Answer:
Step-by-step explanation:
(4 , 1) ; x₁ = 4 and y₁ = 1
(4 , -5) ; x₂ = 4 and y₂ = -5
The slope of the the line is undefined as the line is parallel to y-axis
In response to nutrition concerns raised last year about food served in school cafeterias, the Smallville School District entered into a one-year contract with the Healthy Alternative Meals (HAM) company. Under this contract, the company plans and prepares meals for 2,500 elementary, middle, and high school students, with a focus on good nutrition. The school administration would like to survey the students in the district to estimate the proportion of students who are satisfied with the food under this contract. Two sampling plans for selecting the students to be surveyed are under consideration by the administration. One plan is to take a simple random sample of students in the district and then survey those students. The other plan is to take a stratified random sample of students in the district and then survey those students. (a) Describe a simple random sampling procedure that the administrators could use to select 200 students from the 2,500 students in the district. (b) If a stratified random sampling procedure is used, give one example of an effective variable on which to stratify in this survey. Explain your reasoning>
The students corresponding to those 200 numbers would beasked to participate in the survey.
What is corresponding ?
Having or participating in the same relationship (such as kind, degree, position, correspondence, or function) especially with regard to the same or like wholes (such as geometric figures or sets) corresponding parts of similar triangles. : related, accompanying.
Have given,
a) The administrators could number an alphabetical list of students from 1 to 2,500.Then use a random number generator from a calculator or computer to generate 200 unique random numbers from 1 to2,500.(if you don’t say “unique”, then say “ignoring repeats”)The students corresponding to those 200 numbers would beasked to participate in the survey.
b) One advantage is that stratified random sampling guarantees that each of the school-level strata will have some representation, because it is possible that a simple random sample would miss one or more of the strata completely.(NOTE: It is NOT sufficient to say that a stratified sample “makes it MORELIKELY that all school-levels are represented in the sample”… the student must state that stratifying by school level GUARANTEES or ENSURES that all school levels are represented in the sample.)
The students corresponding to those 200 numbers would beasked to participate in the survey.
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Kelvin spends 1/4 of his $100 on a ticket to a play and then buys a shirt for $22.50. How much
of the $100 does Kelvin have left?
A $5.50
B $10.00
C $52.50
D $73.50
need answer right now
Please help me, I need to get this now
Answer:
see the attachment for a graph
Step-by-step explanation:
You seem to want a graph of the inequalities ...
y ≤ -3/2x -2y > 1/2x +6Boundary linesThe equations of the boundary lines are given by replacing the inequality symbol with an equal sign:
y = -3/2x -2y = 1/2x +6These are graphed in the usual way. It is often convenient to find the y-intercept, then use the slope to locate other points on the line.
y = -3/2x -2
The y-intercept is (0, -2). The line has a rise/run of -3/2, so goes down 3 units for each 2 to the right. Another point on the line is (2, -5).
y = 1/2x +6
The y-intercept is (0, 6). The line has a rise/run of 1/2, so goes up 1 unit for each 2 to the right. Another point on the line is (2, 7).
Line typeWhen the "or equal to" symbol (≤ or ≥) is used, the boundary line is solid. When the "or equal to" case is not part of the solution, the boundary line is dashed.
The line with negative slope through (0, -2) is solid; the line with positive slope through (0, 6) is dashed.
ShadingAll you need to determine shading is a variable with a positive coefficient, and the inequality symbol.
y ≤ . . . . . tells you shading is below the solid line
y > . . . . . tells you shading is above the dashed line
We notice x has a positive coefficient in the second inequality, so we could determine shading from ...
> x . . . . . tells you shading is left of the line (where x values are less than those on the line)
Of course, you can rearrange the inequality so a variable of interest has a positive coefficient. For example, we could add 3/2x to the first inequality to get ...
3/2x + y ≤ -2
Then, looking at the x-variable, we see ...
x ≤ . . . . . tells you shading is to the left of the line
Answer:
See attachment.
Step-by-step explanation:
When graphing inequalities:
< or > : draw a dashed line.≤ or ≥ : draw a solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Treat the inequalities as equations (swap the inequality sign for an equals sign) to find two points on the line to help draw the lines.
Inequality 1
[tex]y \leq -\dfrac{3}{2}x-2[/tex]
[tex]\begin{aligned}x=0 \implies y&=-\dfrac{3}{2}(0)-2\\y&=-2\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=-\dfrac{3}{2}(2)-2\\y&=-5\end{aligned}[/tex]
Plot the points (0, -2) and (2, -5).
Draw a solid straight line through the points.
Shade under the line.
Inequality 2
[tex]y > \dfrac{1}{2}x+6[/tex]
[tex]\begin{aligned}x=0 \implies y&=\dfrac{1}{2}(0)+6\\y&=6\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=\dfrac{1}{2}(4)+6\\y&=8\end{aligned}[/tex]
Plot the points (0, 6) and (4, 8).
Draw a dashed straight line through the points.
Shade above the line.
The solution to the two inequalities is the overlap of the shaded parts.
Select the correct answer from each drop-down menu.
The function f(x) = 500(1+004 models the balance in a savings account.
The savings account had an initial balance of
$500
$515
and compounds
Reset
Next
at an interest rate of
Answer:
Initial balance 500, compounds 4 times at an interest rate of 15%
Step-by-step explanation:
Initial balance 500, compounds 4 times at an interest rate of 15%
Answer the questions below about the quadratic function
f(x)=-x^2-10x-27
a) Does the function have a minimum or maximum value?
b) What does the functions minimum or maximum value?
c) Where does the minimum or maximum value occur?
Answer:
a) The function has a minimum value.
b) The minimum value of the function is -27.
c) The minimum value occurs at x=3.
Step-by-step explanation:
Use the points A(1,5), B(1,-4), C(-3,5), D(-3,-4)
Pls lmk by Thursday
Using the points A(1,5), B(1,-4), C(-3,5), D(-3,-4) the following are matched:
Distance between points B and C = √97.
Distance between points A and B = 9.
Midpoint between points B and C = (-1, 1/2).
Midpoint between C and D = (-3, 1/2).
Slope of the line through B and D = 0.
What is the distance between two points of a line?The distance between two points of a line is given as:
Distance = [tex]\sqrt{c - a)^2 + (d - b)^2}[/tex]
We have,
A(1,5), B(1,-4), C(-3,5) and D(-3,-4).
The distance between A and B.
= [tex]\sqrt{(1 - 1)^2 + (-4 - 5)^2}[/tex]
= √81
= 9
The distance between B and C.
= [tex]\sqrt{(-3 - 1)^2 + (5 + 4)^2}[/tex]
= √(16 + 81)
= √97
The midpoint (x, y) between B and C.
x = (1 - 3)/2 = -1
y = (-4 + 5) / 2 = 1/2
The midpoint (x, y) between C and D.
x = (-3 -3) / 2 = -6/2 = -3
y = (5 - 4) / 2 = 1/2
The slope of the line through points B and D.
= (-4 + 4) / (-3 - 1)
= 0/ -4
= 0
Thus,
The distance between A and B is 9.
The distance between B and C is √97.
The midpoint between B and C is (-1, 1/2).
The midpoint between C and D is (-3, 1/2).
The slope of the line through B and D is 0.
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(20points) Let A be a 4 x 4 matrix and let A be a eigenvalue of multiplicity 3. If A - AI has rank 1, is A defective? Explain.
Answer: No
Step-by-step explanation: If A − λI has rank 1, then the geometric multiplicity of λ is 4 − 1 = 3, equal to the algebraic multiplicity of λ.
The Matrix A is not defective.
What is the rank nullity theorem?A theorem in linear algebra known as the rank-nullity theorem states that the domain dimension of a linear map is equal to the sum of the rank (or the dimension of its image) and the nullity of the map (the dimension of its kernel).
Given:
We have A be a 4 x 4 matrix
let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have
Rank(A-λI) + Nullity((A-λI) =4
dimN(N-λI) = Nullity(A-λI)
dimN(N-λI) = 4 - Rank(A-λI)
dimN(N-λI) = 4-1
dimN(N-λI) = 3
As a result, eigenvalue is made up of 3 linearly independent eigenvectors.
This guarantees that there is another eigenvalue other than since is an eigenvalue of multiplicity 3. This provides us 4 linearly independent eigenvectors in the matrix A, in addition to the 3 linearly independent eigenvectors in the eigenspace of. Now we If and only if A has n linearly independent eigenvectors, then A is diagonalizable. A thus has no defects.
Hence, matrix A is not defective.
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What is the solution of the system? Use elimination.
3x +9y=33
-10x-6y=-14
a. (-4,5)
b. (4,-1)
c. (-10, 3)
d. (-1,4)
To solve the given system of equations using elimination, we can add the two equations together to eliminate one of the variables. Doing this, we get 3x + 9y + (-10x - 6y) = 33 + (-14), which simplifies to -7x + 3y = 19. We can then solve for y by dividing both sides of the equation by 3, giving us y = 19/3 = 6.33. We can substitute this value for y in either of the original equations to solve for x. For example, if we substitute 6.33 for y in the first equation, we get 3x + 9 * 6.33 = 33, which simplifies to 3x = 3.67. Dividing both sides of the equation by 3, we get x = 1.22. Therefore, the solution of the system is (1.22, 6.33), which is approximately (1, 6). The answer choice that is closest to this solution is (d) (-1, 4). Thus, the solution of the system is (-1, 4).
18) What is the slope of the line that contains points (–6, –6) and (–3, 1)?
The slope of the line is 7/9
How to determine the slope of the lineIt is important to note that the equation of a line is represented as;
y = mx + c
Where;
y is a point on the linem is the slope of the linex is a point on the x - axisc is the intercept of the y-axisThe formula for calculating the slope of a line is expressed as;
Slope, m = y₂ - y₁/x₂ - x₁
Now, let's substitute the values into the formula from the points given we have;
Slope, m =1 -(-6)/ -3 - (-6)
expand the bracket
Slope, m = 1 + 6/ 3 + 6
add the values
Slope, m = 7/9
Hence, the value is 7/9
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Use distributive property to solve 4/7x4 5/8
Applying distributive property of multiplication the solution of the multiplication problem is 5 11/56
What is distributive property of multiplication?The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.
This applied mathematically in the problem
4/7 x 4 5/8
dividing by 4 for the multiplicand and multiplier
4/7 ÷ 4 = 1/7
4 5/8 ÷ 4 = 37/32
4/7 x 4 5/8
= 4 * (1/7 + 37/32) - distributive property applied
= 4 * (291/224)
= 291 / 56
= 5 11/56 as mixed number
using distributive property the solution of the multiplication is 5 11/56
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The table shows a proportional relationship between x and y.
x 3.6 12.2 2.1
y 7.2 24.4 4.2
Which of the following correctly describes the graph of the relationship?
A line that goes through (3.6, 7.2) and (24.4, 12.2)
A line that goes through (7.2, 3.6) and (12.2, 24.4)
A line that goes through (0, 0) and (3.6, 7.2)
A line that goes through (0, 0) and (7.2, 3.6)
Answer:
(c) A line that goes through (0, 0) and (3.6, 7.2)
Step-by-step explanation:
You want to find the correct descriptor of the proportional relationship that includes points (x, y) = (2.1, 4.2), (3.6, 7.2), (12.2, 24.4).
GraphThe graph of the points in the table will go through points with coordinates that have the x-value of the table listed first. Points (24.4, 12.2), (7.2, 3.6) are not on the graph. (The table y-value is listed first for those ordered pairs.)
A proportional relationship graphs as a straight line through the origin, so this graph can be described as ...
A line that goes through (0, 0) and (3.6, 7.2)
Answer:
(c) A line that goes through (0, 0) and (3.6, 7.2)
Step-by-step explanation:
(20points) Let A be a 4 x 4 matrix and let A be a eigenvalue of multiplicity 3. If A - AI has rank 1, is A defective? Explain.
No, A is not defective.
What is the rank nullity theorem?The rank–nullity theorem is a theorem in linear algebra, which asserts that the dimension of the domain of a linear map is the sum of its rank (the dimension of its image) and its nullity (the dimension of its kernel).
Given here A be a 4 x 4 matrix and let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have
Rank(A-λI) + Nullity((A-λI) =4
⇒dimN(N-λI) = Nullity(A-λI)
⇒dimN(N-λI) = 4 - Rank(A-λI)
⇒dimN(N-λI) = 4-1
⇒dimN(N-λI) = 3
Therefore 3 linearly independent eigenvectors belong to eigenvalue λ. Since λ is an eigenvalue of multiplicity 3, this ensures that there is a different eigenvalue different from λ. Along with 3 linearly independent eigenvectors in the eigenspace of λ, this gives us 4 linearly independent eigenvectors in the matrix A. Now we An n × n matrix A is diagonalizable if and only if A has n linearly independent eigenvectors. Thus A is nondefective
Hence, matrix A is not defective.
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what is the standard form, degree and leading term of 21y - 3y^2 + 4 +y^3
Answer:
Standard form: [tex]y^3 -3y^2 + 21y + 4[/tex]
Degree: [tex]3[/tex]
Leading term: [tex]y^3[/tex]
Step-by-step explanation:
Standard form:
⭐ Standard form is a way you can order the terms of an equation so that the exponents of each term decrease in number when reading the equation from left to right.
Find the term in the given equation with the largest exponent and put that term first. The terms with exponents are [tex]y^3, -3y^2,[/tex] and [tex]21y[/tex](remember that a single variable has an exponent of 1). 3 is greater than 2 and 1, so [tex]y^3[/tex] will be the first term.Find the term with the next largest exponent and put that term after the new first term, and repeat. Remember that constants (terms without a variable) will always be the last term in your new, rewritten equation.Degree:
⭐ The degree of an equation is the highest exponent of the equation. You should always write equations in standard form in order to find the degree.
The highest exponent in this equation is 3. Therefore, the degree of this equation in 3.Leading term:
⭐ The leading term is the term that has the highest exponent. In standard form, it is the first term in the equation.
The highest exponent in this equation is 3, and the term with an exponent of 3 is [tex]y^3[/tex]. Therefore, the leading term of this equation is [tex]y^3[/tex]8. A material in which thermal energy is transferred rapidly is an insulator
True or false
Answer:This statement is not necessarily true
Step-by-step explanation:In general, the rate at which thermal energy is transferred depends on several factors, including the temperature difference between the material and its surroundings, the type of material, and its thermal conductivity. Some materials, such as air and glass, are poor conductors of heat and are therefore considered insulators. However, other materials, such as metal, are good conductors of heat and are not considered insulators.
A small town has two local high schools. High School A currently has 700 students and is projected to grow by 65 students each year. High School B currently has 900 students and is projected to grow by 40 students each year. Let A(t) represent the number of students in High School A in t years, and let B(t) represent the number of students in High School B after t years. Write the equation for each function and determine how many students would be in each high school in the year they are projected to have the same number of students. A(t) = B(t) =
Answer:
1. A(t) = 65t + 700
2.B(t) = 40t + 900
3. High School A and High School B will both have 1,220 students in the 8th year
Step-by-step explanation:
1. The equation for the number of students in High School A represents a linear function.
⭐ What is a linear function?
A linear function is a type of equation where every y-value increases by a constant, additive amountOne way to write the equation for a linear function is: [tex]y = mx+b[/tex], where m is the constant, additive amount, and b is the y-intercept, or the initial value.Let's write the equation for High School A in the [tex]y = mx+b[/tex] format, known as slope-intercept form:
The constant, additive amount for High School A is 65 (m)The initial value for High School A is 700 (b)∴ High School A: [tex]y = 65x + 700[/tex]
2. Let's write the equation for High School B in the [tex]y = mx + b[/tex] format, known as slope-intercept form:
The constant, additive amount for High School B is 40 (m)The initial value for High School B is 900 (b)∴ High School B: [tex]y = 40x + 900[/tex]
3. To find at what year High School A and High School B will have the same number of students, we need to solve a system of linear equations.
⭐What is a system of linear equations?
A system of linear equations is two or more linear equations that intersect at one point (x,y)For this problem, let's set both linear equations equal to each other to see at what point will the high school populations be the same.
[tex]A(t) = B(t)[/tex]
[tex]65t + 700 = 40t + 900[/tex]
[tex]25t = 200[/tex]
[tex]t = 8[/tex]
Now we know that in the 8th year, High School A will have the same population as High School B.
We need to find what the population will be in year 8.
Thus, substitute the value of t into one of the functions and solve.
I am choosing to substitute t into A(t), but you can also do B(t).
[tex]A(8) = 65(8) + 700[/tex]
[tex]A(8) = 520 + 700[/tex]
[tex]A(8) = 1,220[/tex]
⚠️!!! CAUTION !!! ⚠️
Some people may stop at this point and write that in the 8th year, both high schools will have a population of 1,220 students.
However, you should also substitute 8 into the other function you didn't substitute it into to make sure that 8 is correct.
[tex]B(8) = 40(8) + 900[/tex]
[tex]B(8) = 320 + 900[/tex]
[tex]B(8) = 1,220[/tex]
∴ In the 8th year, both high schools will have a population of 1,220 students.
8. Sketch a model to represent the equation
3x - 5 = 10. Then, solve the equation.
Answer:
x=5
Step-by-step explanation:
(Not sure how I was supposed to do the model..so I ended up doing it this way..)
3x-5=10
Add 5 on both sides and then you get
3x=15
divide both sides by 3 and then you get
x=5
(Hopefully you can see my model even if it's just a little...)
For the model I drew 3 rectangles and put an x inside each one of them. for the -5, I drew 5 squares with a minus symbol/sign inside. And then I put an equal sign beside and I drew 10 squares with nothing inside but you can draw positive signs in it to show that it's positive..
So basically mines was
3 rectangles with x inside -5 squares with - inside = 10 squares
#7
Write an equation in
slope-intercept form of
the line shown.
Please help
Answer:
y = -x - 4
Step-by-step explanation:
m = y2-y1 / x2-x1
(-4, 0) and (1, -5)
m = -5+0 / 1+4
m = -5 / 5
m = -1
y = -x + b
0 = -(-4) + b
0 = 4 + b
b = -4
y = -x - 4
Under certain conditions, the number of feet a car will skid after the brakes are fully applied is given by the function d(x)=0.05x2+x, where x is the speed of the car in miles per hour. For what values of x will the car skid at most 120ft ?
Answer:
x ≤ 40 . . . miles per hour
Step-by-step explanation:
You want to know the values of x for which d(x) = 0.05x² +x is at most 120.
Solutiond(x) ≤ 120 . . . . . . . . the required limit
0.05x² +x ≤ 120 . . . . . substitute the expression for d(x)
x² +20x -2400 ≤ 0 . . . . . multiply by 20, subtract 2400
(x -40)(x +60) ≤ 0 . . . . . . . . factor. Factors are zero for x=40, x=-60.
The product will be negative for x-values between the zeros:
-60 ≤ x ≤ 40
We only care about positive values of x:
0 ≤ x ≤ 40 . . . . . miles per hour
Drag and drop a statement or reason to each box to complete the proof. Given: parallelogram MNPQ Prove: ∠N≅∠Q Parallelogram M N P Q with diagonal M P drawn. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Statement Reason parallelogram MNPQ Given MN¯¯¯¯¯¯¯≅QP¯¯¯¯¯MQ¯¯¯¯¯¯≅NP¯¯¯¯¯¯ Response area Response area Response area △MQP≅△PNM Response area Response area CPCTC
After solving the problems the answers obtained are MN ≅ QP and MQ ≅ NP, MP ≅ MP, Δ MQP ≅ Δ PNM, ∠ N ≅ ∠ Q.
What is Parallelogram?The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.
1. According to the parallelogram's feature that its opposed sides are congruent, the opposite sides of the given parallelogram MNPQ,
So, MN ≅ QP and MQ ≅ NP.
2. According to the reflexive feature of congruence, a line or other geometric figure is both a reflection of and consistent with itself. Therefore, in the example of the parallelogram MNPQ,
So,
MP ≅ MP
3. The SSS congruence postulate, which stands for Side-Side-Side congruence postulate, argues that when three adjacent sides of two triangles are congruent, the two triangles are congruent. As the sides MNQ, MQ, NP, and MP are in the given parallelogram MNPQ
Hence,
Δ MQP ≅ Δ PNM
4. Part 4 demonstrated that MQP and PNM are congruent, hence in accordance with a CPCTC property,
∠ N ≅ ∠ Q
5. The acronym CPCTC stands for congruent portions of congruent triangles.
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lObjective 6-6) The following are various management assertions (a. through m.)
related to sales and accounts receivable.
Management Assertion
a. Recorded sales transactions have occurred.
b. There are no liens or other restrictions on accounts receivable.
c. All sales transactions have been recorded.
d. Receivables are appropriately classified as to trade and other receivables in the financial statements and are clearly described.
e. Sales transactions have been recorded in the proper period.
f. Accounts receivable are recorded at the correct amounts.
g. Sales transactions have been recorded in the appropriate accounts.
h. All required disclosures about sales and receivables have been made.
i. All accounts receivable have been recorded.
j. Disclosures related to receivables are at the correct amounts.
k. Sales transactions have been recorded at the correct amounts.
1. Recorded accounts receivable exist.
m. Disclosures related to sales and receivables relate to the entity.
a. Explain the differences among management assertions about classes of transactions and events, management assertions about account balances, and management assertions about presentation and disclosure.
b. For each assertion, indicate whether it is an assertion about classes of transactions and events, an assertion about account balances, or an assertion about presentation and disclosure.
c. Indicate the name of the assertion made by management. (Hint: See Table 6-2)
The management assertions for the given parts is explains below.
What is assertion?
Management assertions are statements made about specific elements of a business by members of management. The idea is mainly applied to the auditing of financial statements of a company, where the auditors rely on various business assertions.
Consider, the following.
(a) Recorded sales transactions have been recorded
Category of management. Classes of transactions
Name of assertion. . Occurance
(b) There are no lines are other restrictions in accounts receivable
Category of management. Account balances
Name of assertion. Rights and obligations.
(c) All sales transactions have been recorded
Category of management. Classes of transactions
Name of assertion. Completeness
(d) Receivables are appropriately classified as to trade and other receivables in the financial statements and are clearly described.
Category of management. Presentation and disclosure
Name of assertion. Classification and understandabilty
(e) sales transactions have been recorded in proper period
Category of management. Classes of transactions.
Name of assertion. Cut off.
(f) Account receivables recorded at correct amounts
Category of management. Account balances
Name of assertion. Valuation and allocation
(g) sales transactions recorded at appropriate accounts
Category of management. Class of transactions
Name of assertion. Classification
(h) All required disclosure about sales and receivables are at recorded amounts
Category of management. Presentation and disclosure
Name of assertion. Completeness
(k) Sales transactions have been recorded at correct amounts
Category of management. Account balances
Name of assertion. Completeness
(L) Recorded accounts receivable exist
Category of management. Account balances.
Name of assertion. Existence
(m) Disclosure related to sales and receivable relate to entity
Category of management. Presentation and disclosure
Name of assertion. Occurance and obligation
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Given a metric space M with metric d, verify that any ε-ball is an open set.
Answer:
Prove that for any x0∈X and any r>0, the open ball Br(xo) is open. My attempt: Let y∈Br(x0). By definition, d(y,x0)<r
Step-by-step explanation:
Prove that for any x0∈X and any r>0, the open ball Br(xo) is open. My attempt: Let y∈Br(x0). By definition, d(y,x0)<r
Find all values f x that make the equation true: 4/x+4=x-2/x
Step-by-step explanation:
4/x + 4 = x - 2/x
multiply everything by x
4 + 4x = x² - 2
x² - 4x - 6 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-6))/(2×1) =
= (4 ± sqrt(16 + 24))/2 = (4 ± sqrt(40))/2 =
= (4 ± sqrt(4×10))/2 = (4 ± 2×sqrt(10))/2 =
= 2 ± sqrt(10)
x1 = 2 + sqrt(10) = 5.16227766...
x2 = 2 - sqrt(10) = -1.16227766...
For the first week of August, Eric Washington worked 43 hours. Eric earns $18.30 an hour. His employer pays overtime for all hours worked in excess of 40
hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the first week of August (round your responses to the nearest cent if necessary):
1. Regular pay amount:
2. Overtime pay:
3. Gross pay:
Suppose f left parenthesis x right parenthesis equals 1 minus x squared and g left parenthesis x right parenthesis equals 2 x plus 5. Find the value of f(g(-1).
Answer:
f(g(-1)) = -8
Step-by-step explanation:
⭐ The two equations we are given are:
[tex]f(x) = 1-x^2[/tex][tex]g(x) = 2x + 5[/tex]This problem is an example of composite functions.
⭐What are composite functions?
Composite functions are functions inside of a functionYou compute the value of an x-value for one function, and use that value for another function.First, we have to compute the value for the 2nd function you see. The 2nd function is inside f(x), and it is g(-1).
Essentially, we have to find the corresponding y-value for when x = -1 in g(x)
[tex]g(-1) = 2(-1) + 5[/tex]
[tex]g(-1) = 3[/tex]
Next, take this value and substitute it as the x-value for f(x).
[tex]f(3) = 1-x^2[/tex]
Now we have to find the y-value for f(x) for when x = 3.
[tex]f(3) = 1 -3^2[/tex]
⚠️⚠️⚠️!!! CAUTION !!! ⚠️⚠️⚠️
Some people may make the mistake of computing f(3) like this:
[tex]f(3) = 1 - 3^2[/tex]
[tex]f(3) = 1+9\\f(3) = 10[/tex]
This is wrong because only 3 is being squared, not -3. Make sure to read the equations you are given carefully to avoid mistakes like this.
[tex]f(3) = 1-3^2\\f(3) = 1-9\\f(3) = -8[/tex]
∴ f(g(-1)) = -8
Marijuana legalization: In a Public Policy Institute of California (PPIC) poll, 53% of 1,706 California adult residents surveyed say that marijuana 10 points should be legal. Based on the results, the 95% confidence interval is (0.506, 0.554). Which of the following is an appropriate interpretation of this confidence interval? A. We are 95% confident that between 50.6% and 55.4% of California residents say that marijuana should be legal. B. We can conclude that 95% of states have 50.6% to 55.4% of adult residents who say that marijuana should be legal. C. We are 95% confident that between 50.6% and 55.4% of all American adults say that marijuana should be legal. D. If we took many samples of adults from around the nation, between 50.6% and 55.4% of them would say that marijuana use should be legal.
The correct interpretation of the confidence interval is: "We are 95% confident that between 50.6% and 55.4% of California adult residents say that marijuana should be legal." (Option A)
The confidence interval represents the range of values within which we are 95% confident that the true population parameter (in this case, the percentage of California adult residents who say that marijuana should be legal) lies. It is specific to the population of California adult residents that was surveyed, and cannot be generalized to other states or to all American adults.
Therefore, Option A is the correct answer that we are 95% confident that between 50.6% and 55.4% of California adult residents say that marijuana should be legal.
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The confidence interval denotes the range of values within which we are 95% certain that the true population parameter (in this case, the proportion of adult Californians who support marijuana legalization) resides. It cannot be extrapolated to adults in other states or to all Americans as a whole because it is specific to the demographic of adult inhabitants of California who were polled.
Accordingly, Option A is the right response, and we are 95% certain that between 50.6% and 55.4% of adult inhabitants of California agree that marijuana should be legal.
The following contingency table summarizes the drug test results for 429 test-takers:
For a randomly selected test administration, find the following probabilities. (Round the answers to 4 decimal places.)
Table
Top right: [tex]5+194=199[/tex]
Middle right: [tex]217+13=230[/tex]
Bottom left: [tex]5+217=222[/tex]
Bottom middle: [tex]194+13=207[/tex]
Bottom right: [tex]222+207=429[/tex]
Question 1
[tex]\frac{207}{429} \approx \boxed{0.4825}[/tex]
Question 2
[tex]\frac{13}{429} \approx \boxed{0.0303}[/tex]
Question 3
[tex]\frac{194+217}{429} \approx \boxed{0.9580}[/tex]
Rain is flowing into 2 containers at different rates. The figure below shows the volume of water in each container what is the difference in rate of change between the two containers
With the help of Linear relationships The difference in the rate of change between the two containers is 1/5 gallon per minute.
what is Linear relationships?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association). Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships. In everyday life, linear relationships are quite prevalent.
Given:
Volume of water in each container.
To find:
Difference in the rate of change.
Solution:
Take any two points on container 1.
Let the points are (10, 2) and (20, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 20 - 10 )
= 2/ 10
= 1/ 5
Rate of change for container 1 is .
Take any two points on container 2.
Let the points are (5, 2) and (10, 4).
m = (y2 - y1) / ( x2 - x1 )
= ( 4 - 2 ) / ( 10 - 5)
= 2 / 5
Rate of change for container 2 is 2/5
Difference = (2 /5 ) - ( 1/ 5 )
= 1 / 5
Hence, The difference in the rate of change between the two containers is 1/5 gallon per minute.
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Each of 8 students reported the number of movies they saw in the past year. Here is what they reported 10,4,8,.15,17,6,19,16. Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
to find mean you add all numbers and divide by the amount of numbers, 10+4+8+15+17+6+19+16 is 95, 95 divided by 8 is 11.875
What is the maximum height of the firework? How long is the firework in the air before it explodes?
See attached picture
The maximum height of the firework is; 387.78 ft
The time for which the firework is in the air before it explodes is; 1 second
How to solve projectile equations?
We are given the function;
h = -(500/9)t² + (1000/3)t + 10
where;
h is height after time of t seconds
At height of zero, the firework would either be about to launch or when it has come down.
Thus, let us set h = 0 to find the times.
0 = -(500/9)t² + (1000/3)t + 10
Using quadratic equation calculator, we have;
t ≈ 2 seconds
Now the firework explodes at the highest point which will be the mid point of where the launching started and the endpoint where it stopped.
This means time at midpoint = (0 + 2)/2 = 1 sec
It explodes after 1 second.
Thus maximum height at this time is;
h = -(500/9)(1)² + (1000/3)(1) + 10
h = 387.78 ft
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The model t = 16.708 ln(x/(x-705)) approximates the term of a mortgage of $150,000 at 6% interest rate, where t is the term of the mortgage in years and x is the monthly payment plan in dollars.
a. Approximate in terms (in yr) of a $150,000 mortgage at 6% when the monthly is $897.72 and when the monthly payment is $1526.49 (Round your answers to the nearest whole number).
$897.72 ________ yr
$1526.49_________ yr
b. Approximate the total amounts paid (in dollars) over the term of the mortgage with a monthly payment plan of $897.72 and with a monthly payment plan of $1526.49. (Round your answers to 2 decimal places.)
$897.72 $_____________
$1526.49 $_____________
What is the amount of the total is interest costs (in dollars) in each case? (Round your answers to 2 decimal places)
$897.72 $__________
$1526.49 $__________
c. What is the vertical asymptote for the model? ____________
Interpret its meaning in the context of the problem.
The monthly payment must be (more or less) than $________, and the close to this value is, the (quicker you will be able or longer it will take) to pay off the mortgage.
Answer:
(a) $897.72: 26 yr
$1526.49: 10 yr
(b) See below.
(c) x = 705
more, $705, longer it will take
Step-by-step explanation:
Given equation:
[tex]t=16.708 \ln \left(\dfrac{x}{x-705}\right)[/tex]
where:
t = term of the mortgage (in years)x = monthly payment plan (in dollars)Part (a)[tex]\begin{aligned}x=897.72 \implies t& =16.708 \ln \left(\dfrac{897.72}{897.72-705}\right)\\& =16.708 \ln \left(4.65815691...\right)\\&=16.708(1.53861985...)\\&=25.70726...\\&=26\; \rm years\end{aligned}[/tex]
[tex]\begin{aligned}x=1526.49 \implies t& =16.708 \ln \left(\dfrac{1526.49}{1526.49-705}\right)\\& =16.708 \ln \left(1.85819669...\right)\\& =16.708(0.619606496...)\\&=10.352385...\\&=10 \; \rm years\end{aligned}[/tex]
Part (b)To approximate the total amounts paid (in dollars) over the term of the mortgage, multiply the monthly payment by the term.
Please note I have provided two calculations per monthly payment:
(1) by using the exact term, and (2) using the rounded term from part (a).
[tex]\implies \$897.72 \times 25.7072605... \times 12 =\$276935.06[/tex]
[tex]\implies \$897.72 \times 26 \times 12=\$280088.64[/tex]
[tex]\implies \$1526.49 \times 10.3523853... \times 12=\$189633.75[/tex]
[tex]\implies \$1526.49 \times 10 \times 12 =\$183178.80[/tex]
To calculate the amount of interest costs (in dollars) in each case, subtract $150,000 from the total amounts paid:
[tex]\$897.72\implies 276935.06-150000=\$126935.06[/tex]
[tex]\$897.72 \implies 280088.64-150000=\$130088.64[/tex]
[tex]\$1526.49 \implies 189633.75-150000=\$39633.75[/tex]
[tex]\$1526.49\implies 183178.80-150000=\$33178.80[/tex]
Part (c)The natural logarithm of a negative number cannot be taken.
Therefore, x > 705.
So the vertical asymptote for the model is:
x = 705The monthly payment must be more than $705, and the closer to this value the payment is, the longer it will take to pay off the mortgage.