Answer:
2+2=4, not 6
Step-by-step explanation:
A college has a financial aid formula that applies to applicants whose family's income is below a certain threshold. The financial aid can be determined by the function f(x)=10000+1000x,f(x)=10000+1000x, where xx is the number of siblings (including half siblings and step siblings) that the applicant has living in their household. Find and interpret the given function values and determine an appropriate domain for the function.
The numeric values of the function are given and explained as follows:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.The domain is: {x is a whole number and x ≥ 0}.How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the function is given by:
f(x) = 10000 + 1000x.
In which:
The output f(x) is the financial aid.The input x is the number of siblings in the family.When x = -2, we have that:
f(-2) = 10000 + 1000(-2) = 8000.
Hence:
f(-2) = 8000, meaning a qualifying applicant with -2 siblings would receive a financial aid of $8,000. This interpretation does not make sense in the context of the problem.
When x = 4, we have that:
f(4) = 10000 + 1000(4) = 14,000.
Hence:
f(4) = 14,000, meaning a qualifying applicant with 4 siblings would receive a financial aid of $14,000. This interpretation makes sense in the context of the problem.
The number of siblings is a discrete number, and has to be of at least 0, hence:
The domain is: {x is a whole number and x ≥ 0}.
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A total of 52 microphones are to be purchased. Each microphone costs $548. Estimate the total purchase price by using rounded numbers.
The total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A total of 52 microphones are to be purchased. Each microphone costs $548.
Let x be the total purchase price
x = 52x548
x = $28496
Thus, the total purchase price is $28496 if a total of 52 microphones are to be purchased. Each microphone costs $548.
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1. The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make? pizzas ?
2. Dan purchased 3 ½ yards of mulch for his garden. Mulch costs $25 a yard. How much did Dan pay for his mulch? $
3. Mr. Hamilton owns 2 ¾ acres of land. He plans to buy 1 and 1/3 more acres. How many acres will he own? Write your answer as an improper fraction. acres
1) The soccer team can make 48 pizzas using 12 one-pound packages of cheese.
2) The total cost Dan paid for the mulch was $87.50.
3) The number of acres that Mr. Hamilton will own after the planned purchase is 3¹³/₁₂.
How are the values determined?The above values are determined using mathematical operations of addition, division, and multiplication.
For instance, Mr. Hamilton's land increased to 3¹³/₁₂ through the addition of 2¾ and 1¹/₃ acres.
The total cost that Dan paid for the mulch was a multiplication operation.
The number of pizzas the soccer team could make resulted from a division operation.
Data and Calculations:1) Quantity of cheese on each pizza = 1/4 lb
The total quantity of cheese = 12 lb
The number of pizzas to make = 48 (12/1/4) or (12/0.25)
2) The number of yards of mulch purchased = 3¹/₂ yards
Cost of mulch per yard = $25
The total cost for the mulch = $87.50 ($25 x 3¹/₂)
3) Measurement of land owned = 2¾ acres
The planned purchase of additional land = 1¹/₃
The total acres Mr. Hamilton will own = 3¹³/₁₂ (2¾ + 1¹/₃)
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Your answer is incorrect.
Suppose 2 quarts of pure antifreeze is mixed with 3 quarts of a solution that is 18% antifreeze.
Answer the questions below. Do not do any rounding.
(a) How many quarts of antifreeze are in the resulting mixture?
(b) What percentage of the resulting mixture is antifreeze?
a) There is 2.54 quarts in the resulting mixture (b) The percentage of the resulting mixture is 50.8% antifreeze.
Percentage is defined as parts per hundred. Percentage is calculated by dividing the given amount by the total amount and multiplying by 100.
a) 18% of 3 quarts antifreeze contains (18/100) × 3 quarts of antifreeze.
amount of antifreeze = 0 .18 × 3 = 0.54 quarts
Now to this solution 2 quarts of antifreeze is added.
Therefore total amount of antifreeze in the resulting mixture = 2 + 0.54 = 2.54 quarts.
b) Total amount of the resulting mixture = 2 + 3 = 5 quarts
amount of antifreeze in the mixture = 2.54 quarts
Percentage antifreeze in the mixture = (2.54 / 5) × 100 % = 50.8 % .
Therefore there is 2.54 quarts of antifreeze in the mixture and its percentage is 50.8% of the total mixture.
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Please help me with 7, 11, 15, 9, 13, 17, . Please explain your answer for each one. I will give an Brainly and extra points.
The truth values of the composite propositions are listed below:
Case 7: T, Case 9: T, Case 11: F, Case 13: T, Case 15: F, Case 17: F
What are the truth values of composite proposition?
Propositions are constructions that contain itself a truth value. This exercise presents a proposition p is false and proposition q is true. Then, we proceed to find the truth value of each composite proposition, that is, a combination of propositions and operators.
Case 7
p → F Given¬ p → T Definition of negation / ResultCase 9
p → F, q → T Givenp ∨ q → T Definition of disjunction / ResultCase 11
p → F, q → T Given¬ q → F Definition of negationp ∨ ¬ q → F Definition of disjunction / ResultCase 13
p → F, q → T Given¬ p → T, ¬ q → F Defintion of negation¬ p ∨ ¬ q → T Definition of disjunction / ResultCase 15
p → F, q → T Givenp ∧ q → T Definition of conjunction¬ (p ∧ q) → F Definition of negation / ResultCase 17
p → F, q → T Given¬ p → T, ¬ q → F Definition of negation ¬ q ∨ p → T Definition of disjunction¬ p ∧ (¬ q ∨ p) → T Definition of conjunction¬ (¬ p ∧ (¬ q ∨ p)) → F Defintion of negation / ResultTo learn more on propositions: https://brainly.com/question/13011669
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Give the slope and the y-intercept of the line with the
given equation. Then, graph the linear equation.
y = 3x +5
What is the slope? Select the correct choice below and
fill in any answer boxes within your choice.
OA. The slope is
(Simplify your answer.)
OB. The slope is undefined.
What is the y-intercept? Select the correct choice
below and fill in any answer boxes within your choice.
OA. The y-intercept is
(Type an integer or a simplified fraction.)
OB. There is no y-intercept.
Graph the equation.
Click to
enlarge
graph
help pls i gyg soonn
Answer:
Step-by-step explanation:
8806
Karen must choose a number between 49 and 95 that is a multiple of 2, 8, and 10. Write all the numbers that she could choose. If there is more than one
number, separate them with commas.
Answer:
80
Step-by-step explanation:
80 is the only number that is a multiple of ALL 2, 8 and 10
Answer:
the only answer that is a multiple of 2,8 and 10 between 49 and 95, is 80.
Determine the following geometric probabilities:
A. Tal-mart parking lot is 500 feet by 800 feet. You just parked your car, which is
approximately a rectangle with the dimensions 6 feet by 10 feet. A bird flying
overhead has just relieved himself by having a bowel movement. If the waste
material has an equal chance of landing anywhere in the parking lot then what are
the chances of it hitting your car.
The geometric probability which represents the chances of having the waste material hit the car as described in the task content is; 3/20,000.
What is the probability of having the waste material hit the car?It follows from the task content that the probability which is to be evaluated is the chance of having the waste material hit the car.
First, since the dimension of the parking lot is; 500 by 800 feet. It follows that;
Area of parking lot = 500 × 800 = 400,000.
Also, since the dimension of the rectangular car is approximately 6 by 10. It follows that;
Area occupied by car = 6 ×10 = 60.
Consequently, the chances of the waste material hitting the car is the ratio of desired outcome to the possible outcome and hence is;
P = 60/400,000
P = 3/20,000.
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20 push-ups in 2days
Answer: ok?
Step-by-step explanation:
i need help assap dont judge
Find the equation of the exponential function represented by the table below:
x
0
1
2
3
Y
5
2.5
1.25
0.625
Answer:
x = r ,r is a whole number
y = 5(.5)^r
y=5(.5)
Step-by-step explanation:
The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
Function:
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
For x=0 for f(0)=(5)[tex](0.5^{0} )[/tex]=5
⇒ x=1 for f(1)=(5)[tex](0.5^{1} )[/tex]=2.5
⇒ x=2 for f(2)=(5)[tex](0.5^{2} )[/tex]=1.25
⇒ x=3 for f(3)=(5)[tex](0.5^{3} )[/tex]= 0.625
Therefore,The equation of the exponential function represented by the table given is f(x)=(5)[tex](0.5^{x} )[/tex].
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College Level Quantitative Reasoning - See Screenshot
The absolute and relative errors are 0. 8 and 0. 01 respectively.
What is absolute error?Absolute error can be defined as the difference between the inferred or measured value and the actual value of a given quantity.
The formula for absolute error is expressed as;
Absolute error = | VA - VE |
Where;
VA is the actual value = 60. 8 InchesVE is the expected value = 60. 0 InchesSubstitute the values into the formula
Absolute error = | 60. 8 - 60. 0|
Find the difference
Absolute error = | 0. 8|
Absolute error = 0. 8
Relative error = Absolute error/ actual value
Relative error = 0. 8/ 60. 0
Relative error = 0. 01
Thus, the absolute and relative errors are 0. 8 and 0. 01 respectively.
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Bob sells cars. His income is based on a graduated scale. If he earns %5 commission for the first $50,000 in scales %8 commission for sales over $50,000, then how much would he earn if his total sales were $95,000
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
I need help I give a lot of points and answer all of them for star
Step-by-step explanation:
1. 10.58
2. 15.87
3. 20.37
4 25.88
5. 8.89
6. 2.24
7. 9.95
8. 4.80
could someone help me understand what I need to do in this problem?
[tex]p(x-1)[/tex] is a quadratic in the form
[tex]a(x-1)^2 + b(x-1) + c[/tex]
We want to write [tex]p(x-1)[/tex] instead in the form
[tex]a' x^2 + b' x + c[/tex]
To do this, simply expand the first form completely.
[tex]a(x-1)^2 + b(x-1) + c = a(x^2 - 2x + 1) + b(x-1) + c \\\\ ~~~~~~~~ = ax^2 + (-2a + b)x + (a - b + c)[/tex]
Then [tex]a'=a[/tex], [tex]b'=-2a+b[/tex], and [tex]c'=a-b+c[/tex].
Given
[tex]p(x-1) = 2(x-1)^2 + 3(x-1) + 4[/tex]
(so [tex]a=2[/tex], [tex]b=3[/tex], and [tex]c=4[/tex]) it follows that
[tex]a' = a = 2[/tex]
[tex]b' = -2a + b = -2^2 + 3 = -1[/tex]
[tex]c' = a - b + c = 2 - 3 + 4 = 3[/tex]
[tex]\implies p(x-1) = \boxed{2}\,x^2 - \boxed{1}\,x + \boxed{3}[/tex]
There is exactly 1 pair of parallel sides in the
following shape.
Base=6 base=8 height=5
What is the area of the shape?
The area of the shape with parallel sides is 35 unit² of trapezoid .
Describe the trapezoid shape?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.A = (1/2) * (a + b)h
Where a, b is the length of the parallel sides and h is the height of the trapezoid.
Given that a = 8, b = 6 and h = 5, hence:
A = (1/2) * (8 + 6) * 5 = 35 unit²
The area of the shape with parallel sides is 35 unit².
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what is 3 11/12 - 3/4? I have an upcoming test, and I need someone to explain it step-by-step.
Answer:
3 1/6
Step-by-step explanation:
First, we turn 11/12 and 3/4 to have the same denominator
3/4 x 3 is 9/12
11/12- 9/12 is 2/12
Now we add the extra 3 to 2/12 which is 3 2/12
3 2/12 can be simplified to 3 1/6
x^2+48=14x
Show work please
Answer:
Step-by-step explanation:
x^2 - 14x = -48
x^2 +48 -14 x
x^2 - 14x - 48 = 0
a = 1
b = -14
c = 48
x=8, x=6
Based on the graph of z (x), what is the value of z-¹ (-2)?
Answer:
-9
Step-by-step explanation:
[tex]z^{-1}(-2)=k \implies z(k)=-2 \\ \\ k=-9 \implies z^{-1}(-2)=-9[/tex]
I need help with question!
given line A has a slope of m=-2/5, what is the slope of a line parallel to line A
Given line A has a slope of m = -2/5, the slope of a line parallel to line A is m = -2/5
What is the slope of a line?The slope of a line y = mx + c where
m = slope of line and c = y - interceptIs given by m = Δy/Δx where
Δy = change in y and Δx = change in xHow to find the slope of a line [parallel to another line?Given a line y = mx + c where
m = slope of line and c = y - interceptAlso, given another line y' = m'x + c' where
m' = slope of line and c' = y - intercept.If y is parallel to y' then their slopes are equal. That is m = m'
How to find the slope of the line parallel to line A?Given that line A has a slope of m = -2/5, then by the condition above, the slope of a line paralllel to line A must also equal m.
So, the slope of a line parallel to line A is m = -2/5
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Insert brackets in this expression
to make it correct:
8 – 2 + 1 × 5 – 3 = 2
Answer: 8 – (2 + 1) × (5 – 3) = 2
Step-by-step explanation:
8 – 2 + 1 × 5 – 3 = 2
8 – 2 + 1 × 5 – 3 = 2 ==> notice there is an '8-' in the equation, Let's solve for the difference between 8 and 2.
8 – (2 + 1 × 5 – 3)+(2 + 1 × 5 – 3) = 2 + (2 + 1 × 5 – 3)
8=2 + (2 + 1 × 5 – 3)
8-2=2-2+(2 + 1 × 5 – 3)
6=2 + 1 × 5 – 3 ==> 6 is a multiple of 2 and 3. Let's see how we can convert 2 + 1 × 5 – 3 into the product of 2 and 3
6=(2 + 1) × (5 – 3)
6=3 × 2
6=6√ ==> since this is right, let's substitute the parentheses to the original equation
8 – 2 + 1 × 5 – 3 = 2 ==> 8 – (2 + 1) × (5 – 3) = 2
Find the values of a and b that make f continuous everywhere.
f(x) =
x2 − 4
x − 2 if x < 2
ax2 − bx + 1 if 2 ≤ x < 3
4x − a + b if x ≥ 3
The function is a continuous function. Then the value of variables a and b will be 2.5 and 3.5, respectively.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The piecewise function is given below.
[tex]f\left ( \rm x \right ) = \left\{\begin{matrix} \rm \dfrac{x^2 - 4}{x-2} \ or \ x + 2,& \rm x < 2\\ \rm ax^2 - bx + 1, & \rm 2\leq x < 3\\ \rm 4x - a + b, & \rm x \geq 3\end{matrix}\right.[/tex]
At x = 2, the function is continuous, then we have
2 + 2 = a(2²) - 2b + 1
4a - 2b = 3 ...1
At x = 3, the function is continuous, then we have
a(3²) - 3b + 1 = 4(3) - a + b
10a - 4b = 11 ...2
From equations 1 and 2, we have
8a - 10a = 6 - 11
2a = 5
a = 2.5
Then the value of b will be
10(2.5) - 4b = 11
25 - 4b = 11
4b = 14
b = 3.5
The value of the variable a and b will be 2.5 and 3.5, respectively.
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Write the equation of a line perpendicular to 3x - 8y = - 7 that passes through the point (-3,3).
3y = -8x -27
Solution :
A line equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Given line: 3x - 8y = -7
-8y = -7 -3x
y=- (-7 -3x)/8
y= 7+3x/8
So, the slope (m1) = 3/8
Let’s consider the slope of the line perpendicular to the given line as m2
Then, m1 x m2 = -1
3/8 x m2 = -1
m2 = -8/3
Now,
The equation of the line perpendicular to the given line and passing through the point (-3, -3) will be
y – y1 = m (x – x1)
y – (-3) = -(8/3) (x – (-3))
y + 3 = (-8/3) (x +3)
3y + 3 = - 8x - 24
3y = -8x -24-3
3y = -8x -27
Thus, the equation of the required line is 3y = -8x -27
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How many grams are in 0.0564 mol of sodium?
Answer:
1.296623028 grams
Step-by-step explanation:
your answer is 1.296623028 grams because you multiply the given number of moles which was 0.0564 by the molar mass to get the grams
The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost?
The total cost based on the equation illustrated as y= 10x is $230.
How to illustrate the information?It should be noted that from the information, the equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost.
Therefore, it should be noted that the total cost when x is 23 will be illustrated thus:
y = 10x
y = 10 (23)
y = 230
Therefore, the total cost based on the equation illustrated as y= 10x is $230.
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The equation y= 10x models the cost to attend the aquarium, where x is the number of students in the class and y is the total cost. Calculate the total cost when x is 23.
1/4 minus 3/8 in fraction form
Answer: -1/8 is the answer
Write a sequence that has the stated property.
The 1st difference of the sequence can be modeled with the expression 8x-5.
The sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
How to determine the sequence that can be modeled by the expression?The expression of the first difference is given as
8x - 5
Rewrite properly as
d = 8x - 5
Where the common difference is represented by d
The common difference of an arithmetic sequence is calculated as
d = T2 - T1
So, we have
T2 - T1 = 8x - 5
Add T1 to both sides of the equation
So, we have
T2 = T1 + 8x - 5
Express 2 as 1 + 1
So, we have
T(1+1) = T1 + 8x - 5
Express 1 as n
So, we have
T(n+1) = Tn + 8x - 5 where n >= 1
Hence, the sequence that can be modeled by the expression is T(n+1) = Tn + 8x - 5 where n >= 1
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Help help me me me me
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)
Step-by-step explanation:
Answer:
(-6, 26),( -4, 8,) (0, -4), (2,2), (8,68)