The population in the year 2000 is 21
How to determine the population in 2000?The function is given as:
P(t) = 21e^0.01823t
The year 2000 is 0 years after 2000.
This means that
t = 0
So, we have:
P(0) = 21e^(0.01823 *0)
Evaluate the product
P(0) = 21e^0
Evaluate the expression
P(0) = 21
Hence, the population in the year 2000 is 21
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The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.
Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.
Which is correct regarding the angles of the triangle?
mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX
Answer:
Option (2)
Step-by-step explanation:
The angle opposite the shortest side is the smallest and the angle opposite the longest side is the largest.
Since m is greater than or equal to 6, we know that:
2m+3 > m+8 > m-3
For 7,440 blank shares could have been bought ?
Answer:
$2,000
Step-by-step explanation:
7,440/3.72
please help meeee ………..
Answer:
x = 5
Step-by-step explanation:
The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.
Application[tex]\dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}[/tex]
__
Additional comment
Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.
[tex]\log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5[/tex]
What is the solution to the equation 2^x+4 -12=20
Answer:
2^x = 28Step-by-step explanation:
What is the solution to the equation?
[tex]2^{x}[/tex] + 4 - 12 = 20
[tex]2^{x}[/tex] = 20 - 4 + 12
[tex]2^{x}[/tex] = 16 + 12
[tex]2^{x}[/tex] = 28
Answer:
x-1
Step-by-step explanation:
because i said so
if m²+1/m = 4, find m²+ 1/m²
A) The solution to m² + (1/m²) is gotten as; 14
B) The solution to m³ + ¹/₃ is gotten as; 52.312
How to simplify Algebra?We are given the algebraic equation;
(m² + 1)/m = 4
Multiply through by m to get;
m² + 1 = 4m
m² - 4m + 1 = 0
From online quadratic equation calculator, we have;
m = 3.732 or 0.268
A) Thus;
m² + (1/m²) = 3.732² + (1/3.732²)
⇒ 14
B) m³ + ¹/₃ gives;
3.732³ + (1/3) = 52.312
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Select the equivalent expression. 2^-4=
Choose 1 answer
a)1/2^4
b)-2^4
c)(-2)^4
Answer: A 1/2 ^4
Step-by-step explanation:
Answer:
a)1/2^4
Step-by-step explanation:
First solve 2^-4.
Use negative power rule: x^-a = 1/xa
⇒ 1/2^4
Simplify 2^4 to 16
⇒ 1/16
Just evaluate the other options.
The first one is correct.
Here's why:
⇒ Simplify 2^4 to 16.
⇒ 1/16
They have the same steps, therefore making Option A correct.
Note: This is the longer way, there is a easier way of dealing with these types of problems. Example: Without using a calculator problem.
In your opinion, which is the best and simplest way to factor polynomials (including quadratics)? Explain why you chose this method compared to other methods. Are there some exceptions to this, maybe a polynomial that might factor better with another method?
The simplest way to factor polynomials is to use the greatest common factor.
How to illustrate the polynomial?It should be noted that the polynomial simply means the expression of more than two algebraic terms.
In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.
Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.
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3. Find the point of intersection of the graphs for each system. a.2x + 2y = 3 and 6x-6y = -1
Given :
2x + 2y = 3 (Equation #1)6x - 6y = -1 (Equation #2)Multiply Equation #1 by 3 :
3(2x + 2y) = 3(3)6x + 6y = 9 (Equation #3)Add Equations 2 and 3 :
6x - 6y + 6x + 6y = -1 + 912x = 8x = 2/3Now, input x in Equation #3 to find y :
6(2/3) + 6y = 94 + 6y = 96y = 5y = 5/6∴ Hence, the point of intersection is (2/3, 5/6).
Multiply:
-9w(w + 10)
asap answer plsss
Answer:
-9w^2-90w
Step-by-step explanation:
You just use the distributive property and watch the negatives and positives.
[tex]\huge\boxed{-9w^2-90w}[/tex]
Distribute [tex]-9w[/tex] to both [tex]w[/tex] and [tex]10[/tex] as shown in the attached image. Then, just simplify the terms with multiplication.
[tex](-9w)\cdot w+(-9w)\cdot10\\\boxed{-9w^2-90w}[/tex]
A circus is composed of acrobats, ballerinas, clowns, and dogs. The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Twice the combined number of acrobats and ballerinas is five more than three times the number of clowns. If the number of dogs is one more than the number of clowns, how many people and animals belong to the circus
If we make appropriate equation then we can find that there are 21 people and animals belong to the circus.
Given The number of acrobats and ballerinas, minus the number of clowns, is one fewer than the number of dogs. Double the combined number of acrobats and ballerinas is five more than three times the number of clowns.
We have to find total people and animals belong to the circus.
An equation is relationship between variables that are expressed in equal to form. It is solved to find the variables in equal to form Equations of two variables look like ax+ by=c.
let the number of acrobats be x, ballerinas be y, clowns be z, clowns be u.
According to given information in question the equations are:
x+ y-z=u-1-----------------------1
2(x+ y)=3z+5-------------------2
u=z+1----------------------------3
Put the value of u from 3 in 1
x+y- z=z+1-1
x+y-2z=0
from 2
z=2x+2y-5/3
put the value of z in x+y-2z=0
x+y-2(2x+2y-5/3)=0
-x-y+10=0
x+ y=10-------------------------4
put put the value of x+y=10 in 1
10-z=u-1
u+z=11-----------------------------5
solving 3
u-z=1------------------------6
Now add 5&6
u+z+u-z=11+12
2u=12
u=6
Put the value of u in 6
6-z=1
z=5
From above we get x+y=10, u=6, z=5
Add all three we get the total number of people and animals belong to circus.
x+y+u+z=10+6+5
=21
Hence there are total 21 people and animals belong to the circus.
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What is the inverse of function ??
f(x) = 64x³ - 1
Answer:
The inverse of the function f(x) = 64x³ - 1 is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]
Step-by-step explanation:
First replace x with y.
[tex]x=64y^3-1[/tex]
Then solve for y.
[tex]y^3=\frac{x+1}{64}[/tex]
Cube root both sides.
[tex]y=\frac{\sqrt[3]{x+1}}{4}[/tex]
Hence, the inverse is [tex]\frac{\sqrt[3]{x+1}}{4}[/tex]
There were three parts to Rita's race. She ran the first part, which was 4/9
of the total distance, in 20 minutes. She ran the second part, which was 2/5
of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at a speed of 300 meter per minute.
A) How long was the first part of the race? What was Rita's speed in that section of the race?
B)How long was the second part of the race? What was Rita's speed in that section of the race?
Answer:
300 meters per minute
Step-by-step explanation:
Step 1
Determine the fraction of the total distance for each part of the race.
Given:
1st part of race = 4/9 of total distance
2nd part of race = 2/5 of remaining distance
Step 2
Determine the distance of the third part of the race.
Given:
time = 15 minutes
speed = 300 meters per minute
Step 3
If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:
Step 4
Determine the distance of the 1st part of the race:
Step 5
Determine the speed of the 1st part of the race:
Given:
time = 20 minutes
distance = 6000 m
Which expression is equivalent to 14 times 14?
2 squared
2 Superscript 14
14 squared
14 Superscript 14
Answer:
[tex]14^{2}[/tex]
Step-by-step explanation:
14*14
14 is the base. We are multiplying 14 two times. Two would be the exponent
14 ^2
Find the volume of the prism.
Answer:
216kmStep-by-step explanation:
The formula for finding the volume of a triangular prims is:
0.5 * b * h * length, where b is the length of the base of the triangle, h is the height of the triangle and length is prism length.
So, let's substitute those variables with the base length, height length, and prism length
The base length is 6km, the height length is 8km, and the prism length is 9km
So, we get:
0.5 * 6 * 8 * 9
= 1/2 * 6 * 8 * 9
= 1/2 * 48 * 9
= 1/2 * 432
= 216
The volume of this prism is 216km.
19. What is the coordinate for the vertex of the function f(x)=-16x² + 64x?
Answer:
vertex = (2, 64 )
Step-by-step explanation:
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = - 16x² + 64x ← is in standard form
with a = - 16, b = 64, c = 0 , then
x = - [tex]\frac{64}{-32}[/tex] = 2
substitute x = 2 into f(x) for corresponding y- coordinate
f(2) = - 16(2)² + 64(2) = - 16(4) + 128 = - 64 + 128 = 64
vertex = (2, 64 )
Maria bought a stock for x dollars, and she sold it at a profit of 20 %. Write a
mathematical expression for the selling price.
Answer: 1.2x
Step-by-step explanation:
Profit = Selling price - Cost
She bought the stock at a cost of x dollars
Her profit was 20% of that, which is 0.2x dollars
Selling price = Profit + Cost = x + 0.2x = 1.2x
PLEASE HELP
This table contains an Arithmetic Sequence. Find the missing terms in the table.
D
A fabric mill produces 4953 metres of fabric in a day. How much fabric will it
365 days]
produce in a year? [1 year =365 days
The fabric mill produce 1,807,845 meters of fabric in 365 days.
A fabric mill produces 4953 meters of fabric in a day.
What is simplification?operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.
We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845
Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.
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What is the range of the function shown in this table?
OA. (3, 4), (4, 4), (5, 2), (6, 5)
OB. (3,4)
O C. (2, 4, 5)
O D. (3, 4, 5, 6}
Answer: A
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
The range is just the y-values. You don't have to write any of the repeated values. You do need to write them in numerical order.
4, 4, 2, 5
becomes
2,4,5
Please need help ASAP
Answer:
Can u please upload more clearer pictures ?
You buy 12 packages of discounted socks for a total cost of $85.50, which includes a 5% discount.
Before the discount, how much did a single package of socks cost?
a.)
$7.50
b.)
$4.75
c.)
$6.78
d.)
$10.68
Answer:
a) $7.50
Step-by-step explanation:
The total cost of $85.50 includes a 5% discount, so 95% of what price is $85.50?
[tex].95x = 85.50[/tex]
[tex]x = 90[/tex]
So the original price is $90. Divide this by 12, obtaining $7.50.
Answer:
a)$7.5
Step-by-step explanation:
Solution:
Let X represents socks
Given,
Selling price (SP) of 12x=$85.50
Discount precent (d%)=5%
So,
SP=(100-d)% of MP. [this formula really exist believe it or not]
85.50= (100-5)/100 ×MP
or, 85.50×100 =95×MP
or, 8550/95=MP
So,MP=$90
Now At last ,
cost of 1 shocks before discount is 90/12
which is $7.50 ans√
Which explains why the graph is not a function? It is not a function because the points are not connected to each other. It is not a function because the points are not related by a single equation. It is not a function because there are two different x-values for a single y-value. It is not a function because there are two different y-values for a single x-value.On a coordinate plane, solid circles appear at the following points: (negative 2, negative 5), (negative 1, 3), (1, negative 2), (3, 0), (4, negative 2), (4, 4).
The given points of the expression is not a function because there are two different y-values for a single x-value.
Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)
Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.
We have been given points (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).
These are not points of a function because of a simple reason that it has two values of y for each one value of x.
Value of relation at x=-2 is -5.
Value of relation at x=-1 is 3.
Value of relation at x=1 is -2.
Value of relation at x=3 is 0.
Value of relation at x=4 is -2.
Value of relation at x=4 also equal to 4.
It has two values at x=4 one is -2 and other one is 4.
Hence the relation is not a function because there are two different y-values for a single x-value.
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The given points of the expression is not a function because there are two different y-values for a single x-value.
Given The points are : (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4)
Function refers to a relation or expression involving one or more variables. In a function each value of x corresponds to each value of y. A relation which is having two or more values of y for x values is not a function.
We have been given points (-2,-5), (-1,3), (1,-2) , (3,0) ,(4,-2) (4,4).
These are not points of a function because of a simple reason that it has two values of y for each one value of x.
Value of relation at x=-2 is -5.
Value of relation at x=-1 is 3.
Value of relation at x=1 is -2.
Value of relation at x=3 is 0.
Value of relation at x=4 is -2.
Value of relation at x=4 also equal to 4.
It has two values at x=4 one is -2 and other one is 4.
Hence the relation is not a function because there are two different y-values for a single x-value.
What effect does it have when there are exceptions to the overall trend in a relationship between two variables?
Option 3. The effect that it has when there are exceptions to the overall trend between two variable is that It is irrelevant to the relationship.
What is a trend between two variables?This is used in statistics to show that there is the existence of two variables that are positively correlated.
These two variables would then have a positive slope trend line. Hence the answer to the question is option 3.
Complete questionWhat effect does it have when there are exceptions to the overall trend in a relationship between two variables?
O It increases the relationship
O It decreases the relationship
O It is irrelevant to the relationship.
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Watch help video
Mason is a songwriter who collects royalties on his songs whenever they are played in
a commercial or a movie. Mason will earn $30 every time one of his songs is played in
a commercial and he will earn $80 every time one of his songs is played in a movie.
Mason earned a total of $470 in royalties on 9 commercials and movies. Write a
system of equations that could be used to determine the number of commercials and
the number of movies on which Mason's songs were played. Define the variables that
you use to write the system.
Answer:479
Step-by-step explanation:470+9=479
We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as → 30x + 80y = 470 and x + y = 9. The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
What is equation modelling?
Equation modelling is a method of writing a mathematical relation from a mathematical statement for mathematical analyses of the problem given.
Given is Mason who collects royalties on his songs whenever they are played in commercials or movies.
Assume that his song played in 'x' commercials and 'y' movies.
Cost per song when played in commercial = $30
Then for 'x' commercials, total cost will be = $30x
Cost per song when played in movie = $80
Then for 'y' movies, total cost will be = $80y
Total money earned through both = $470
We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as -
30x + 80y = 470
The total number of commercials and movies combined -
x + y = 9
The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
Therefore, We can write the system of equation that determines the number of commercials and the number of movies on which Mason's songs were played as → 30x + 80y = 470 and x + y = 9. The variables used in the system of equations are -
x - Number of times his song played in a commercial
y - Number of times his song played in a movie.
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ABC is a triangle. ACD is an isosceles triangle. Find ACB and ABC.
Answer:
∠ ACB = 128° and ∠ABC = 32°
Step-by-step explanation:
∠ ADC = ∠ CAD (base angles theorem)
∠ ACD = 82° (angles in a triangle add to 180°)
∠ ACB = 128° (angles around a point add to 360°)
∠ ABC = 32° (angles in a triangle add to 180°)
The radius of a sphere is 3 inches. Which represents the volume of the sphere?
• 12t cubic inches
• 367 cubic inches
• 647T cubic inches
• 817 cubic inches
Answer:
Step-by-step explanation:
The formula for the volume of a sphere of radius r is V = (4/3)(pi)r^3.
Here, with r = 3 in, the volume is
V = (4/3)(3.14)(3 in)^2, or V = 36(pi)(27 in)^3 = 36pi in^3
One can convert temperature from fahrenheit into newton using the formula . what is the temperature in fahrenheit corresponding to n degrees newton?
Which exponential function has a faster rate f(x)=5^x or g(x)=(1/3)^x. How do you know?
Answer:
f(x)
Step-by-step explanation:
This question isn't to difficult, since all you need to know is: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. If the you're not quite sure why this is true, I'll try to express this in another way. [tex](\frac{a}{b})^x=\frac{a}{b}*\frac{a}{b}*\frac{a}{b}...\text{ x amount of times}[/tex], and as you may know when multiplying fractions, you simply multiply the numerators by the numerators and the denominators by the denominators, this means that you can simplify it to: [tex]\frac{a*a*a...\text{ x amount of times}}{b*b*b...\text{ x amount of times}}[/tex] this is literally what an exponent is which is why you can distribute the exponent as such: [tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]. The next thing you need to know is that: [tex]1^x=1[/tex] for any real number. This is you can express this as: [tex]1*1*1...\text{ x amount of times} = 1[/tex], since 1 times 1 times 1, will always remain 1. You may think this will not apply for rational exponents, but it still does since: [tex]1^{\frac{a}{b}}=\sqrt[b]{1}^a[/tex], and no matter what b is, it's going to be 1. The square root of 1, is 1..., the cube root of 1 is 1.... This is because the very definition of a radical is what number times times it self index amount of times is equal to the number under the radical, and no matter how many times you multiply 1, you're going to get 1. If that's a bit confusing what I'm saying is: [tex]\sqrt[n]{b}\implies\text{?}^n=b[/tex].
Anyways hopefully you understand that, if not I'm sorry if I went a bit overboard trying to explain it. Anyways all you need to really know is that: [tex](\frac{1}{3})^x=\frac{1^x}{3^x}=\frac{1}{3^x}[/tex]. So this means as x increases, all you're really doing is increasing the denominator which is decreasing the number. The f function has an integer as a base, so the function will overall be increasing. This is not true for g(x) since as x increases the y-value decreases. So this means that f(x) has a faster rate. This is because the g(x) has a horizontal asymptote, since as x approaches infinity, g(x) approaches 0, since the denominator is increasing towards infinity. So the rate of change will be slowing down as x increases, since there is only so much the g(x) can change, since it has a horizontal asymptote. This is not true for f(x) as it has no horizontal asymptote and just goes towards infinity. So the f(x) has a faster rate.
To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym.
A triangle has points gym, Lin apostrophe s house, and lecture hall. The distance between the lecture hall and gym is 910 feet. The distance between the gym and Lin apostrophe s house is 615 feet. The distance between the lecture hall and Lin apostrophe s house is 651 feet.
What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?
Lin walked south, creating a right triangle.
Lin walked southwest, creating an obtuse triangle.
Lin walked southeast, creating an acute triangle.
Lin walked directly east, creating a right triangle.
The general direction that Lin walked from the gym to his house is; B: Lin walked southwest, creating an obtuse triangle.
How to interpret distance bearing?
We are given;
Distance between the lecture hall and gym = 910 feet.
Distance between the gym and Lin apostrophe's house = 615 feet.
Distance between the lecture hall and Lin apostrophe's house = 651 feet.
Now, since this 3 distances form a triangle and the 3 distances are unequal, then we can call it an obtuse triangle since he walked west and then walked northwest.
Now, since he walked back to his house from the gym, we can say that he walked southwest if we picture the bearing of his first two directions.
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Which of the following could represent the interval −4 ≤ x ≤ 6?
Answer:
Step-by-step explanation:
-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6
x = {-4,-3,-2,-1,0,1,2,3,4,5,6}
Hope I helped...