1. The linear function that models the town's population is given as follows:
P(t) = -640t + 26,700.
i. The domain for the function is of: t ≥ 0.
ii. The range for the function is of: 0 ≤ P(t) ≤ 26700.
iv. The slope of -640 means that the population decayed by an average of 640 habitants each year.
What is the linear function?The function is defined as follows:
P(t) = mt + b.
In which the parameters are listed as follows:
m is the slope, representing the rate of change.b is the intercept, representing the initial population.In 10 years, the population decreased from 26,700 to 20,300, hence the slope is of:
m = (20,300 - 26,700)/10 = -640.
Considering the population in 1995, the intercept is given as follows:
b = 26,700.
Hence the equation is given by:
P(t) = -640t + 26,700.
The domain and range of the function are given as follows:
i. The domain for the function is of: t ≥ 0, as it is the number of years after 1995.ii. The range for the function is of: 0 ≤ P(t) ≤ 26700, as it is the values assumed by the population.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Answer:b-of the AAS congruence theorem.
Step-by-step explanation: I guessed and got it right
The element astatine is created during the radioactive decay process of uranium. Based on the location of astatine in group 17 (VIIB) of the periodic table of the elements, which of these is a characteristic of astatine?
Compared to other halogens, astatine is rare and highly radioactive due to its unstable nuclei.
Define the characteristic of astatine?As a member of Group 17 (also known as the halogen group or VIIA), astatine shares several characteristics with other halogens such as fluorine, chlorine, bromine, and iodine. These characteristics include:
Having seven valence electrons in their outermost energy level.High reactivity due to their tendency to gain an electron to form a stable negative ion.Having similar chemical properties, such as forming diatomic molecules and acidic solutions when dissolved in water.Existing in different physical states at room temperature (For instance, iodine is a solid, bromine is a liquid, and fluorine and chlorine are gases).However, compared to other halogens, astatine is rare and highly radioactive due to its unstable nuclei. It has no stable isotopes and its properties have not been well-studied due to its scarcity and short half-life.
To know more about astatine, visit:
https://brainly.com/question/23932284
#SPJ1
Calculate the scale factor of LMN to OPQ. Enter answer as a whole
number or as a fraction in lowest terms, using the slash mark ( / ) for the
fraction bar.
Step-by-step explanation:
the scale factor is 1/1
both triangles are similar, and the scale factor is 1/1
Which expression is NOT equivalent to 60+1260+12?
Answer:60+1260+13 isnt equivalent
Step-by-step explanation:
what is a Pythagoras theorem
The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
What is mathematical representation of Pythagoras theorem?From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;
C² = a²+b²
Where:
'C' represents the hypotenuse which is the longest part of the triangle and is always diagonal connecting the two other points.'a' represents the perpendicular length that forms the angle 90° of the right angle triangle.'b' represents the base of the triangle.Learn more about Pythagorean formula here:
https://brainly.com/question/28981380
#SPJ1
i need help!
Check all that are solutions to −0.25 ≤ 0.5sin(2x) and over 0° ≤ x ≤360°
Answer:
A C E
Step-by-step explanation:
Math help please and thanks
Answer:
idek and i dont ;like how this is working!
Step-by-step explanation:
For the problem 4 x 2/3, Dawn says the answer is 6. Marry Anne says the answer is 3 1/3. Stacy says it is 2 2/3. Who is correct?
Answer:
Stacy is correctStep-by-step explanation:
Solving the problem
4×2/3 = 8/3 = 2 2/3Stacy is correct
Answer:
\(\huge 4 \times \frac{2}{3} = \frac{8}{3} =\boxed{2 \frac{2}{3} }\)
Hence, Stacy is correct.Question 1 (10 points). (a) Explain the difference between linear and logistic regression. (Explain at least two differences and one similarity in detail). (b) Give an example of a modeling problem (ie, using X to predict Y, where X and Y are real life examples) for each type.
Answer:
(a) Linear regression is used to estimate dependent variable which is continuous by using a independent variable set. Logistic regression we predict the dependent variable which is categorical using a set of independent variables.
(b) Finding the relationship between the Number of doors in the house vs the number of openings. Suppose that the number of door is a dependent variable X and the number of openings is an independent variable Y.
Step-by-step explanation:
(a) Linear regression is used to estimate dependent variable which is continuous by using a independent variable set .whereas In the logistic regression we predict the dependent variable which is categorical using a set of independent variables. Linear regression is regression problem solving method while logistic regression is having use for solving the classification problem.
(b) Example: Finding the relationship between the Number of doors in the house vs the number of openings. Suppose that the number of door is a dependent variable X and the number of openings is an independent variable Y.
If I am to predict that increasing or reducing the X will have an effect on the input variable X or by how much we will make a regression to find the variance that define the relationship or strong relationship status between them. I will run the regression on any computing software and check the stats result to measure the relationship and plots.
Solve the equation using square roots. Write your answer in simplest form.
Question in picture
Answer:
The solutions to the quadratic equation involving square roots are:
\(x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8\)
Step-by-step explanation:
Given the equation
\(\frac{1}{4}\left(x-8\right)^2+8=1\)
subtract 8 from both sides
\(\frac{1}{4}\left(x-8\right)^2+8-8=1-8\)
\(\frac{1}{4}\left(x-8\right)^2=-7\)
\(\left(x-8\right)^2=-28\)
\(\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)
solving
\(x-8=\sqrt{-28}\)
\(x-8=\sqrt{-1}\sqrt{28}\)
\(x-8=\sqrt{28}i\) ∵ \(\sqrt{-1}=i\)
\(x=2\sqrt{7}i+8\)
similarly solving
\(x-8=-\sqrt{-28}\)
\(x-8=-2\sqrt{7}i\)
\(x=-2\sqrt{7}i+8\)
Therefore, the solutions to the quadratic equation involving square roots are:
\(x=2\sqrt{7}i+8,\:x=-2\sqrt{7}i+8\)
How much would it cost for a customer to purchase 20 subscriptions for each of their 20 employees after a free 30-day trial period, with each subscription costing $10 per month for a yearly commitment? Additionally, they will need 1 extra subscription for a different service for every two employees, with each of these subscriptions costing $5 per month for a yearly commitment. What would be the total cost for the customer for the entire year
The total cost for the customer for the entire year is $48,600.
How to the total cost for the customer for the entire yearThe customer wants to purchase 20 subscriptions for each of their 20 employees, so they need a total of 20 x 20 = 400 subscriptions.
Each subscription costs $10 per month for a yearly commitment,
so the cost for one subscription for a year would be $10 x 12 = $120.
Therefore, the total cost for 400 subscriptions for a year would be $120 x 400 = $48,000.
In addition, they need 1 extra subscription for a different service for every two employees, so they need 20 / 2 = 10 extra subscriptions.
Each extra subscription costs $5 per month for a yearly commitment, so the cost for one extra subscription for a year would be $5 x 12 = $60.
Therefore, the total cost for 10 extra subscriptions for a year would be $60 x 10 = $600.
Adding the cost of the extra subscriptions to the cost of the regular subscriptions, the total cost for the customer for the entire year would be $48,000 + $600 = $48,600.
Learn more about total cost at:https://brainly.com/question/25109150
#SPJ1
(−12 3/4) ÷ (−5 1/2)
Answer:
\(\frac{51}{22}\)
\(2\frac{7}{22}\)
Step-by-step explanation:
Answer:
2 7/22
Step-by-step explanation:
(−12 3/4) ÷ (−5 1/2)
(−12 3/4) = -51/4
(−5 1/2) = -11/2
-51/4 ÷ -11/2
= 51 × 2 / 4 × 11
= 51/22
= 2 7/22
A class of 118 students went on a field trip. They took 10 vehicles, some vans (x) and some buses (y). Find the number of vans and the number of buses they took if each van holds 6 students and each bus hold 35 students. Express your answer as a solution set {x, y} or (x, y).
Answer:
Solve for x+y=10
6x+35y=118
Step-by-step explanation:
I would solve it for you but my calculator isn't working rn. You could also use a picture calculator and it will give you a more in depth explanation. Hope this helps!
Answer:
{ 8, 2}
Step-by-step explanation:
Basic algebra, the object which is not in a set quantity, which we have to find, is the "some vans" and the "some buses"
So let the number of van be x
Let the number of buses be y
So, since there are 10 vehicles,
x+y=10
Makes sense right
Now, it says that every car can carry 6 students, and every van can carry 35 students, so in another way, we could represent this by saying
6 x Number of van + 35 x Number of buses
thus,
6x + 35y
And since 118 students went on the field trip, this means that
6x +35y = 118
So now we have two equations,
x + y = 10
6x + 35y = 118
We can solve this with substitution
x + y = 10
x = 10 - y
Thus, x = 10-y
Put this in this
6(10-y)+ 35y= 118
60-6y+35y=118
60+29y=118
29y=118-60
29y= 58
y = 58/29
y = 2
Thus, the number of buses, y, is 2
Now since there are 10 vehicles, and 2 are buses, then the other are 8 van
Jenna made 10 cookies on blah buster day. She ate one of them her brother 0.2o f the cookies her little sister ate 1/5 of them how many cookies were left
Answer:
Jenna has 6 and 4/5 cookies left.
Step-by-step explanation:
Jenna starts with 10 cookies. She eats 1, her brother eats 2, and her little sister eats 1/5. If you add up all the cookies they ate. that would be 3 1/5 cookies they ate. So, 6 and 4/5 cookies are left.
ps. give me brainliest pls
Which expressions are completely factored?
Select each correct answer.
Responses
16a5−20a3=4a3(4a2−5)
16 a begin power 5 end power minus 20 a cubed equals 4 a cubed left parenthesis 4 a squared minus 5 right parenthesis
12a3+8a=4(3a3+2a)
12 a cubed plus 8 a equals 4 left parenthesis 3 a cubed plus 2 a right parenthesis
30a6−24a2=3a2(10a4−8)
30 a begin power 6 end power minus 24 a squared equals 3 a squared left parenthesis 10 a begin power 4 end power minus 8 right parenthesis
24a4+18=6(4a4+3)
24 a begin power 4 end power plus 18 equals 6 left parenthesis 4 a begin power 4 end power plus 3 right parenthesis
The expressions that are completely factored are:
16a5−20a3=4a3(4a2−5) is correct.12a3+8a=4(3a3+2a) is correct.24a4+18=6(4a4+3) is correct.Why are they considered to be correct?The expressions are considered correct because they have been completely factored, meaning they have been written in the form of "a common factor times another expression". This means that the expression on the right side of the equal sign can be simplified into its simplest form.
For example, in the expression 16a5−20a3=4a3(4a2−5), the 4a3 factor is common to both 16a5 and 20a3, so it can be factored out. The expression then becomes 4a3 times (4a2−5), which is the completely factored form.
Similarly, in the expression 12a3+8a=4(3a3+2a), the factor of 4 is common to both the expressions on the right side, so it can be factored out. This results in the completely factored form of 4 times (3a3+2a).
learn more about factorization: https://brainly.com/question/10718512
#SPJ1
Answer:
16a^5−20a^3=4a^3(4a^2−5)
and
24a^4+18=6(4a^4+3)
Step-by-step explanation:
63=7p can someone solve this?? i mean i know one step equations but im still confused on this one
Answer:
p= 9
Step-by-step explanation:
you can rewrite the equation as 7p = 63 if that makes more sense for you
then divide both sides by 7
you get 9
help me please :)))))
Answer:
a number. 5. b number. 7 fourth one. c number. 1. d number 0
Step-by-step explanation:
mark me as brainliest
You and your best friend are meeting at
Starbucks on the corner
of Asbury Avenue and
11th Street. Presently, you are on 11th Street
eight miles north of Starbucks. Meanwhile, your
best friend is on Asbury Avenue seven miles
west of Starbucks. How far away from each other
are you and your best friend? Round your
answer to the nearest tenth.
Answer:
10.6 miles
Step-by-step explanation:
The corner where Starbucks is located could be considered to be the right angle in a right triangle having legs of 8 miles (distance to you) and 7 miles (distance to your friend). The straight-line distance (d) from you to your friend is the hypotenuse of that triangle. Its length can be found from the Pythagorean theorem.
d² = 8² +7²
d² = 64 +49 = 113
d = √113 ≈ 10.6
You and your friend are about 10.6 miles from each other.
What is GTPAL? I'm Stuck
Answer:
What does gtpal stand for? GTPAL stands for Gravidity (number of pregnancies including current), Term (number of pregnancies carried to 37+ weeks), Preterm (number of pregnancies carried between 20 and 36.6 weeks ), Abortion (number of losses prior to 20 weeks), and Living (number of living children).
Step-by-step explanation:
please help!!!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of A?
Answer:
∠ A = 59°
Step-by-step explanation:
ABCD is a cyclic quadrilateral.
the opposite angles in a cyclic quadrilateral sum to 180° , then
∠ A + ∠ C = 180°
∠ A + 121° = 180° ( subtract 121° from both sides )
∠ A = 59°
Solve for X (look at photo for answer choices)
The numerical value of x in the inscribed angle and intercepted arc is 4.
What is the numerical value of x?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
From the image:
Inscribed angle XZY = 14x + 4
Intercepted arc XY = 30x
Value of x = ?
Plug these values into the above formula and solve for x.
Inscribed angle = 1/2 × intercepted arc.
14x + 4 = 1/2 × 30x
14x + 4 = 15x
15x = 14x + 4
15x - 14x = 4
x = 4
Therefore, x has a value of 4.
Option D) 4 is the correct answer.
Learn more about inscribed angles here: brainly.com/question/29017677
#SPJ1
Solve the following equation, answer as a reduced, mixed number. Then place the correct number in the box provided. 4(7 - 3x) = 7(4 - 2x)
Answer:
x = 0
Step-by-step explanation:
4(7 - 3x) = 7(4 - 2x)
28 - 12x = 28 - 14x distributed
28 + 2x = 28 added 14x to both sides
2x = 0 subtracted 28 from both sides
x = 0 divided both sides by 2
Step-by-step explanation:
Skylar models the volume of a popcorn box as a right rectangular prism and the box can hold 69 cubic inches of popcorn when it is full. Its width is 33 in and its height is 5 3/4 in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer:
4/11 of an inch (about .4 of an inch)
Step-by-step explanation:
\(l \times 33 \times 5.75 = 69\)
\(189.75l = 69\)
\(l = \frac{69}{189.75} = \frac{4}{11} = .3636\)
So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.
Solve the inequality 1.5g + 12.5 ≤ 35.
Answer:
Inequality Form: g≤15
Interval Notation: (−∞,15]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Detailed explanation and solution is available in the photo. I wish you success. If there is something you do not understand, please do not hesitate to ask.
Find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field T(x,y). Temperature Field: T(x,y)= 100 - x^(2) - 2y^(2).
As a result, the following parametric equations describe the motion of the heat-seeking particle: x = a - 2t and y = b - 4t
As per the question given,
To find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field T(x,y) = 100 - x^(2) - 2y^(2), we need to use the gradient vector of T(x,y).
The gradient of T(x,y) is given by:
∇T(x,y) = (-2x, -4y)
The heat-seeking particle moves in the direction of maximum increase of temperature, so it moves in the direction of the gradient vector, that is, (-2x, -4y).
To find the path of the particle, we need to integrate the gradient vector starting at point P = (a,b), where a and b are the coordinates of the point on the metal plate where the particle is placed.
So the path of the heat-seeking particle is given by the following parametric equations:
x = a - 2t
y = b - 4t
where t is the parameter that represents time.
These equations represent a straight line in the direction of the gradient vector of T(x,y). The particle moves from point P in the direction of the gradient vector, with a speed proportional to the magnitude of the gradient vector.
For such more questions on Temperature
https://brainly.com/question/25677592
#SPJ4
-2(x + 2) =
Please help
Answer:
-2x - 4
Step-by-step explanation:
Is your expression
-2 x x = -2x
-2 x 2 = 4
therefore, your expression would be:
-2x - 4
Answer:
-2(x + 2)= -2x - 4
Step-by-step explanation:
A theater production charges $21 for adult tickets and $15 for student tickets. If the production sold 102 tickets for its opening night and made $1,932 in ticket sales, how many of each type of tickets were sold?
Answer:
67 adult tickets
35 student tickets
How many solutions does this equation have? 8m = 10 + 8m
Answer:
8m-10=8-m
We move all terms to the left:
8m-10-(8-m)=0
We add all the numbers together, and all the variables
8m-(-1m+8)-10=0
We get rid of parentheses
8m+1m-8-10=0
We add all the numbers together, and all the variables
9m-18=0
We move all terms containing m to the left, all other terms to the right
9m=18
m=18/9
m=2
can someone help me with this question?
Help a bab out, please?
Answer:
sorry yrr im also not sure
You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,
determine how long it will take for the object to hit the ground below. NEAREST TENTH
You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second, 64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.
What is law of conservation of energy?Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.
Given that,
Height of the cliff, h= 55 Foot
Initial speed of the projectile, u = 85 m/s
Let, the projectile hit the ground with velocity "v"
Applying the law of conservation of energy,
mgh + 1/2 mu² = 1/2 mv²
or, m (gh + 1/2 u²) = 1/2 mv²
or, (gh + 1/2 u²) = 1/2 v²
or, 10 × 55 + (1/2 × (55)²) = 1/2 v²
or, 550 + 1512.5 = 1/2 v²
or, 2062.5 = 1/2 v²
or, 4125 = v²
or, v = 64.23 feet/second
To know more about law of conservation of energy refer to:
https://brainly.com/question/23590186
#SPJ1