The cost of the Chicago Cubs ticket in the year 2000 was $97.50.
What is defined as the constant rate of change?A rate of change is defined as the ratio of change in dependent values as well as outputs to change in independent variables or inputs. The change, also known as the function's slope, describes what numbers change between 2 points on the a coordinate plane.For the given question.
The price of the Chicago Cubs ticket in year 2005 is $77.50.
The price of the ticket reduced in year 2012 as $49.50.
There is a constant amount of decrease in the price.
Thus, difference in years;
= 2012 - 2005
= 7 years.
Difference in amount;
= 49.50 - 77.50
= -28
Price decreased in one year = 28/ 7 = -4 per year.
For the price of the ticket in the years 2000.
= 2005 - 2000
= 5 years.
Price decreased in 5 years is;
= -4 x 5
= -20
The price is 2000 is 77.50 + 20 = 97.50
Thus, the cost of the Chicago Cubs ticket in the year 2000 was $97.50.
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is it true that all whole numbers are rational numbers ? why or why not
all whole numbers are rational numbers
because we can write 21 as 21/1 in rational form.
.
We can write any whole number (a) into the form of
[tex]\frac{a}{b}[/tex]where b = 1,
so all whole numbers can be written in form of rational numbers.
A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2,3,4. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Red 1 is an example of which of the following events? Select all correct answers.
The event Red 1 is an example of these following events:
R and O.E'.E or R.Which events are included into Red 1?Red cards are represented by the letter R, while the number 1, which is odd, is represented by the letter O.
Both events R and O happen in the, hence the event R and O is one of the possible events to this problem, as the card is both red and has an odd number.
The number is not even, hence the event E' is another one of the events in this problem.
The final event is E or R, as the card has a red number, meaning that at least one of the options E or R are satisfied.
Missing informationThe options which the event respect are missing, and are given by the image at the end of the answer.
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I need help I am doing 8th grade conversion factors and there is only one way my teacher wants me to do it.
Conversion factors are the numbers for which we need to multiply a certain variable to convert it to another unit. In this case we need to convert gallons to cups, which have a conversion factor of 16 and minutes to seconds, which has a conversion rate of 60. Doing this we have:
[tex]\text{capacity = 24 gallons }\cdot\text{ 16 = }384\text{ cups}[/tex][tex]\text{time = 5 minutes }\cdot\text{ 60 = }300\text{ s}[/tex]The rate is:
[tex]\text{rate = }\frac{384}{300}\text{ = }1.28\text{ }\frac{cups}{s}[/tex]use the graph to find the following A) find the slope of the lineB) is the line increasing or decreasingC) estimate the vertical intercept(x y)=
The Solution.
To find the slope of the line from the given graph:
First, we shall pick two coordinates in the graph, that is
[tex](0,2),(2,-1)[/tex]This implies that
[tex]\begin{gathered} (x_1=0,y_1=2)\text{ and} \\ (x_2=2,y_2=-1) \end{gathered}[/tex]By formula, the slope is given as below:
[tex]\text{ slope=}\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the values in the above formula, we get
[tex]\begin{gathered} \text{ Slope=}\frac{-1-2}{2-0} \\ \\ \text{ Slope =}\frac{-3}{2} \end{gathered}[/tex]So, the slope of the line is -3/2
b. From the graph, and from the slope being a negative value, it is clear that the line graph is Decreasing.
c. To estimate the vertical intercept is to find the y-intercept of the line.
Clearly from the graph, we can see that the vertical intercept is (0,2), that is, the point where the line cut the y-axis.
Therefore, the vertical intercept is (0,2).
Mrs. Navarro has 36 students in her class, 16 boys and 20 girls.Select all ratios below that correctly describe the ratio of boys to girls in Mrs.Navarros's class.
First, we need to know the ratio of boys to girls in Mrs. Navarro's class. There are 16 boys and 20 girls. The ratio would be 16:20.
From this given, we can choose from the options which rations are equivalent to our given ratio.
8 to 10 is a ratio that is equivalent from our given. If we scale are ratio by 2, we can get 8:10.
5:4, 8:18, and 5 to 9, however, are NOT equivalent to 16:20.
4:5 is equivalent. We just need to scale 16:20 by 4, and we will get 4:5.
10:8 is another ratio that is NOT equivalent to 16:20.
*Scaling ratios are similar to finding the lowest terms of fractions.
I'm not sure how to do this. This is a long one that's why.
We have the following:
For the area surface:
[tex]As=2\pi rh[/tex]repacing:
r = 1.5 in
h = 7 in
[tex]\begin{gathered} As=2\cdot3.14\cdot1.5^{}\cdot7 \\ As=65.94 \end{gathered}[/tex]The answer is 65.9 in^2
For volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=3.14\cdot1.5^2\cdot7 \\ V=49.455 \end{gathered}[/tex]The answer is 49.5 in^3
Shown in the equation are the steps a student took to solve the simple interest formula A=P(1+rt) for r
Given:
We're given the steps a student took to solve the simple interest formula.
To find:
The algebraic error in student's work.
Step-by-step solution:
Let us first solve the equation and then we will spot the error in the solution:
A = P(1 + rt)
A = p + prt
A - p = prt
A - p / pt = r
Upon comparing both solutions, we can clearly see that the student made a mistake in the second step in the multiplication process.
The student should write A = p + prt in the second step in place of
A = p + rt, because p is multiplied with the whole bracket.
7. The cylinder shown has a radius of 3inches. The height is three times the radiusFind the volume of the cylinder. Round yoursolution to the nearest tenth.
Answer:
250 cubic inches
Explanation:
Given that:
Radius of the cylinder, = 3 in.
Height of the cylinder = 3r
= 3(3)
=9 in.
The formula to find the volume of a cylinder is
[tex]V=\pi r^2h[/tex]Plug the given values into the formula.
[tex]\begin{gathered} V=\pi3^29 \\ =81\pi \\ =254.469 \end{gathered}[/tex]Rounding to nearest tenth gives 250 cubic inches, which is the required volume of the cylinder.
A car can travel 43/1/2 miles on 1/1/4 gallons of gas. What is the unit rate for miler per gallon
The unit rate for the car is 34.8 miles per gallon.
How to get the unit rate for mile per gallon?
The unit rate will be given by the quotient between the distance traveled and the gallons of gas consumed to travel that distance.
Here we know that the car travels 43 and 1/2 miles on 1 and 1/4 gallons of gas, then the quotient is:
U = (43 + 1/2)/(1 + 1/4) mi/gal = (43.5)/(1.25) mi/gal = 34.8mi/gal
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Y + 41 = 67 solve y using one step equation
Answer:
Y = 26
Step by step explanation:
[tex]y\text{ + 41 = 67}[/tex]
Then we pass the 41 to substract.
[tex]y\text{ = 67 - 41 = 26}[/tex]Lisa is a software saleswoman. Let y represent her total pay (in dollars). Let “x”represent the number of copies of History is Fun she sells. Suppose that “x”and “y”are related by the equation 90x + 2200 =v.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Explanation
Part A
Given that x and y are related by the by the equation 90x + 2200 =y. We can find the change by comparing the formula with the original equation of a line.
[tex]\begin{gathered} y=mx+c \\ where\text{ m is the slope\lparen change in y for x\rparen} \end{gathered}[/tex]Comparing the above with the given question, m becomes change in Lisa's pay for each copy of history is fun. Therefore,
Answer: 90 dollars
Part B
If Lisa does not sell any copies of history is fun, therefore, the value of x becomes zero. We can then have the total pay as
[tex]\begin{gathered} y=90(0)+2200 \\ y=2200 \end{gathered}[/tex]Answer: 2200 dollars
7 singles, 13 fives, 4 twenties, and 3 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
So,
The probability to obtain one bill of the four, is 1/4.
So, the expected value is:
[tex]\begin{gathered} \frac{1}{4}(7)+\frac{1}{4}(13)+\frac{1}{4}(4)+\frac{1}{4}(3) \\ \\ =6.75 \end{gathered}[/tex]Therefore, the fair price to play this game is 6.75.
Writing the equation of a quadratic function given its graph
Answer:
[tex]y=-(x-1)^2+2[/tex]Step-by-step explanation:
A quadratic function in vertex form is represented as:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex} \end{gathered}[/tex]Given the vertex (1,2) substitute it into the function:
[tex]y=a(x-1)^2+2[/tex]As you can see, we still do not know the value for ''a'', use the point given (4,-7) substitute it (x,y) and solve for ''a'':
[tex]\begin{gathered} -7=a(4-1)^2+2 \\ -7=a(3)^2+2 \\ -7=9a+2 \\ 9a=-7-2 \\ a=-\frac{9}{9} \\ a=-1 \end{gathered}[/tex]Hence, the equation of the function would be:
[tex]y=-(x-1)^2+2[/tex]Write the slope-intercept form of the equation. Put your answer in y = mx + b form.Passing through (-4, -8) and (-8, -13)
Answer:
[tex]y=\frac{5}{4}x-3[/tex]Step-by-step explanation:
Linear functions are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]The slope of a line is given as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex](-4,-8) and (-8,-13):
[tex]\begin{gathered} m=\frac{-8-(-13)}{-4-(-8)} \\ m=\frac{5}{4} \end{gathered}[/tex]Use the slope-point form of a line, to find the slope-intercept form:
[tex]\begin{gathered} y_{}-y_1=m(x_1-x_{}) \\ y+8=\frac{5}{4}(x+4) \\ y+8=1.25\mleft(x+4\mright) \\ y=\frac{5}{4}x-13 \\ y+8=\frac{5}{4}x+\frac{20}{4} \\ y=\frac{5}{4}x+5-8 \\ y=\frac{5}{4}x-3 \end{gathered}[/tex]whic fracción is equivalente to 8/10
Given data
*The given fraction is 8/10
[tex]\frac{80}{100}=\frac{8}{10}[/tex]80/100 is the fraction equivalent to 8/10
Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.)
Answer:
0
Explanation:
Let us call
[tex]f(x)=\frac{\sqrt[]{x}}{\csc x}[/tex]The function is continuous on the interval [0, 2pi]; therefore,
[tex]\lim _{x\to\pi^+}f(x)=\lim _{x\to\pi^-}f(x)[/tex]To evaluate the limit itself, we use L'Hopital's rule which says
[tex]\lim _{x\to c}\frac{a(x)}{b(x)}=\lim _{x\to c}\frac{a^{\prime}(x)}{b^{\prime}(x)}[/tex]Now in our case, we have
[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{\frac{d\sqrt[]{x}}{dx}}{\frac{d \csc x}{dx}}[/tex][tex]=\lim _{n\to\pi}\frac{d\sqrt[]{x}}{dx}\div\frac{d\csc x}{dx}[/tex][tex]=\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex]since
[tex]\frac{d\csc x}{dx}=-\frac{\cos x}{\sin^2x}[/tex]Therefore, we have
[tex]\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=\lim _{n\to\pi}\frac{1}{2\sqrt[]{x}}\div(-\frac{\cos x}{\sin^2x})[/tex][tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}[/tex]Putting in x = π into the above expression gives
[tex]-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}\Rightarrow-\frac{1}{2\sqrt[]{\pi}}\times\frac{\sin^2\pi}{\cos\pi}[/tex][tex]=0[/tex]Hence,
[tex]=\lim _{n\to\pi}-\frac{1}{2\sqrt[]{x}}\times\frac{\sin^2x}{\cos x}=0[/tex]Therefore, we conclude that
[tex]\boxed{\lim _{n\to\pi}\frac{\sqrt[]{x}}{\csc x}=0.}[/tex]which is our answer!
The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -4) ; m = -3 y=
Answer
y = -3x - 13/4
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept.
Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:
[tex]\begin{gathered} -4=(-3)\cdot\frac{1}{4}+b \\ -4=-\frac{3}{4}+b \\ -4+\frac{3}{4}=-\frac{3}{4}+b+\frac{3}{4} \\ -\frac{13}{4}=b \end{gathered}[/tex]Substituting into the general equation with m = -3 and b = -13/4, we get:
[tex]\begin{gathered} y=(-3)x+(-\frac{13}{4}) \\ y=-3x-\frac{13}{4} \end{gathered}[/tex]Can someone help me with 7? I’m desperate
Determine which of the following are true statements. Check all that apply.
Substitute in each inequality the given corresponding solution (x,y) and prove if it makes a true math expression:
1.
[tex]\begin{gathered} -5x-9y\ge60 \\ (-3,-5) \\ \\ -5(-3)-9(-5)\ge60 \\ 15+45\ge60 \\ 60\ge60 \end{gathered}[/tex]As 60 is greater than or equal to 60, (-3,-5) is a solution for the inequality.2.
[tex]\begin{gathered} 4x-3y>1 \\ (5,7) \\ \\ 4(5)-3(7)>1 \\ 20-21>1 \\ -1>1 \end{gathered}[/tex]As -1 isn't greater than 1, (5,7) is not a solution for the inequality3.
[tex]\begin{gathered} -10x+8y<12 \\ (-9,-10) \\ \\ -10(-9)+8(-10)<12 \\ 90-80<12 \\ 10<12 \end{gathered}[/tex]As 10 is less than 12, (-9,-10) is a solution for the inequality.4.
[tex]\begin{gathered} 9x+7y\le98 \\ (9,3) \\ \\ 9(9)+7(3)\le98 \\ 81+21\le98 \\ 102\le98 \end{gathered}[/tex]As 102 is not less than or equal to 98, (9,3) is not a solution for the inequalityhelp me solve the volume of the cylinder? 20 ft x 17 ft
Remember that the formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
• r, is the ,radius, of the base
,• h ,is the height of the cylinder
Notice that the base has a diameter of 20 ft. Therefore, the radius is 10 ft.
Using this data and the formula, we get that:
[tex]\begin{gathered} V=\pi(10^2)(17) \\ \rightarrow V=5340.71 \end{gathered}[/tex]The volume of the cylinder is:
[tex]2540.71ft^3[/tex]Simplify.1,5m^7(-4m^50^2A. -6m^14B. 24m^17C. 24m^14D. 12m^17There is a picture too if you need it.
The expression can be simplified as,
[tex]\begin{gathered} 1.5m^7(-4m^5)^2 \\ =1.5m^7(16m^{10}) \\ =24m^{17} \end{gathered}[/tex]Thus, option (b) is the correct solution.
Calculate the five-number summary of the given data. Use the approximation method.19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Answer:
Explanation:
Given the data:
19, 2, 23, 25, 20, 2, 4, 8, 16, 11, 10, 12, 8, 2, 18
Step 1: Write in an order (we are writing in an ascending order here)
2, 2, 2, 4, 8, 8, 10, 11, 16, 18, 19, 20, 23, 25,
An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to carefor each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs onMonday. Gavin found a record showing that there were a total of 18 cats and dogs onMonday. How many cats were at the shelter on Monday?
4 cats and 14 dogs.
Explanation:
Data :
Amount of cats : c = ?
Cost per cats : $1.50
Amount of dogs : d = ?
Cost per dogs : $6.50
Total spent for dogs and cats : $97.00
Total number of dogs and cats : 18
Formulas:
1.50c + 6.50d = 97.00
c + d = 18
Solution:
c + d = 18 => c = 18 - d
1.50(18 -d) + 6.50d = 97.00
27 - 1.50d + 6.50d = 97.00
27 - 1.50d + 6.50d - 27 = 97 -
If f(x) = x² is vertically stretched by a factor of 18 to g(x), what is the equation of g(x)?
We need to find the equation of the new function g(x) obtained by vertically stretching the function:
[tex]f\mleft(x\mright)=x²[/tex]Vertically stretching a function by a factor of k corresponds to multiplying the whole expression of function by k:
[tex]g(x)=k\cdot f(x)[/tex]In this problem, we have k = 18. Thus, we obtain:
[tex]g(x)=18\cdot f(x)=18x²[/tex]Answer: C. g(x) = 18x²
[tex]8.25 \div 6[/tex]8.25 divid by 6
We want to calculate the following number
[tex]\frac{8.25}{6}[/tex]To make the calcul.ation easier, we will transform the number 8.25 into a fraction. Recall that
[tex]8.25=\frac{825}{100}[/tex]So, so far, we have
[tex]\frac{8.25}{6}=\frac{\frac{825}{100}}{6}[/tex]Also, recall that
[tex]6=\frac{6}{1}[/tex]So, we have
[tex]\frac{\frac{825}{100}}{6}=\frac{\frac{825}{100}}{\frac{6}{1}}[/tex]Now, recall that when we divide fractions, we have
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]In this case, we have a=825,b=100,c=6,d=1.
So we have
[tex]undefined[/tex]what will the y-intercept be if the graph is proportional?
A graph is proportional if the line intersects at the origin (0, 0)
and the y-intercept will always equal to 0
Since y-intercept is the value of y when x =0, and it passes the origin at x = 0, y= 0.
The answer is 0
Several friends go to a casino and do some gambling. The following are the profits each of these friends make: $120, -$230, $670, -$1020, $250, -$430, and -$60. What is the average profit of this group? A. $100 B. -$100 C. -$1020 D. $397
The average profit of this group is B. -$100.
The average represents the total profits and losses generated by the group of friends, divided by the number in the group.
The average is the data set's mean after performing the mathematical operations of addition and division on the data values.
Friends Profits
A $120
B -$230
C $670
D -$1020
E $250
F -$430
G -$60
Total -$700
Average profit = -$100 (-$700/7)
Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.
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how do I find the coefficient the queshtion is the expression -5p+20 factored is __
Factor the coefficient of the expression.
[tex]-5p+20=-5(p-4)[/tex]So answer is -5(p - 4).
Colin is playing a video game. He wins 25 points for each gold coin he finds. His goal is to win more than 200 poijts. He wants to know how many gold coins he needs to find.
25 points for each gold coin
He wants more tha 200 points
Number of coins to get 200 points: = 200/25 = 8
Answer:
He needs to find 8 gold coins or more
>= 8
[tex] - \frac{5}{6} e - \frac{2}{3} e = - 24[/tex]cual es la respuesta
Resolvamos esta ecuación para la variable "e":
[tex]\begin{gathered} -\frac{5}{6}e-\frac{2}{3}e=-24 \\ \frac{5}{6}e+\frac{2}{3}e=24 \\ \frac{5}{6}e+\frac{4}{6}e=24 \\ \frac{(5+4)e}{6}=24 \\ \frac{9e}{6}=24 \\ 9e=24\cdot6 \\ 9e=144 \\ e=\frac{144}{9} \\ e=16 \end{gathered}[/tex]Entonces, el valor de "e" es 16.
