An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.
Unlike an equation, which has one unique solution, an inequality can have multiple solutions or no solution at all. The solutions of an inequality are the values that make the inequality true.
Inequalities are used to model real-world situations where there are constraints or limitations, such as determining the range of possible values for a variable. They are also used to describe relationships between variables, such as when one variable is greater than or less than another variable.
There are different types of inequalities, such as linear inequalities, quadratic inequalities, and absolute value inequalities, each with their own set of rules and methods for solving them.
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Use the drawing tool(s) to form the correct answer on the provided number line. Consider the given functions. Function 1 Function 2 Graph shows a polynomial function plotted on a coordinate plane with vertical axis g of x. A curve enters quadrant 3 at (minus 5, minus 40), goes through (minus 4, 0), (minus 2, 32), (0, 15), (2, 0), and exits quadrant 1 at (4, 30). Represent the interval where both functions are decreasing on the number line provided.
Both functions decrease at (-1, 2)
How to determine the decreasing intervals of the function?The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
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The mass of a proton is about 1.7 x 10^-24 g. The mass of a neutron is about the same as a proton. The nucleus of an atom of carbon has 6 protons and 6 neutrons. The mass of the nucleus is about 2 x 10^-26 units. Circle the best choice for the units this measurement is given in: g/kg/tons
The density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
How to estimate the density of proton?Given:
[tex]$r = 2 * 10^{-26[/tex] units.
[tex]mass = 1.7 * 10^{-24[/tex] grams
Formula, V [tex]= 4/3 * \pi * r^3[/tex]
Density = mass / Velocity
Put the givens into the formula.
Find the value for [tex]r^3[/tex]
[tex]V = (4/3) 3.14 * (1 * 10^{-13})^3[/tex]
To estimate the volume indicate divide by 3
[tex]V = (4/3) 3.14 * 1 * 10^{-39[/tex]
[tex]V = 1.256 10^{-38/3[/tex]
[tex]V = 4.1867 * 10^{-39[/tex]
Density = mass / velocity
Density = [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
Therefore, the density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
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How many terms are in the sequence shown?
38, 36, 34, ..., -20
Answer:
30 terms
Step-by-step explanation:
In the sequence, the value of each term decreases by 2.
38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20.
1+ (38 - (-20))/2 = 1+ 29 = 30
A group of restaurant owners surveyed a list of people to determine how preferences of meats compared to preferences of grains, and if they are related. The results are in the table above. Based on the table, is there evidence of association between chicken preferences and rice preferences
There is no association between the chicken preferences and rice preferences. Option C
What is association?There is an association between two variables when they both decrease or increase simultaneously. In many cases, the association between the variables can be shown using the correlation coefficient when the relationship is plotted on Cartesian coordinates.
If we look at the table, we can see that there is no association between the chicken preferences and rice preferences because because the proportion of chicken and rice eaters to all chicken eaters is lower than all rice eaters to all eaters; and because the proportion of chicken and rice eaters to all rice eaters is lower than all chicken eaters to all eaters.
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Javid travels to work by bus or by train.
The daily bus fare is £2.50
The daily train fare is £3.50
In 5 days he spends a total of £14.50
On how many days did he travel by bus?
Javid travelled by bus for 3 days using a simultaneous equation
What is simultaneous equation?
This refers to equations that are solved together in order to determine the values of unknown variables.
In this case, the total amount spent on daily bus or train can be determined as the fare price multiplied by the number of days
Let X be the number of days that Javid took bus
total spent on bus=2.50X
Let Y be the number of days that Javid took train
total spent on train=3.50Y
Total spent=2.50X+3.50Y
14.50=2.50X+3.50Y
Secondly, X plus Y gives 5 days
5=X+Y
multiply the second equation by 2.50 and the first by 1
14.50=2.50X+3.50Y
12.50=2.50X+2.50Y
subtract the second equation from first
2=Y
substitute for Y
5=X+Y
5=X+2
X=5-2
X=3
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The number of days that he travelled by bus is; 3 days
How to Solve Simultaneous Equations?Let x be the number of days that Javid travelled by bus.
Let y be the number of days that Javid travelled by train.
Thus;
Total spent on bus = 2.50x
Total spent on train = 3.50y
Overall total spent is;
2.5x + 3.5y = 14.50 -----(1)
Total number of days is 5 days and so;
x + y = 5 -----(2)
Making x the subject in eq 2 gives us;
x = 5 - y -----(3)
Put eq 3 in eq 1 to get;
2.5(5 - y) + 3.5y = 14.50
12.5 - 2.5y + 3.5y = 14.5
y = 14.5 - 12.5
y = 2 days
Thus;
x = 5 - 2
x = 3 days
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Help ASAP will give 20 points!!!!!
use six unit multipliers to convert 33 cubic feet to cubic centimeters
Converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
How to determine the conversionIt is important to note that conversion of units requires the appropriate equivalent values
For
I cubic foot is equivalent to 28316. 8 cubic centimeters
But we were given
33 cubic feet for the conversion
If 1 cubic foot = 28316. 8 cubic centimeters
Then 33 cubic feet = x
Cross multiply, we get
x = 28316. 8 × 33
x = 934454. 4 cubic centimeters
Thus, converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters
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help me please omg im in a rush
Answer:48
Step-by-step explanation:
Geometry question need help finding the answers to this
Answer:
L' (-1, 1)
M' (1, 2)
N' (1, -1)
if you were to solve the following system by substitution, what would be the best variable to solve for and what from what equation 3x 6y
so here you the answer is 9
can someone please help mee
Answer:
[tex]\frac{\sqrt{731}}{30}[/tex]
Step-by-step explanation:
We first observe that the angle is located in quadrant III
This allows us to draw a triangle as attached in the attachments.
Using this triangle, we can find sin([tex]\theta_1[/tex]).
Remembering that sin(theta) = [tex]\frac{opp}{hypo}[/tex], we can see from the attached image that it is [tex]\frac{\sqrt{30^2 - 13^2}}{30}[/tex], then simplifying [tex]\sqrt{30^2 - 13^2}[/tex] using a calculator, we get [tex]\sqrt{731}[/tex].
So our final answer is the answer shown above.
You may be wondering how did the side lengths appear on the triangle.
From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.
Simplify :-
(3x-2y) (3x+2y) (9x²+4y²)
Answer:
[tex]\huge\boxed{\sf 81x^4 - 16y^4}[/tex]
Step-by-step explanation:
Given expression:= (3x - 2y)(3x + 2y)(9x² + 4y²)
Using formula:[tex](a+b)(a-b)=a^2-b^2[/tex]= [(3x)² - (2y)²] (9x² + 4y²)
= (9x² - 4y²)(9x² + 4y²)
Using the above formula again
= (9x²)² - (4y²)²
= 81x⁴ - 16y⁴[tex]\rule[225]{225}{2}[/tex]
5. Jigsel has 6 more years of teaching experience than Wangmo, and the two of themhave 16 years of teaching experience altogether. How many years of teaching experience does Wangmo have?
Answer:
10 just find the difference between the two
Step-by-step explanation:
16-6=10
Wangmo have 6 years of teaching experience.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Let Wangmo has x years of experience.
Jigsel has 6 more years of teaching experience than Wangmo.
So, Jigsel has x + 6 years of experience.
According to the question,
the two of them have 16 years of teaching experience altogether.
That means,
we have the equation,
(x+6) + x = 16
2x = 16 -6
2x = 10
x = 10/2
x = 5
Therefore, Wangmo has 6 years of experience.
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(08.01)Angela wants to know how many families in her neighborhood plan to attend the parade. She puts all 120 of the neighborhood addresses in a hat and draws a random sample of 30 addresses. She then asks those families if they plan to attend the parade. She finds that 40% of the families plan to attend the parade. She claims that 40% of the neighborhood families would be expected to attend the parade. Is this a valid inference?
A) Yes, this is a valid inference because the 30 families speak for the whole neighborhood
B)Yes, this is a valid inference because she took a random sample of the neighborhood
C)No, this is not a valid inference because she did not take a random sample of the neighborhood
D) No, this is not a valid inference because she asked only 30 families
Using sampling concepts, the correct option regarding the validity of the inference is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
For example:
I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So I ask, lets say, 1000 randomly selected New York state residents whether they are Buffalo Bills fans, and expand this to the entire population of New York State residents. If I had taken 1000 residents just from Buffalo, it would not be a representative sample.
In this problem, all addresses in the neighborhood are considered, hence a random sample was taken and the correct option is given as follows:
B) Yes, this is a valid inference because she took a random sample of the neighborhood.
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Which of the following steps would you perform to the system of equations
below so that the equations have opposite y-coefficients?
4x+2y = 4
12X - Y = 26
A. Divide both sides of the top equation by 3
•
B. Divide both sides of the bottom equation by 3
• C. Multiply both sides of the bottom equation by 2
• D. Multiply both sides of the top equation by 2
Answer: Choice C
Multiply both sides of the bottom equation by 2
Reason:
The y coefficient of the first equation is 2. For the other equation, that y coefficient is -1. We need these coefficients to be equal but opposite. One way to do this is to double everything in the bottom equation
The bottom equation 12x-y = 26 doubles to 24x - 2y = 52
At this point we have the equivalent system of
[tex]\begin{cases}4x+2y = 4\\24x-2y = 52\end{cases}[/tex]
And we can see that we have equal but opposite y coefficients (2 and -2). The y terms add to 0 since 2y + (-2y) = 0y = 0 meaning we've eliminated y.
Question 1
Which equation represents the relationship shown in the table
at the right?
Answer:
Option (4)
Step-by-step explanation:
When x = 0, y = -3.
Eliminate Option 1.Also, the slope is
[tex]\frac{-1-(-3)}{1-0}=2[/tex]
So, the equation is y = 2x - 3.
Desiree opens an account with one deposit of $6500. she receives a statement twice a year, just after the interest is applied. which type of account is desiree most likely using?
From Longman Dictionary of Contemporary English opens an account to start an account at a bank or other financial organization by putting money into it Mary was in the bank to ask about opening a current account.
Step 1: Visit the official website of the bank in which you wish to open an account. Step 2: Fill in the application form online along with a digital copy of address proof, identity proof, age proof, income/employment proof, and photographs.
You need to be at least 18 years old to open an account. However, you can open a joint account as a minor with a parent or legal guardian as an account co-owner. Some banks do offer accounts tailored for minors.
Please check the attached file for a complete answer.
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v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws and 2 pairs of appendages per body segment
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment: FALSE
What are Centipedes?Their bodies have an elongated, cylindrical form that can appear flat at times. Adults can range in size from half an inch to 6.5 inches. Despite its "thousand-legger" moniker, most have less than 100 legs. Despite having so many legs, these arthropods move slowly.Most centipedes can only bite with their poison claws just under the head, causing a bee-like sting; however, Scolopendra can harm a person with the sharp claws of its many walking legs.Centipedes have only one pair of legs on each body segment, which can be seen protruding from their flattened bodies. The number of body segments varies by species, and the number of pairs of legs ranges from 15 to 177, plus or minus one.As it is given in the description, centipedes have only one pair of legs on each body segment. So, the whole statement becomes False.
Therefore, the statement "centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment" is FALSE.
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Complete question:
Centipedes differ from millipedes in that centipedes are cylindrical, have poison claws, and 2 pairs of appendages per body segment. TRUE or FALSE
What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
What is the range of the function graphed below?
y
-8 -6
B.
C.
+
O D.
-2
8
6+
4+
2+
-2-
-4-
-6+
OA -∞0 < y < 2
-∞ < y < ∞
-2 < y < ∞
-∞0 < y < -2
-8-
N
10
--00
Y
+x
Answer:
D
Step-by-step explanation:
Range is the 'y' values a graph can have
you can see that the 'y' values can be anythig from - inf to + 2
The range of the function is [2, -∞].
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
We see that the function line y values are from 2 to negative infinity.
This means,
The range is [2, -∞].
Thus,
The range of the function is [2, -∞].
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Answer fast in steps
Suppose the number of residents within five miles of each of your stores is asymmetrically distributed with a mean of 19 thousand and a standard deviation of 7.6 thousand. What is the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores
The 95th percentile for the average number of residents within five miles of each store is 20219.86.
Given mean of 19000 , sample size of 75 stores and standard deviation of 7600.
We have to find the 95th percentile for the average number of residents within five miles of each store in a sample of 75 stores.
We have to first find the margin of error to calculate the upper level of confidence interval.
Margin of error is the difference between the real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of z at given confidence level.
σ is standard deviation
n is the sample size.
z value at 95% confidence level is 1.39. (one tailed)
Put the values in the formula to get margin of error.
Margin of error=1.39*7600/[tex]\sqrt{75}[/tex]
=10564/8.66
=1219.86
Upper level=19000+1219.86
=20219.86
Hence the 95th percentile is 20219.86 for the average number of residents within five miles of each store in a sample of 75 stores.
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Geometry question need explanation on finding the answer
A client has just inherited a property. the deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. the shape is an irregular quadrilateral and the other three sides have distances of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. more importantly, it is known that the front left corner of the property is a right angle.
Answer:
sorry ❣️ bro you halp me
PQ has endpoints P(0, 0) and Q(8, 4). Find the coordinates of the midpoint of PQ
O
O
O
(4,4)
(2,4)
(4,2)
A: Identify the function type in the graph, and then describe a relationship that could be modeled by the function represented by the graph.
B: Identify and interpret the key features of the function in the context of the situation you described in part A.
The function type in the graph is a decreasing function.
What is a function?It should be noted that a function is simply used to illustrate the relationship between variables.
In this case, the function type in the graph is a decreasing function. As the number in X axis increases, the value in the y axis is decreased.
This illustrates a decreasing function.
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Identify the domain of the function shown in the graph
Answer:
C. All real numbers.
Step-by-step explanation:
The domain is the set of all x values that are used by points on the graph. This is a sine wave, and we assume it extends infinitely far to the left and right. Even without that assumption, you can eliminate the other answers.
A. This describes the numbers on the x-axis between 0 and 5, inclusive. But the graph includes many more points with x-coordinates beyond that interval.
B. The same sort of thing: the graph extends well beyond the interval of x values between -5 and 5, inclusive.
D. This would mean the graph has only points with positive x-coordinates, but there are many with negative (or 0) x-coordinates.
a 90% confidence interval for a proportion is found to be (0.22,0.28). What is the sample proportion
The value of sample proportion is found to be 0.253.
What is the sample proportion?The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.
Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.
Now, according to the question;
The 90% confidence interval for a proportion is found to be (0.22,0.28).
The confidence interval for the sample is given as-
Confidence interval = Sample proportion ± Margin of Error
Let [tex]\hat{p}[/tex] be the sample proportion.
The level of significance = 1 - 0.90
= 0.10 (10%)
From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.
90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Thus, 0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and
0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.
[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]
Take square root,
[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]
Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]
Therefore, the value of sample proportion is 0.253.
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Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y 2 and ys x
B. x>2 and yz x
C. x22 and y> x
D. y 22 and y
The system is:
y < x
y ≥ 2
So we conclude that the correct option is D.
Which system of inequalities is represented in the graph?On the graph, we can see two lines. One with a positive slope that is dashed.
And a solid line that is constant of the form y = c.
We can see that the shaded region is above the constant line and below the line with a positive slope, so the system of inequalities is of the form:
y < line.y ≥ constant line (≥ is used because this line is solid).The only option that has this form is option d:
y < x
y ≥ 2
So we conclude that the correct option is D.
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A function is a relation where each input value is assigned to (1) ___ one output value.the (2) ___ of a function is the set of all input values, or x-values, for which the function is defined. the (3) ___ of a function is the set of all output values, or y-values, for which the function is defined. to write the equation y = ax + b in function notation, substitute (4) ___ for y. options for 1: a. exactly b. at least c. less than options for 2: a. range b. interval c. domain d. rate of change options for 3: a. range b. rate of change c. interval d. domain options for 4: a. f(x) b. a c. b d. x
The blanks can be filed by exactly, domain, range, and, f(x) respectively.
While we've got a feature in formulation form, it also includes a simple count to assess the function. For example, the feature f(x)=5−3x2 f ( x ) = 5 − 3 x 2 can be evaluated with the aid of squaring the enter cost, multiplying by means of three, and then subtracting the product from 5.
You write capabilities with the function name observed by way of the established variable, together with f(x), g(x), or maybe h(t) if the function depends upon time. You read the function f(x) as "f of x" and h(t) as "h of t". functions no longer need to be linear. The feature g(x) = -x^2 -3x + 5 is a nonlinear characteristic.
A user is an actual-valued feature on a vector area, usually of functions. as an example, the electricity practical at the unit disk assigns various to any differentiable feature, For the practical to be non-stop, it's miles necessary for the vector space. of capabilities to have the perfect topology.
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