Therefore, the interval (0, 1) must be countless and infinite. Since the interval (0, 1) is as large as R, R is also infinite.
Interval:
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing (0, 1), and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Open Interval:
Open intervals do not include endpoints and are indicated by parentheses. For example, (0, 1) means greater than 0 and less than 1. This is (0, 1) = {x | 0 This interval can also be expressed as ]0, 1[ . Please refer to the following.
Closed Interval:
A closed interval is an interval that contains all boundary points and is indicated by square brackets. For example, [0, 1] means greater than or equal to 0 and less than or equal to 1.
Half- Open Interval:
A half-open interval contains only one of its endpoints and is represented by a combination of open and closed interval notation. Example: (0, 1) means greater than 0 and less than or equal to 1, [0, 1) means greater than or equal to 0 and less than 1.
Complete Question:
II. Identify the following terms described in each item. Quantitative & Quaeritated. It can be separated into different categories that are distinguished by some nonnumeric characteristics. 2. It consists of numbers representing counts or measurements. Quantitative Quantitative 3. The result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on 4. The result from infinitely many possible values that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions 5. It is characterized by data that consist of names, labels, or categories only. 6. It involves data that may be arranged in some order, but differences between data values either cannot be determined or are meaningless. 7. It involves meaningful amounts of differences between data. It has no true zero point or absolute zero. 8. It contains all the properties of the interval level but has true zero point or absolute zero. 9. It is a complete collection of all elements to be studied. 10. It is a branch of Mathematics that deals with the collection, organization presentation, analysis, and interpretation of data.
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Winston has a savings in a bank and was surprised that his money
accumulated to P 65. 000 after 3 years. He knew that the bank offered him 5%
interest rate compounded bimonthly. How much was his sayings at the start?
The initial saving of the Winston was $55952.48
Compound InterestCompound interest is when you receive interest on both your interest income and your savings.
According to the question given,
Let the initial savings amount be P
We know Compound interest =
[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest is applied per year
t = number of time periods elapsed
Given,
A = $65000
t = 3 years
r = 5% = 0.05
n = 2 *12 = 24
So
65000 = P(1 + (0.05/24))^72
P = $55952.48
Therefore the initial savings was $55952.48
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please answer correctly
cans someone please help me
Answer:
8 x 16 = 128 (area of rectangle)
Area of triangle:
16 - 12 = 4
6 x 4 = 24
24 divided by 2 = 12 (area of triangle)
Now lets add both areas:
128 + 12 = 140 ft2 is your answer.
Solve the inequality x-4 < - 3.Then graph the solution set.show your work.
Answer:
x < 1
Step-by-step explanation:
x - 4 < - 3
+ 4 +4 Do inverse operations by adding 4 on both sides
x < 1
Therefore, the answer is x < 1.
(It isn't allowing me to attach a photo but I am just going to try make a visual of the graph below)
<------------------------------o------------------>
-4 -3 -2 -1 0 1 2 3 4
The circle is open because based on the concept that in inequalities, less/greater than and/or equal to (such as these ≥ ≤ ) signs are graphed with closed circles, while less/greater than (like these > <) signs are graphed with open circles. The direction of the arrow is moving to the left on the number line because all possible values for x would be less than 1. When graphing the inequality you would use a solid line rather than a dashed line (I had to improvise since I could not attach an image).
HELP!!! NO LINKS PLEASE!!!
a) A designer has a circular tablecloth with radius 0.5 m. He wants to sew a fringe around the cloth. The fringe is sold by the tenth of a meter.
(i) What length of fringe is needed?
(ii) One meter of fringe costs $4.70. How much will the fringe cost?
b) A semicircular mat has a diameter of 18 m. What is the area of the mat?
Step-by-step explanation:
a) (i) length = 2(pi)r = 2(3.14)(.5 m) = 3.14 m
(ii)3.14 m × ($4.70/m) = $14.76
b) A = (pi)r^2 = (3.14)(18 m)^2 = 1017.9 m^2
Consider the directed line segment from M(−3, 1) to N(3, 4). Determine which of the following statements are true.
A
The point P(1, 3) partitions the segment in the ratio 2 to 1.
B
The point Q(−1, 2) partitions the segment in the ratio 1 to 2.
C
The point R(0, 2.5) partitions the segment in the ratio 1 to 2.
D
The point S(0, 2.5) partitions the segment in the ratio 1 to 1.
E
The point T(−1, 4.5) partitions the segment in the ratio 1 to 1.
Help please! Thank you
Answer:
the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.
Please answer!!! I’m stuck on it and need help fast <3
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Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (- 1, 8) ← 2 ordered pairs from the table
m = [tex]\frac{8-6}{-1-1}[/tex] = [tex]\frac{2}{-2}[/tex] = - 1 , then
y = - x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (1, 6 ) , then
6 = - 1 + c ⇒ c = 6 + 1 = 7
y = - x + 7 → B
Type ONLY your numeric answer. You do not need the degree symbol.
Answer: 54
Step-by-step explanation:
1) First, we need to find what 'x' is. We know that the exterior angles of a triangle equal to 360. So, we will add up all the expressions and set them equal to 360.
7x-2 + 9x-31 + 4x +33 = 360.
2) We will add all the like terms, which will give us: 20x + 0 = 360. We don't need to add the 0.
3) Now, we will isolate the 'x' by dividing 360 by 20 and we will get: x= 18.
4) To find the measure of angle DCE, we just have to substitute x in '7x-2' with 18, which then would equal to: 124.
5) Now, that we have the adjacent angle of DCE, we just have to subtract 124 from 180, and we will get the answer.
6) Angle DCE equals to 54.
To the nearest square centimeter, what is the area of the shaded sector in he circle shown below? Radius= 12 cm, angel = 110 degrees
Answer:
138.23 cm²
Step-by-step explanation:
The formula for the area of a sector is given as:
θ/360 × πr²
θ = 110°
Radius = r = 12 cm
Hence
Area of a sector = 110/360 × π × 12²
= 138.23007676 cm²
Approximately, Area of a sector = 138.23 cm²
Please help! Due tomorrow!!!
Homework assignments are worth 12 points and tests are worth 100 points. A teacher records the homework averages and test averages for 10 students. Use a graphing calculator to find an equation of the line of best fit. Round each value in your equation to the nearest tenth.
Answer:
y=7.5x+6.2
Step-by-step explanation:
Hopefully this is the answer
Answer:
y=7.5x+6.2
Step-by-step explanation:
Hopefully this is the answer
Calculate the slope of the following line:
m=
Answer:
m= -1/3
Step-by-step explanation:
slope is rise/run or change in y/change in x
i pick out point (9,0) to (6,1)
the increase in y of this triangle is 1 and increase in x is 3
note that this line will have a negative slope as it goes downwards from left to right instead of upwards
hence m= rise/run= -1/3
A scientist studies the population of an insect colony. She begins her study with 10,000 insects in the colony and measures the population of the colony
each year. She uses the given formula to model the insect population, P, é years since the beginning of the study.
P= 10,000(1.08)
By what percent does the Insect population grow each year?
%
Please help! Due Soon - You will get 30 points and brainliest! - 4 pictures in total - links=reported - thanks!
Answer:
(the last one) i think its B
Step-by-step explanation:
Select the correct answer.
How many solutions does this system of equations have?
y = 2x + 5
y = x^3 + 4x^2 + x + 2
A. No solution
B. 1 solution
C. 2 Solutions
D. 3 Solutions
An equation is formed of two equal expressions. The number of solutions that the given system of equation will give is 3. Thus, the correct option is D.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The number of solutions that the system of equations will have can be found by plotting both the equation on the graph.
Since the point at which the graph intersects is the solution of the system of equations.
Hence, the number of solutions that the given system of equation will give is 3. Thus, the correct option is D.
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Please help me with this question:
What is 2x-2?
Answer:
as a factor 2(x-1) this should help or be the correcr answer
Solve the equation using the quadratic formula. X^2-9x+3=0
Answer:
The answer is x= [tex]\frac{9+\sqrt{69}}{2}[/tex], x= [tex]\frac{9-\sqrt{69}}{2}[/tex]
Step-by-step explanation:
x^2=a
-9x=b
3=c
Plug into formula.
Equation: [tex]\frac{9+-\sqrt{(-9)^2-4(1)(3)}}{2}[/tex]
Simplify the equation.
Equation: [tex]\frac{9+-\sqrt{81-12}}{2}[/tex]
Subtract 81 and 12.
Equation: [tex]\frac{9+-\sqrt{69}}{2}[/tex]
Spit into two equations
Equation 1: [tex]\frac{9+\sqrt{69}}{2}[/tex]
Equation 2: [tex]\frac{9-\sqrt{69}}{2}[/tex]
Hope this helps!
Yolanda's Flower Shop sells long-stem roses for $5 each. In addition, the
shop charges a $15 shipping fee. How many roses can Santo purchase if he
plans to spend $90?
Answer:
15
Step-by-step explanation:
5x + 15 <= 90
5x<=75
x=15
Answer:
15 roses
Step-by-step explanation:
90 (Amount Santo wants to spend)
15 (Shipping fee)
You first subtract Shipping Fee from the total amount Santo wants to spend
90-15=75
Next it's time to figure out how many roses he can buy with the $75
Each roses is $5, so you divide the left over money after shipping by the price of the rose.
75÷5=15
2. Tell whether the segment lengths form an acute, right, or obtuse? 9, 12, 17
Answer:
obtuse angled triangle
Step-by-step explanation:
Given 3 segments , say a, b and c , with c the longest then
• If a² + b² = c² ⇒ right triangle
• If a² + b² > c² ⇒ acute triangle
• If a² + b² < c² ⇒ obtuse triangle
Here c = 17 and 17² = 289
9² + 12² = 81 + 144 = 225
Since 225 < 289 , then triangle is obtuse
In the diagram, two circles, each with center $D$, have radii of $1$ and $2$. The total area of the shaded region is $\frac5{12}$ of the area of the larger circle. How many degrees are in the measure of (the smaller) $\angle ADC$
Angle ADC = 120 degrees.
What is area of sector?A certain portion of a circle that is created based on two radius of the same circle and one arc. Area of sector for a circle with radius r is given by π r²Ф/ 360°
What is the angle of ADC in the smaller circle?
Given, two circles of radius 1 unit and 2 unit which have same center D.
We know area of a circle = π r²
Area of larger circle = π 2² = 4π
it is said that the total area of the shaded region that means area of a particular sector is 1/12 of the area of the larger circle.
area of sector, ACD = 1/12 ×4π
as per the question, the ACD sector is located in the smaller circle that has radius 1 unit.
formula for area of sector ACD = π r² ×Ф/360°
where,Фis the central angle of ACD sector
and Ф = ADC
from the above statement, 4π/12 = π r² ADC/360
ADC = 1/3×360°
ADC = 120 degrees
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How many 1/3 cup servings are there in 10 cups of cereal?
Answers:
30
1/10
1/3
9
Answer:
30
Step-by-step explanation:
Solve for x. *they are similar* NO BOTS OR ELSE U WILL BE REPORTED
Answer:
x = 5
Step-by-step explanation:
i will insert an image of my work below
Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
The best answer is t = 7. Option C
What is a quadratic equation?A quadratic equation is simply defined as an equation that could be rearranged in standard form.
It is also described as an algebraic equation having the highest exponent of as 2.
It is so arranged such that;
x represents an unknown valueVariables, a, b, and c represent known numbersAlso, a is not equal to 0, a ≠ 0It is important to note that the three methods of solving quadratic equation are;
FactorizationUsing the quadratic formulaUsing completing the square methodFrom the information given, we have that the form is;
x² = c
Given t squared minus 49 = 0
First, represent mathematically
t² - 49 = 0
Now, collect like terms, we have;
t² = 49
Take square root of both sides
t = √49
t = 7
Hence, the equation is t = 7
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Seven netball teams played in a school's competition. Each team had 7 players. If 3/7 of the number of players were disqualified for poor conduct, how many pupils were qualified?
y = -11x - 25 ...........(i)
y = 5x - 7 ...............(ii)
Answer:
3/2
Step-by-step explanation:
5x-7=-11x-25
5x+11x=-25+7
16x=18
x=18/16
x=3/2
How do you find the difference between two different numbers?
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.
Subtracting two integers from each other is a type of subtraction.
The process for determining the difference between two decimals and two whole numbers is the same.
We only add a new step.
Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.
To give them all the same amount of decimal places, we must first convert each decimal.
7.2 becomes 7.200 as a result.
The computation may now be done as before:
8.967 - 7.200 = 1.767
Therefore, there is a 1.767 discrepancy between these figures.
In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.
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If { 4x+y=13
x−y=2
, then y=
Answer:
2.5
Step-by-step explanation:
Taking eguation i
4x+y=13
x= 13-y/4
Taking equation ii
x-y = 2
Substituting the value of x in eq i from ii
x- y =2
13-y/4- y=2
13-y-y=2×4
13-2y =8
-2y=8-13
y=-5/-2
Therefore y=2.5
Please Answer ASAP!
Will give 85 points for answer!
Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class. If the ratio of students who prefer free time at the beginning of class to students who prefer free time at the end of class is 13 over 17, what does the ratio 13 over 17 represent?
Answer:
Step-by-step explanation:
Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
What is a Ratio?
This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.
Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.
Answer:
Step-by-step explanation:
the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning
Calculate the slope of the line.
m=
Answer:
m=4
Step-by-step explanation:
look at the traingle formed with line with points (6,5) and (4, -3)
look at change in y (how tall the triangle is) and change in x (the base of triangle)
change in y=8
change in x=2
m=rise/run also known as change in y/change in x
=8/2
=4
note that this is a positive gradeint line