The approximate values for the percent of persons that are 65 years and over with a family income below the poverty level and the rate of change of the percent, obtained from the function P and the derivative of P
a. 20.86%, -1.166%
b. 12.77%, -0.29%
c. 8.735%, -0.15%
d. The rate of change decreases
What is a derivative?The derivative of a function is an indication of the measure of the sensitivity of the change in the function value (output value) to a change in the argument or input value.
The function for the percentage of persons that are 65 years and older with a family income which is lower the poverty level is; P(t) = 30.24 - 5.83·ln(t)
a. In 1970, the percentage was; t = 1970 - 1965 = 5, therefore;
P(5) = 30.24 - 5.83 × ln(5) = 20.86%
The percent of persons 65 years and over with a family income below the poverty level in 1970 was 20.86%
The rate of change of the function P(t) = 30.24 - 5.83·ln(t) is the derivative of P(t), which is; P'(t) = d/dt(30.24 - 5.83·ln(t)) = -5.83/t
Therefore, in 1970, we get; P'(5) = -5.83/5 = -1.166%
b. The percentage in 1990, can be obtained from the value of t in 1990, which is t = 1990 - 1970 = 20
Therefore; P(20) = 30.24 - 5.83·ln(20) ≈ 12.77%
The rate of change of the percentage is; P'(20) = -5.83/20 ≈ -0.29%
c. The percentage of persons in the year 2010 is; P(2010 - 1970) = P(40) = 30.24 - 5.83·ln(40) ≈ 8.73%
The rate of change of the percentage is; P'(40) = -5.83/40 ≈ -0.15%
d. The rate of change of the percentage over time is; P'(t) = -5.83/t
Therefore, as the value of t increases, the magnitude of P'(t) decreases, which indicates that the rate of change of the percent of 65 years and over with a family income below the poverty level decreases over time.
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PLSSS HELP!! Simplify the expression.
-1/2 + 1/6
Write an equation of the line that passes through the point (2,3) and is perpendicular to the line x+4y-8
Answer:
\(y = 4x - 5\)
Step-by-step explanation:
rewrite the equation
\(x + 4y - 8 = 0 \\ 4y = - x + 8 \\ y = - \frac{1}{4} x + 2\)
perpendicular slope is a negative reciprocal. we will use the negative reciprocal to find the y-intercept
\(3 = 4(2) + b \\ 3 = 8 + b \\ b = - 5\)
If Hailey divides 150 ounces of sports drink with her volleyball team equally into 12 bottles, what is the weight of sport drink in one bottle?
Answer:
12.5 oz
Step-by-step explanation:
150 oz / 12 = 12.5 oz
-10-9-8-7 -6 -5 -4 -3
-2.1
0
1 2 3 4 5
6
7 8 9 10
3) Which inequality matches the graph?
A) X > .2
B) X <-2
C) x = -2
D) 3.2
Answer:
I think its D
Step-by-step explanation:
The dot starts on -2 and decreases so the answer would = -2 or be less than -2 :)
Advertising a business. Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.
Show all work
The inequality representing the given situation is -
300x + 700y ≤ 7500
What is advertising?Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.
Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.
We can write the inequality as -
300x + 700y ≤ 7500
where -
{x} - number of online ads posted
{y} - number of TV ads poste
Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.
Therefore, the inequality representing the given situation is -
300x + 700y ≤ 7500
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What is the degree of the polynomial, y^2+7x^14-10x^2?
The degree of the polynomial is 14
How to determine the degree of the polynomial?The polynomial is given as:
y^2+7x^14-10x^2
Here, we assume that the variable of the polynomial is x
The highest power of x in the polynomial y^2+7x^14-10x^2 is 14
Hence, the degree of the polynomial is 14
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. Translate parallelogram ABCD 2 units down and plot it. 2. Translate rhombus EFGH 2 units to the left, 4 units down, and plot it. 3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,-2), N(-2,-2). What are the coordinates for O? 4. If the coordinates of the vertices of a triangle XYZ are X (2,1), Y(4,4) and Z(5,2). Translate the triangle XYZ 4 units down. What are the new coordinates? 5. Write the coordinates down for the following points: Please Write The answers
To translate a shape, all of its vertices must be moved in the same direction and by the same amount. The responses to the five sections of the question are as follows:
What are coordinates?Coordinates are used to identify the position of an object on a two-dimensional grid or in three-dimensional space. They are usually written as pairs of numbers, separated by a comma.
1. We must deduct 2 from all of the y-coordinates of the vertices of the parallelogram ABCD in order to translate it two units down. Let's assume that the vertices' initial coordinates are A(a,b), B(c,d), C(e,f), and D. (g,h). The vertices will then have the new coordinates A'(a,b-2), B'(c,d-2), C'(e,f-2), and D' (g,h-2). To obtain the translated parallelogram, plot these new vertex points.
2. To move the rhombus EFGH 2 units to the left and 4 units down, we must deduct 2 from all of its vertices' x-coordinates and 4 from all of its y-coordinates. Let's assume that the vertices' initial coordinates are E(a,b), F(c,d), G(e,f), and H. (g,h). The vertices will then have the new coordinates E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H' (g-2,h-4). To obtain the translated rhombus, plot these additional vertices.
3. If we want to translate a square with coordinates L(-5,5), M(-5,5), N(5,5), and O(5,5) 3 units to the right and 2 units up, we must add 3 to all of its x-coordinates and subtract 2 from all of its y-coordinates. The vertices' new coordinates are L'(-2,-7), M'(-2,3), N'(8,3), and O' (8,-7). To obtain the translated square, plot these new vertex points.
4. The new coordinates of triangle XYZ after translating 4 units down will be X' (2,-3), Y' (4,1) and Z' (5,-2). This is happening because when a triangle is translated 4 units down, the y-coordinate of each vertex is decreased by 4 units, while the x-coordinate remains the same.
5. I (4,-2) P (-4,-2) G (5,2) Q (6,-4) R (-2,2)
S (6,4) J (1,-1) U (-5,0) H (3,-1) K (-6,-5)
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Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. 3X1 + 6x2 = 18 4x1 +5X2 = 30 Find the solution to the system of equations.
Solution to the system by using elementary row operations of equations is \(x1 = 3\) and \(x2 = 1\).
This can be understand by:
Step 1: Subtract 3 times the first equation from the second equation:
\(4x1 + 5x2 = 30\\-3(3x1 + 6x2) = 18\\ -x1 + -x2 = -12\)
Step 2: Add the equations to eliminate x2:
\(3x1 + 6x2 = 18\\-x1 + -x2 = -12\\2x1 = 6\)
Step 3: Divide both sides by 2 to solve for x1:
\(2x1 = 6\\x1=6/2\\x1 = 3\)
Step 4: Substitute x1 = 3 into either equation to solve for x2:
\(3(3) + 6x2 = 18\\6x2 = 6\\x2 = 1\)
Therefore, the solution to the system of equations is x1 = 3 and x2 = 1.
To reduce a matrix into row-echelon form, a series of procedures known as elementary row operations is used. These operations include multiplying one row by a nonzero value and adding it to another row, adding two rows together, switching two rows, and adding two rows together. They can be used to determine a matrix's inverse and to resolve linear equations.
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find the difference between points (3,5) and (-1,5)
b'
Let the given points be A(3,-5) and B(5,-1).
AB= sqrt of (5−3) ² +(−1+5)²
= sqrt of 4+16
= sqrt of 20
=2 sqrt of 5 units
Nvm I found the answer
247 1372 as a number
Answer:
Do you mean in words?
Step-by-step explanation:
then it is
Two million,four hundred and seventy one thousand,three hundred and seventy two.
Find the value of 72% of 90 kg
Answer:
64.8 kg kilograms
Step-by-step explanation:
please mark brainiest
hope it works out for you
Answer:
the value of 72% of 90 kg:
72 * 90 / 100 = 64,8 kg
Error Analysis A sports team with 17 members is planning an end-of-season awards banquet. It costs $6 for each meal. To find the total cost of the meals, the team uses the expression 6(g + 17) where g is the number of guests attending the banquet. One team member in correctly claims that the expression is equivalent to 6g + 17. Use the Distributive Property to write an expression equivalent to 6(g + 17). What was the likely error? Use the Distributive Property to write an equivalent expression. Will send image.
we distribute the multiplication of 6 by each term of the parenthesis
\(\begin{gathered} (6\times g)+(6\times17) \\ 6g+107 \end{gathered}\)the the equivalent expression is (6g+107)
what does 2(-3+5) + 7× (-4) + (-1) equal?
Answer:
-25
Step-by-step explanation:
= 2*(2) - 28 - 1
= 4 - 29
= -25
Given:-
\( \tt \: 2(- 3+5 ) + 7× (-4) + (-1) = ?\)\( \: \)
Solution:-
\( \tt \: 2(- 3+5 ) + 7× (-4) + (-1) \)\( \: \)
\( \tt \: 2( 2 ) - 28 - 1\)\( \: \)
\( \tt \: 4 - 29\)\( \: \)
\( \boxed{ \: \tt \pink{-25 }\: \: } \)\( \: \)
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
BRAINLIEST QUESTION ON PIC THANK YOU
Answer:
No Solution
Step-by-step explanation:
√-121=No Solution
There would be a solution if the equation was -v²=-121.
Answer:
the answer is no solution there is no possible way to get a negative
What is the surface area of the cylinder with height 6 m and radius 4 m? Round your answer to the nearest thousandth.
Step-by-step explanation:
Right cylinder
Solve for surface area
A≈251.33m²
r Radius
4
m
h Height
6
m
Solution
A=2πrh+2πr2=2·π·4·6+2·π·42≈251.32741m²
Answer:
I think 251.33m² is your answer
Step-by-step explanation:
A $5000 investment pays 3% interest compounded monthly. To the nearest cent, what will be the value of the investment after 10 years?
Answer:
We can use the formula for compound interest to solve this problem. The formula is:
A = P * (1 + r/n)^(n*t)
where:
A = the amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, P = $5000, r = 0.03, n = 12 (since the interest is compounded monthly), and t = 10. Plugging these values into the formula, we get:
A = 5000 * (1 + 0.03/12)^(12*10)
A = 5000 * (1.0025)^120
A ≈ $6,621.36
So the investment will be worth approximately $6,621.36 after 10 years.
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Subtract and write in standard form
(8x – 6x3 + 5x2) - (2x2 + 2x - 7x3)
Answer:
x^3 +3x^2 +6x
Step-by-step explanation:
Eliminate parentheses using the distributive property. Collect terms. Standard form has the exponents decreasing.
= 8x -6x^3 +5x^2 -2x^2 -2x +7x^3
= x^3(-6 +7) +x^2(5 -2) +x(8 -2)
= x^3 +3x^2 +6x
Which expression is equivalent to 1/5×15: 5÷15, 1÷5, 15÷5, 15÷1
Answer:
the question is not valid with "obj."
Evaluate the expression
if x = 2, y = 3, and z = 4.
2x²-y + 2(z-1)
Answer:
11
Step-by-step explanation:
Substituting the values of x, y, and z into the expression, we get:
2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)
= 2(4) - 3 + 2(3)
= 8 - 3 + 6
= 11
Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.
Answer:
11
Step-by-step explanation:
if x = 2, y = 3, and z = 4.
2x²-y + 2(z-1)
Substituting the given values of x, y, and z, we get:
2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)
= 2(4) - 3 + 2(3)
= 8 - 3 + 6
= 11
Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.
BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).
Choose the best domain and range, with justification for the relation shown below.
the domain is (-7, 1]
the range is (2, 7]
So the correct option is the third one.
How to identify the domain and range of the graphed function?For a given function we identify the domain as the set of the inputs of the function, in this case, represented by the horizontal axis, while the range is the set of the outputs of the function, in this case, represented by the vertical axis.
So, to identify the domain of the function, we just need to find the smallest and largest x-values graphed, these are:
x = -7
x = 1
Then the domain is (-7, 1]
(the parenthesis is because the point (-7, 1) is in an open circle, which means that it does not belong to the graph).
For the range we can do the same thing, but on the vertical axis, the smallest and largest values are:
y = 2
y = 7
So the range is (2, 7]
Then the correct option is the third one.
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John invested in a savings bond for 4 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was $48. How much did he invest?
the principal or invested amount is $41.38
The computation of the invest amount is given below:
As we know that
Principal = Amount ÷ (1 + rate × time)
= $48 ÷ (1 + 0.04 × 4)
= $48 ÷ 1.16
= $41.38
Hence, the principal or invested amount is $41.38
Basically we have applied the above formula so that the same would be calculated
Can you explain to me how did we get the answer
The end behavior of the polynomials are as follows;
(a) y = x³ - 9·x² + 8·x - 14
End behavior; y → ∞ as x → ∞
\({}\) y → -∞ as x → -∞
(b) y = -8·x⁴ + 13·x + 800
End behavior; y → -∞ as x → -∞
\({}\) y → -∞ as x → ∞
What is the end behavior of a a polynomial?The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.
The factors that effect the end behavior of a polynomial are;
The degree of the polynomial, (even or odd)
The sign of the leading coefficient of the polynomial (positive or negative)
The leading coefficient is the coefficient of the term with the highest degree.
(a) The polynomial, function, y = x³ - 9·x² + 8·x - 14
The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;
y tends to positive infinity as x tends to positive infinity
y tends to negative infinity as x tends to negative infinity
End behavior;
y → ∞ as x → ∞
y → -∞ as x → -∞
(b) The polynomial function can be expressed as follows;
y = -8·x⁴ + 13·x + 800
The above polynomial of degree 4 is an even degree polynomial
The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative
The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;
y-values approaches negative infinity as x approaches negative infinity
y-values approaches negative infinity as x approaches positive infinity
End behavior;
y → -∞ as x → -∞
y → -∞ as x → ∞
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Consider the function y = √4-x.
What are the domain and range of this function?
Answer:
For the function y = √4-x, we know that the value inside the square root must be non-negative. Therefore, we have the inequality:
4 - x ≥ 0
Solving for x, we get:
x ≤ 4
So the domain of the function is all real numbers less than or equal to 4.
For the range, we know that the square root of any non-negative number is always non-negative. Therefore, the smallest value that y can take is 0, which occurs when x = 4. As x decreases, y increases without bound. So the range of the function is [0,∞).
Step-by-step explanation:
Which graph shows function f?
The graph of f(x) is the second one, so the correct option is B.
Which graph shows function f?Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.
You can see that the first domain of the function is:
x ≤ -4
So we must have a closed circle at x = -4, when the parabola ends.
The second domain is:
-4 < x < 1
So x here is not equal to -4 nor 1, so this part starts and ends with open circles.
finally, the linear part starts with a closed circle.
Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.
Then we can see that the correct option is the second graph.
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f(x)= 1/2x-1 what is the function
The domain of the given function f(x)= 1/2x-1 is ( -∞ , 1/2) ∪ (1 /2 , ∞) .
The set of all potential values that qualify as inputs to a operate is understood because the domain of the operate, or it also can be outlined because the entire set of values potential for freelance variables. The domain is found in – the divisor of the fraction isn't up to zero and also the digit underneath the root bracket is positiveWe have given an function f(x)= 1/2x-1 .
To find the domain, we'd like to appear at the values of the freelance variables that area unit allowed to use as explained on top of, i.e. no zero at all-time low of the fraction and no negative sign within the root.
2x - 1 ≠ 0
2x ≠ 1
x ≠ 1/2
Domain is given by ( -∞ , 1/2) ∪ (1 /2 , ∞) .
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The complete question is given below :
Find domain of the function f(x)= 1/2x-1
find the values of p and q such that 4x^2+12=4(x-p)^2+q
!!!!!
Answer:i dont know please answer this
Step-by-step explanation: