Answer:
C. postulate; theorem
Step-by-step explanation:
While a "given" is taken as true without proof, and a "problem" sometimes involves an assertion that can be proven, the answer choices involving these terms are not correct here.
The dictionary definitions of "postulate" and "theorem" apply. It is useful to learn the meaning of these terms so you can understand problems and descriptions that use them.
The number of users of a cell tower in a small, developing town increased by a factor of 1.5 every year from 2010 to 2019. The function below shows the number of cell tower users, f(x), after x years from the year 2010:
f(x) = 5,000(1.5)x
Which of the following is a reasonable domain for the function?
A.2,010 ≤ x ≤ 2,019
B.0 ≤ x ≤ 5,000
C.0 ≤ x ≤ 9
D.All positive integers
Answer:
Option C) [tex]0 \leq x \leq 9[/tex]
Step-by-step explanation:
We are given the following information in the question:
The number of users of a cell tower increased by a factor of 1.5 every year from 2010 to 2019.
[tex]f(x) = 5000(1.5)^x[/tex]
where f(x) is the number of cell tower users and x is the years from the year 2010.
We have to find the domain for the given function.
Domain of a function is defined as the possible values of x the function can take, so that the function is defined.
Since this function gives the number of cell users from 2010 to 2019, thus, it is applicable from year 2010 to 2019.
x takes the value of years after 2010.
Thus for year 2010, x = 0 and for year 2019, x = 9
Thus, the domain of the given function is given by:
[tex]0 \leq x \leq 9[/tex]
I will mark brainliest to the best answer!! Please please help!!
Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution:
2x-y=4
X+2y=2
A) no solution
B) one solution
C) infinitely many solutions
Answer:
B) one solution
Step-by-step explanation:
The ratio of x-coefficient to y-coefficient is different in the two equations, so the lines have different slopes. Two lines with different slopes will always have exactly one point of intersection. You don't need to graph the equations to know there is ...
one solution
__
A graph is attached. As it happens, the two lines are perpendicular. The solution is (2, 0).
Solve for x: √3-x+13=1
Answer:
√3 + 12 = x
Step-by-step explanation:
Simplify both sides of the equation, isolating the variable.
The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars per bin, is
p
(
x
)
=
253
−
2
x
Find the cost function.
C
(
x
)
=
syntax error
Find the revenue function.
R
(
x
)
=
syntax error
Find the profit function.
P
(
x
)
=
syntax error
At what quantity is the smallest break-even point?
Answer:
Revenue , Cost and Profit Function
Step-by-step explanation:
Here we are given the Price/Demand Function as
P(x) = 253-2x
which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.
Now let us revenue generated from this demand i.e. x units
Revenue = Demand * Price per unit
R(x) = x * (253-2x)
= [tex]253x-2x^2[/tex]
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 3*x
= 3x
Fixed Cost = 6972 as given in the problem.
Hence
Cost Function C(x) = 3x+6972
Let us now find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
= [tex]253x-2x^2 - (3x+6972)\\253x-2x^2-3x-6972\\253x-3x-2x^2-6972\\250x-2x^2-6972\\-2x^2+250x-6972\\[/tex]
Now we have to find the quantity at which we attain break even point.
We know that at break even point
Profit = 0
Hence P(x) = 0
[tex]-2x^2+250x-6972[/tex]=0
now we have to solve the above equation for x
[tex]-2x^2+250x-6972 = 0[/tex]
Dividing both sides by -2 we get
[tex]x^2-125x+3486 = 0\\[/tex]
Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83
Hence we now solve the above quadratic equation using splitting the middle term method .
[tex]x^2-42x-83x+3486 = 0\\x(x-42)-83(x-43)=0\\(x-42)(x-83)=0\\[/tex]
Hence
Either (x-42) = 0 or (x-83) = 0 therefore
if x-42= 0 ; x=42
if x-83=0 ; x=83
Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.
Final answer:
The cost function is C(x) = $6972 + ($3 × x). The revenue function is R(x) = 253x - 2x². The profit function is P(x) = (253x - 2x²) - ($6972 + $3x). The smallest break-even point is where P(x) = 0.
Explanation:
To answer the student's series of questions involving cost, revenue, and profit functions, as well as the break-even quantity, we need to derive these functions from the given information and perform the necessary calculations. The unit cost to produce bins of cat food is $3, and the fixed cost is $6972. Meanwhile, the price-demand function is given by p(x) = 253 - 2x.
The cost function, C(x), which represents the total cost of producing x units, can be expressed as:
C(x) = Fixed Costs + (Variable Cost per Unit × x)
Thus, C(x) = $6972 + ($3 × x).
The revenue function, R(x), is the total income from selling x units, defined by:
R(x) = Price per Unit × x
So, using the price-demand function, R(x) = (253 - 2x)x = 253x - 2x².
The profit function, P(x), is found by subtracting the cost function from the revenue function:
P(x) = R(x) - C(x)
Therefore, P(x) = (253x - 2x²) - ($6972 + $3x).
To calculate the break-even point, where profit is zero, you need to solve the equation P(x) = 0 for x.
Step 1: Collect and organize your data.
a) Using the Super Survey Simulator, survey 10 students of your choice and gather data. Create an organized representation of your data below.
3.6
2.7
3.0
3.3
1.7
1.5
2.7
3.0, 3.0,3.8
b) What do you think the purpose of this survey is? Explain.
Answer:
To better understand the data you're working with
Step-by-step explanation:
Note that, the sample is a subset of your whole population (population here is a general definition, it could be a population of cars for example), which means that if you want to understand your population your best "bet" would be using a sample to try to estimate some unknown characteristics of your population. Let's suppose you want to estimate the true mean of your population, then you would need a sample, and if this sample is big enough you could approximate the estimative to the true mean.
It's hard to say exactly what this survey could mean, but the general idea is to understand your data a little more, see if there is any pattern, if a certain value occurs more than others, to calculate the sample mean, median and standard deviation, and so on...
Hope it helped!
Answer:
For b, the answer is that your trying to find out what the type of funtion may be. It could be either exponential, linear, or quadratic.
Step-by-step explanation:
That's what the lesson in edg is all about.
please help asap will mark brainliest
Answer:
29; 30
Step-by-step explanation:
1. To the nearest whole number.
Whole numbers are numbers like 27, 28, 29, and 30.
A is between 28 and 29, but it is closer to 29.
To the nearest whole number, A = 29.
2. To the nearest 10
The tens are numbers like 10, 20, 30, and 40.
A is between 20 and 30, but it is closer to 30.
To the nearest ten, A = 30.
The function p(x) = –2(x – 9)2 + 100 is used to determine the profit on T-shirts sold for x dollars. What would the profit from sales be if the price of the T-shirts were $15 apiece?
Answer:
$28
Step-by-step explanation:
Put the given value into the formula and do the arithmetic.
p(15) = -2(15 -9)^2 +100
= -2(6^2) +100
= -72 +100
= 28
The profit on T-shirts selling for $15 would be $28.
Answer:
B -$28
Step-by-step explanation:
If 2x-3y=14 and 5x+3y=21 then what is the value of x?
A) -1
B) 0
C) 7/3
D) 5
Answer:
D
Step-by-step explanation:
Given the 2 equations
2x - 3y = 14 → (1)
5x + 3y = 21 → (2)
Adding the 2 equations term by term will eliminate the y - term
(5x + 2x) + (- 3y + 3y) = (14 + 21)
7x = 35 ( divide both sides by 7 )
x = 5 → D
which of the following is NOT equal to 50 millimeters?a. 5,000,000 nanometersb. 0.05 metersc. 5 centimetersd. 50,000 micrometers
Answer:its a. 5,000,000
Step-by-step explanation:
Final answer:
Option a, 5,000,000 nanometers, is the correct choice as it does not equate to 50 millimeters; it equates to 5 millimeters instead, making it not equal to the other options listed.
Explanation:
The question asks which of the provided options is not equal to 50 millimeters. We can convert each option to see which one does not equal 50 mm:
a. 5,000,000 nanometers (nm) - This equates to 5,000,000 nm × 1 m / 1,000,000,000 nm = 0.005 m or 5 mm, which is not equal to 50 mm.
b. 0.05 meters (m) - This is equal to 0.05 m × 1000 mm / 1 m = 50 mm, which is equal to 50 mm.
c. 5 centimeters (cm) - This is equal to 5 cm × 10 mm / 1 cm = 50 mm, which is equal to 50 mm.
d. 50,000 micrometers (µm) - As 1 µm is 1/1000 mm, this is equal to 50,000 µm × 1 mm / 1000 µm = 50 mm, which is equal to 50 mm.
Therefore, the correct answer is a. 5,000,000 nanometers, as it is the only option that does not equate to 50 mm.
Can someone please help me? Will give the brainlest!!
Step-by-step explanation:
The ratio of the perimeters = the scale
P₂ / P₁ = 6 / 4 = 3 / 2
The ratio of the areas = the square of the scale
A₂ / A₁ = (6 / 4)² = (3 / 2)² = 9 / 4
Same for the triangles:
P₂ / P₁ = 6 / 3 = 2
A₂ / A₁ = (6 / 3)² = (2)² = 4
Find the area of this kite
For this case we have that the area of the kite is given by the area of two triangles, the triangles share the same base of 2 + 2 = 4. One of the triangles has height of 6 and the other has height of 7.
So, the total area is given by:
[tex]A = \frac {1} {2} * 4 * 6 + \frac {1} {2} * 4 * 7\\A = \frac {1} {2} 24+ \frac {1} {2} 28\\A = 12 + 14\\A = 26[/tex]
So, the kite area is 26
ANswer:
Option D
Harriet used the work below to determine the percent equivalent to 1/8.
Step 1: 1/8=?/100
Step 2: 8 divided by 100 = 0.08
Step 3: 0.08 multiplied by 1 = 0.08
Step 4: 0.08
What was Harriet’s error?
-In Step 1, she set up the proportions incorrectly.
- In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.
-In Step 3, she multiplied the numerator instead of the denominator by the factor. -In Step 4, she forgot to move the decimal.
Answer:
Its B ''In Step 2, she divided 8 by 100 instead of 100 by 8, so she cannot multiply the numerator by the factor.''
Hence, in step [tex]2[/tex] she did the mistake.
What is the multiplication?
Multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here given that,
Step 1: [tex]\frac{1}{8}=\frac{?}{100}[/tex]
Step 2: [tex]8[/tex] divided by [tex]100 = 0.08[/tex]
Step 3: [tex]0.08[/tex] multiplied by [tex]1 = 0.08[/tex]
Step 4: [tex]0.08[/tex]
She did the mistake in step [tex]2[/tex] it would be,
[tex]\frac{100}{8}=12.5[/tex]
Hence, in step [tex]2[/tex] she did the mistake.
To know more about the multiplication
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Answer the following questions.
1. How many favorable outcomes are expressed in the probability 7/9 ?
2. How many possible outcomes are expressed in the probability 14/25 ?
3. What fraction correctly shows the probability of 14 favorable outcomes out of 21 possible outcomes?
(Enter
as a reduced fraction using / for the fraction bar. Do not use any spaces in your answer.. Example: 1/2 is 1/2
4. Which probability is least likely; 17/35, 5/13, 132/425, 1/2?
Answer:
1. 7
2. 25
3. 2/3
4. 132/425
Step-by-step explanation:
Probability is the likelihood of an event occurring and it can be computed by:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}[/tex]
1. So when you are given a probability of 7/9:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{7}{9}[/tex]
So the answer is 7.
2. Given the probability is 14/25:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{25}[/tex]
The number of possible outcomes is 25.
3. You have 14 favorable outcomes out of 21 possible outcomes.
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{21}\div \dfrac{7}{7}=\dfrac{2}{3}[/tex]
The answer is 2/3.
The least likely even would be the smallest fraction. If you want to do this the easy way, just change them all to decimal and find the value with the least.
17/35 = 0.49
5/13 = 0.38
132/425 = 0.31
1/2 = 0.5
Since 132/425 = 0.31 is the smallest, then it is the least likely probability.
Given the statement "If a line is horizontal, then it has slope equal to zero," what is its contrapositive?
Answer:
if a line has a slope equal to zero, then it is horizontal
Step-by-step explanation:
Answer:
If a line does not have zero slope, then it is not a horizontal line.
Step-by-step explanation:
edg
Over 6 days jim jogged 6.5 miles 5 miles 3 miles 2 miles 2 miles 3.5 miles and 4 miles. What is the mean distance that jum jogged
Mean means average.
To find the average, add the data then divide it by the amount of individual data you have.
(6.5 + 5 + 3 + 2 + 2 + 3.5 + 5)/2 = mean
27/2 = mean
13.5 = mean
13.5 miles is the mean distance that Jim jogged.
PLZ HELP ME!!! I NEED THIS DONE BY TONIGHT!!!
1. This kite has a 90 degree angle, which is equivalent to angle B.
2. Distance RB is 2.
3. Distance SB is 1.
4. The kite forms a right triangle.
5. Distance RS is the hypotenuse which has not been given. We can call RS by any variable of choice.
A zip line is setup 150ft in the air, where a person can expect to zip line at a safe declining speed to the ground as they pass over a body of water, said to be 40 ft in length. Assuming that this cable were stretched tight, where the zip liner is approaching the ground at a 40∘ angle (not the top angle), how many feet of ground would be covered horizontally by the zip liner, not including the body of water? Round to the nearest foot
Answer:
139 ft
Step-by-step explanation:
So the zip line forms a right triangle. The height of the triangle is 150 ft, and the opposite angle is 40°. The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.
tan 40° = 150 / x
x = 150 / tan 40°
x ≈ 179 feet
But this includes the 40 ft long body of water, so the amount of ground covered is:
179 ft - 40 ft = 139 ft
What is the volume of the cone with radius 6 in. and height 10 in.? Express the answer in terms of π.
Answer:
120*pi in^3
Step-by-step explanation:
We are given
Radius of cone=r=6 in
Height of cone=h=10 in
We know that the formula for finding the volume of cone is:
[tex]V=\frac{1}{3}\pi *(r)^{2}*h[/tex]
Putting the values of radius and height:
[tex]V=\frac{1}{3}\pi *(6)^{2}*10\\=\frac{1}{3}\pi *36*10\\=\frac{360}{3}\pi\\=120\pi[/tex]
So, the volume of cone in terms of pi is 120pi cubic in^3 ..
Answer:
The volume of cone = 120π cubic inches
Step-by-step explanation:
Points to remember
Volume of cone = (πr²h)/3
Where r - Radius of cone and
h - Height of cone
To find the volume of cone
Here r = 6 in and h = 10 in
Volume = (πr²h)/3
= (π * 6² * 10)/3
= (π * 36 * 10)/3
= 360π/3
= 120π cubic inches
Therefore volume of cone = 120π cubic inches
I coach a soccer team with 15 members. i want to choose a starting lineup consisting of 11 players, two of whom will represent the team in the captains meeting at the beginning of the game. in how many ways can i choose my starting lineup, including designating the two captains?
[tex]{_{15}C_{11}}\cdot {_{11}C_2}=\dfrac{15!}{11!4!}\cdot\dfrac{11!}{2!9!}=\dfrac{12\cdot13\cdot14\cdot15}{2\cdot3\cdot4}\cdot\dfrac{10\cdot11}{2}=75,075[/tex]
Answer: There are 715 ways to choose his starting lineup which includes designating the two captions.
Step-by-step explanation:
Since we have given that
Number of members = 15
Number of players = 11
Number of captions must be included = 2
So, Number of remaining members = 15-2 = 13
Number of remaining players = 11 - 2 = 9
So, Number of ways to choose starting line up is given by
[tex]^{13}C_9\\\\=715[/tex]
Hence, there are 715 ways to choose his starting lineup which includes designating the two captions.
A basket contains 13 pieces of fruit five apples five oranges and three bananas Jonas takes piece of fruit at random from the basket in Bethex if you summon what is the probability that Jonas will get orange and Beth will get an apple
Answer:1 out of 13
Step-by-step explanation:
because you take both of them and add them together and if one gets a banana and the other one gets an orange that will be one out of thirteen
What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9
Answer:
Step-by-step explanation:
Let [tex]u^2=x^4\\u = x^2[/tex]
Subbing in:
[tex]9u^2-2u-7=0[/tex]
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
[tex]9u^2-9u+7u-7=0[/tex]
Group together in groups of 2:
[tex](9u^2-9u)+(7u-7)=0[/tex]
Now factor out what's common within each set of parenthesis:
[tex]9u(u-1)+7(u-1)=0[/tex]
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
[tex](u-1)(9u+7)=0[/tex]
Remember that [tex]u=x^2[/tex]
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
[tex](x^2-1)(9x^2+7)=0[/tex]
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring [tex](x^2-1)[/tex] gives us that x = 1 and -1. The other set is a bit more tricky. If
[tex]9x^2+7=0[/tex] then
[tex]9x^2=-7[/tex] and
[tex]x^2=-\frac{7}{9}[/tex]
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
[tex]x=[/tex]±[tex]\sqrt{-\frac{7}{9} }[/tex]
which will simplify down to
[tex]x=[/tex]±[tex]\frac{\sqrt{7} }{3}i[/tex]
Those are the 4 solutions to the quartic equation.
Given cos =4/3 sqrt 3 and tan-sqrt 11/4,find sin
Solve for a.
a = 0
a = -1
a = 1
none
Answer:
None.
Step-by-step explanation:
5/a - 2 / (1 - a) = 2 (a - 1)
Multiply each term by a(1 - a)(a - 1):
5 (1 - a)(a - 1) - 2a(a - 1) = 2a(1 - a)
5( a - 1 - a^2 + a) - 2a^2 + 2a = 2a - 2a^2
5(-a^2 + 2a - 1) - 2a^2 + 2a = 2a - 2a^2
-5a^2 + 10a - 5 - 2a^2 + 2a - 2a + 2a^2 = 0
-5a^2 + 10a - 5 = 0
-5(a^2 - 2a + 1) = 0
= -5(a - 1)^2 = 0
So a = 1.
But a = 1 cannot be a root because 2/ 1 - a would be 2/0 which is undefined.
Also 2 / (a - 1) is undefined.
can anyone help with problems 6 and 8 those are the only ones I cannot figure out
Answer:
[tex](f + g) (x)=x^2 +x +3[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
Step-by-step explanation:
We have the following functions:
[tex]f(x)=3x +2\\[/tex] and [tex]g(x) = x^2 -2x +1[/tex]
First we find [tex](f + g) (x)[/tex]
To find [tex](f + g) (x)[/tex] we must add the function f(x) with the function g(x)
[tex](f + g) (x)=3x +2 + x^2 -2x +1[/tex]
[tex](f + g) (x)=x^2 +x +3[/tex]
Now we find [tex](f - g) (x)[/tex]
To find [tex](f - g) (x)[/tex] we must subtract the function f(x) with the function g(x)
[tex](f - g) (x)=3x +2 - (x^2 -2x +1)[/tex]
[tex](f - g) (x)=3x +2 - x^2 +2x -1[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
PARKS Anika is hiking on a rectangular trail at the national park. There are four resting spots along the corners of the trail. On the map, they are marked with coordinates of (-2, 2), (1, 2), (1, -2), and (-2, -2). If each unit represents 1 mile, find the perimeter of the trail in miles, using the coordinates.
Answer:
[tex]14\ miles[/tex]
Step-by-step explanation:
Let
[tex]A(-2, 2), B(1, 2), C(1, -2),D(-2, -2)[/tex]
Plot the coordinates
see the attached figure
we know that
The perimeter is equal to
[tex]P=2(AB+AD)[/tex]
we have
[tex]AB=(1-(-2))=3\ units[/tex]
[tex]AD=(2-(-2))=4\ units[/tex]
substitute
[tex]P=2(3+4)=14\ units[/tex]
Convert to miles
If each unit represents 1 mile
then
[tex]14\ units=14\ miles[/tex]
Answer:
15 units sq
Step-by-step explanation:
Good job
Solve the following equation: -4x - 6 = 10
4
-4
1
-1
A new unit has been formed in the army . In this until, 1 member is a staff sergeant , 3 are sergeants,21 are PFC's and 35 are PVT's . What percent of the soldiers are in the army
Answer:
93%
Step-by-step explanation:
1 + 3 + 21 + 35 = 60 = 100%
21 + 35 = 56 = x%
60 = 100%
56 = x%
60x = 56 * 100
x = 56* 100 / 60
x = 2*23*2*2*5*5 / 2*2*3*5
x = 23*2*5/3
x = 93%
To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.
Explanation:The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are
percent
,
total soldiers
, and
army unit
.
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Solve for the zeros
x^2+10x+21
(x+3)(x+7)= 0
x^2+7x+3x+21= x^2+10x+21
x+3-3= 0-3
x+7-7= 0-7
Answers are :
x= -3 , x= -7
Answer:
x=-7,-3
Step-by-step explanation:
okay so what is a independent variable
Hello There!
In an experiment, The independent variable is the variable that the person doing the experiment changes on purpose so they can see if it affects another variable in the experiment. Independent variables are also called "The Manipulated Variables"
I Hope This Helped You!
Have Great Day!
Be Safe,
TheBlueFox
You plan to use 170 feet of fencing to enclose a Rectangular play area of 2800 square feet. You plan to build the play area so it is centered against the back of your home which is 50 feet in length. Determine the dimensions necessary to enclose the required area.
Answer:
40 ft by 70 ft
Step-by-step explanation:
The 50 ft side of the house can add to the total perimeter of the play area, allowing it to be 170+50 = 220 feet. Then the sum of length and width will be half that, or 110 feet.
Factors of 2800 that have a sum of 110 are 40 and 70.
The play area fence can extend 10 ft either side of the house, out 40 ft, then 70 ft across the back, for a total length of 170 ft. Dimensions of the play area are 40 ft by 70 ft.