If f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
What is a function?
In mathematics, a function is a rule that assigns a unique output to each input in a set. A function is continuous if the output value changes smoothly as the input value changes, without any sudden jumps or breaks.
To prove that if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem.
The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], and if y is any value between f(a) and f(b), then there exists at least one x in the interval [a,b] such that f(x) = y.
In our case, f is a function from [0,1] to R, which is a closed interval, and f is continuous on this interval. Therefore, the intermediate value theorem applies to f.
To prove that there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem with y = 0. Since 0 is between f(0) and f(1), the intermediate value theorem guarantees that there exists at least one x in [0,1] such that f(x) = 0.
Hence, if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
To learn more about the function, visit:
https://brainly.com/question/11624077
#SPJ4
Solve the system.
2x + y + 3z = 20
X + 2y - z = -11
3x - 2z = -3
Enter your answer as an ordered triple.
The solution to the system, as an ordered triple is: (3, -4, 6).
How to Solve a System of Equations?To solve the following given system of equations:
2x + y + 3z = 20 --> eqn. 1
x + 2y - z = -11 --> eqn. 2
3x - 2z = -3 --> eqn. 3
Multiply equation 1 by 2 to get eqn. 4:
4x + 2y + 6z = 40 --> eqn. 4
Subtract eqn. 4 from eqn. 2:
x + 2y - z = -11 --> eqn. 2
4x + 2y + 6z = 40 --> eqn. 4
-3x - 7z = -51 --> eqn. 5
Add equations 3 and 5 together:
3x - 2z = -3 --> eqn. 3
-3x - 7z = -51 --> eqn. 5
-9z = -54
z = -54/-9
z = 6
Substitute the value of z into equation 5:
-3x - 7(6) = -51 --> eqn. 5
-3x - 42 = -51
-3x = -51 + 42
-3x = -9
-3x/-3 = -9/-3
x = 3
Find the value of y by substituting the values of x and z into equation 1:
2(3) + y + 3(6) = 20 --> eqn. 1
6 + y + 18 = 20
24 + y = 20
y = 20 - 24
y = -4
The solution as an ordered triple is: (3, -4, 6).
Learn more about the solution of a system on:
https://brainly.com/question/28048601
#SPJ1
PLEASE HELP WILL GIVE 100 POINTS
Answer:
72y
Step-by-step explanation:
Perfect square monomials are in the form:
[tex]x^2+bx+\left(\dfrac{b}{2}\right)^2[/tex]
They factor as:
[tex]\left(x + \dfrac{b}{2}\right)^2[/tex]
To find the middle term of this polynomial, first factor 16 out of the expression.
[tex]16(y^2 \: + \: ?+5.0625)[/tex]
We know that the middle term will be in the form [tex]by[/tex], and the last term will be in the form [tex]\left(\dfrac{b}{2}\right)^2[/tex]. Using this information, we can solve for b.
[tex]5.0625 = \left(\dfrac{b}{2}\right)^2[/tex]
[tex]\sqrt{5.0625} = \dfrac{b}{2}\right[/tex]
[tex]4.5 = b[/tex]
Then, we can substitute that into the term [tex]by[/tex].
[tex]16(y^2 + 4.5y+5.0625)[/tex]
Finally, distribute the 16 and then take the middle term as the answer.
[tex]16y^2 + 72y+81[/tex]
72y
Answer:
72y or -72y-----------------------------
We are given a binomial and need to add a monomial to make it a perfect square.
Recall the identities for a square of a sum or difference of two numbers:
(a ± b)² = a² ± 2ab + b²Analyze the given and compare with the identity above:
16y² + ... + 81Here 16y² = (4y)² and 81 = 9², so a = 4y and b = 9.To complete the square we need to add ± 2ab, which is:
± 2ab = ± 2(4y*9) = ± 72yBy adding this we get:
16y² + 72y + 81 = (4y + 9)²or
16y² + (-72y) + 81 = (4y - 9)²4. *
This pattern of squares continues. Which equation below relates the number of squares, n, in a picture to the size number, s ?
Size 1
Size 2
a) n=s+4
b) n=4 s
c) n=4 s+1
d) s=4 n
A
B
c
D
The required equation that following the pattern is n = 4s+1. So the option c is correct.
In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.
The given options are:
a) n = s+4
b) n = 4s
c) n = 4s+1
d) s = 4n
We find the pattern we firstly observe the given diagram closely.
As we can see that in first diagram have 5 blocks.
In second diagram have 9 blocks.
In third diagram have 13 blocks.
So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.
To learn more about finding pattern link is here
brainly.com/question/29023099
#SPJ4
Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data.
Researcher A
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 26 0.17 0.17
2-4 30 0.20 0.37
4-6 49 0.33 0.70
6-8 25 0.17 0.87
8-10 12 0.08 0.95
10-12 8 0.05 1
Researcher B
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 48 0.32 0.32
2-4 51 0.34 0.66
4-6 24 0.16 0.82
6-8 12 0.08 0.90
8-10 11 0.07 0.97
10-12 4 0.03 1
Give a reason why the data may differ.
A) The researchers are studying different statistics, so there will be some variation in the data.
B) The researchers are studying different parameters, so there will be some variation in the data.
C) The researchers are studying the same statistic, so there will be some variation in the data.
D) The researchers are studying different samples, so there will be some variation in the data.
E) The researchers are studying the same population, so there will be some variation in the data.
The reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
What is meant by data?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Write types of data.Qualitative, quantitative, discrete, continuous, primary and secondary are the types of data.
Since researches choose same school but group of 150 people is randomly chosen and different therefore, the reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
To learn more about data visit the link:
https://brainly.com/question/26711803
#SPJ4
Kyra is blocking off several rooms in a hotel for guests coming to her wedding. The hotel can reserve large rooms that can hold 4 people, and small rooms that can hold 3 people. Kyra reserved twice as many large rooms as small rooms, which altogether can accommodate 77 guests. Determine the number of small rooms reserved and the number of large rooms reserved.
Answer:
19 small room and 25 big room
Step-by-step explanation:
Which figure has four sides that are the same length
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The cone will fit in 4 times and the volume of the cone is 535.89 in³
Volume of a ConeTo solve this problem, we have to find the volume of the cone and the volume of the sphere.
The formula of volume of a cone is given as;
V = 1/3πr²h
v = volume of the coner = radius of the coneh = height of the coneWe need to calculate the volume of the sphere which is given as
V = 4/3 πr³
The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³
The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³
The number of times it will fit into will be 2143.57 / 535.89 = 4
It will fit in 4 times
b)
The volume of the cone is 535.89in³
Learn more on volume of a cone here;
https://brainly.com/question/12004994
#SPJ1
A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 24 feet across at its opening and 2 feet deep at its center, where should the receiver be placed?
Find the equation of the parabola?
How far above the vertex should the receiver be placed?
Equation of parabola: y =ax² and receiver should be placed 18 feet above vertex.
Explanation:
Considering satellite dish as parabola we can have vertex as origin and concave upward.
So, equation of parabola will be justifying structure of satellite dish i.e
y = ax² -------(1)
Two points other than (0,0) are (-12,2) and (12,2), unit being feet.
This points will satisfy equation of parabola, substituting them in equation 1, we will calculate the value of constant 'a'.
a = [tex]\frac{2}{12^{2} }[/tex]
[tex]\frac{2}{2*6*12}\\ =\frac{1}{72}[/tex]
Substituting value of a = 1/72 in equation 1 we get
72y = x²
As receiver need to be located at focus, so it will be places at a distance of 'p' above the vertex
4p = 72
Dividing both sides by 4, we get
p = 18 feet
So, receiver will be placed at a distance of 18 feet above vertex.
Learn more about parabola here:
https://brainly.com/question/64712
#SPJ4
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The cone would fit into the beachball two times, and has a volume of 134 in^3. Answers required are:
Blank 1 - two
Blank 2 - 134 in^3.
A beachball has the shape of a sphere, so that its volume can be determined by;
volume of a sphere = 4/3 [tex]\pi r^{3}[/tex]
where r is the radius of the sphere.
Given that the diameter of the beachball is 8 inches, then;
its radius = 8/ 2
= 4 inches
volume of beachball = 4/3 x 22/7 x 4^3
= 268.19 cubic in.
The volume of a cone can be determined by;
volume of a cone = 1/3 [tex]\pi r^{2} h[/tex]
where r is its radius, and h is its height.
Given a cone of radius 4 inches and height 8 inches, then;
its volume = 1/3 x 22/7 x 4^2 x 8
= 134.1cubic inches
Thus,
268.19/ 134.10 = 1.999993
≅ 2.0
Thus the cone would fit into the beachball twice, and its volume is 134.10 in^3.
Learn more about volume of a cone and sphere at https://brainly.com/question/16123866
#SPJ1
What is the measure of angle I? (number only)
If H is
102°
Answer:<I=78
Step-by-step explanation:
<1 and 102 are supplementary angles so they add to 180 degrees
<1 + 102 = 180
Subtract 102 from each side
<1 + 102 -102 = 180-102
<1 = 78
Question 6 A test of hypothesis was performed to determine, at 5% level of significance, if the majority of the engineering graduates pass the PE exam in their first try. If the computed value of the test statistic Z based on the sample information is z = 2.10, then the p-value for this test is: 0.00895 O 0.05 0.9821 None of these O 0.0179 N • Previous Not saved S
The p-value for the test is 0.9821.
What is hypothesis?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
What is z-score?
You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.
Given that the test statistic Z based on the sample information is z = 2.10.
z = 2.1 + 0.00
From the z-score table the value of p is 0.9821.
To learn more about p-value, click on below link:
https://brainly.com/question/29101924
#SPJ4
d) an undeclared major thinks that the time it takes for a freshmen to pick their major has a standard deviation of 1 year. to find the average he surveys 10 freshmen and finds out how long it took them to pick a major. he does a confidence interval to find the average time it takes.
The time it takes a freshman to choose their major is thought to have a standard deviation of one year by an undeclared major. A t-distribution table can be used to determine the crucial value.
The confidence interval for the average time it takes for freshmen to pick a major can be found by taking the sample mean of the 10 freshmen surveyed and adding and subtracting
The margin of error is calculated by multiplying the sample standard deviation by the critical value from a t-distribution with degrees of freedom equal to (n-1), where n is the sample size.
The sample size in this instance is 10. A t-distribution table can be used to determine the crucial value.
Learn more about standard deviation here
https://brainly.com/question/13905583
#SPJ4
Please help with attached linear function question. Thank you!!
The graph of cubic equations, a to d and the associated cubic equations are as follows;
Equation (B) ⇒ Graph a
Equation (C) ⇒ Graph b
Equation (D) ⇒ Graph c
Equation (A) ⇒ Graph d
What is a cubic equation?A cubic equation that has only one variable is an equation of the form a·x³ + b·x² + c·x + d, where a ≠ 0.
The evaluation of the graphs are as follows;
Graph a
The y-intercept of the graph a, is 1, and the x-intercept, which is a solution of the equation is x = -1,
Therefore, when x = 0, y = 1, and when y = 0, x = -1
The function in graph a represents the translation of the parent function, y = x³, one unit, upwards, which corresponds with the function;
y = x³ + 1
Therefore, graph a corresponds to cubic equation (B) y = x³ + 1
Graph b
The y-intercept is one (1), and the turning point is at the point x = -1, which represents a shift of one unit to the left, and which can be obtained by the equation; y = (x + 1)³
Therefore, graph b corresponds with the cubic equation (C) y = (x + 1)³
Graph c
The turning point of the graph and the y-intercept is shifted one unit down, which corresponds with the equation; (D) y = x³ - 1
Graph d
The turning point is shifted 1 unit to the right and is located on the x-axis, The y-intercept is located at the point y = 1, therefore, the graph corresponds with the equation y = (x - 1)³
Graph d corresponds to equation (A), y = (x - 1)³
Learn more about the graphs of cubic equations here:
https://brainly.com/question/9401169
#SPJ1
In the case of Regression Analysis, the dependent variable must be ________; in multiple discriminant analysis, the dependent variable is______ in nature.
a. Metric; nonmetric
b. Metric; nominal
c. Nominal; categorical
d. Categorical; nonmetric
b. Metric; nominal
In the case of regression analysis, the dependent variable must be metric; in multiple discriminant analysis, the dependent variable is nominal in nature. (Option B)
Regression analysis refers to a collection of statistical methods which are used for the estimation of relationships between a dependent variable and one or more independent variables. It can used to assess the strength of the relationship between variables and for modeling their future relationship. In regression analysis the dependent variable is metrically scaled (where distance between values can be calculated). Multiple discriminant analysis is a regression technique used in statistics to group objects into categories for analysis. In multiple discriminant analysis the dependent variable is nominally scaled (where characteristics can be distinguished).
Learn more about Regression analysis:
https://brainly.com/question/7781679
#SPJ4
standard form of (2 ten thousands 7 thousands) divided by 10
Answer:
2,700
Step-by-step explanation:
10,000x2=20,000+7,000=27,000÷10=2,700
Is this correct? Or no?
Answer:
No
Step-by-step explanation:
No, this is not correct. When you divide both sides of an inequality by a negative number, the inequality symbol must be reversed. So in this case, dividing both sides of the inequality -3x > 9 by -3 would give us x < -3, which is not what Diego claimed.
the model that includes as predictors all independent variables but no quadratic or interaction terms.
When each independent variable is changed by one unit, use linear regression to get the mean change in the dependent variable. Polynomials can be used to simulate curvature as well as to add interaction effects.
An entire second order model is what?
The x1 and x2 linear terms, the x12 and x22 second-degree terms, and the x1x2 interaction term make up the entire second degree polynomial model. As could be used to represent the estimated model.
Which kind of model would you apply to discover the relationship between the dependent and independent variables?
Considering a one-unit change in each independent variable, use linear regression to determine the mean change in a dependent variable. To represent curvature and take interaction effects into account, you may also employ polynomials.
To know more about independent variables visit:
https://brainly.com/question/29430246
#SPJ4
The complete question is "Consider a regression analysis with three independent variables x1,x2, and x3. Give the equation for the following regression models: a. The model that includes as predictors all independent variables but no quadratic or interaction terms. b. The model that includes as predictors all independent variables and all quadratic terms. c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model)."
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)? i need this now
-3
3
1/3
-1/3
Answer:
m = -1/3
Step-by-step explanation:
(-1, 2) and (-4, 3)
m = 3-2/-4+1
m = 1/-3
m = -1/3
3x+5y = 4
Constant?
Change?
4x2 + y = 4
Constant?
Change?
6x + 1 = y
Constant?
Change?
Answer:
Step-by-step explanation:
Ian's car can go 165 miles on 5 gallons of gas. During a drive last weekend, Ian used 6 gallons of gas. How far did he drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas he used.
The distance that Ian can drive is 198 miles.
How far did Ian drive?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Here, Ian's car can go 165 miles on 5 gallons of gas. The mile per gallon will be:
= 165 / 5
= 33 miles per gallon.
Therefore, the miles in 6 gallons will be:
= 33 × 6
= 198 miles.
The distance is 198 miles.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Answer:
She will have a balance of more than $18 for up to 6 days
Step-by-step explanation:
Start with $30.
Each day, x, subtract $1.99 from $30.
30 - 1.99x
The amount must be greater than $18.
30 - 1.99x > 18
Subtract 30 from both sides.
-1.99x > -12
Divide both sides by -1.99. Remember than when you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction.
-1.99x/(-1.99) < -12/(-1.99)
x < 6.03
The number of days must be less than 6.03. Since we deal with whole days, she will have a balance of more than $18 for up to 6 days.
HELP PLEASE ASAP!!!
The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.
Answer:
D= [-4,-1) U (2,4)
R = [-3,5)
PLEASE HELP WILL MARK BARINLIEST
Answer:
d= 120
Step-by-step explanation:
c+d = 180 degree
d = 180-60 =120 degree
Find the sum.
17x³ + (3x + 8x³) =
Calculate and then write the reciprocal of your answer.
2/43 of the difference of 3 2/15 and 2 5/12
The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
Here, we have to subtract 2 mixed fractions i.e
=> (3 2/15) - (2 5/12)
which when converted to a proper fraction is equal to,
=> (47/15) - (29/12)
= 43/60
∵ (3 2/15) - (2 5/12) = 43/60
now, 2/43 of the difference of 3 2/15 and 2 5/12,
=> (2/43) × (43/60) = 1/30............(i)
taking the reciprocal of the value obtained above,
∴ reciprocal of 1/30 = 30.
Thus, The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.
To learn more about reciprocal,
https://brainly.com/question/2534506
Find the slope.
x
012345
y 3 6 9 12 15 18
The slope of the line is 3.
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Given that, are points of a line,
The slope of a line passing through two points is = (y₂-y₁)/(x₂-x₁)
Considering the points (0, 3) and (1, 6)
Therefore, slope = (6-3)/(1-0) = 3
Hence, the slope of the line passing through the given points is 3.
For more references on slope, click;
https://brainly.com/question/3605446
#SPJ1
Find the derivative of f(x) = 3x² + 2x at 3. That is, find f '(3).
Answer:
20
Step-by-step explanation:
To find the derivative of f(x) = 3x² + 2x at x = 3, we can use the power rule:
f'(x) = 2*3x + 2
When x = 3, the derivative of f(x) is:
f'(3) = 2*3(3) + 2
f'(3) = 18 + 2
f'(3) = 20
Therefore, the derivative of f(x) = 3x² + 2x at x = 3 is f'(3) = 20.
Carli is comparing two phone companies. Big Phone Company charges $0.39 for the connection fee and $0.03 per minute. Little Phone Company charges $0.25 for the connection fee and $0.07 per minute. Which system of equations could be used to determine the total cost, y, for using x minutes?
Answer:
Step-by-step explanation:
I also need help.
finding missing angle of 32 and 17 with trigonometry
What is 2 1/5 divided by 4/5 in mixed number form???