Answer:
When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.
Using a union:
A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."
Using an intersection:
An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."
Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.
When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).
A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.
When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.
Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.
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An experienced census official feels that she can accurately estimate the number of inhabitants of a city block by simply noting the size of the block and the types of buildings (single family homes, apartments, businesses, etc.) that are found on the block. This procedure, if accurate, would be much quicker and cheaper than visiting each residence and taking a survey of its inhabitants. The data below are estimates of block populations provided by the official for 10 blocks in a large city, and the actual numbers of inhabitants for the same 10 blocks. Inhabitants of City Blocks Estimate 193 86 81 87 223 226 151 126 120 76 Actual 163 140 150 179 204 128 73 89 136 145 Step 1 of 2: Find the value of the test statistic for testing whether there is a linear relationship between the actual number of inhabitants and the estimated number. Round your answer to two decimal places, if necessary.
Answer:
035
Step-by-step explanation:
193
86
81
87
223
226
151
126
120
76
Y:
163
140
150
179
204
128
73
89
136
145
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
Will someone please help me with finding the median
Answer:
remember this rhyme
Step-by-step explanation:
hey diddle diddle,
the median in the middle
you add and divide for the mean
the mode is the one you see the most
and the range is the differences between.
for median put them in order and then it's the one in the middle
so what you have to do is you have to get all the numbers put them in least to greatest order and slowly you're going to mark one off on the side and then on the other side Mark went off and keep on doing that until you get into the middle and then that should be your median
Dilate the line shown by a scale factor of 1/4 with the center as (-3,9). Graph the dilated line
On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r
A fixed point serves as the dilation's center.
Dk is used to represent dilation, where k is the scale factor.
Dk (x, y) = for a dilation centered on the origin (kx, ky)
Let's assume that you have a PQRS rectangle where
P = (0,0)
Q = (4,0)
R = (4,4)
S = (0,4)
You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.
P' = (0.0)
Q' = (1,0)
R' = (1,1)
S' = (0,1)
You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.
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<4?
What is the solution of 3+
X-2
X-3
O x <3
O XS3
Ox>3
0 x23
Answer:
x < 3
Step-by-step explanation:
3 + x-2/x-3 ≤ 4, x ≠ 3
3 + x-2/x-3 -4 ≤ 0
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3, x ≠ 3
x < 3
x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation can be rewritten as 3 + (x-2) / (x-3) ≤ 4.
To solve for x, we need to multiply both sides by (x-3)
3(x-3) + (x-2) ≤ 4(x-3).
3 + x-2/x-3 -4 ≤ 0
Solve the above equation.
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3
Hence, x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
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find the value of x thanks! :D brainliest will be awarded!
Answer:
19
Step-by-step explanation:
point y is 90
x is 3x - 5
w is 2x
so
3x - 5 + 2x = 90
5x - 5 = 90
5x = 95
x = 19
In 2012, the population of Cincinnati, Ohio, was 296,550 with a population density of approximately 3800 people per square mile. What is the approximate land area of Cincinnati in square miles to the nearest whole number?
Answer:
≈ 78mi^2
Step-by-step explanation:
To find approximate land area:
296,550/3,800 = 78.039
Round to nearest whole number:
Area = 78
HELP WILL GIVE BRANLIEST! No links!!!
Answer:
11.5
Step-by-step explanation:
[tex]14^{2} - 8^{2} = 132\\\sqrt{132}= 2\sqrt{33} = 11.48912529\\answer-is -11.5[/tex]
Answer:
11.48
Step-by-step explanation:
Pythagoras Therum
8^2 + x^2 = 14^2
64 +×^2 = 196
x^2 = 132
sqrt both sides
11.48
can you help me for this math?
Answer:
3
Step-by-step explanation:
27-6=7q
21/7=q
3=q
hope it helps
27 = 7q + 6
=> 27 - 6 = 7q
=> 21 = 7q
=> 21/7 = q
=> 3 = q
So, q = 3.
onsider the transformation.
Which statement about the transformation is true?
O It is isometric because the side lengths remained the
same,
• It is isometric because all
angle measures remained
the same.
It is not isometric because the side
lengths did not
remain the same.
O It is not Isometric because the
not remain the same.
angle measures did
Mark this and return
Save and Exit
The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.
What is isometric transformation?An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.
The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.
Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.
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how many 5-digit even numbers can be formed with the digits 1,2,3,4,5, and 6 if repetition is allowed?
Given:
The given digits are 1,2,3,4,5, and 6.
To find:
The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).
Solution:
To form an even number, we need multiples of 2 at ones place.
In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.
We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.
Total number of ways to form a 5 digit even number is:
[tex]Total=6\times 6\times 6\times 6\times 3[/tex]
[tex]Total=3888[/tex]
Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.
Y
P
Q
S
R
Part A
Rectangle PQRS is rotated 90° counterclockwise about the origin to create rectangle PQR'S' (not shown). What are the coordinates of point R?
0 (-7,6)
O (7,6)
• (-6,7)
O (6,7)
Part B
Answer:
The coordinates of point R are (7,6), second option
Step-by-step explanation:
Coordinates of point R:
The coordinates of point R are , so (6,-7).
90° counterclockwise rule:
The rule for a rotation of 90º counterclockwise is given by:
(x,y) -> (-y,x)
What are the coordinates of point R?
(6,-7) -> (-(-7),6) = (7,6).
The coordinates of point R are (7,6), second option
The foot of a ladder is placed 7 meters from a wall. If the top of the ladder rests 9 meters up on the wall, how long is the ladder?
Answer:
8 meters
step-by-step explanation:
8 is in between 9 and 7
A bakery sells cupcakes and cookies. No more than 750 total items
can be produced a day. Production costs cannot exceed $1200 per day. It costs
$0.50 to make a cupcake and $0.25 to make a cookie. Given that you have the
constraints0.5x +0.25y < 1200 and 2 + y < 750, how would you
write an additional constraint to represent that the bakery can produce at most 85
cookies?
Answer:
The question doesn't make since so random guess
If you multiply $0.50 by 750 you get 375
If you multiply $0.25 by 750 you get 187.5
divide that by 85 and you get 2.2.
Step-by-step explanation:
Solve for x.
x - 6 = 8
x = [?]
x=14
Step-by-step explanation:
the answer is 14
I just added 8 with 6
:)
A hexagon forms a semi-regular tessellation with which of the following
regular polygons?
A. Square and equilateral triangle
B. Dodecagon and equilateral triangle
C. Trapezoid and pentagon
D. Trapezoid and octagon
Answer:
A.
Step-by-step explanation:
I NEED HELP FAST PLS
Answer:
234 feet cubed
Step-by-step explanation:
6 1/2 * 8 = 52
52 * 4 1/2 = 234
Drag each question to the correct location on the table.
Classify the questions as statistical or not statistical.
Each of the questions should be correctly classified as statistical or not statistical as follows:
Not statistical question: "How many hours did I jog yesterday?"Not statistical question: "How many students in my class can swim?"Not statistical question: "How many students in my class watch television?"Statistical question: "How many hours a day do the students in my class watch television?"Statistical question: "How many TV shows did each student in my class watch yesterday?"Statistical question: "How many days a week did each student in my class go swimming in the last month?"What is a statistical question?In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"
What is a non-statistical question?A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"
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Question 1-1
Barrett earns $15 per hour cutting grass and $10 per hour tutoring reading. In one month, Barrett needs to save at least $400 for a
new lawnmower but does not want to work more than 35 hours.
Part A: Let z represent the hours cutting grass and y represent the hours tutoring. Given z 20 and y ≥ 0, select all the inequalities
that represent the situation.
On solving the inequality we know, Barrett should work 25 hours tutoring and 10 hours cutting grass to make $400.
What exactly does inequality mean?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality results from a lack of balance.
Solution:-
given,
z=hours of cutting grass
y=hours of tutoring
Two equation can be made using given condition
15z+10y=400
and
z+y=35
Solving both equation simultaneously,
we get
y=25
z=10
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Given the triangle below what is the length of the third side rounded to the nearest whole number?
Will Give brainliest
No links please.
Sorry I over complicated the answer that i wrote, I think the answer is 18
Draw a diagram of x + 2, and a separate diagram of 3x, when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
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Correct Answer= Brainliest
Answer:
49
Step-by-step explanation:
Convert the dot plot into numbers
40, 40, 40, 45, 45, 50, 55, 55, 60, 60
Add all together
40+40+40+45+45+50+55+55+60+60 =490
Divide by amount of numbers there are
Amount of numbers = 10 --> 490/10 = 49
Mean = 49
29. For all values of X,
x^2+2x+4 = (x + 2)^2 + a(x+2) + b,
where a and b are constants. What is the value
of a?
(A) -2
(b) - 1
(c) 0
(d) 1
Peter and his four brothers combined all of their money to buy a video game. If 30% of the total money is Peter's, and $6.00 of the total money is Peter's, how much do all five brothers have combined?
A.
$26.00
B.
$20.00
C.
$14.00
D.
$1.80
Two brothers are allowed to spend a maximum of 5.90 money as pocket money.the elder brother spent 2.97 money. How much was left for the younger brother?
During the last class period of the semester, each student in a graduate computer science class with 10 students is required to give a brief report on his or her class project. The professor randomly selects the order in which the reports are to be given. Two students have been working on similar projects and would like to give their reports consecutively. What is the probability that this will happen
Answer:
Probability = 1/5
Step-by-step explanation:
Total ways of arrangement for 10 students = 10 !
Ways to arrange 2 students consecutively & other 8 students = 9 ! x 2
( As 9! to arrange 9 units, as 2 considered together ; & 2 for arranging 2 consecutive students - respectively )
So, Probability = Favourable outcomes / Total outcomes
= ( 2 x 9! ) / 10! = ( 2 x 9 x 8 x ..... 2 x 1 ) / 10 x 9 x ....... 2 x 1)
= 2 / 10 = 1/5
Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What is the expected value of the number shown if we add one additional 3 to the bag?
(c) What is the expected value of the number shown if we add two additional 3's (instead of just one) to the bag?
The expected values for each experiment are:
A) 3.4
B) 3.36
C) 3.33
How to get the expected values?If we have an experiment with the outcomes:
{x₁, x₂, ..., xₙ}
Each one with the correspondent probability:
{p₁, p₂, ..., pₙ}
Then the expected value of that experiment will be:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.
So the outcomes are:
{3, 5}
The probabilities are:
{8/10, 2/10}
Then the expected value is:
EV = 3*(8/10) + 5*(2/10) = 3.4
B) If we add another slip of paper with a number 3 on it, the new probabilities are:
{9/11, 2/11}
Then the new expected value is:
EV = 3*(9/11) + 5*(2/11) = 3.36
C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:
{10/12, 2/12}
So the new expected value is:
EV = 3*(10/12) + 5*(2/12) = 3.33
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summarize how you can find the slope of a parallel line.
Summary of slope of parallel lines:
Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.
If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.
The coefficients for "x" and "y" in the equations that depict parallel lines are identical.
Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.
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The effectiveness of two types of textbook is compared. A class of 30 students is randomly divided into two groups. One group uses digital textbooks and the other group uses paper textbooks. A summary of their test scores at the end of the session is given below. Digital Textbook: Paper Textbook: Construct a 90% confidence interval for the difference in scores between the two groups assuming underlying normal distributions with equal variance. Find the lower bound of the confidence interval (round off to first decimal place).
Answer:
- 18.377
Step-by-step explanation:
n1 = 17 ; xbar1 = 78.4 ; s1² = 90.3
n2 = 13 ; x2bar = 92 ; s2² = 107.8
Confidence interval :
(x1 - x2) ± Tcritical * sqrt[(sp²/n1 + sp²/n2)]
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
df = n - 1
Sp² = (16*90.3 + 12*107.8) / 28
Sp² = 97.8
Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)
Tcritical = 1.313
(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]
Margin of Error = Tcritical * sqrt[(sp²/n1 + sp²/n2)] Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473
Lower boundary :
(78.4-92) - 4.7771473
-13.6 - 4.7771473
= −18.3771473
= - 18.377
88 student said they watch TV everyday. This number represents 80% of the students body. What is the total number of students in the student body? And i need you to give me the part,whole,and percent
The total number of students in the student body is 110.
How many students are in the student body?Percentage is the ratio of an amount expressed as a number out of 100. The sign that is used to represent percentage is %.
In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.
In order to determine the total number of students in the student body, divide the number of students that watch TV everyday by the given percentage.
Number of students in the student body = number of students that watch TV everyday / percentage
88 / 80%
= 88 / 0.8 = 110
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Bea T. Howen, a sophomore college student, lost her scholarship after receiving a D in her "Music Appreciation" course. She decided to buy a snow plow to supplement her income during the winter months. It cost her $6312.50. Fuel and standard maintenance will cost her an additional $8.75 for each hour of use. Find the cost function C(x) associated with operating the snow plow for x hours. C(x)= If she charges $34.00 per hour write the revenue function R(x) for the amount of revenue gained from x hours of use. R(x)= Find the profit function P(x) for the amount of profit gained from x hours of use. P(x)= How many hours will she need to work to break even? hours
Answer:
[tex](a)\ C(x) = 6312.50 + 8.75x[/tex]
[tex](b)\ R(x) = 34x[/tex]
[tex](c)\ P(x) = 6312.50 -25.25x[/tex]
[tex](d)\ Break\ Even = 250\ hours[/tex]
Step-by-step explanation:
Solving (a): The cost function.
Given
[tex]Cost = \$6312.50[/tex] --- cost of saxophone
[tex]Additional = \$8.75[/tex] per hour
The cost function is: sum of the cost of the saxophone and the extra cost per hour.
If an hour costs 8.75, then x hours will cost 8.75x
So, the cost function is:
[tex]C(x) = Cost + Additional[/tex]
[tex]C(x) = 6312.50 + 8.75x[/tex]
Solving (b): The revenue function
Given
[tex]Charges = \$34.00[/tex] per hour
The revenue function is the product of the unit charge by the number of hours.
If in an hour, she charges $34.00, then in x hours, she will cost 34x
So, the revenue function is:
[tex]R(x) = Charges * Hours[/tex]
[tex]R(x) = 34.00 * x[/tex]
[tex]R(x) = 34x[/tex]
Solving (c): The profit function
This is the difference between the cost function and the revenue function
i.e.
[tex]P(x) = C(x) - R(x)[/tex]
So, we have:
[tex]P(x) = 6312.50 + 8.75x - 34x[/tex]
[tex]P(x) = 6312.50 -25.25x[/tex]
Solving (d): The break even hours.
To do this, we simply equate the cost function and the revenue function, then solve for x
i.e.
[tex]C(x) =R(x)[/tex]
[tex]6312.50 + 8.75x = 34x[/tex]
Collect like terms
[tex]6312.50 =- 8.75x + 34x[/tex]
[tex]6312.50 = 25.25x[/tex]
Solve for x
[tex]x = \frac{6312.50}{25.25}[/tex]
[tex]x = 250[/tex]