Answer:
a.1
b.10
c.120
Step-by-step explanation: don't know that last one
A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph represents the system of inequalities for this scenario?
x + y ≥ 4
y – x ≤ 1
A graph which represents the system of inequalities for this scenario include the following: graph B.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of developed acres and number of open acres, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of developed acres.Let the variable y represent the number of open acres.Since a planned community must have at least 4 acres of developed and open space, a linear inequality which represents this situation is given by;
x + y ≥ 4
Additionally, since the difference between the number of developed acres and the number of open acres can be no more than 1, we have;
y – x ≤ 1
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by graph B.
Read more on inequality here: https://brainly.com/question/12952773
#SPJ1
Prob 5. Suppose that the number of cans of soda pop filled in a day at a bottling plant is a random variable with an espected valefiance of 1.,00. (a) Use Markov's inequality to obtain an upper bound on the probability that the plant will fill more than 11,000 cans on a particular day. (b) Use Chebyshev's inequality to obtain a lower bound on the probability that the plant will fill between 9,000 and 11,000 cans on a particular day.
The lower bound on the probability that the plant will fill between 9,000 and 11,000 cans on a particular day is at least 1 - 1/10 = 9/10.
What is probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur.
(a) P(X > 11,000) ≤ E[X] / 11,000
Where X is the random variable representing the number of cans filled in a day, and E[X] = 1,000 is the expected value.
So, P(X > 11,000) ≤ 1,000 / 11,000 = 1/11
(b) P(|X - E[X]| ≥ kσ) ≤ 1/k^2
Where X is the random variable representing the number of cans filled in a day, E[X] = 1,000 is the expected value, and σ is the standard
As we know that for any random variable X, E[X^2] >= (E[X])^2
therefore Var(X) = E[X^2] - (E[X])^2 >= 0.
so the standard deviation of X is
σ = √(Var(X)) = √(1000) = 31.62
We can choose k = (11000-9000)/(2*31.62) = 3.16
so P(|X - E[X]| ≥ 3.16σ) = P(|X - 1000| ≥ 10000) ≤ 1/3.16^2= 1/10
Therefore, the lower bound on the probability that the plant will fill between 9,000 and 11,000 cans on a particular day is at least 1 - 1/10 = 9/10.
To learn more about probability visit : brainly.com/question/30034780
#SPJ4
not sure what the answer is
The truth table for ~p ∨ q is as shown below.
~p ∨ q
T
F
T
T
How to construct the truth table for ~p ∨ q?A truth table is a table for evaluating the truth value of a truth-functional compound sentence on the basis of the truth value of its part
The truth tables for negation and disjunction are shown below:
Negation
p ...... ~p
T F
F T
Disjunction
p ..... q ..... p v q
T T T
T F T
F T T
F F T
Note:
T and F stand for True and False respectively.
In disjunction, if one of the inputs is true then the output will be True.
Negation reverses the input i.e if the input is True, the output will be False. The symbol for negation is ~ i.e the negation of p is ~p
Truth table for ~p ∨ q?
p ----- q ----- ~p ----- q ----- ~p ∨ q
T T F T T
T F F F F
F T T T T
F F T F T
Learn more about truth table on:
brainly.com/question/14458200
#SPJ1
estimate 718-331 to nearest 100
Answer: 400
Step-by-step explanation: Max has rounded off the difference of two numbers. Max's estimate of the difference is 400.
Given information:
The first number = 718.
The second number = 331
Now, according to the question, Max estimates their difference by taking the number rounded off.
Hence, the rounding off the given number to nearest 100,
we get,
First number as 700 and Second number as 300.
Hence the difference of the obtained number can be written as:
Hence, one can conclude that, max's estimate of the difference is 400.
Tolerance The height and radius of a right circular cylinder are equal, so the cylinder's volume is The volume is to be calculated with an error of no more than 1of the true value. Find approximately the greatest error that can be tolerated in the measurement of expressed as a percentage of
The greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h.
The given data is the height and radius of a right circular cylinder are equal.
[tex]$$\begin{aligned}V & =\pi h^3 \\\frac{d V}{d h} & =3 \pi h^2 \\d V & =3 \pi h^2 d h\end{aligned}$$[/tex]
A differentiable function is a function in one variable in calculus such that its derivative exists at each point in its entire domain. The tangent line to the graph of a differentiable function is always non-vertical at each interior point in its domain.
A differentiable function does not have any break, cusp, or angle.
Find the derivative of V in terms of h. Then multiply both sides by dh.
The maximum percentage error of the volume is 1%.
[tex]$$\begin{aligned}0.01 \pi h^3 & =3 \pi h^2 d h \\\frac{0.01}{3} h & =d h \\\frac{1}{300} h & =d h\end{aligned}$$[/tex]
The maximum percentage error of the volume is 1% which means
dV=0.01=0.01[tex]\pi[/tex][tex]h^{3}[/tex]. Substitute this into the equation and then solve for
dh.
The maximum error in the height is then [tex]\frac{1}{300}h=\frac{1}{3}[/tex]%h.
Therefore, the greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h
For more such questions on Tolerance
https://brainly.com/question/28782231
#SPJ4
i don’t get this :(
The value of x, which is the measure of the remaining angle, is equal to 180° - 70° - 30°, or 80°.
Find the value of each variable?The sum of the two angles, a and b, is equal to the total of the two angles, x and y, in a linear pair.This relationship can be expressed through the equation a + b = x + y. In this case, a is equal to 70° and b is equal to 30°.To solve for x and y, we must rearrange the equation to solve for each variable individually.First, we can subtract b from both sides to get a = x + y - b. Then, we can add b to both sides to get a + b = x + y.This simplifies to x + y = a + b, or x + y = 70° + 30° = 100°. By subtracting y from both sides, we can solve for x by getting x = 100° - y.To solve for y, we can subtract x from both sides to get y = 100° - x.Since the sum of the two angles is equal to 100°, the value of x must be 90° and the value of y must be 60°.a=70° and b=30° are two angles that together form a straight line.The sum of these two angles is equal to 180°, which is the measure of a straight line.Therefore, the value of x, which is the measure of the remaining angle, is equal to 180° - 70° - 30°, or 80°.The value of y, which is the measure of the remaining angle, is equal to 180° - 70° - 80°, or 30°.Therefore, the value of x is equal to 80°, and the value of y is equal to 30°.To learn more about The Law of Sines refer to:
https://brainly.com/question/27174058
#SPJ1
Does changing the compound inequality x > −3 and x < 3 from “and” to “or” change the solution set? explain.
Changing the compound inequality x > −3 and x < 3 from “and” to “or” will change the solution set
What is compound inequality?A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality.
The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect.
The conjunction "or" means that the entire compound sentence is true as long as either statement is true. When "or" appears in a compound inequality, a disjunction is created.
Hence changing “and” to “or” changes the solution set
Learn more about compound inequality at:
https://brainly.com/question/24761100
#SPJ1
h(t)=(t+3) 2 +5h, left parenthesis, t, right parenthesis, equals, left parenthesis, t, plus, 3, right parenthesis, squared, plus, 5 Over which interval does h have a negative average rate of change?
The interval over which h(t) has a negative rate of change is given as follows:
(-∞, -3).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The equation for this problem is given as follows:
h(t) = (t + 3)² + 5.
The leading coefficient is positive, hence the function is concave up.
Considering the t-coordinate of t = -3 at the vertex, the decreasing and increasing intervals are given as follows:
Decreasing: (-∞, -3).Increasing: (3, ∞).More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
Which of the following dot plots would most likely have the highest standard
deviation?
Option A is the dot plots which would most likely have the highest standard
deviation.
What is Standard deviation?This is referred to as the measure of the amount of variation or dispersion of a set of values and the one with a higher standard deviation will usually have its average points farther away from the mean which is located at the center while those with a lower standard deviation will usually have its average points closer to the mean.
From the options provided , option A has a lot of points on 2 and 14 which are further way from the center (mean) and is therefore the reason why it was chosen as the correct choice.
Read more about Standard deviation here https://brainly.com/question/24298037
#SPJ1
How can you add 3/10 and 2/5
Answer:
7/10
Step-by-step explanation:
steps linked below
Y=-(x+3)^2-3
vertex form to standard form please help
Therefore , the solution of the given problem of equation comes out to be the vertex (h,k) is (3,3).
Equation explainedAn expression is a mathematical representation of two equal variables , one on each end of a "equals" sign. Typical issues can be resolved using equations. We commonly look to pre algebra for solutions to problems in real life. The fundamental concepts of mathematics are covered in pre-algebra lessons.
Here,
use the vertex form y=a(x-h)2+k to get the values of a, h, and k.
Given : a =1
h=3
k=−3
Discover the vertex (h,k) (3,3).
So, we discovered the vertex of given equation.
Therefore , the solution of the given problem of equation comes out to be the vertex (h,k) is (3,3).
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
You create a recipe for slime by mixing some 20% pure slime and some 80% pure slime to create 1000 gallons of a 65% pure slime mixture. How many gallons of the 20% mixture are needed?
Answer:
We can start solving this problem by using a system of linear equations. Let x be the number of gallons of the 20% pure slime mixture and y be the number of gallons of the 80% pure slime mixture. We know the following:
The total amount of slime mixture is 1000 gallons. This means that x + y = 1000.
The final mixture is 65% pure slime, which means that 0.65 = (0.20)x + (0.80)y. This is because we are mixing 20% pure slime and 80% pure slime to get the final mixture.
We can use these two equations to solve for x, which is the number of gallons of the 20% pure slime mixture needed.
First, we'll use the first equation to solve for y in terms of x:
y = 1000 - x
Then we'll substitute this expression into the second equation:
0.65 = (0.20)x + (0.80)(1000 - x)
Simplifying we get:
0.65 = 0.20x + 800 - 0.80x
0.45x = 200
x = 200/0.45
x = 444.44 gallons
So, you would need 444.44 gallons of the 20% pure slime mixture to make 1000 gallons of a 65% pure slime mixture.
Step-by-step explanation:
Which function represents the graph of f (x) = 1/2 (3)^x
On solving the provided question, we can say that from the graphs the function = [tex]f(x) = 1/2 (3)^x[/tex], it represents a half parabola
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
from the graphs
the function = [tex]f(x) = 1/2 (3)^x[/tex]
it represents a half parabola
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. v(x)
The volume, V of box as a function of x that is V(x) = 4x³ - 64x² + 240x , where x is side of square cut out from each corner.
We have, a box open from top and constituted from rectugular pieces of dimensions 12 inches and 20 inches. As we know, The volume of a box is V
= width (w) × height(h) ×length (l).
Now, equal squares of side x are cut from each corner of box and folded. We draw our box it looks like as seen above figure. We will notice here that the height will be x and that the height and length depend on x. Length of box, l = 20 - 2x and
Width of box, w = 12 - 2x
So the volume is, V(x) = w×h×l
= (12 - 2x)(x)(20 - 2x)
Expand it for further calculation,
V(x) = ( 12 - 2x ) ( 20x - 2x²)
V(x) = 4x³ - 64x² + 240x
Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.
To learn more about volume function of x , refer:
https://brainly.com/question/29258657
#SPJ4
The volume, V, of a box is defined as V(x) = 4x3 - 64x2 + 240x.
We have a box that opens from the top and is made of rectangular components that are 12 inches and 20 inches in length. As is common knowledge, a box's volume is V.
V = height (h) + width (w) + length (l).
From each corner of the box, equal squares of side x are now cut and folded. We create a box that resembles the image above. Here, we'll see that the height is x and that the relationship between height and length is x-dependent.
Box length, l = 20 - 2x, and
Box width, w = 12 - 2x
Thus, V is the volume (x) = W * H * I
V(x) = (12 - 2x) (x) (20 - 2x)
V(x) = ( 12 - 2x ) ( 20x - 2x²)
V(x) = 240x - 24x² - 40x² -4x³
V(x) = 4x³ - 64x² + 240x
Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.
For such more question on box:
brainly.com/question/13073134
#SPJ4
Find the sum of the first 7 terms of the
following series, to the nearest integer.
10,4, 8/5,…
The required sum of the 7 terms in the geometric sequence is 16.6.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given geometric series,
10, 4, 8/5 . . . . . .
Common ratio = 4 / 10 = 2/5
first term = 10
the sum of the first seven terms is given as,
S₇ = a[r⁶ - 1] / r - 1
S₇ = 10[{2/5}⁶ - 1] / {2/5 - 1}
S₇ = 16.6
Thus, the required sum of the 7 terms in the geometric sequence is 16.6.
Learn more about geometric progression here: https://brainly.com/question/4853032
#SPJ1
how can I Write an expression to show 4 thirds times the product of 2 and 1 third.
Answer:
as: 4/3 * (2 * 1/3)
Step-by-step explanation:
Note: parentheses, 2 and 1/3 are being multiplied together first, before being multiplied by 4/3.
A function is represented by the values in the table. x y 2 4 4 8 5 10 7 14 8 16 Choose from the drop-down menu to complete the statement. The function represented in the table___linea
Chose; is or is not
Option A is appropriate since the table's function is linear.
Equation: What is it?The equals sign is used in equations to indicate the equality of two expressions in a formula. The expressions relate two or more variables with each other.
Given that:
x = 2 and y =4
x= 4 and y= 8 and so on.
In all the values given, the value of y is two times the value of x.
Also, these values satisfy the condition of linear expression:
y=mx
where, m =2 for the represented value.
This means that the function is linearly dependent on x.
The function shown in the table is linear.
Learn more about equation here:
https://brainly.com/question/29657992
#SPJ1
Which equation represents a circle with the endpoints of its diameter at (4, –11) and (12, –9)?
Answer:
Out of all possible choices you've shown, I'd say the best answer would be D
Step-by-step explanation:
Write an equation in slope-intercept form for the line with y-intercept 7 and slope
-3
Answer: y= -3x+7
Step-by-step explanation:
the equation is y=Mx+b you gave me the slope (-3) and the y-intercept (7) so the answer is y=-3x+7
←
Find the sample variance and standard deviation.
22, 15, 4, 7, 9
Part 1 of 2
Choose the correct answer below. Fill in the answer box to complete your choice.
(Type an integer or a decimal. Round to one decimal place as needed.)
OA. ²=
OB. s² =
Variance and standard deviation are two common measures of spread in statistics. The standard deviation is √30.25 = 5.5.
What is variance and standard deviation?OB. s² = The sample variance is a measure of the spread of a set of data. To calculate the sample variance, the sum of the squares of the differences between each data point and the mean is divided by the number of data points minus one. In this case, the mean of the data set is (22+15+4+7+9)/5 = 11.
The differences between each data point and the mean are 11-22=-11, 11-15=-4, 11-4=7, 11-7=4, and 11-9=2. The sum of the squares of these differences is (-11)² + (-4)² + 7² + 4² + 2² = 121.
Dividing this by the number of data points minus one, which is 5-1=4, gives us a sample variance of 121/4 = 30.25.
The standard deviation is the square root of the sample variance, so in this case, the standard deviation is √30.25 = 5.5.
To learn more about variance and standard deviation refer to:
brainly.com/question/12402189
#SPJ1
Find m
I don’t get it
49 679 find the quotient
The quotient of the given answer is 0.
Define quotient and remainder.The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
On dividing 49 by 679 we will get quotient 0 and remainder 49
To know more about Ratio visit:
brainly.com/question/13419413
#SPJ1
A bag contains 1 green, 4 red, and 5 yellow balls. Two balls, are selected at random. Find the probability of each selection. Express your answers as a percent. Show your work for credit. 20. P (2 red) 21. P (I red and 1 yellow) 22. P (I green and 1 yellow) 23. P (2 green) 24. P (2 yellow and I red)
The probability of getting 2 reds will be 13.3%.
The probability of a red and a yellow will be 22.2%.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true
From the information the bag contains 1 green, 4 red, and 5 yellow balls. Two balls, are selected at random.
The probability of getting 2 reds will be:
= 4/10 × 3/9
= 12/90
= 13.3%
The probability of a red and a yellow will be:
= 4/10 × 5/9
= 20/90
= 22.2%
Learn more about probability on
brainly.com/question/24756209
#SPJ1
Let $x = -1$. Find the answer to:
Answer:
-1
Step-by-step explanation:
Since -1 to a power will either be negative or postive 1, looking at whether the exponent is odd or even can determine if the answer is -1 or 0 (x + x^2 for instance equals 0 but x + x^2 + x^3 is -1)
[tex]\it (-1)^{2k}=1;\ \ \ (-1)^{2k+1}=-1,\ \ \forall\ k \in\mathbb{N}\\ \\ S=-1+(1-1)+(1-1)+\ ...\ (1-1)=-1[/tex]
Find the curvature of r(t) = (3t, t^2, t^3) at the point (3, 1, 1).
The curvature of r(t) at the point (3,1,1) is 2/3
The curvature of a space curve is given by the formula:
k(t) = |r'(t) x r''(t)| / |r'(t)|^3 where,
r(t) is the position vector of the curver'(t) is the first derivative of r(t) r''(t) is the second derivative of r(t).r(t) = (3t, t^2, t^3)
r'(t) = (3, 2t, 3t^2)
r''(t) = (0, 2, 6t)
So we can substitute these in the above formula:
k(t) = |(3, 2t, 3t^2) x (0, 2, 6t)| / |(3, 2t, 3t^2)|^3
By cross-product, we get
k(t) = |(6t, -6, -6t^2)| / |(3, 2t, 3t^2)|^3
Now substituting the point (3,1,1) we get
k(t) = |(6(1), -6, -6(1)^2)| / |(3, 2(1), 3(1)^2)|^3 = 6/9 = 2/3
So the curvature of r(t) at the point (3,1,1) is 2/3
Learn more about curvature here:
https://brainly.com/question/14598632
#SPJ4
Robert is purchasing shirts for his weekend soccer team. The shirts he wants to buy are normally $12 each but are on sale for $5 off. His team has a total of 9 players. How much will he spend to buy the shirts?
Answer:
$63
Step-by-step explanation:
12-5=7
9*7= 63
Answer:
$63 Is the answer.
Step-by-step explanation:
$12 - $5 = $7
$7 x $9 = $63
Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
A. parallel
B. same line
C. perpendicular
D. neither perpendicular nor parallel
The given two lines are parallel to each other. The correct answer would be an option (A).
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The lines will be parallel if they have the same slope and they will be perpendicular if the product of the slopes of the two lines is -1.
The slope of the first line can be found using the formula:
m₁ = (-2 - (-5))/(5-9) = -3/4
The slope of the second line can be found using the formula:
m₂ = (1 - (-2))/ (-8 - (-4)) = -3/4
They have identical slope, so the lines will be parallel.
Hence, the given two lines are parallel to each other.
Learn more about the Slope of the Line here:
brainly.com/question/14511992
#SPJ1
Line L1 has the equation x - 10y = 10.
Express the equation of L1 in slope-intercept form.
Answer:
[tex]y = \frac{1}{10}x - 1[/tex]
Step-by-step explanation:
Pre-SolvingWe are given the equation x - 10y = 10.
We want to write it in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
SolvingNotice how in slope-intercept form, only y is on one side.
This is because the equation is basically solved for y in slope-intercept form.
So, we should solve the equation for y.
Start by subtracting x from both sides.
x - 10y = 10
-x -x
_______________
-10y = -x + 10
Now, divide both sides by -10 to isolate y.
-10y = -x + 10
÷10 ÷10
_______________
[tex]y = \frac{1}{10}x - 1[/tex]
Select the table that represents a linear function. (Graph them if necessary.)
OA. x 0 1 2 3
y 0136
OB. x 0 1 2 3
y 0149
OC. XO 1 2 3
y 13 9 5 1
OD. x 012 3
y 5797
SUBMIT
Answer:
Step-by-step explanation:
The table that represents a linear function is ob x 0 1 2 3 y 0149
Please help will mark Brainly
Therefore , the equation problem is 15 fraction of 72 is the number 480. The expressions published here on left & right sides appear to be equivalent in their relationship.
An equation is what?Mathematical statements with two algebraic in the middle and also the means total (=) sign from either side are called equations. Variables, contractors, diffusion coefficients, terms, and the equatable to sign are just a few of the elements that compose an equation. The "=" sign but also terms both on sides are always necessary when writing an equation.
Here,
Using the value A = 480 as a guide
Let y become the ratio of the number, or the opposite.
It is equivalent to 72%.
The equation that results is
72 is equivalent to x% of 480.
When the expression is condensed, we get
72 = y % x 480
72 = ( y/100 ) x 480
Divide each side by 480 to obtain
y/100 = 0.15
Multiply by 100 on each side to arrive at
y = 15
Consequently, the value is y = 15.
Therefore, out of 480, 72 represents 15%.
To know more about equation visit :-
brainly.com/question/29657992
#SPJ1