles is 90 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
In this problem we have that
m∠ABD and m∠DBC are complementary
so
m∠ABD + m∠DBC=90° -----> by complementary angles
and
(m∠ABD + m∠DBC)+m∠EBC=180° -----> by a linear pair
Find the measure of angle EBC
substitute the given values
(90°)+m∠EBC=180°
∠EBC=180°-90°=90°
Answer:
Statements B and A
Step-by-step explanation:
GIven are some statements and we have to identify the one which justifies the measure of angle EBC as 90 degrees.
We have to use two statements here for the complete proof
B) SInce given that angles ABD and DBC are complementary we have sum of these angles = angle ABC = 90 degrees
A)since linear pair form supplementary angles and since one pair ABC =90 other pair EBC has to be 90 degrees.
Which combination of integers can be used to generate the Pythagorean triple (5,12,13)
Answers
Answer:
x=3 and y=2
Step-by-step explanation:
The pythagorean triples are generated by two integrers x and y that can be found by solving the following system of equations:
[tex]\left \{ {{x^{2}-y^{2}=5}\atop {2xy=12}} \atop {x^{2}+y^{2}=13}}\right.[/tex]
Solve the system of equations, and we get that the solution is x=3 and y=2.
Therefore, the combination of integrers that ca be used to generate the pythagorea triple are: x=3 and y=2
Answer:
[tex]x=3[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
The Pythagorean triples can be generated by two values x, y, and a given system of equations:
[tex]x^{2}-y^{2}=5\\2xy=12\\x^{2}+y^{2}=13[/tex]
You can see that each coordinate of the triple is included in each equation.
Remember that Pythagorean triples refers to the values of each side of a right triangle, where is used the Pythagorean Theorem. But, at a higher level, to construct this triples we use the system of equations, with two integers x and y., like this case.
Now we solve the system, the best first step is to just sum the first and third equations, because they have like terms:
[tex]2x^{2}=18\\x^{2}=\frac{18}{2}=9\\x=3[/tex]
Now, we just replace it in the second equation:
[tex]2xy=12\\y=\frac{12}{2x}=\frac{6}{3}=2[/tex]
Therefore the integers that generate the Pythagorean triple [tex](5,12,13)[/tex] are [tex]x=3[/tex] and [tex]y=2[/tex]