ANSWER:
Height = 80 yds
Base = 50 yds
STEP-BY-STEP EXPLANATION:
Given:
Area = 2000 square yards
Height = h
Base = 5/8h
We can calculate the value of the height using the triangle area formula, just like this:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ \text{ We replacing} \\ 2000=\frac{h\cdot \frac{5}{8}h}{2} \\ h^2=\frac{2000\cdot2\cdot8}{5} \\ h=\sqrt{6400} \\ h=80\text{ yd} \\ \text{ therefore, the base is:} \\ b=\frac{5}{8}\cdot80 \\ b=50\text{ yd} \end{gathered}[/tex]Height = 80 yds
Base = 50 yds
An ordinary (Pair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in successionand that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of andereCompute the probability of each of the following svents.Event A: The sum is greater than 7.Event B: The sum is divisible by 3 or 6 (or both).Write your answers as fractions
1) We are going to tackle this question starting with the total outcomes of dice rolled twice in succession.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So we can see that there are 36 possibilities.
2) Let's examine the events.
a) P (>7)
Let's bold the combinations of outcomes whose sum is greater than 7
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
So, we can see that there are 15 favorable outcomes.
Now, we can find the Probability of rolling the dice twice and get a sum greater than 7:
[tex]P(A)=\frac{15}{36}=\frac{5}{12}[/tex]b) Now, for the other event: The sum is divisible by 3 or 6, or both:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Hence, the favorable outcomes are: 12
So now, let's find the probability of getting a sum that way:
[tex]P(B)=\frac{12}{36}=\frac{1}{3}[/tex]what is the answer and how do i solve it?
EXPLANATION
Since we have the expression:
[tex]\frac{x}{x^2+x-6}-\frac{2}{x+3}[/tex]First, we need to find the least common multiplier as follows:
Least common multiplier of x^2 + x - 6, x+3: (x-2)(x+3)
Ajust fractions based on the LCM:
[tex]=\frac{x}{\left(x-2\right)\left(x+3\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]\mathrm{Apply\: the\: fraction\: rule}\colon\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]=\frac{x-2\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}[/tex][tex]Expand\text{ x-2(x-2)}[/tex][tex]=\frac{-x+4}{\left(x-2\right)\left(x+3\right)}[/tex]The final expression is as follows:
[tex]=\frac{-x+4}{(x-2)(x+3)}[/tex]
in ️RST, RS ~=TR and m
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ΔRST
RS ≅ TR
∠ T = 15
∠ S = ?
Step 02:
We must apply the properties of isosceles triangles.
∠ T = ∠ S = 15
The answer is:
∠ S = 15 °
simplify 5(3c-4d)-8c
Answer:
7c - 20d
Step-by-step explanation:
5(3c - 4d) - 8c ← distribute parenthesis by 5
= 15c - 20d - 8c ← collect like terms
= 7c - 20d
Use the formula for the probability of the complement of an event.A single card is drawn from a deck. What is the probability of not drawing a 7?
occur
the answer is 12/13 or 0.932
Explanation
when you have an event A, the complement of A, denoted by.
[tex]A^{-1}[/tex]consists of all the outcomes in wich the event A does NOT ocurr
it is given by:
[tex]P(A^{-1})=1-P(A)[/tex]Step 1
find the probability of event A :(P(A)
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible
[tex]P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}[/tex]so
let
favorable outcome = 4 (there are four 7 in the deck)
total outcomes=52
hence,replacing
[tex]\begin{gathered} P=\frac{4}{52}=\frac{1}{13} \\ P(A)=\frac{1}{13} \end{gathered}[/tex]Step 2
now, to find the probability that the event does NOT ocurrs ( not drawing a 7)
let's apply the formula
[tex]P(A^{-1})=1-P(A)[/tex]replace
[tex]\begin{gathered} P(A^{-1})=1-\frac{1}{13} \\ P(A^{-1})=\frac{13-1}{13}=\frac{12}{13} \\ P(A^{-1})=0.923 \end{gathered}[/tex]therefore, the answer is 12/13 or 0.932
I hope this helps you
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?
From the information available, the mixture will test negative if all 6 samples are negative.
The probability of each is independent of the other for all 6 samples.
The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be
[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;
[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]Therefore if we have the probability of the mixture testing negative as
[tex]P_{\text{neg}}=0.4969[/tex]The probability of the mixture testing positive would be;
[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]ANSWER:
The probability that the mixture will test positive is 0.5031
Rounded to 2 decimal places,
[tex]P_{\text{pos}}=0.50[/tex]Converting between metric units of volume and capacityA water tower has a volume of 874 m³.Find how many liters of water it would take to completely fill thewater tower. Use the table of conversion facts, as needed.LXS?Conversion facts for volume and capacity1 cubic centimeter (cm³) = 1 milliliter (mL)1 cubic decimeter (dm³) = 1 liter (L)1 cubic meter (m³) = 1 kiloliter (KL) I need help with this math problem
Given: A water tower has a volume of 874 m³
To Determine: How many liters of water it would take to completely fill the
water tower
Solution
Please note that 1 cubic meter (m³) = 1 kiloliter (KL)
Therefore
[tex]\begin{gathered} 1m^3=1KL \\ 874m^3=xKL \\ Cross-multiply \\ x=874KL \end{gathered}[/tex]Also note that Kilo means 1000
Therefore
[tex]\begin{gathered} 874KL=874\times1000L \\ =874000L \end{gathered}[/tex]Hence, the water tower will be completely fill with 874000 liters(L)
3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:
A sequence is called arithmetic if the difference between two consecutives is a constant
In the first case we see a constant difference of 5
every two consecutives have difference of 5, for example 20-15, 30-25 and so on.
In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.
the constant in this case is 18/6 =3
lets return to the 1st case find the explicit
An = Ao +(n-1) d
An means the n term in the sucession
Ao means the first term
d means the constant
with that in mind we replace the values obtained
An= 5 + (n-1) •5
now for the recursive
a1= 5
An = An-1 + 5
Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula
so then
An = A1 •(3)^(n-1)
An = 2• (3)^(n-1)
Which of the following actions will best help her find out whether the two equations in the system are in fact parallel
Check to see whether the slope of both lines are the same (option A)
Explanation:[tex]\begin{gathered} \text{Given} \\ y\text{ - x = }21 \\ 2y\text{ = 2x + 16} \end{gathered}[/tex]When two system of equations do not intersect, the lines are said to be parallel lines.
This means there is no solution.
To determine if the lines are trully parallel, the slope of each equation need to be determined.
For parallel lines, the slope will be the same
The best action to help her find out whether the two equations are inded parallel, Check to see whether the slope of both lines are the same (option A)
ocupo encontrar la x con procedimiento
les regalare coronas!!!!
La variable x asociada al sistema geométrico con dos ángulos alternos externos es igual a 23.
¿Cómo determinar la variable asociada a dos ángulos alternos externos?
En esta pregunta tenemos un sistema geométrico conformado por dos líneas paralelas atravesadas por una tercera línea. Este conjunto incluye dos ángulos alternos externos, que guardan la siguiente relación según la geometría euclídea:
6 · x - 28 = 4 · x + 18
A continuación, despejamos la variable x:
6 · x - 4 · x = 28 + 18
2 · x = 46
x = 23
El valor de la variable x es 23.
ObservaciónNo existen preguntas en español sobre ángulos alternos externos, por lo que se añade una pregunta en inglés.
Para aprender más sobre ángulos alternos externos: https://brainly.com/question/28380652
#SPJ1
Plot ( 0 -5/8) on the coordinate axes. Where is it located? State the axis or the quadrant.
We need to plot the coordinate (0, -5/8).
An ordered pair (x, y) represents the location of the point in the coordinate plane. Based on the given, we have x = 0 and y = -5/8. No movement will happen around the x-axis since we have x = 0. Since y is a negative number, we will go down on the y axis from the origin depending on the value of y.
We see that our y value is equal to -5/8. What we can do first is to represent each grid to be equal to 2/8. There are 4 grids that we will encounter before going to -1. At the second grid, the value is (2/8)*2 = 4/8. At the third grid, we have (2/8)*3 = 6/8. The middle term for these two fractions is equal to 5/8, hence, the plot of (0, -5/8) will be around:
Based on the plot above, the coo
Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)
First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.
The first step is to subtract x from both sides, doing this we get:
[tex]2y=6-x[/tex]Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:
[tex]y\text{ = }\frac{6-x}{2}[/tex]which can also be written as
[tex]y=\frac{-x}{2}+3[/tex]The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is
[tex]y=\frac{-0}{2}+\text{ 3}[/tex][tex]y=0\text{.}[/tex]The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is
[tex]0=\frac{-x}{2}+3[/tex][tex]-3\text{ = }\frac{-x}{2}[/tex][tex]x\text{ = 6.}[/tex]Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.
On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
Find the length to the nearest whole number of the diagonal (hypotenuse) of a square with 30 cm on a side. Round answers to the nearest tenth if necessary. Your answer
Notice that we can draw a triangle in the square , and that the length of the square's diagonal is the same as the length of the triangle's hypotenuse. The triangle is a right triangle therefore it satisfies the Phytagorean Theorem. To calculate for it's hypotenuse , we will use:
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse, and a, b are the other legs of the triangle.
[tex]\begin{gathered} c^2=30^2+30^2 \\ c^2=1800 \\ c=\sqrt[]{1800} \\ c=42.43 \end{gathered}[/tex]Since the hypotenuse of the triangle is 42.43 cm. Therefore, the square's diagonal is also 42.43 cm
Answer:
The square's diagonal is 42.43 cm
help me pleaseeeeeeeee
The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.
According to the question,
We have the following information:
The value of the car is given by V(x) where x is the number of years.
V(x) = -1500x + 21,000
(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:
V(5) = -1500*5+21000
V(5) = -7500+21000
V(5) = $13,500
(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:
V(9) = -1500*9+21000
V(9) = -10500+21000
V(9) = $10,500
(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.
Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.
To know more about value here
https://brainly.com/question/20593631
#SPJ1
Greg's youth group is collecting blankets to take to the animal shelter. There are 38 people in the group, and they each gave 2 blankets. They got an additional 29 by asking door-to-door. They set up boxes at schools and got another 52. Greg works out that they have collected a total of 121 blankets. Does that sound about right?
We want to know the total of blankets that Greg's collected.
As there are 38 people in the group, and they each gave 2 blankets, they brough a total of 79 blankets.
As they got 29 asking door-to-door, and got another 52, we will sum the values, as shown:
[tex]79+29+52=160[/tex]This means that the Greg group collected a total of 160 blankets, instead of 121, and the Greg statement is false.
Find the area of the prism in the figure shown.
TherWe are asked to determine the area of the triangular prism. To do that we will add the area of the surfaces of the prism and add them together.
we have that the front and back areas are the areas of a triangle which is given by the following formula:
[tex]A_t=\frac{bh}{2}[/tex]Where:
[tex]\begin{gathered} b=\text{ length of the base} \\ h=\text{ height of the triangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} b=3 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_t=\frac{\left(3\right)\lparen4)}{2}[/tex]Solving the operations:
[tex]A_t=6[/tex]Since the front and back faces are the same triangle we can multiply the result by 2:
[tex]A_t=2\times6=12[/tex]Therefore, the areas of the front and back faces add up to 12.
Now, we determine the area of the right side. This is the area of a rectangle and is given by the following formula:
[tex]A_r=lh[/tex]Where:
[tex]\begin{gathered} l=\text{ length of the rectangle} \\ h=\text{ height of the rectangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} l=5 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_r=\left(5\right)\left(4\right)[/tex]Solving the operation:
[tex]A_r=20[/tex]Now, we determine the area of the left face which is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=5 \end{gathered}[/tex]Substituting we get:
[tex]A_l=\left(5\right)\left(5\right)=25[/tex]Therefore, the area of the left side is 25.
The area of the bottom face is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=3 \end{gathered}[/tex]Substituting we get:
[tex]A_b=\left(5\right)\left(3\right)=15[/tex]Now, the total surface area is the sum of the areas of each of the faces:
[tex]A=A_t+A_r+A_l+A_b[/tex]Substituting the values we get:
[tex]A=12+20+25+15[/tex]Solving the operations:
[tex]A=72[/tex]Therefore, the surface area is 72.
Statistics: a professor recorded 10 exam grades but one of the grades is not readable. if the mean score on the exam was 82 and the mean of the 9 readable scores is 84 what is the value of the unreadable score?
To mean of a set is given by the sum of all values in the data-set divided by the number of values.
We have that the mean of the whole set is 82.
The mean of the 9 readable scores is 84.
So:
[tex]\begin{gathered} \frac{x}{9}=84 \\ x=84\cdot9 \\ x=756 \end{gathered}[/tex]So, we 9 readable scores add up to 801. If we add 756 to a number, y, and divide by 10, we'll have the mean score of the exam, 82.
[tex]\begin{gathered} \frac{756+y}{10}=82 \\ 756+y=820 \\ y=820-756 \\ y=64 \end{gathered}[/tex]So, the grade of the unreadable score was 64.
From question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*
Answer:
The complete table:
6 18 2 42
9 27 3 63
Explanation:
We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is
[tex]\frac{\min}{\text{song}}=\frac{9}{6}[/tex]Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get
[tex]song\times\frac{\min}{\text{song}}=\frac{9}{6}\times\text{song}[/tex]which gives
[tex]min=\frac{9}{6}\times\text{song}[/tex]This means the number of minutes practised is 9/6 of the number of songs played.
Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get
[tex]\frac{9\div3}{6\div3}=\frac{3}{2}[/tex]therefore, we have
[tex]min=\frac{3}{2}\times\text{song}[/tex]Now we are ready to fill the table.
If Montell plays 18 songs then we have
[tex]\min =\frac{3}{2}\times18[/tex][tex]\min =27[/tex]the minutes practised is 27 for 18 songs.
If Montell practices for 3 minutes then we have
[tex]3=\frac{3}{2}\times\text{song}[/tex]then the value of song must be song = 2, since
[tex]\begin{gathered} 3=\frac{3}{2}\times2 \\ 3=3 \end{gathered}[/tex]Hence, for 3 minutes of practice, Montell sings 2 songs.
Now for 42 songs, the number of minutes played would be
[tex]\min =\frac{3}{2}\times42[/tex]which simplifies to give
[tex]\min =63[/tex]Hence, for 42 songs played, the practice time is 63 minutes.
To summerise, the complete table would be
songs 6 18 2 42
minutes 9 27 3 63
For scenarios of statistical studies are given below decide which study uses a sample statistic
The sample statistic is defined as any number computed from the sample data. This means that the data must be a sample and not the entire population. Looking at the options,
option D is correct
In general, what points can have coordinates reversed and still have the same location?Choose the correct answer below.O the points with x-coordinates 0o the points with y-coordinates 0o the points with the same x- and y-coordinatesO the points with opposite coordinates
SOLUTION
The Point of a co-ordinate is always written as
[tex](x,y)[/tex]Giving a point
[tex]\begin{gathered} A(x,y) \\ \text{if the coordinates of x and y are the same } \end{gathered}[/tex]For instance x=2 and y=2, the point will be
[tex](2,2)[/tex]If the coordinate of x and y are reversed, the point will remain the same
Hence
the points with the same x- and y-coordinates will give the same location if the coordinate is reversed.
Therefore The Third option is correct (c)
Use the given instructions to answer question 17 to question 20.
Given
The boxplot.
And, the total number of students in the class is 60.
To find:
a) The percentage of students who received one or more moving violation.
b) The number of parking violations received by at least 50% of students.
c) How many students received two or more parking violation.
Explanation:
a) From the figure,
The percentage of students who received one or more moving violation is,
[tex]Percentage\text{ of students}=75\%[/tex]Because the number of students having minimum moving violation is 0, and the number of students having maximum moving violation is 4.
b) The number of parking violation received by at least 50% of students is,
[tex]\begin{gathered} Number\text{ }of\text{ }parking\text{ }violation\text{ received by at least 50}\%\text{ of students } \\ is\text{ }2\text{ }or\text{ }more. \end{gathered}[/tex]c) The number of students who received two or more parking violation is,
[tex]\begin{gathered} Number\text{ of students}=75\%\times60 \\ =\frac{75}{100}\times60 \\ =45 \end{gathered}[/tex]Hence, the number of students who received two or more parking violation is 45.
3. For the polynomial: ()=−2(+19)3(−14)(+3)2, do the following:A. Create a table of values that have the x-intercepts of p(x) in the first column and their multiplicities in the second column.B. State the degree and end behavior for p(x). C. Hand sketch a rough graph of p(x). You should have the x-int labeled, but you do not need tick marks for all numbers in between.
Part A. We are given the following polynomial:
[tex]\mleft(\mright)=-2\mleft(+19\mright)^3\mleft(-14\mright)\mleft(+3\mright)^2[/tex]This is a polynomial of the form:
[tex]p=k(x-a)^b(x-c)^d\ldots(x-e)^f[/tex]The x-intercepts are the numbers that make the polynomial zero, that is:
[tex]\begin{gathered} p=0 \\ (x-a)^b(x-c)^d\ldots(x-e)^f=0 \end{gathered}[/tex]The values of x are then found by setting each factor to zero:
[tex]\begin{gathered} (x-a)=0 \\ (x-c)=0 \\ \text{.} \\ \text{.} \\ (x-e)=0 \end{gathered}[/tex]Therefore, this values are:
[tex]\begin{gathered} x=a \\ x=c \\ \text{.} \\ \text{.} \\ x=e \end{gathered}[/tex]In this case, the x-intercepts are:
[tex]\begin{gathered} x=-19 \\ x=14 \\ x=-3 \end{gathered}[/tex]The multiplicity are the exponents of the factor where we got the x-intercept, therefore, the multiplicities are:
Part B. The degree of a polynomial is the sum of its multiplicities, therefore, the degree in this case is:
[tex]\begin{gathered} n=3+1+2 \\ n=6 \end{gathered}[/tex]To determine the end behavior of the polynomial we need to know the sign of the leading coefficient that is, the sign of the coefficient of the term with the highest power. In this case, the leading coefficient is -2, since the degree of the polynomial is an even number this means that both ends are down. If the leading coefficient were a positive number then both ends would go up. In the case that the leading coefficient was positive and the degree and odd number then the left end would be down and the right end would be up, and if the leading coefficient were a negative number and the degree an odd number then the left end would be up and the right end would be down.
Part C. A sketch of the graph is the following:
If the multiplicity is an odd number the graph will cross the x-axis at that x-intercept and if the multiplicity is an even number it will tangent to the x-axis at that x-intercept.
What is 120 percent of 118?
120 percent of 118 is expressed mathematically as;
120% of 118
120/100 * 118
= 12/10 * 118
= 6/5 * 118
= 708/5
= 141.6%
Hence 120 percent of 118 is 141.6%
Solve for y.
|6y + 12| = -18
Answer: y=-5
Step-by-step explanation:
12-12=0
-18-12=-30
6y=-30
y=-5
Drag each number to the correct location on the statements. Not all numbers will be used. Consider the sequence below. --3, -12, -48, -192, ... Complete the recursively-defined function to describe this sequence. f(1) =...... f(n) = f(n-1) × .....for n = 2, 3, 4... 3, 2, 3, 4, 12, -4
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following sequence:
[tex]-3,-12,-48,-192...[/tex]f(1), is the first term of the sequence, therefore, it would be:
[tex]f(1)=-3[/tex]Now, we calculate the common ratio, just like this:
[tex]\begin{gathered} r=\frac{-192}{-48}=4 \\ \\ r=\frac{-48}{-12}=4 \\ \\ r=\frac{-12}{-3}=4 \end{gathered}[/tex]So the sequence would be:
[tex]f(n)=f(n-1)\cdot4[/tex]You need to measure the depth of a large lake. Since the sonar equipment is very expensive, you decide to use your friend's boat. The boat has an anchor on a 100 ft line. You take the boat out to the middle of the lake on a
windy day. You drop the anchor and let the wind push the boat until the anchor line is tight. Your GPS tells you that the boat has moved 82 feet. Assuming the bottom of the lake is flat, what is the depth of the lake?
Using the Pythagorean Theorem, the depth of the lake is 57.24 feet.
What is the depth?According to the Pythagorean Theorem, the depth or height is the difference between the squared root of the hypothenuse and the base.
The Pythagorean Theorem Formula is as follows:
a² + b² = c²
Where:
a = side of the right triangle (height, depth, or perpendicular)
b = side of the right triangle (the base)
c = hypotenuse (the longest part or hypothenuse)
Therefore, the depth is:
a² = c² - b²
a² = 100² - 82²
a² = 10,000 - 6,724
a² = 3,276
a = √3,276
a = 57.24
= 57.24 feet
Thus, assuming a flat-bottom lake, its depth is 57.24 feet.
Learn more about the Pythagorean Theorem at https://brainly.com/question/343682
#SPJ1
Create a table of values to represent the equation y = x - 9
Answer:
Explanation:
Here, we want to create a table of values to represent the given equation
To do this, we need to select a range of values for x
This can be a range of any set of numbers
With respect to this question, we shall be choosing -2 to +2 with an increment of 1
The values of x are thus: -2,-1 , 0, +1 and +2
So, now let us get the corresponding y-values using the equation rule
Now, let us get the y-values
when x = -2
y = -2-9 = -11
when x = -1
y = -1-9 = -10
when x = 0
y = 0-9 = -9
when x = 1
y = 1-9 = -8
when x = 2
y = 2-9 = -7
Thus,we have the table of values as follows:
Cindy eats 12 oz of candy in 4 days how long will it take her to eat 1 pound of candy
We should know that:
1 pound = 16 oz
given Cindy eats 12 oz in 4 days
She will eat 1 pound in x days
So, we need to find the number of days to eat 1 pound which is equal to 16 oz
Using the ratio and proportion
12 : 4 = 16 : x
[tex]\begin{gathered} 12\colon4=16\colon x \\ \frac{12}{4}=\frac{16}{x} \\ x=\frac{4\cdot16}{12}=\frac{16}{3}=5\frac{1}{3} \end{gathered}[/tex]so, the number of days = 5 1/3
18
If p percent of an adult's daily allowance of
potassium is provided by x servings of Crunchy
Grain cereal per day, which of the following
expresses p in terms of x ?
Express p in terms of x : p = 5x
What is Percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
If 5% of an adult's daily potassium requirement is provided by each serving of Crunchy Grain cereal, then x servings will offer x times 5%.
Five times as many servings, or p, of potassium are required for an adult's daily requirement.
As a result,
p = 5x can be used to describe the proportion of potassium in an adult's daily allotment.
To learn more about Percent click on the link
https://brainly.com/question/24304697
#SPJ13
