Answers
From the question
We are given the function
[tex]y=-0.5x+29[/tex]Comparing the function with the equation
[tex]y=mx+c[/tex]Then the slope of the function is
m = - 0.5
Using the function
[tex]y=-0.5x+29[/tex]When x = 1
[tex]\begin{gathered} y=-0.5(1)+29 \\ y=28.5 \end{gathered}[/tex]When x = 2
[tex]\begin{gathered} y=-0.5(2)+29 \\ y=28 \end{gathered}[/tex]When x = 3
[tex]\begin{gathered} y=-0.5(3)+29 \\ y=27.5 \end{gathered}[/tex]By comparing the values of y, we will notice a decrease of 0.5
Hence,
The value of the function decreased by 0.5 per year after 1990
Related Questions
When finding the composition of f (g (x) )substitute f (x) for the x in g (x)multiply f (x) by g (x)substitute g (x) for the x in f (x)
Answers
Okay, here we have this:
Considering that the composition of function is formed by taking the outputs of one function and converting them into the inputs of another function. We obtain that, f(g(x)), consists of taking the result obtained by evaluating g (x) and replacing it by x in f (x). Then the correct answer is the third option.
What is the purchase price of a 50-day T-bill with a maturity value of S1,737 that eams an annual interest rate of 2 802% (Assume a 360 day year)The purchase price is (Round to two decimal places)
Answers
We need to use the next simple interest formula:
[tex]A=P(1+rt)[/tex]Where
P= Present value
r= annual interest rate in decimal form
T=time in years
A=amount after time
Hence, we have that
A= S1,737
r=2.802%/100=0.02802
t=50/360
P=?
Replacing on the given formula:
[tex]\begin{gathered} 1,737=P(1+0.02802\cdot\frac{50}{360}) \\ P=\frac{1,737}{1+0.02802\cdot\frac{50}{360}} \\ P=1730.27 \end{gathered}[/tex]Hence, the purchase price is $1730.27
Jungle Gym Print On the new jungle gym there are 4 ladders that lead to a landing. From the landing you can get to the big platform by climbing up either the rope or the fireman's pole How many different ways are there to get to the big platform?
Answers
Answer: 12 ways
Total number of ladder = 4
Yo can get to the platform either by climbing up the rope or fire mans hope
We have two options to get to the big platform
[tex]\begin{gathered} ^nP_r\text{ = }\frac{n!}{(n\text{ - r)!}} \\ ^4P_2\text{ = }\frac{4!}{(4\text{ - 2)!}} \\ =\text{ }\frac{4!}{2!} \\ \text{= }\frac{4\text{ x 3 x 2 x 1}}{2\text{ x 1}} \\ =\text{ 4 x 3} \\ \text{= 12 ways} \end{gathered}[/tex]A line passes through (4,3) and (8,6). Another line has a slope of -3/4. The two lines are parallel. *1 pointTrueFalse
Answers
ANSWER
False
EXPLANATION
The formula for the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The slope of the first line is:
[tex]m=\frac{3-6}{4-8}=\frac{-3}{-4}=\frac{3}{4}[/tex]The other line has a negative slope, so the lines are not parallel.
Try AgainAt the city museum, child admission is $6.00 and adult admission is $9.20. On Monday, twice as many adult tickets as childtickets were sold, for a total sales of $780.80. How many child tickets were sold that day?
Answers
32 child tickets were sold on that day
Explanation:Given:
The cost per child = $6.00
let the number of child tickets = c
The cost per adult ticket = $9.20
let the number of adult tickets = a
To find:
the number of child tickets sold
On Monday:
Adult tickets = 2(children tickets)
a = 2c
Total sales on Monday = $780.80
Total sales = The cost per child (number of child tickets) + The cost per adult (number of adults tickets)
780.80 = 6(c) + 9.2(a)
substitute for a:
780.8 = 6c + 9.2(2c)
780.8 = 6c + 18.4c
780.8 = 24.4c
divide both sides by 24.4:
[tex]\begin{gathered} \frac{780.8}{24.4}\text{ = }\frac{24.4c}{24.4} \\ \\ c\text{ = 32} \end{gathered}[/tex]Hence, 32 child tickets were sold on that day
Gloria, an experienced bungee jumper, leaps from a tall bridge and falls toward the river below. The bridge is 200 feet above the water and Gloria's bungee cord is 130 feet long unstretched. When will Gloria's cord begin to stretch? Round your answer to two decimal places.
Answers
We are given that Gloria jumps from a bridge using a bungee cord. The quadratic expression that models an object falling freely is the following:
[tex]h=h_0+v_0t-\frac{1}{2}gt^2[/tex]Where:
[tex]\begin{gathered} h_0=\text{initial height} \\ v_0=\text{initial velocity} \\ g=\text{acceleration of gravity} \\ t\text{ = time} \end{gathered}[/tex]A representation of the problem is the following:
If we assume that the initial velocity is zero, we get the following values:
[tex]\begin{gathered} h_0=200 \\ h=200-130 \\ g=32 \\ \end{gathered}[/tex]The height is equivalent to the total height of the bridge minus the longitude of the cord. The value for "g" is a constant equivalent to 32 feet per second.
Replacing we get:
[tex]200-130=200-\frac{1}{2}(32)t^2[/tex]Now we solve for "t", first by subtracting 200 to both sides:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Solving the operation:
[tex]-130=-\frac{1}{2}(32)t^2[/tex]Multiplying both sides by -2:
[tex]260=32t^2[/tex]Dividing both sides by 32:
[tex]\frac{260}{32}=t^2[/tex]Taking square root on both sides of the equation:
[tex]\sqrt[]{\frac{260}{32}}=\sqrt{t^2}[/tex]Solving the operations:
[tex]2.85=t[/tex]Therefore, the cord starts stretching at 2.85 seconds.
Find the equation of the line. Write the equation of the line in standard form Vertical line through (-1,-1)
Answers
Solution
We have the following point given (-1, -1)
The equation of a line is given by:
y= mx+b
For this case since we have a vertical line the equation would be:
x= -1
Lucas made a recipe that needed five-sixths cup of flour. Sarah's recipe calledfor 1/6 cup of flour. How much moreflour did Lucas need?
Answers
Answer:
2/3 cups of flour
Explanation:
Lucas recipe needed 5/6 cup of flour.
Sarah's recipe needed 1/6 cup of flour.
The difference
[tex]\begin{gathered} \text{Difference}=\frac{5}{6}-\frac{1}{6} \\ =\frac{4}{6} \\ =\frac{2}{3}\text{ cups} \end{gathered}[/tex]Therefore, Lucas needed 2/3 cups more of flour.
Hello I really need help with this question I’m not understanding it
Answers
The subset of the event " The two spins have a sum of 5 " is { (2,3), (3,2), (1,4) and (4,1) }
It is given that the sum of Jae's two spins was 5.
S is the sample space of spinning the spinner twice.
The collection of all the possible outcomes is termed the sample space
Subset: If every element in set A is also an element in set B, then set A is a subset of set B. Set A is therefore contained within set B.
Now, the subset of the event " The two spins have a sum of 5 "
In the spinner, there are 1, 2, 3, and 4.
So, the values that would give us a 5 are (2,3), (3,2), (1,4), and (4,1)
These are the terms that will be in the required subsets,
So, Required subset = { (2,3), (3,2), (1,4) and (4,1) }
To read more about subsets, visit https://brainly.com/question/17514113
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Classify the slope as upward downward vertical or horizontal. m = -7
Answers
Answer:
downward
Explanation:
A negative slope decreases from left to right.
a line with a negative slope can be thought of as a downward side of a hill. Therefore we classify negative slopes as downward (because our idea of 'upward' is something that increases from left to right).
Therefore, the slope m = - 7 since it is negative is classified as downward.
The upward slope is
a vertical slope is
a horizontal slope is
A catering service offers 3 appetizers, 7 main courses, and 4 desserts. A customer is to select 2 appetizers, 3 main courses,and 3 desserts for a banquet. In how many ways can this be done?
Answers
General category: Mathematics
Sub-category: Probability
Topic: counting techniques
Introduction:
The combination formula C(n,r) shows us the number of ways of picking r unordered outcomes from n possibilities. For n ≥ r ≥ 0, C(n,r) is given by the following formula:
[tex]C(n,r)=\frac{n!}{r!(n\text{ -r})!}[/tex]Explanation:We can use combinations and fundamental counting principles to answer this question.
Let us denote by "a", the number of selection of appetizers. This number can be calculated as follows:
[tex]C(3,2)=\frac{3!}{2!(3\text{ -2})!}=3[/tex]Now, let us denote by "b", the number of selection of main courses. This number can be calculated as follows:
[tex]C(7,3)=\frac{7!}{3!(7\text{ -3})!}=35[/tex]Finally, let us denote by "c", the number of selection of desserts. This number can be calculated as follows:
[tex]C(4,3)=\frac{4!}{3!(4\text{ -3})!}=4[/tex]Now, applying the multiplication principle we get the desired number:
[tex]C(3,2)\cdot C(7,3)\cdot C(4,3)=3\cdot35\cdot4\text{ = 420}[/tex]We can conclude that the correct answer is:
The table below shows the birth months for all 25 students in Mr. Battistini's class.Student Birth MonthsWhat is the probability of selecting a student at random from this class who was NOT bornin June?А. 4%B. 16%C.21%D.84%
Answers
Given data:
The given table.
The probability that the student not born in june is,
[tex]\begin{gathered} P(J^{\prime})=1-\frac{4}{25} \\ =\frac{21}{25} \\ =0.84 \\ =84\text{ percent} \end{gathered}[/tex]Thus, the option (D) is correct.
How much must be deposited today into the following account in order to have 40,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%how much should be deposited today? $(Do not round until the final answer. Then round to the nearest cent as needed.)
Answers
The formula to calculate the compound interest is:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{ Where } \\ A\text{ is the total amount at the end of t years.} \\ P\text{ is the initial amount deposited.} \\ r\text{ is the interest rate.} \\ t\text{ is the time.} \end{gathered}[/tex]From the word problem, we have:
[tex]\begin{gathered} A=40,000 \\ P=? \\ r=7\%=\frac{7}{100}=0.07 \\ n=1\Rightarrow\text{ It was compounded once in a year.} \\ t=6 \end{gathered}[/tex]Then, we can replace the above values in the compound interest formula and solve for P.
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 40,000=P(1+\frac{0.07}{1})^{(1)(6)} \\ 40,000=P(1+0.07)^6 \\ 40,000=P(1.07)^6 \\ \text{ Divide by }1.07^6\text{ from both sides} \\ \frac{40,000}{1.07^6}=\frac{P(1.07)^6}{1.07^6} \\ 26,653.69\approx P \\ \text{ The symbol is read 'approximately'.} \end{gathered}[/tex]AnswerYou should deposit today $26,653.69.
I need help answering it I don’t know howTo do it
Answers
Okay, here we have this:
Considering the provided graph we obtain that:
Recall that the slope is undefined when lines are vertical. So in this case we can see that this description is fulfilled, therefore, finally we obtain that the Type of slope is Undefined
find the slope of the line through each pair of points (3,0) , (-11, -15)
Answers
Given:
points (3,0) , (-11, -15)
Required:
Slope
Solution:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{slope}=\frac{-15-0}{-11-3_{}}=\frac{-15}{-14}=\frac{15}{14}[/tex]Answer:
[tex]\text{slope}=\frac{15}{14}[/tex]What is the area, in square inches, of the shape below? 8.4 in 9.7 in
Answers
Problem:
The area of the triangle is
[tex]A\text{ = }\frac{bxh}{2}[/tex]here, b is the base of the triangle and the variable h is its height so :
[tex]A\text{ = }\frac{bxh}{2}\text{ = }\frac{9.7\text{ in x 8.4 in}}{2}\text{ = }\frac{81.48in^2}{2}=40.74in^2[/tex]We can conclude that the area of the shape is 40.74 in^2
Solve this system of equations by graphing. First graph the equations, and then type the solution.3x+2y=6y=–5/2x+1
Answers
System of equations:
[tex]3x+2y=6[/tex][tex]y=-\frac{5}{2}x+1[/tex]The solution of the system of equations using the graph is the coordinate in which both functions collide:
In our function, this occurs in (-2, 6).
Answer: ( -2, 6 )
A. Make box-and-whisker plots to represent the temperature data for Oakville and Fairview.
B. What conclusions can you make about the temperatures in August in the two cities?
C. Luis finds that the average August temperature in Fairview in 2004 was 73°. How would including this additional data value change the box-and-whisker plot you made in part (a)? Would it change the conclusions you made in part (b)?
Answers
Answer:
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
lower air temperature and less precipitation
Graphs that Describe Climate Climographs show monthly average temperatures and precipitation totals on a single graph.
Step-by-step explanation:
Part 2: Consider this word problem: "Professor has several tarantulas and frogs. She counts 104 legs and 80 eyes in the room (not including her own). How many of each creature does she have?" Answer the question in a paragraph form. Answer the following: • What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up orpull some information from the back of your head?• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!)
Answers
Okay, here we have this:
Considering the provided information we are going to calculate how many of each creature does she have, so we obtain the following:
• What bits of information are not explicitly stated in the problem that would help us figure out the answer? Do you need to look anything up or
pull some information from the back of your head?:
The missing information of the exercise is the amount of legs and eyes of each type of animal
• Which mathematical concept(s) that we've gone over so far would be helpful for solving this problem?:
The mathematical concept that we apply to solve this exercise will be the systems of equations of two equations by two incognites.
• Now, solve the problem and explain your solution. (It's OK if your answer isn't completely right. We're here to learn!):
According to the given information we obtain the following systems of equations:
8x+4y=104 (Equation of the legs)
8x+2y=80 (Eye equation)
"X" corresponds to the number of tarantulas and "y" to the number of frogs.
Solving:
We will clear x in the second equation:
8x+2y=80
8x=80-2y
x=(80-2y)/8
x=10-2y/8
Replacing in the first equation:
8x+4y=104
8(10-2y/8)+4y=104
80-2y+4y=104
80+2y=104
2y=24
y=24/2
y=12
Using this value of y in the equation of x:
x=10-2y/8
x=10-2(12)/8
x=10-24/8
x=10-3
x=7
Finally we obtain that she has 7 tarantulas and 12 frogs.
Label the sides of the right triangle.*2 pointsCaptionless ImageA) Hypotenuse = 8 m, Adjacent = 15 m, Opposite = 17 mB) Hypotenuse = 17 m, Adjacent = 8 m, Opposite = 15 mC) Hypotenuse = 15 m, Adjacent = 17 m, Opposite = 8 mD) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m
Answers
Given:
There are given that the right angle triangle, UVW.
Where,
[tex]\begin{gathered} UV=8m \\ VW=15m \\ UW=17m \end{gathered}[/tex]Explanation:
According to the concept:
The hypotenuse is defined as the longest side in the right-angle triangle.
The perpendicular side is defined by the perpendicular base angle.
And,
The adjacent side is defined by the leg of the right-angle triangle.
Final answer:
Hence, the correct option is D.
How many solutions does this equation have? Solve on paper and enter your answer on Zearn.
9x +7x+8=-4+4(3x+5)
No solutions
One solution
Infinitely many solutions
Answers
Answer: One solution
Step-by-step explanation:
Simplify to find x:
9x +7x+8=-4+4(3x+5)
16x + 8 = -4 +12x +20
4x = -4 +20 -8
4x = 8
x=2
which conversion factors are used to multiply to 12m/s to get kilometers per minute A. 1000m over 1kmB. 60S Over 1 minC.1 km over 1000mD.1min over 60s
Answers
To convert 12 meter per seconds to kilometer per minute
We need kilometer in the denominator and minute in the denomiator
But 1 km = 1000 m and 60 seconds = 1 minute
12m / s x 60s / 1 min x 1km / 1000m
Hence the correct option is;
B and C
please solve it and identify what was wrong in solving it the first time
Answers
we have that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
In the triangle ABE
A+B+E=180
substitute given values
60+55+E=180
E=65 degrees
so
mRemember that
m by vertical angles
so
mIn the triangle EDC
msubstitute given values
65+85+D=180
D=30 degreesmHow is the function in the following picture graphed on a chart?
Answers
Okay, here we have this:
Which inequality is true when the value of c is −11?−c−4≤−3c-4≥3-c-4≤3c-4≤3
Answers
In order to find which inequality is true, let's use the value of c in each one and check if they are true or false:
[tex]\begin{gathered} -c-4\le-3 \\ 11-4\le3 \\ 7\le-3\text{ (false)} \\ \\ c-4\ge3 \\ -11-4\ge3 \\ -15\ge3\text{ (false)} \\ \\ -c-4\le3 \\ 11-4\le3 \\ 7\le3\text{ (false)} \\ \\ c-4\le3 \\ -11-4\le3 \\ -15\le3\text{ (true)} \end{gathered}[/tex]Therefore the correct option is the fourth one.
3. From a boat on the lake, the angle of elevation to the top of a cliff is 25.2°. If the base of the cliff is 1384 ft from the boat, how high is the cliff? Round results to an appropriate number of significant digits.
Answers
Using trig function Tan to get the height of the cliff;
[tex]\begin{gathered} \tan25.2=\frac{h}{1384} \\ h=tan25.2\times1384 \\ =0.471\times1384 \\ =651.26096 \end{gathered}[/tex]ANSWER
[tex]651.26ft[/tex]1. Solve the given system of equations. X + y + z = 9 x - z = 5 X + y = 6the solution is: x = y = and z =
Answers
x=8
y=-2
Z=3
Explanation
Step 1
Let
[tex]\begin{gathered} x+y+z=9\text{ Equation (1)} \\ x-z=5\text{ Equation(2)} \\ x+y=6\text{ Equation(3)} \end{gathered}[/tex]Step 2
isolate x from equation (1) , (2) and (3)
[tex]\begin{gathered} x+y+z=9 \\ x=9-y-z\text{ Equation (4)} \end{gathered}[/tex][tex]\begin{gathered} x-z=5 \\ x=5+z\text{ equation (5)} \\ \\ x+y=6 \\ x=6-y\text{ equation(6)} \\ \end{gathered}[/tex]Step 3
combining equation (4) and (5)
[tex]\begin{gathered} 9-y-z=5+z \\ 9-y-2z=5 \\ -y-2z=5-9 \\ -y-2z=-4\text{ Equation(7)} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} x=x \\ \text{equation (5) = equation (6)} \\ 5+z=6-y\text{ equation (8)} \end{gathered}[/tex]Step 5
using equation(7) and (8) find y and z
[tex]\begin{gathered} -y-2z=-4\text{ (7)} \\ 5+z=6-y(8) \\ \text{isolate y from equation (7)} \\ -y=-4+2z \\ y=4-2z \\ \text{replace in equation (8)} \\ 5+z=6-4+2z \\ 5+z=2+2z \\ z-2z=2-5 \\ -z=-3 \\ z=3 \end{gathered}[/tex]replace the value of z= 3 in equation (7) to find y
[tex]\begin{gathered} -y-2z=-4 \\ -y-2\cdot3=-4 \\ -y-6=-4 \\ -6+4=y \\ y=-2 \end{gathered}[/tex]finally, replace the value of y in equation (3) to find x
[tex]\begin{gathered} x+y=6 \\ x-2=6 \\ x=6+2 \\ x=8 \end{gathered}[/tex]I hope this helps you
Hello I don't know if you can help me with this
Answers
we have that
In this problem we have an arithmetic sequence
the general equation is equal to
an=a1+D(n-1)
where
a1 is the first term
D is the common difference
n is the number of terms
so
a1=7
D is the difference between consecutive terms
D=11-7=4
an=7+4(n-1)
change the variables
d=7+4(n-1)
d=7+4n-4
d=4n+3
For n=30
d=4(30)+3
d=123Find the value of the variable that is not given: V=I w h; Given V = 90,1 = 10, h = 3 (Round the answer to 2 decimal places if necessary)
Answers
V= l*w*h
V=90
l=10
h=3
Replace the values in the expression and clear w
V= l*w*h
90=10*w*3
90=30w
w=3
Find the area and perimeter of each polygon:
6
5
4
8
Area:
unit2
Perimeter:
unit2
OK
Answers
Part a
The area of the figure is equal to the area of two rectangles
Area of the top rectangle
A=(6)*(5)=30 unit2
Area of the bottom rectangle
A=(8)*(4)=32 unit2
therefore
The total area is
A=30+32
A=62 unit2Part b
Find out the perimeter
To find out the perimeter adds all the length sides
so
P=8+4+(8-6)+5+6+5+4
P=34 units