hello! i need help on this question and the (select) questions have the options of 1997 to 2006
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To find the average rate of change, we use the following formula
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Where a = 1998, f(a) = 856, b = 2001, and f(b) = 1591.
[tex]r=\frac{1591-856}{2001-1998}=\frac{735}{3}=245[/tex](a) The average rate of change between 1998 and 2001 is 245.We use the same formula between 2002 and 2006, where a = 2002, f(a) = 1483, b = 2006, and f(b) = 745.
[tex]r=\frac{745-1483}{2006-2002}=\frac{-738}{4}=-184.5[/tex](b) The average rate of change between 2002 and 2006 is -184.5.(c) As you can observe, the population was increasing from 1997 to 2001.(d) The population was decreasing from 2001 to 2006.Related Questions
Joe is painting his wooden fence post before putting them in his yard. They are each 8 feel tall and have a diameter of 1 foot. There are 12 fence post in all. How much Paint will Joe need to paint all the surfaces of the 12 fencepost? Use 3:14 for tt and round your final answer to the nearest number Total paint needed: _______
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Given
The number of fence post is 12.
The dimension of each fence post is 8ft tall and 1ft diameter.
To find: How much paint is needed to paint all the surfaces of the 12 fenceposts.
Explanation:
It is given that,
The number of fence post is 12.
The dimension of each fence post is 8ft tall and 1ft diameter.
Therefore,
The fencepost is cylindrical in shape.
Then, the total surface area of the cylinder is,
[tex]\begin{gathered} TSA\text{ of cylinder}=2\pi r(h+r) \\ =2\times3.14\times\frac{1}{2}\times(8+\frac{1}{2}) \\ =3.14\times\frac{17}{2} \\ =26.69ft^2 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} Required\text{ }quantity\text{ }of\text{ }paint=12\times26.69 \\ =320.28 \\ =320ft^2 \end{gathered}[/tex]Hence, the required quantity of paint is 320ft^2.
Hello! Need help with this, please explain in an easy way I am in year 9
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Let's factor the trinomial step by step:
1. Multiply and divide the whole trinomial by the leading coefficient. For the middle term, leave it expressed:
[tex]3x^2-20x+12\rightarrow\frac{9x^2-20(3x)+36}{3}[/tex]2. We'll factor just like a regular x^2+bx+c trinomial:
• Open two sets of parenthesis and put the square root of the first term on each one
[tex]\frac{(3x)(3x)}{3}[/tex]• Put the sign of the second term of the trinomial in the first set of parenthesis, and the result of multiplying the sign of the second term by the sign of the third term on the second set:
[tex]\frac{(3x)(3x)}{3}\rightarrow\frac{(3x-)(3x-)}{3}[/tex]• Find two numbers whose product is 36 and whose sum is 20
[tex]\begin{gathered} 18\cdot2=36 \\ 18+2=20 \\ \\ \rightarrow18,2 \end{gathered}[/tex]• Fill both sets with such numbers, in ascending order:
[tex]\frac{(3x-)(3x-)}{3}\rightarrow\frac{(3x-18)(3x-2)}{3}[/tex]3. Simplify one of the terms with the denominator:
[tex]\frac{(3x-18)(3x-2)}{3}\rightarrow\frac{3(x-6)(3x-2)}{3}\rightarrow(x-6)(3x-2)[/tex]Therefore, the factorization of our trinomial is:
[tex](x-6)(3x-2)[/tex]identify the terms ,coefficients constants in 5c2 + 7d
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Algebraic expressions are compound by algebraic terms that are compound by a signed number or coefficient, one or more variables and one or more exponents.
In the given expression:
[tex]5c^2+7d[/tex]There are 2 terms which are 5c^2 and 7d, its coefficients are 5 and 7 respectively and there is not any constant, which are independent terms.
subtract 7 1/4 - 4 3/4 simplify the answer and write as a mixed number .122 1/21/43 1/2
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Answer
The simplified fraction is 2 1/2
Step-by-step explanation:
[tex]\begin{gathered} \text{Substract 7}\frac{1}{4}\text{ - 4}\frac{3}{4} \\ \text{Step 1: convert the mixed fraction into an improper fraction} \\ 7\frac{1}{4}\text{ = }\frac{(7\text{ x 4) + 1}}{4} \\ 7\frac{1}{4}\text{ = }\frac{29}{4} \\ \\ 4\frac{3}{4}\text{ = }\frac{(4\cdot4)+3}{4} \\ 4\frac{3}{4}\text{ = }\frac{19}{4} \\ We\text{ have} \\ \frac{29}{4}\text{ - }\frac{19}{4} \\ \text{ Find the common denominator} \\ \text{The common denominator is 4} \\ \frac{29\text{ - 19}}{4} \\ =\text{ }\frac{10}{4} \\ =\text{ }\frac{5}{2} \\ =\text{ 2}\frac{1}{2} \\ \text{Hence, the answer is 2}\frac{1}{2} \end{gathered}[/tex]Third-degree, with zeros of -3, -2, and 1, and passes through the point (4, 10).
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The required third degree expression is 1/7 (x³ + 2x² - 5x - 6)
Given,
Find a third degree expression f(x) that has zeros -3, -2, 1 and the equation y = f(x) passes through (4, 10). ,
If the roots/zeroes of a nth order expression are given as r₁, r₂, r₃....rₙ, the expression is given by f(x) = c(x - r₁) (x - r₂) (x - r₃)....(x - rₙ)
Since we know the three roots of the third degree expression, the function is;
f(x) = c(x - (-3)) (x - (-2)) (x - 1)
= c(x + 3) (x + 2) (x - 1)
= c (x³ + 2x² - 5x - 6)
Also y = f(x), passes through(4, 10) , so
10 = c(4³ + 2 x 4² - 5 x 4 - 6)
10 = c(64 + 32 - 20 - 6)
10 = 70c
c = 10/70 = 1/7
∴Required expression is 1/7 (x³ + 2x² - 5x - 6)
Learn more about third degree expressions here;
https://brainly.com/question/13917875
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Find the parabola with focus (2,7) and directrix y = -1.
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A parabola with focus (a, b ) and directrix y = c has the equation
[tex](x-a)^2+b^2-c^2=2(b-c)y[/tex]In our case, (a, b) = (2, 7) and c = -1; therefore, the above becomes
[tex](x-2)^2+7^2-(-1)^2=2(7-(-1))y[/tex][tex](x-2)^2+48=16y[/tex][tex]\Rightarrow\textcolor{#FF7968}{(x-2)^2=16(y-3)}[/tex]which is our answer!
Use the deck of 52 standard playing cards to answer the question.
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Given:
A deck of 52 playing cards is given.
Required:
Probability of selecting a number card, a red card and an ace.
Answer:
There are 40 number cards.
Therefore, probability of selecting a number card=
[tex]\frac{1}{40}[/tex]There are 26 red cards.
Therefore, probability of selecting a red card=
[tex]\frac{1}{26}[/tex]The probability of selecting an ace =
[tex]\frac{1}{52}[/tex]Final Answer:
The Probabilities of selecting a number card, a red card and an ace are,
[tex]\frac{1}{40},\frac{1}{26},\frac{1}{52}[/tex]respectively.
I need help with a math question. I linked it below
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1) We can fill in the gaps, this way since we can write the following when we translate into mathematical language:
[tex]\begin{gathered} \frac{b}{55}+8>6 \\ \frac{b}{55}>-8+6 \\ \frac{b}{55}>-2 \\ 55\cdot\frac{b}{55}>-2\cdot55 \\ b>-110 \end{gathered}[/tex]Note that we could do it in two steps. Subtracting and then multiplying and dividing
3/4 = m + 1/4
What is m? m = ?
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Answer 3/4 = m + 1/4 is 2/4
Explanation.3/4 = m + 1/4
m = 3/4 - 1/4
m = (3 - 1)/4
m = [tex]\frac{2}{4}[/tex]
__________________
Class: Elementary School
Lesson: Fractions
[tex]\boxed{ \colorbox{lightblue}{ \sf{ \color{blue}{ Answer By\:Cyberpresents}}}}[/tex]
use the figure at the right . if JK=5x+23 and NO=29, what is the value of x?
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From the triangle midpoint theroem,
[tex]\begin{gathered} NO=\frac{1}{2}JK \\ 29=\frac{1}{2}(5x+23) \\ 58=5x+23 \\ 58-23=5x \\ 35=5x \\ x=7 \end{gathered}[/tex]A positive integer is 38 more than 27 times another their product is 5057. Find the two integers.
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Answer:
13 and 389
Explanation:
Let the two positive integers be x and y
If a positive integer is 38 more than 27 times another, then;
x = 27y+ 38 ...1
If their product is 5057, then;
xy = 5057 .....2
Substitute equation 1 into 2
(27y + 38)y = 5057
Expand the bracket
27y^2 + 38y = 5057
27y^2 + 38y - 5057 = 0
Factorize
27y^2 -351y + 389y - 5057 = 0
27y(y-13) + 389(y-13) =0
(27y+389)(y−13) = 0
27y + 389 = 0 and y - 13 = 0
27y = -389 and y = 13
Since y is a positive integer, hence y = 13
Substiute y = 13 into equation 1;
x = 27y+ 38 ...1
x = 27(13)+ 38
x = 351 + 38
x= 389
Hencethe two positive integers are 13 and 389
if f(x)=3x-2/x+4 and g(x)=4x+2/3-x,prove that f and g are inverses of each other
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Find the slope of the line passing through the points(-2,6) and (-6, 3).
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Answer:
3/4
Step-by-step explanation:
To find the slope (gradient) of the line = change in y / change in x
[tex]slope=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\(x_{1} ,y_{1} ) = (-2,6)\\(x_{2} ,y_{2} ) = (-6,3)[/tex]
insert those coordinates in the equation:
[tex]slope=\frac{3-6}{-6-(-2)} =\frac{-3}{-4} =\frac{3}{4}[/tex]
Write an equation that expresses the following relationship.u varies jointly with p and d and inversely with wIn your equation, use k as the constant of proportionality.
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Answer:
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]Explanation:
If a varies jointly with b, we write the equation
a = kb
If a varies inversely with b, we write the equation
a = k/b
So, if u varies jointly with p and d and inversely with w, the equation is
[tex]u=k\cdot\frac{p\cdot d}{w}[/tex]Logan wants to know how many skateboards have defective parts. He inspects 20000 skateboards and keeps track of the number of defects per board. Use his probability distribution table to find the expected value for defects on a skateboard.(Rest of the problem needs to be sent as an image)a. 1/25b. 4/25c. 3/25d. 2/25
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ANSWER:
2nd option: 4/25
STEP-BY-STEP EXPLANATION:
To find the expected value of the distribution, we multiply each outcome by its probability and the sum of this would be the expected value, like so:
[tex]\begin{gathered} E(x)=0\cdot\frac{9}{10}+1\cdot\frac{1}{20}+2\cdot\frac{1}{25}+3\cdot\frac{1}{100} \\ \\ E(x)=0+\frac{1}{20}+\frac{2}{25}+\frac{3}{100} \\ \\ E(x)=\frac{5}{100}+\frac{8}{100}+\frac{3}{100}=\frac{16}{100}=\frac{4}{25} \end{gathered}[/tex]Therefore, the correct answer is the 2nd option: 4/25
it says how many one eights are in the product of 9x7/8
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Answer
63
Explanation
Given the product 9 * 7/8
We are to find the number of one eighths that are in the product
Finding the product;
= 9 * 7/8
= (9*7)/8
= 63/8
= 63 * 1/8
= 63 * one-eighth
This shows that there are 63 one eighth in the product
Find the median:1,4,2,7,3,9,5,12,4,8
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Take into account that the median of a data set is given by the element of the set that is at the center of the ordered list of elements. If there is no possible to determine a central element in the list, then, you take two elements of the center and calculate the average value in between such elements.
Then, first order the elements, as follow:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
THe number of elements is 10, then, you conisder the two elements at the center of the list, that is, the 5th and 6th elements:
1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12
and calculate the average in between these numbers:
median = (4 + 5)2 = 9/2 = 4.5
Hence, the median of the given data set id 4.5
Identify the quadrant or ask is that the following points lie on if the point lies on an axis specify which part positive or negative of which axis X or Y
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ANSWER
Quadrant II
EXPLANATION
There are four (4) quadrants on the coordinate plane:
Let us now plot the point:
Therefore, the point (-1, 9) lies on quadrant II.
Match each expression to the equivalents value. 4. i^121 A. 15. i^240 B. -16. i^90 C. -i7. i^43 D. i
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Let's find the value of each expression.
[tex]undefined[/tex]Sort the sequences according to whether they are arithmetic, geometric, or neither. (98.3, 94.1, 89.9, 85.7,) (1, 0, -1, 0) (1.75, 3.5, 7, 14) (-12, -10.8, -9.6, -8.4) (-1, 1, -1, 1)
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hello
to know what type of sequence they are, we need to test either for common difference of common ratio
first sequence
(98.3, 94.1, 89.9)
first term = 98.3
in this case there's a common difference here
we can find that by subtracting the second term from the first term or the third term from the second term
[tex]\text{common difference (d) = 94.1-98.3=-4.2}[/tex]first sequence is an arithmetic progression
second sequence
(1, 0, -1, 0)
first term = 1
common difference or common ratio does not exist here
third sequence
(1.75, 3.5, 7, 14)
first term = 1.75
in this case, there's no common difference but rather common ratio
common ratio (r) can be found by dividing the second term by the first term or the third term by the second term
[tex]\begin{gathered} \text{common ratio(r) = }\frac{3.5}{1.75}=2 \\ \frac{14}{7}=2 \end{gathered}[/tex]the common ratio here is 2 and this is a geometric progression
fourth sequence
(-12, -10.8, -9.8, -8.4)
first term = -12
in this sequence, there's no common difference or common ratio
fifth sequence
(-1, 1, -1, 1)
the fifth sequence is neither a geometric or artimethic progression because there no common difference or ratio
Are there no more tutors for mathematics, I can’t seem to find the option anymore for a tutor.
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A quadratic equation is represented graphically as:
[tex]y=a(x-h)^2+k[/tex]Here the graph represents the parabola where (h,k) is the vertex of the parabola.
Put any value of h, k and a to get the graph as follows:
The graph of a quadratic equation is parabolic in nature.
Suppose that you have a quadratic equation given by:
[tex]y=x^2-5x+6[/tex]Convert the equation into perfect square by completing the square method
[tex]\begin{gathered} y=(x^2-5x+\frac{25}{4})+6-\frac{25}{4} \\ y=(x-\frac{5}{2})^2-\frac{1}{4} \end{gathered}[/tex]This is the method of conversion of quadratic to plot the graph.
2) What is the sum of all the angles in the rectangle
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the sum of all the angles in a rectangle is 360°
Which of the sketches presented in the list of options is a reasonable graph of y = |x − 1|?
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ANSWER
EXPLANATION
The parent function is y = |x|. The vertex of this function is at the origin.
When we add/subtract a constant from the variable, x, we have a horizontal translation, so the answer must be one of the first two options.
Since the constant is being subtracted from the variable, the translation is to the right. Hence, the graph of the function is the one with the vertex at (1, 0).
For the following scores:a. construct a frequency distribution table.b. sketch a histogram of the frequency distribution.5, 4, 3, 5, 4, 2, 4, 15, 4, 6, 1, 4, 5, 2, 3
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Given the data set:
5, 4, 3, 5, 4, 2, 4, 1, 5, 4, 6, 1, 4, 5, 2, 3
Using the given data set, let's answer the following questions:
• (a). Construct a frequency distribution table.
Let's first arrange the terms in ascending order:
1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6
Here, we can have the following:
1 ==> Occurs twice
2 ==> Occurs twice
3 ==> Occurs twice
4 ==> Occurs 5 times
5 ==> Occurs 4 times
6 ==> Occurs once.
Therefore, for the frequency distribution table, we are to use the number of times each data occur (this is the frequency).
We have the table below:
• Part b.
Let's sketch a histogram of the frequency distribution.
• We have the histogram of the frequency distribution below:
Find P on line segment CD that is 3/4 the distance from C(0, 0) to D (0, 12).
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We have two points C(0, 0) and D (0, 12).
P is on the line segment and 3/4 of the distance from C to D.
u(x) = 4x - 2 w(x) = - 5x + 3The functions u and w are defined as follows.Find the value of u(w(- 3)) .
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Solution
- We are given the two functions below:
[tex]\begin{gathered} u(x)=4x-2 \\ \\ w(x)=-5x+3 \end{gathered}[/tex]- We are asked to find u(w(-3)).
- In order to find u(w(-3)), we need to first find u(w(x)) and then we can substitute x = -3.
- Since we have been given u(x), then, it means that we can find u(w) as follows:
[tex]\begin{gathered} u(x)=4x-2 \\ u(w),\text{ can be gotten by substituting w for x} \\ \\ u(w)=4w-2 \end{gathered}[/tex]- But we have an expression for w in terms of x. This means that we can say:
[tex]\begin{gathered} u(w)=4w-2 \\ \\ w(x)=-5x+3 \\ \\ \therefore u(w(x))=4(-5x+3)-2 \\ \\ u(w(x))=-20x+12-2 \\ \\ \therefore u(w(x))=-20x+10 \end{gathered}[/tex]- Now that we have an expression for u(w(x)), we can proceed to find u(w(-3)) as follows:
[tex]\begin{gathered} u(w(x))=-20x+10 \\ put\text{ }x=-3 \\ \\ u(w(-3))=-20(-3)+10 \\ \\ u(w(-3))=60+10=70 \end{gathered}[/tex]Final Answer
The answer is
[tex]u(w(-3))=70[/tex]If the discriminant is 22, then the roots of the quadratic equation are ________________.irrationalrationalreal and equalcomplex
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Given:
The discriminant is 22.
Required:
To choose the correct option for the roots.
Explanation:
The desciminant is 22 means
[tex]b^2-4ac=22[/tex]We know that if
[tex]b^2-4ac>0[/tex]the equation has two distinct real number roots.
Therefore the roots are irrational or rational.
Final Answer:
The roots are irrational or rational.
You deposit $6000 in an account earning 6% interest compounded continuously. How much will you have in the account in 10 years?
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Solution
Step 1:
Write the compounded interest continuously formula.
[tex]\text{A = Pe}^{rt}[/tex]Step 2:
Given data
P = $6000
r = 6% = 0.06
t = 10 years
Step 3:
Substitute in the formula
[tex]\begin{gathered} A\text{ = Pe}^{rt} \\ A\text{ = 6000 }\times\text{ 2.7183}^{10\times0.06} \\ A\text{ = 6000 }\times\text{ 2.7183}^{0.6} \\ A\text{ = 6000 }\times\text{ 1.822126} \\ A\text{ = \$10932.76} \end{gathered}[/tex]Final answer
A = $10933 ( nearest whole number)
9.State the slope and y-value of the y-intercept of the equation, y = 6x + 9Slopey-intercept
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The slope is 6 and the y-intercept is 9
Explanation:The given equation is:
y = 6x + 9
The general form of the equation of a line is
y = mx + c
where m is the slope and c is the y-intercept.
Comparing these equations, we see that
m = 6 and c = 9
Therefore, the slope is 6 and the y-intercept is 9
how long does it take the snail to crawl 86 inches enter answer in decimal number
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To get the equation of the line graph, first, we have to find its slope. The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the picture, the line passes through the points (0,0) and (10, 1), then its slope is:
[tex]m=\frac{1-0}{10-0}=\frac{1}{10}_{}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
From the graph, the line intersects the y-axis at y = 0, this means that b = into
the equation. Therefore, the equation is:
y = 1/10x
where x is distance (in inches) and y is time (in minutes).
To find how long it takes the snail to crawl 86 inches, we have to replace x = 86 into te equation as follows:
[tex]\begin{gathered} y=\frac{1}{10}\cdot86 \\ y=8.6 \end{gathered}[/tex]The snail takes 8.6 minutes to crawl 86 inches