Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex]
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
What is the difference between 4Σn=1, 2n+1 and 4Σi=1, (2i+1)?
a. 0
b. 3
c. 4
d. 7
Answer:
0
Step-by-step explanation:
Each expression is a way to write the sum ...
3 + 5 + 7 + 9
That sum in each case is 24, so the difference is 24-24 = 0.
Answer:
it is not 0 !!!
Step-by-step explanation:
got it wrong bc of top answer
Jose can paint an entire house in seven hours and brandon can paint the same house in eight hours. Write an equation that can be used to find the time in hours, t, it would take jose and brandon to paint the house together. You do not need to solve the equation.
Answer:
t/8 + t/7 = 1
Step-by-step explanation:
Given in the question that,
time require for Jose to paint the house = 7 hours
time require for Brandon to paint the house = 8 hours
Suppose t means Full house painted.
To solve the question we have to figure out how much each of them can paint in ONE hour.7 hours----t
1 hour ---- t/7
8 hours----t
1 hour ---- t/8
Equationt/8 + t/7 = 1 (in one hour)
(7t + 8t)/8(7) = 1
15t/56 = 1
15t = 56
t = 56/15
t = 3.73 hours
Sarah, Natasha and Richard share some sweets in the ratio 4:5:3. Sarah gets 36 sweets. How many sweets are there altogether?
Answer:
108
Step-by-step explanation:
36÷4= 9
9 is the unit rate
5×9=45
Natasha has 45 sweets
3×9= 27
Richard has 27 sweets
36+ 45+ 27= 108
All together they have 108 sweets
In total, there are 108 sweets. This answer is derived by finding the value of one part of the ratio and then multiplying this by the sum of all parts of the ratio.
Explanation:The question is about the distribution of sweets among Sarah, Natasha and Richard in the ratio 4:5:3. You have been given that Sarah, represented by the first term of the ratio, gets 36 sweets. To find how many sweets there are altogether, we first need to determine the value of one part of the ratio.
In this case, if 4 parts are equivalent to 36 sweets, then one part is equivalent to 36 divided by 4 which equals 9 sweets.
Now, to find the total sweets, we need to sum all parts of the ratio which is 4 parts for Sarah, 5 parts for Natasha and 3 parts for Richard. Total parts = 4 + 5 + 3 = 12. This total is then multiplied by the value of one part of the ratio. Here, total sweets = 12 parts * 9 sweets = 108 sweets.
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50 POINTS!!! Which of the following expressions are equivalent to 2/x^8-y^8
Answer:
it's A&B
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{\bold{A.} } \ \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}} \\\\\\ \large \boxed{\mathrm{\bold{B.} } \ \frac{2}{(x^4)^2 -(y^4)^2 } }[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x^8-y^8 }[/tex]
Factor the denominator.
[tex]\displaystyle \frac{2}{(x^4)^2 -(y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)^2 }[/tex]
[tex]\displaystyle \frac{2}{(x^4-y^4)(x^4 +y^4) }[/tex]
Split the fraction into two fractions.
[tex]\displaystyle \frac{2}{x^4-y^4} \cdot \frac{1}{x^4 +y^4}[/tex]
The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?
Show all work
Answer:
possible values of 4th term is 80 & - 80
Step-by-step explanation:
The general term of a geometric series is given by
[tex]a(n)=ar^{n-1}[/tex]
Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term
Given, 5th term is 40, we can write:[tex]ar^{5-1}=40\\ar^4=40[/tex]
Given, 7th term is 10, we can write:[tex]ar^{7-1}=10\\ar^6=10[/tex]
We can solve for a in the first equation as:
[tex]ar^4=40\\a=\frac{40}{r^4}[/tex]
Now we can plug this into a of the 2nd equation:
[tex]ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}[/tex]
Let's solve for a:
[tex]a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640[/tex]
Now, using the general formula of a term, we know that 4th term is:
4th term = ar^3
Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:
[tex]ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80[/tex]
possible values of 4th term is 80 & - 80
Using point slope form write the equation of the line that passes through the point (-1/2, 1/2) and has a slope of -1
Answer: [tex]y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]
Step-by-step explanation:
The point-slope form of the equation of the line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope of the line and [tex](x_1,y_1)[/tex] is a point of the line.
You know the value of the slope and you also know a point of the line, then you need to substitute values into [tex]y-y_1=m(x-x_1)[/tex].
Therefore, you get that the equation of this line in point-slope form is:
[tex]y-\frac{1}{2}=-1(x-(-\frac{1}{2})\\\\y-\frac{1}{2}=-(x+\frac{1}{2})[/tex]
Answer:
y = -x
Step-by-step explanation:
Given in the question,
co-ordinate(-1/2 , 1/2)
gradient of the line = -1
Standard equation form of a straight line
y - y1 = m(x - x1)here y1 = 1/2
x1 = -1/2
m = -1
Plug values in the equation
y - 1/2 = -1(x + 1/2)
y -1/2 = -x - 1/2
y = -x
What is the surface area of the rectangular prism below?
A. 496 units^2
B. 248 units^2
C. 490 units^2
D. 980 units^2
Answer:
The correct answer is option C. 490 units ²
Step-by-step explanation:
Area of cuboid = 2(lb + bh + lh)
From the figure we can see that a rectangular prism.
To find the surface area of prism
Here l = 14 units
b = 7 units and h = 7 units
Surface area = 2((14 * 7) + (7 * 7) + (14 * 7))
= 490 units ²
Answer:
490 units squared
Step-by-step explanation:
Kristin bought eight boxes.A week later half of all her boxes were destroyed in a fire.There are now only 17 boxes left.With how many did she start
Answer:
She started with 26 boxes.
Step-by-step explanation:
She started with x boxes. Then she bought 8 more boxes. Now she had x + 8 boxes. Then half the boxes were destroyed, so she has the other half of the boxes. Half of the boxes is (x + 8)/2. She has now 17 boxes, so (x + 8)/2 = 17.
(x + 8)/2 = 17
Multiply both sides by 2.
x + 8 = 34
Subtract 8 from both sides.
x = 26
She started with 26 boxes.
Please help me with these questions
Thank u
Answer:
4(a + b)^2
p = 6/5 or 1.2
Step-by-step explanation:
Question One
z = a^2 + b^2
y = ab
4z = 4*a^2 + 4*b^2
8y = 8*ab
=================
4z + 8y = 4a^2 + 8ab + 4b^2
4z + 8y = 4(a^2 + 2ab + b^2)
4z + 8y = 4(a + b)^2
Question Two
2(p + 1) + 8(p - 1) = 5p
2p + 2 + 8p - 8 = 5p
2p + 8p + 2 - 8 = 5p
10*p - 6 = 5p
10*p = 5p + 6
10p - 5p = 6
5p = 6
p = 6/5 or 1.2
Mary covered her kitchen floor with 10 tiles. The floor measures 6 feet long by 5 feet wide. The tiles are each 3 feet long and w feet wide. Write an equation to represent each situation
Answer:
Step-by-step explanation:
Some foundation pieces:
Floor is 30 ft^2
tiles are 3w
Equation:
30=(3w)*10
3=3w
1=w
Now that you know that w has to 1 you can write the formula 30=(3w)×10
Which function best fits the following points?
A. Exponential
B. Quadratic
C. Linear
D. None of the above
Answer:
Option B. Quadratic
Step-by-step explanation:
In a regression model, the value of [tex]r ^ 2[/tex] tells us how accurately the model fits the data.
That closer the value of [tex]r ^ 2[/tex] of 1 is, better is the model.
This can be used to compare what type of model is most convenient to use in some cases.
In this problem the attached table shows a comparison of the value of [tex]r ^ 2[/tex] for 3 models
Linear
Quadratic
Exponential
Note that the value of [tex]r ^ 2[/tex] that is closest to 1 is that which corresponds to the quadratic model.
[tex]r ^ 2 = 0.89[/tex]
Therefore the function that best fits the points is the quadratic
What is the root of the polynomial equation x(x-2)(x+3)=18
Answer:
The root of the polynomial is 3
Step-by-step explanation:
To find the root of the polynomial x(x-2)(x+3)=18
We can use a graphing utility and the system of equations.
We can have the equations;
y = x(x-2)(x+3) ......(i)
Therefore, from the initial equation;
y = 18 ..................... (ii)
We can then plot the graph using the equations, and the x-coordinate of the point of intersection will be the root of the equation.
From the graph, the x-coordinate is 3, since the intersection point is (3,18).
Therefore; the root of the equation is 3.
Which algebraic expression is a trinomial? x3 + x2 – 2x3 – x2 4x3 + x2 – x6 – x +
ANSWER
D.
[tex] {x}^{6} - x + \sqrt{6} [/tex]
EXPLANATION
A trinomial is a simplified polynomial with three terms.
The first option is not a polynomial because of the presence of √x.
The second option is not a trinomial because it has only two terms.
The third option is not a polynomial because of the presence of
[tex] \frac{1}{x} [/tex]
The last option:
[tex] {x}^{6} - x + \sqrt{6} [/tex]
This is trinomial because it has three terms and cannot be simplified further.
There is not fractional exponent.
Answer:
x^8 - x + √6
Step-by-step explanation:
The fourth expression is a trinomial (a polynomial with three terms). The term √6 is acceptable because it's a constant; it's the coefficient of x^0.
Which expression could be used to determine the cost of a 50$ video game after a 20 percent discount?
Answer:
50x.2 is the correct expression. :)
Step-by-step explanation:
50x.2 =10
So you would get a $10 discount off of a $50 video game.
Hope this helps! If you don't mind, please mark as brainliest! Thx :)
Answer:
0.80($50)
Step-by-step explanation:
1.00 times the $50 cost is the initial price of the video.
(1.00 - 0.20) times $50 is the discounted price.
0.80($50) is the desired expression.
Next time, please be sure to share the answer choices. Thanks.
please help me with this geometry question
image attached
Answer:
32
Step-by-step explanation:
Since AP and BP are tangents from the same point, they are equal. So 2x+12=4x-8. So solving for x, we get 2x=20. So x=10. Plugging that in, we get 20+12=32. So the answer is 32.
The linear parent function f(x) = x is transformed to g(x) = 1/3x-5. Which statement correctly compares the graphs of the functions?
Answer:
A
Step-by-step explanation:
The graph of the parent function f(x)=x is the straight line that passes trough the origin and is the bisector of first and third coordinate quadrants (red line in attached diagram).
The graph of the function g(x)=1/3x-5 is the straight line that passes through the point (0,-5) and is less steep (because the slope 1/3 is less than the slope 1). This line is blue line in attached diagram.
So, correct option is option A
If $315 is invested at an interest rate of 3% per year and is compounded continuously, how much will the investment be worth in 9 years? Use the continuous compound interest formula: A = Pert.
$206.23
$412.64
$2,343.56
$4,687.11
Answer:
[tex]\$412.64[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=9\ years\\ P=\$315\\ r=0.03[/tex]
substitute in the formula above
[tex]A=\$315(e)^{0.03*9}=\$412.64[/tex]
Answer: $412.64
Step-by-step explanation: you’re welcome :)
What is the sum of 2 / 3x^2 +12x and 8 / c. Need steps
Answer:
[tex]\frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c} [\tex]
Step-by-step explanation:
We need to find sum of 2 / 3x^2 +12x and 8 / c
So, solving:
[tex](\frac{2}{3x^2} + 12 x ) +\frac{8}{c}[/tex]
Taking LCM of 3x^2 and 1 i.e. 3x^2
[tex]=(\frac{2 + 12 x(3x^2)}{3x^2} ) +\frac{8}{c}\\=(\frac{2 + 36x^3}{3x^2} ) +\frac{8}{c}\\=\frac{2 + 36x^3}{3x^2} +\frac{8}{c}\\LCM \,\, 36x^2 c\\=\frac{(2 + 36x^3)c + 8(3x^2)}{3x^2c}\\=\frac{2c + 36x^3c + 24x^2}{3x^2c}\\= \frac{2c}{3x^2c}+ \frac{36x^3c}{3x^2c} +\frac{24x^2}{3x^2c}[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Select Parameter or Statistic to classify each statement.
Answer:
Statistics;Parameter;Statistics;Parameter.Step-by-step explanation:
According to southeastern.edu,
parameters summarize data from an entire population, whereasstatistics summarize data from a sample of the population.The first statement is true for the sample "those surveyed" the population but not necessarily the entire population. Statistic.
The second statement implies that the soccer team is the population. All members of the population are surveyed. Parameter.
The third statement states that a sample of 100 of all swimming teams are surveyed. Statistic.
The fourth statement implies that the population is all members of the golf team, and that all members of the population are surveyed. Parameter.
A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth. Enter your answer in the box.
The sides of the box are 12in by 12in by 30in.
The interior diagonal =[12^2+12^2+30^2]0.5
=[144+144+900]^0.5
=1188^0.5
The final answer is 34.47in.
My deepest apology if this is not what you meant.
= 34.47in.
Answer:
34.47
Step-by-step explanation:
Assume that there are 2 trials.
X = 2 where X represents the number of successes.
Which probability matches the probability histogram?
Round the answer to one decimal place.
A. P(success) = 0.2
B. P(success) = 0.4
C. P(success) = 0.6
D. P(success) = 0.8
Step-by-step explanation:
According to the graph, the probability of 2 successes is 0.36, which rounds to 0.4.
The number of success is X = 2, the P(success) = 0.4 according to the given histogram.
What is probability?It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.
Number of successes is represented by X (given)
X = 2
The number of successes are plotted on the X - axis of the histogram
So according to the graph , P(success at X = 2) = 0.36
Rounding off the probability to 0.4
Hence, the P(success at X = 2) = 0.4 according to the histogram.
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Please answer this question only if you know it! 30 points and brainliest!
5 out of 20 people said that they like the new packaging of Toasty Toasts.
Which row of the input/output table is incorrect?
y = 2x - 3
x y
Row A 3 3
Row B 5 7
Row C 7 11
Row D 10 15
Row A
Row B
Row C
Row D
Row A: x = 3
y = 2x - 3
y = 2(3) - 3 = 3 This is correct
Row B: x = 5
y = 2x - 3
y = 2(5) - 3 = 7 This is correct
Row C: x = 7
y = 2x - 3
y = 2(7) - 3 = 11 this is correct
Row D: x = 10
y = 2x - 3
y = 2(10) - 3 = 17 THIS IS INCORRECT, SO ROW D
Answer:
Road D
Step-by-step explanation:
The side of a square garden is 12 meters and the total length of the wire brought for fencing the garden is 19 m. Will the wire length be sufficient to fence garden
Answer:
No
Step-by-step explanation:
If its a square garden then that means all 4 sides are 12 meters so 12 times 4 equals 48. This meaning you need 48 meters of wire to wire the entire fence garden.
Answer:
no
Step-by-step explanation:
if the garden is to be fence on all 4 sides then the total length of wire needed is 48 meters as 12*4=48 so since 19<48 it will not be enough
Noah scored 20 points in a game Maya score was 30 points the mean score for Noah Maya and Claire was 40 points what was Claire score explain or show your reasoning
Answer:
70 points
Step-by-step explanation:
Let n represent Noah's score, m as Maya's score, and c as Claire's score.
n=20
m=30
c=?
Let's try make an equation for this problem. The mean score for the three of them is 40, so the following equation is possible:
n+m+c/3=40
Now replace the variable with their values and continue to simplify.
20+30+c/3=40
Multiply both sides by 3.
20+30+c=120
Add 20 and 30 together.
50+c=120
Subtract 50 from 120 to find c.
c=70
Claire's score is 70 points.
Final answer:
To find Claire's score, calculate the total points based on the mean score and then subtract the scores of Noah and Maya. This calculation reveals that Claire's score was 70 points.
Explanation:
The question asks for the score of Claire based on the mean score of Noah, Maya, and Claire combined. Noah scored 20 points, Maya scored 30 points, and the mean score for all three players was 40 points.
To find Claire's score, we first calculate the total points scored by all three. The mean score is the total points divided by the number of scores, which in this case is 3. Therefore, we multiply the mean score (40 points) by 3 to get the total points.
Mean score × number of players = Total points
40 × 3 = 120 points
Next, we subtract Noah's and Maya's scores from the total to find Claire's score.
Total points - Noah's score - Maya's score = Claire's score
120 points - 20 points - 30 points = 70 points
Therefore, Claire's score was 70 points.
In a sale normal prices are reduced by 10% Nathalie bought pair of shoes in the sale for ?54 what was the original price
Answer:
$59.4
Step-by-step explanation:
The original price of the shoes was £60 before the 10% discount was applied, resulting in a final price of £54.
1. First, let's denote the original price of the shoes as [tex]\( x \)[/tex] pounds.
2. Since Nathalie bought the shoes during the sale, she received a 10% discount.
3. Therefore, she paid 90% of the original price after the discount. This can be represented as [tex]\( 0.90x \)[/tex].
4. According to the given information, Nathalie paid £54 for the shoes. So, we can set up the equation:
[tex]\[ 0.90x = 54 \][/tex]
5. To find the original price [tex](\( x \))[/tex], we need to isolate it by dividing both sides of the equation by 0.90:
[tex]\[ x = \frac{54}{0.90} \][/tex]
6. Solving the equation gives us:
[tex]\[ x = 60 \][/tex]
7. Hence, the original price of the shoes was £60 before the 10% discount was applied.
The complete question is here:
In a sale, normal prices are reduced by 10% Nathalie bought a pair of shoes in the sale for £54. What was the original price of the shoes?
sophie makes necklaces by stringing different color beads each necklaces is 15 inches long sophie has 66 inch length of bead string how many necklaces can she make
(I think) you just divide the length of the bead string the the inches of the beads
(Which equals 4.4 so when simplified is 4)
Find the general solution of the given system. dx dt = 3x − y − z dy dt = x + y − z dz dt = x − y + z x(t), y(t), z(t) =
In matrix from, the system is
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}3&-1&-1\\1&1&-1\\1&-1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}[/tex]
The coefficient matrix has eigenvalues [tex]\lambda[/tex] such that
[tex]\begin{vmatrix}3-\lambda&-1&-1\\1&1-\lambda&-1\\1&-1&1-\lambda\end{vmatrix}=-(\lambda-2)^2(\lambda-1)=0\implies\lambda=2_{(2)},\lambda=1[/tex]
(where the subscript denotes multiplicity of the eigenvalue).
[tex]\lambda=2[/tex]:
[tex]\begin{bmatrix}1&-1&-1\\1&-1&-1\\1&-1&-1\end{bmatrix}\vec\eta_1=\vec0[/tex]
[tex]\implies\eta_{1,1}-\eta_{1,2}-\eta_{1,3}=0\implies\eta_{1,1}=\eta_{1,2}+\eta_{1,3}[/tex]
By picking [tex]\eta_{1,1}=1[/tex], we can then set [tex]\eta_{1,2}=1[/tex] and [tex]\eta_{1,3}=0[/tex], and vice versa, to find two corresponding eigenvectors,
[tex]\vec\eta_1=\begin{bmatrix}1\\1\\0\end{bmatrix},\vec\eta_2=\begin{bmatrix}1\\0\\1\end{bmatrix}[/tex]
[tex]\lambda=1[/tex]:
[tex]\begin{bmatrix}2&-1&-1\\1&0&-1\\1&-1&0\end{bmatrix}\vec\eta_3=\vec0[/tex]
[tex]\implies2\eta_{3,1}-\eta_{3,2}-\eta_{3,3}=0\implies2\eta_{3,1}=\eta_{3,2}+\eta_{3,3}[/tex]
We obtain [tex]\vec\eta_3[/tex] independent of [tex]\vec\eta_1,\vec\eta_2[/tex] by picking [tex]\eta_{3,2}=\eta_{3,3}=1[/tex], so that the third corresponding eigenvector is
[tex]\vec\eta_3=\begin{bmatrix}1\\1\\1\end{bmatrix}[/tex]
Then the general solution to this system is
[tex]\begin{bmatrix}x\\y\\z\end{bmatrix}=C_1e^{2t}\vec\eta_1+C_2te^{2t}\vec\eta_2+C_3e^t\vec\eta_3[/tex]
[tex]\begin{cases}x=C_1e^{2t}+C_2te^{2t}+C_3e^t\\y=C_1e^{2t}+C_3e^t\\z=C_2te^{2t}+C_3e^t\end{cases}[/tex]
To find the general solution of the given system of differential equations, we can solve each equation separately and obtain the general solution for x(t), y(t), and z(t).
Explanation:The given system of differential equations is:
dx/dt = 3x - y - z
dy/dt = x + y - z
dz/dt = x - y + z
To find the general solution, we can treat each equation separately.
For dx/dt = 3x - y - z, we can rewrite it as:
dx / (3x - y - z) = dt
Integrating both sides gives us:
ln|3x - y - z| = t + C1, where C1 is the constant of integration.
Exponentiating both sides gives us:
|3x - y - z| = e^(t+C1)
Since |3x - y - z| is always positive, we can remove the absolute value signs:
3x - y - z = e^(t+C1)
Now, we can solve the remaining two equations in a similar manner to find y(t) and z(t).
By solving the three equations, we can obtain the general solution for x(t), y(t), and z(t).
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Three coins are tossed in succession. What is the probability of heads-tails-heads?
1/2
1/6
1/8
Answer:
1/8.
Step-by-step explanation:
The probability of of a head (and a tail) in one toss of a coin being obtained is 1/2.
Each toss is independent of the others so we multiply the probabilities.
So Prob(Head - tail - head) = 1/2*1/2*1/2 = 1/8.
Answer:
1/8.
Step-by-step explanation:
Identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in. HELP PLEASE!!
Answer:
[tex]\boxed{\text{L = 90 in}^{2};\text{ S = 115 in}^{2}}[/tex]
Step-by-step explanation:
Data:
s = 5 in
l = 9 in
1. Lateral surface area
The general formula for the lateral surface area L of a regular pyramid is
L =½pl
where p represents the perimeter of the base and l the slant height.
The base is a square, so
p = 4 × 5 = 20 in
L = ½pl = ½ × 20 × 9 = [tex]\boxed{\text{90 in}^{2}}[/tex]
2. Total surface area
Total surface area = lateral surface area + area of base
S = L + B
B = b² = 5² = 25 in²
S = 90 + 25 = [tex]\boxed{\text{115 in}^{2}}[/tex]