We have 128 teams.
In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:
[tex]T(n)=0.5\cdot T(n-1)[/tex]and we start with n=0 so T(0)=128.
Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):
[tex]\begin{gathered} T(1)=0.5\cdot T(0) \\ T(2)=0.5\cdot T(1)=0.5\cdot0.5\cdot T(0)=0.5^2\cdot T(0) \\ T(n)=0.5^n\cdot T(0)=0.5^n\cdot128 \end{gathered}[/tex]With the last expression we can calculate T for any value of n. Then, for n=4, we have:
[tex]T(4)=0.5^4\cdot128=(\frac{1}{2})^4\cdot128=\frac{1}{2^4}\cdot128=\frac{1}{16}\cdot128=8[/tex]NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.
Answer: after 4 rounds there will be 8 teams left.
Given the following exponential function, identify whether the changerepresents growth or decay, and determine the percentage rate of increase ordecrease.y = 5700(0.94)
Explanation:
[tex]y=5700(0.94)^x[/tex]Using expontia
Graph for 6x - 2y > -11
To graph the inequality:
[tex]6x-2y>-11[/tex]We use the x and y-intercepts.
When x=0
[tex]\begin{gathered} 6x-2y>-11 \\ 6(0)-2y>-11 \\ -2y>-11 \\ \frac{-2y}{-2}<\frac{-11}{-2} \\ y<5.5 \end{gathered}[/tex]We have the point: (0, 5.5)
When y=0
[tex]\begin{gathered} 6x-2y>-11 \\ 6x>-11 \\ x>\frac{-11}{6} \\ x>-1.83 \end{gathered}[/tex]We have the point: (-1.83, 0)
We plot the points (0, 5.5) and (-1.83,0).
The points are joined using a broken line because of the inequality sign: >
The graph is shown below:
To determine which side is required, we use the origin test.
When x=0 and y=0
[tex]\begin{gathered} 6x-2y>-11 \\ 0>-11\text{ (TRUE)} \end{gathered}[/tex]This means the side of the line containing (0,0) is where we need. (Shaded above)
y= ^2 -4x +6 y= -5^2 + 20x - 12 solve by elimination
The required solutions are x = 15/8 and y = 1/2 which is determined by the elimination method.
Given the linear system of equations as
y = 2 - 4x +6 or
4x + y = 8 …(i)
y= - 5² + 20x - 12 or
20x - y = 37 …(ii)
Equations (i) and (ii) constitute a system of two first-degree equations in the two variables x and y.
So, we have to find out the value of 'x’ and 'y’.
Add equation (i) and equation (ii), we get
4x + y + 20x - y = 8 + 37
24x = 45
x = 45/24
x = 15/8
Substitute the value of 'x’ into equation (i) and we get
4(15/8) + y = 8
60/8 + y = 8
y = 8 - 15/2
y = 1/2
Hence, the required solutions are x = 15/8 and y = 1/2.
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Identify the property being demonstrated for each expression.
3+ (5+7)=(3+5) + 7
(3)[5(7)]= (3)[7(5)]
5+0=5
Answer: The property being demonstrated for each expression is the commutative property of addition.
Step-by-step explanation:
Answer:
1.associative property, 2.commutative property, 3.identity property.
Step-by-step explanation: i got it right on edge
A long-distance telephone call from Center City to Smithville costs $3.25 for the first 3 minutes and $0.45 for each additional minute. How many minutes can a person talk if the cost is the call is to be $100.00?
By using linear equation, it is obtained that 218 minutes of phone call cost $100
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here linear equation is used
A long-distance telephone call from Center City to Smithville costs $3.25 for the first 3 minutes and $0.45 for each additional minute
Let the total time for the telephone call be t minutes
So total cost for t minutes telephone talk = $(3.25 + 0.45(t - 3))
By the problem,
3.25 + 0.45(t - 3) = 100
3.25 + 0.45 t - 1.35 = 100
1.9 + 0.45 t = 100
0.45 t = 100 - 1.9
0.45 t = 98.1
t = 218 minutes
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Evaluate the expression when x=-2 z=-1/5
♥ The given parameters are:
x = -2, y = 3 and z = -1/5
The expression is given as xyz
To evaluate the expression when x = -2, y = 3 and z = -1/5, we substitute x = -2, y = 3 and z = -1/5 in expression xyz
This is represented as xyz = -2 * 3 * -1/5
Evaluate the product in the above expression
So, we have xyz = 6/5
Hence, the value of the expression when x = -2, y = 3 and z = -1/5 is 6/5 ♥
Write the equation of the line that has a slope of 1/3 and passes through the point (6,8).
We are asked to determine the equation of a line with a slope 1/3. The general form of a line equation is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept.
Now, we substitute the value of the slope:
[tex]y=\frac{1}{3}x+b[/tex]Now, to determine the value of "b" we will use the fact that the line passes through the point (x, y) = (
6, 8). Now, we plug in these values in the equation:
[tex]8=\frac{1}{3}(6)+b[/tex]Solving the product on the right side we get:
[tex]8=2+b[/tex]Now, we subtract 2 from both sides:
[tex]\begin{gathered} 8-2=2-2+b \\ 6=b \end{gathered}[/tex]Now, we substitute the value in the equation of the line:
[tex]y=\frac{1}{3}x+6[/tex]And thus we get the equation of the line.
ƒ (4) = -8, ƒ (-3) = 1
write a linear function
f(4) = -8 is another way of saying the point is (4 , -8)
f(-3) = 1 is another way of saying the point is (-3 , 1)
to get the equation of any straight line, we simply need two points off of it, so let's use those two provided
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{4}}} \implies \cfrac{1 +8}{-7} \implies \cfrac{ 9 }{ -7 } \implies - \cfrac{9 }{ 7 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{9 }{ 7 }}(x-\stackrel{x_1}{4}) \implies y +8 = - \cfrac{9 }{ 7 } ( x -4) \\\\\\ y+8=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}\implies y=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}-8\implies {\Large \begin{array}{llll} y=- \cfrac{9 }{ 7 }x-\cfrac{20}{7} \end{array}}[/tex]
i need help with this question parts 3 - 7
Explanation
Question 3 wants us to determine the range of the function
The range will be
[tex](-\infty,1]\text{ U \lparen2,}\infty)[/tex]This is
∞
Isabella needs to order some new supplies for the restaurant where she works. The restaurant needs at least 510 glasses. There are currently 231 glasses. If each set on sale contains 18 glasses, which inequality can be used to determine x x, the minimum number of sets of glasses Isabella should buy?
Minimum number of glasses needed by the restaurant be 15
What do you understand by inequality?
Inequalities define the relationship between two different values. Inequality implies not to be equal. The "not equal symbol is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine if they are less than or greater than. If an inequality has just one variable, it is said to be an open sentence.
It is given that the restaurant needs at least 510 glasses.
Currently there are 231 glasses.
Number of glasses each set contain = 18 glasses
x is the minimum number of sets of glasses Isabella should buy.
Number of glasses in x number of sets = 18x glasses
According to question:
231 + 18x ≥ 510
18x ≥ 510 - 231
18x ≥ 279
x ≥ 15.5
Minimum number of sets of glasses ,x = 15
Therefore, minimum number of glasses needed by the restaurant be 15
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Find the distance between the points (20, 15) and (20, 6).
Answer:
5,14
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
O {(-6, -1), (-4, 6), (-8, 2), (3, -1)}
O {(7,4), (9,-8), (-5, -7), (-2,4)}
O {(-3,-3), (4, 5), (8,9), (0,5)}
O {(-1,8), (8,-4), (8, 3), (-5, -6)}
▸
Set of ordered pairs does not represent a function i
= {(2, 2), (0, -8), (2, 7), (-3, 8)}
What is a function?A function relates an input to an output. A function is generally denoted by f(x) where x is the input.
What is a set?
Any collection of objects , which are mathematical or not
Ordered pair are a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.
From question given data is
{(4, 6), (9, -2), (3, -5), (6, 6)}
{(−1,−2),(−4,9),(8,−9),(1,2)}
{(-1, 9), (-7, 8), (3, -1), (4, -1)}
{(2, 2), (0, -8), (2, 7), (-3, 8)}
From the above options we can see that last option has same number in the x axis coordinate. Thus it does not represents a function.
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Could you Please show me how to do this Problem ?
Given:
Number of plants she has = 17
She will put 2 plants in some rows and i plant in other rows.
Let's determine the number of ways in which she plant the tomato plants.
Maximum number of rows with 2 plants = 17/2 = 8.5
There will be a maximum of 8 rows with 2 plants
To determine, let's solve using a table.
We have:
Rows with 2 plants: 1 2 3 4 5 6 7 8
Rows with plants: 16 13 11 9 7 5 3 1
Total plants: 17 17 17 17 17 17 17 17
We can see the maximum number of rows possible is 8 rows.
Therefore, Ms. Hernandez can plant the tomaoto plants 8 ways.
ANSWER:
8 Ways
I need help on in the answer to this question
To find out the value of z we can use the formula
[tex]z=\frac{w+79}{2}[/tex]But we also have to find out the value of w, which be found using the equation
[tex]360=x+79+w+60[/tex]Which needs the value of x, which be found using
[tex]\frac{x+60}{2}=70[/tex]But instead of doing all that and finding the value of x, w and z. We can directly find z using the fact that
Because it's all angles opposite by a vertex, and the sum of them all will be 360º, then we can say that
[tex]\begin{gathered} z+70+z+70=360 \\ \\ 2z+2\cdot70=360 \\ \\ 2z+140=360 \\ \\ 2z=360-140 \\ \\ 2z=220 \\ \\ z=\frac{220}{2} \\ \\ z=110 \end{gathered}[/tex]Therefore, z = 110º.
A bike rental company charges $10 plus a charge per for the distance ridden. the total cost, t, can be represented by the equation t=10+cm , where c is the additional cost per mile and m is the number of miles ridden. solve the equation for c.
Answer:
[tex]c=\frac{t-10}{m}[/tex]
Step-by-step explanation:
[tex]t=10+cm[/tex]
Subtract 10 from both sides:
[tex]t-10=cm[/tex]
Divide both sides by [tex]m[/tex]:
[tex]\frac{t-10}{m}=c[/tex]
Placing [tex]c[/tex] on the left:
[tex]c=\frac{t-10}{m}[/tex]
For example, if the total charge is $27.50 and the distance ridden is 250 mi, we can calculate the additional cost per mile, as such:
[tex]c=\frac{27.50-10}{250}[/tex]
[tex]c=0.07[/tex]
ASAP
forgot this too-
6. Use the data below to make a scatter plot in Desmos and find the exponential regression equation. Round to the nearest hundredth if necessary. Do not type spaces.
7. Using your equation from #6, find out how much the Fire Dragons comic book would be worth in 55 years.
Regression Equation y is 379.9996 ⋅1.04^x . Regression analysis is a set of statistical processes used in statistical modelling to estimate the relationships between a dependent variable and one or more independent variables.
What is Regression analysis ?Regression analysis is a set of statistical processes used in statistical modelling to estimate the relationships between a dependent variable and one or more independent variables.
Linear regression is the most common type of regression analysis, in which the line that best fits the data according to a specific mathematical criterion is found. The ordinary least squares method, for example, computes the unique line that minimises the sum of squared differences between the true data and that line.
This allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values for specific mathematical reasons. Less common types of regression employ slightly different procedures to estimate alternative location parameters or the conditional expectation across a larger set of non-linear models.
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$15,000 to invest and want to keep your money invested for 5 years. You are considering the following investment options. Choose the investment option that will earn you the most money.
A. 1.89% compounded monthly
B. 1.975% compounded quarterly
C. 1.99% compounded annually d.
D. 3.25% simple interest
Answer:
1) 15000*(1+0.0189)^(5*12) = 46130.16346
2) 15000*(1+0.01975)^(5*3) = 20113.9316
3) 15000*(1+0.0199)^5 = 16553.0954
4) 15000*(1+0.0325*5) = 17437.5
The first one is the best option.
What are the coordinates of the vertex?What is the equation of the axis of symmetry?What is/are the x-intercept(s)?What is the y-intercept?
We will find the vertex of the parabola as follows:
*Given a quadratic function of the form:
[tex]y=ax^2+bx+c[/tex]We will have that the vertex is given by:
[tex](-\frac{b}{2a},\frac{b^2-4ac}{4a})[/tex]So, for the function given we will have the following vertex:
[tex](-\frac{(-8)}{2(-1)},\frac{(-8)^2-4(-1)(0)}{4(-1)})\to(-4,16)[/tex]So, the vertex for the function is given by the ordered pair (-4, 16).
We will have that the equation of the axis of symmetry is given by:
[tex]x=-4[/tex]So, the axis of symmetry is x = -4.
We will determine the x-intercepts as follows:
[tex]-x^2-8x=0\Rightarrow x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(-1)(0)}}{2(-1)}[/tex][tex]\Rightarrow\begin{cases}x=-8 \\ \\ x=0\end{cases}[/tex]So, we will have that the x-intercepts are located at x = -8 & x = 0.
From the previous point we can see that the point (0, 0) belongs to the parabola, thus the y-intercept is y = 0.
A set of points is shown on the graph.
Scatter plot with a point at negative 5 comma negative 1, a point at negative 2 comma 4, a point at 1 comma 9, a point at 3 comma 5, and a point at 4 comma 7.
Which of the following equations is the best model for a line of fit for the data?
y equals 1 fourth times x plus 5.
y equals negative 1 fourth times x plus 5.
y equals 3 fourths times x plus.
y equals negative 3 fourths times x plus 5.
y = 3/4x + 5 equations best fits the data as a line of fit.
Given that,
With a point at - 5 comma negative 1, a point at - 2 comma negative 4, a point at 1 comma 9, a point at 3 comma 5, and a point at 4 comma negative 7, a scatter plot is created.
We have to find which of the following equations best fits the data as a line of fit.
We know,
A scatter plot is a particular kind of graph that is used to visually display the values of two variables, with the resulting points indicating any associations (correlations) between the data set.
We can rationally conclude that an equation for the line of best fit (trend line) is given by y = 0.80x + 4.63 by carefully examining the graph that represents the provided data.
We can conclude that y = 3/4x + 5 is the equation that best fits the data as a line of fit.
Therefore, y = 3/4x + 5 equations best fits the data as a line of fit.
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A new bank customer with $4,500 wants to open a money market account. The bank is offering a simple interest rate of 1.6%.
a. How much interest will the customer earn in 20 years?
b. What will the account balance be after 20 years?
a. The customer will earn
in interest.
a. The customer will earn $1440 as a interest after 20 years.
b. The account balance will be $5,940 after 20 years.
What is the simple interest?
Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.
The formula of simple interest is I = Prt.
P = principal
r = rate of interest per year.
t = time.
Given that, a customer deposits $4,500 for 20 years.
According to question, P = $4,500, r =1.6% = 0.016, t = 20 year
Putting the value of P, r, and t in I = Prt:
I =4,500 × 0.016 ×20
I =4,500 × 0.016 ×20
I = 1440
The interest is $ 1440.
The account balance will be $(1440 + 4,500) = $5,940.
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Write an equation for the line that passes through (3,-14) having slope 0. Give the answer in standard form
Slope intercept form:
y= mx + b
where:
m= slope
b= y intercept
m= 0
Replace (x,y) by the given point (3,-14) and solve for b
-14 = 0 (3)+ b
-14 = b
Slope intercept form:
y= - 14
Standard form:
Ax+BY = C
y = -14
Solve the equation. 6(s + 2) − 5s = 16 + s − 4 how many solutions are there
Answer: 0=0
Step-by-step explanation: After simplifying the equation we get 0=0, and 0=0 has infinitely many solutions.
Answer:
it has many solutions :)
Can y’all help me plssss
(a) Solve the inequality: n > 12
(b) The greatest amount of trips that Edwin can take up the mountain and still pay less than Rhea would be 63
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, but two stand out above the rest: wealth inequality as measured by the distribution of wealth and income inequality as measured by the distribution of income.
Edwin and Rhea, two siblings, decide on distinct payment arrangements even though they are both going skiing.
In Edwin's proposal, rentals cost $45 and each lift up the mountain costs $5.25.
Rhea had an arrangement whereby her whole day would cost $108.
An inequaity that simulates the n trips up the mountain that Edwin will pay for out of pocket and Rhea won't.
45 + 5.25n > 108
45 is deducted from both sides.
-45 + 45 + 5.25n > 108 -45
5.25n > 63
5.25 times both sides.
n > 12
Also,
5.25 x 12
= 63
The most trips Edwin could make up the mountain and still make less money than Rhea is 63.
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Casey and Jayden look for animal footprints in the woods.
Casey finds 18 footprints. Casey finds 2 times as many footprints
as Jayden. How many footprints does Jayden find?
Let f stand for the number of footprints Jayden finds.
Which bar model represents the problem?
Casey
Jayden
18
Jayden 18
Casey 18 18
Casey 18
Jayden 18 18
Jayden
Casey
f f
18
Answer:
9
Step-by-step explanation:
Casey = 18
Casey = 2 x James
Because both values for Casey are equal to Casey, they are also the same value
This can then be written as
18 = 2 x James
isolate James by himself by dividing both sides by 2 to get how many footprints James found
18 / 2 = 9
James = 9
Answer:
F or Jayne’s finds 36 Footprints
200 students were asked to name their favorite science class. The results are shown in the two-wayfrequency table. Use the table to answer the following question.
Explanation:
We're told from the question that 200 students took part in the exercise, so if the total number of girls is 100 then the total number of boys will be;
[tex]\text{Total number of boys =}200-100=100[/tex][tex]\text{Total number of boys that chose Biology}=100-44-37=19[/tex][tex]\text{Total number of boys and girls that chose Biology}=40+19=59[/tex][tex]\text{Total number of boys and girls that chose Chemistry}=39+44=83[/tex][tex]\text{Total number of boys and girls that chose Physics}=21+37=58[/tex][tex]\text{Total of the total row}=59+83+58=200[/tex]To find how many more girls than boys chose Biology, we'll have;
[tex]40-19=21[/tex]So 21 more girls than boys chose Biology.
In the equation IX=b, if b<0, then how many solutions are there for x? Think about this: b is a number less than 0
If we assume x and b are real numbers:
|x| = √(x²)
So:
√(x²) = b
Where b<0
x will be always positive, because every number squared is positive
So, the left hand side of the equation will be positive. And since the right hand side of the equation will be always negative, because they tell us that b<0, we can conclude that it is absurd:
√(x²) ≠ b
Therefore, no solutions exist
The answer is Zero
help me..............
I need to find "S"
32 = s - 19
Add 19 in both sides
32 + 19 = s - 19 + 19
51 = s
Result
s = 51
Define the Slope Intercept form of an equation. *
hurry
Step-by-step explanation:
I hope this is helpful for u
10. A square pyramid is shown. The height of the pyramid is 14 centimeters. The area of the base of the square pyramid, B, is 64 square centimeters. 8 64 cm Which measurement is closest to the volume of the pyramid in cubic centimeters? F 900 cm G 450 cm M 300 cm ) 150 cm
ANSWER
The closest measurement is 300cm³
EXPLANATION
The volume of a pyramid is:
[tex]V=\frac{1}{3}Bh[/tex]where B is the ares of the base and h is the height.
In this problem, B = 64cm² and h = 14cm. The volume is:
[tex]V=\frac{1}{3}\cdot64\operatorname{cm}^2\cdot14\operatorname{cm}=298.\bar{6}cm^3[/tex]The one that's closest is 300cm³
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. Group of answer choices 2(x2 + 6x + 9) = –3 + 9 2(x2 + 6x) = 3 2(x2 + 6x + 9) = 3 + 18 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x) = –3
The steps that can be used are:
2(x² + 6x) = 3
2(x² + 6x + 9) = 3 + 18
Options B and C is the correct answer.
The solution for the quadratic equation is
x = (-12 + 2√42) / 4
x = (-12 - 2√42) / 4
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
2x² + 12x - 3 = 0
This is in the form of ax² + bx + c = 0
Now,
a = 2
b = 12
c = -3
We can solve this using the determinant formula.
Where,
D = -b ± √(b² - 4ac) / 2a
D = -12 ± √(144 +24) / 4
D = -12 ± √168 / 4
D = -12 ± √(4 x 42)/4
D = -12 ± 2√42 / 4
So,
x = (-12 + 2√42) / 4
x = (-12 - 2√42) / 4
The solution for the quadratic equation is
x = (-12 + 2√42) / 4
x = (-12 - 2√42) / 4
The following options are given:
2(x² + 6x + 9) = –3 + 9
2x² + 12x + 18 = -3 + 9
2x² + 12x + 18 + 3 - 9 = 0
2x² + 12x + 12 = 0
This is not true.
2(x² + 6x) = 3
2x² + 12x - 3 = 0
This is true.
2(x² + 6x + 9) = 3 + 18
2x² + 12x + 18 = 3 + 18
2x² + 12x - 3 = 0
This is true.
x + 3 = ± 21/2
Not true.
2(x² + 6x) = –3
2x² + 12x + 3 = 0
This is not true.
Thus,
The steps that can be used are:
2(x² + 6x) = 3
2(x² + 6x + 9) = 3 + 18
Options B and C is the correct answer.
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