Answer:
5.4 ft²
Step-by-step explanation:
To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.
[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]
The radius of a circle is half its diameter.
Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.
Given values:
r = 0.6 ftl = 2.25 ftπ ≈ 3.14Substitute the values into the formula and solve:
[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).
Pamela is 3 times older than Jakob. In 10 years from now, Pamela’s age will be twice as Jakob’s age.
How old is Pamela?
Answer:
Pamela is 30 years old.
Step-by-step explanation:
We can find Pamela's age using a system of equations where P represents Pamela's age and J represents Jakob's.First equation:
Since Pamela is 3 times older than Jakob, our first equation is given by:
P = 3J
Second Equation:
Since Pamela will be twice as old as Jakob in 10 years, our second equation is given by:
P = 2J + 10
Method to solve: Substitution:
We can solve with substitution by isolating J in the second equation. This will allow us to substitute it for J in the second equation and find P, Pamela's age:
Isolating J:
Step 1: Divide both sides by 3
(P = 3J) / 3
P/3 = J
Substituting P/3 = J for J in P = 2J + 10:
P = 2(P/3) + 10
Step 1: Distribute the 2 to P/3:
P = 2/3P + 10
Step 2: Multiply both sides by 3 to clear the fraction:
(P = 2/3P + 10) * 3
3P = 2P + 30
Step 3: Subtract 2P from both sides:
(3P = 2P + 30) - 2P
P = 30
Step 4: Divide both sides by 2 to find P, Pamela's age:
(2P = 30) / 2
P = 30
Thus, Pamela is 30 years old.
Optional Steps to check the validity of our answer:
In order to check that our answers for Pamela's age is correct, we will first need to find Jakob's age by plugging in 30 for P in any of the two equations in our system. Let's use the first one:Plugging in 30 for P in P = 3J:
Step 1: Divide both sides by 3:
(30 = 3J) / 3
10 = J
Thus, Jakob is 10 years old.
Checking the validity of answers with verbal statements:
Since 30 (i.e., Pamela's age) is indeed 3 times 10 (i.e., Jakob's age), this satisfies the first statement.
In 10 years, Pamela will be 40 as 30 + 10 = 40.
In 10 years, Jacob will be 20 as 10 + 10 = 20.
Since 40 (i.e., Pamela's age in 10 years) is indeed twice 20 (i.e., Jakob's age in 10 years), this satisfies the second statement.
Thus, our answer for Pamela's age is correct.
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z=?
Step-by-step explanation:
To convert all pulse rates of women to z-scores, we use the formula:
z = (x - μ) / σ
where x is the pulse rate, μ is the mean, and σ is the standard deviation.
Substituting the given values, we get:
z = (x - 77.5) / 11.6
Therefore, after converting all pulse rates of women to z-scores, the mean will be 0 and the standard deviation will be 1.
write equation line passing through (3,7) (-5,-1)
Answer:
Step-by-step explanation:
First find the slope using m = (y2-y1)/(x2-x1)
m = (-1-7)/(-5-3)
= -8/-8
= 1
y = mx + b
find the y-intercept
use 1 of the 2 points
Let's try (3,7)
7 = 1(3) + b
b = 4
Equation of the line is y = x + 4
The equation is:
y = x + 4Work/explanation:
First, we will use the slope formula and determine the slope:
[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
where m = slope.
Plug in the data
[tex]\sf{m=\dfrac{-1-7}{-5-3}}\\\\\\\sf{m=\dfrac{-8}{-8}}\\\\\\\sf{m=1}[/tex]
The slope is 1; the equation so far is y = 1x + b or y = x + b.
Plug in the point:
[tex]\sf{7=3+b}[/tex]
[tex]\sf{3+b=7}[/tex]
Solve for b
[tex]\sf{b+3=7}[/tex]
[tex]\sf{b=4}[/tex]
So the y-intercept is 4; we plug that in and see that the equation is y = x + 4.
Hence, the equation is y = x + 4.Question 6
a) Given (t² + 2ty)y' = y²; where y(1) = 1, show that it is homogenous and find its degree.
b) Find the implicit and the explicit solution to the IVP in Q6.(a).
Formula Table
f(t) (Source) (K, m, a, b, given.)
Ke^at
Kmt^m + ... + Ko
K₁ cos(bt) + K₂ sin(bt)
(Kmt^m+ + ... + Ko)e^at
(K₁ cos(bt) + K₂ sin(bt))e^at
(Kmt^m+ + ... + Ko)(K₁ cos(bt) + K₂ sin(bt)
yp(t) (Guess) (k not given)
ke^at
kmt^m + ... + ko
k₁ cos(bt) + k₂ sin (bt)
(kmt^m + ... + ko)e^at
(k₁ cos(bt) + k₂ sin(bt))e^at
(kmt^m +... + ko) (k₁ cos(bt) + k₂ sin (bt))
TABLE 1. List of sources f and solutions yp to the equation L(yp) = f.
a) The solution to the function is t²(du/dt) + 2tu - u² = 0 and can be expressed in the form F(t, u, du/dt) = 0 which confirms it is homogeneous
b) The implicit solution is t/y + 1/t = 2ln|t| + C₁ and the explicit solution is y = (t + 1)/(2ln|t| + C₁)
Understanding Homogenous Functiona) To show that the given differential equation is homogeneous, we need to verify that it can be written in the form:
F(x, y, y') = 0
where F is a homogeneous function of degree zero.
Given:
(t² + 2ty)y' = y²
Let's rearrange the equation:
(t² + 2ty)y' - y² = 0
Now, let u = y/t. We can rewrite y' in terms of u:
y' = du/dt
Substituting these values into the equation, we get:
(t² + 2ty)(du/dt) - (y/t)² = 0
Expanding the equation:
t²(du/dt) + 2ty(du/dt) - (y²/t²) = 0
Now, let's substitute u = y/t into the equation:
t²(du/dt) + 2tu - u² = 0
We can see that this equation is of the form F(t, u, du/dt) = 0, which is homogeneous. Therefore, the given differential equation is homogeneous.
To find the degree of the equation, we need to determine the power of t in each term. Looking at the equation:
t²(du/dt) + 2tu - u² = 0
The highest power of t is 2, which means the degree of the equation is 2.
b) To find the implicit and explicit solutions to the initial value problem (IVP), we need to solve the homogeneous differential equation and apply the initial condition y(1) = 1.
Let's solve the homogeneous equation:
t²(du/dt) + 2tu - u² = 0
We can rewrite it as:
du/u² - dt/t² = -2dt/t
Integrating both sides:
∫(du/u²) - ∫(dt/t²) = -2∫(dt/t)
This simplifies to:
-1/u - (-1/t) = -2ln|t| + C₁
1/u + 1/t = 2ln|t| + C₁
Since u = y/t, we substitute u back:
1/(y/t) + 1/t = 2ln|t| + C₁
t/y + 1/t = 2ln|t| + C₁
This is the implicit solution to the given initial value problem.
To find the explicit solution, we need to solve for y in terms of t. Let's rearrange the equation:
t/y = 2ln|t| + C₁ - 1/t
Multiply both sides by y:
t = y(2ln|t| + C₁ - 1/t)
Now, let's simplify:
t = 2yln|t| + C₁y - 1
Rearranging the equation:
2yln|t| + C₁y = t + 1
Factoring out y:
y(2ln|t| + C₁) = t + 1
Dividing both sides by (2ln|t| + C₁), assuming C₁ ≠ -2ln|t|, we get:
y = (t + 1)/(2ln|t| + C₁)
This is the explicit solution to the given initial value problem.
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Fabian is painting a wall that is 16 feet wide and 9 feet high. The wall has a window in it that is 4 feet
wide by 2 feet high. What is the total area of the remaining wall that needs to be painted?
O 144 ft²
O 50 ft²
O 136 ft²
O 152 ft²
Answer:
136 [tex]ft^{2}[/tex]
Step-by-step explanation:
Find the area of the wall and subtract out the area of the window
16 x 9 = 144
4 x 2 = 8
144 - 8 = 136
Helping in the name of Jesus.
F i n d space t h e space n u m e r i c a l space v a l u e space o f space
left parenthesis 3 cross times 4 plus 4 ² plus 15 minus 4 right parenthesis cross times 2 plus open parentheses 4.5 plus 5 over 10 close parentheses
Answer:the space is 7 in the text below
Step-by-step explanation:
2
1
-1
-2
Determine the period.
2 4
6 8 10 12 14
Acellus
According to the information we can infer that the period of the graph is 8.
How to determine the period of the graph?To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.
In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.
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Rachel wants to reflect AABC across the y=x line and then reflect the image across the y - axis. Is there a single transformation that would be equivalent to this?
A single 180-degree rotation about the origin is equivalent to the sequence of reflections mentioned, as it accomplishes the same changes to the shape's orientation and coordinates.
Yes, there is a single transformation that is equivalent to reflecting AABC across the y=x line and then reflecting the image across the y-axis. This single transformation is known as a 180-degree rotation about the origin.
When you reflect AABC across the y=x line, each point is transformed to its corresponding point on the opposite side of the line. This reflection effectively swaps the x-coordinates with the y-coordinates for each point, resulting in a new shape.
Now, when you reflect the newly formed image across the y-axis, you essentially negate the x-coordinates of each point. This is equivalent to rotating the shape 180 degrees about the origin.
A 180-degree rotation about the origin involves flipping the shape by exchanging the x and y coordinates and taking their negatives. This transformation achieves the same result as reflecting across the y=x line and then reflecting across the y-axis.
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Find the sum of the following finite geometric series.
The sum of the geometric sequence in this problem is given as follows:
5.77.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.
The first term, the common ratio and the number of terms for this problem are given as follows:
[tex]a_1 = 10, q = -\frac{2}{3}, k = 8[/tex]
The formula for the sum of the first n terms is given as follows:
[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]
Hence the sum for this problem is given as follows:
[tex]S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}[/tex]
[tex]S_8 = 5.77[/tex]
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Find the value of Y using the given diagram below
Answer:
i dont know
Step-by-step explanation:
give proper diagram please
on : to show More... Then click on √x to enter your answers using the Math Equation editor. Question 5 A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = − 16t² +64t + 3. What is the height of the stump? O 3 ft -3 ft O 16 ft O 64 ft ◄ Previous 1 pts M Next ▸
The height of the stump is 3 ft.
The given equation represents the height of the frog, h(t), as a function of time, t. To find the height of the stump, we need to determine the height when the time, t, is equal to 0.
In the equation h(t) = -16t² + 64t + 3, we substitute t = 0:
h(0) = -16(0)² + 64(0) + 3
Since any term multiplied by zero is zero, we can simplify further:
h(0) = 0 + 0 + 3
Therefore, the height of the stump, at time t = 0, is 3 ft. This means that when the frog initially leaps from the stump, the height of the stump itself is 3 ft.
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[tex]x - \dfrac{x-1}{2} = 1 - \dfrac{x-2}{3}[/tex]Solve
No spamming
Don't ignore my questions
[tex]\begin{gathered} \; \color{pink}{\frak{\qquad \: x - \dfrac{x - 1}{2} = 1 - \dfrac{x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{(2 \times x) - x - 1}{2} = \dfrac{(3 \times 1) - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{2x - x - 1}{2} = \dfrac{3 - x - 2}{3}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{x - 1}{2} = \dfrac{1 - x}{3}}} \\ \end{gathered}[/tex]
Cross Multiplying,,
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \dfrac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}[/tex]
What is lim x-1 x3-1/x-1
Answer:
Step-by-step explanation:
[tex]\lim_{x\to 1} \frac{x^3-1}{x-1} \\= \lim_{x \to 1} \frac{(x-1)(x^2+x+1)}{(x-1)} \\= \lim_{x \to 1} (x^2+x+1)\\=(1)^1+1+1\\=1+1+1\\=3[/tex]
Select the correct answer.
Answer:
A
Step-by-step explanation:
the x- axis is a horizontal line. A line perpendicular to it will be a vertical line, parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the only equation fitting this description from the list is
x = 3
Write each fraction in terms of the LCD.
X-2
x2
X + 3x - 28
X
x + 9x + 14
Answer:
a) [tex]\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
b)[tex]\frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Step-by-step explanation:
x² + 3x - 28
= x² + 7x - 4x -28
= x(x + 7) - 4(x + 7)
=
= x² + 7x + 2x + 14
= x(x + 7) + 2(x + 7)
= (x + 7)(x + 2)
LCM of x² + 3x - 28 and x² + 9x + 14 is
(x + 7)(x - 4)(x + 2)
We can write:
[tex]\frac{x-2}{x^2 + 3x - 28}\\ \\= \frac{x-2}{(x + 7)(x - 4)}\\\\= \frac{x-2}{(x + 7)(x - 4)} *\frac{x+2}{x+2} \\\\=\frac{(x-2)(x+2)}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-2^2}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]
and
[tex]\frac{x}{x^2 + 9x + 14 }\\ \\= \frac{x}{(x + 7)(x + 2)}\\\\= \frac{x}{(x + 7)(x + 2)} *\frac{x-4}{x-4} \\\\= \frac{x(x-4)}{(x + 7)(x + 2)(x-4)} \\\\= \frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]
Find f′(x)
1. f(x) = x + 2
2. f(x) =2/x2
f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.
So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.
To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.
Applying the power rule, we differentiate each term separately:
f'(x) = d/dx (x^1) + d/dx (2)
The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.
The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.
Therefore, f'(x) = 1 + 0 = 1.
So, the derivative of f(x) = x + 2 is f'(x) = 1.
To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.
The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).
The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).
In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).
Applying the power rule and the constant multiple rule, we differentiate each term separately:
f'(x) = d/dx (2 * x^(-2))
Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.
Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.
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The table below gives the percent of children under five considered to be underweight.
Percent of Underweight Children Number of Countries
16–21.45 23
21.45–26.9 3
26.9–32.35 9
32.35–37.8 6
37.8–43.25 6
43.25–48.7 2
What is the best estimate for the mean percentage of underweight children? (Round your answer to two decimal places.)
The required answer is: 9.61
Rounding the answer to two decimal places gives the best estimate for the mean percentage of underweight children as 9.61%.
To find the best estimate for the mean percentage of underweight children,
we need to calculate the midpoint of each interval and multiply it by the number of countries in that interval, then add the products and divide by the total number of countries.Below is the table that shows the midpoint of each interval and the corresponding calculations.
MidpointNumber of CountriesProducts16.73 (16 + 21.45) / 22383.29 (21.45 + 26.9) / 33253.13 (26.9 + 32.35) / 97194.08 (32.35 + 37.8) / 61411.025 (37.8 + 43.25) / 6 246.3 (43.25 + 48.7) / 2.
Total471Calculating the average of the above data giv
es:\[\frac{471}{23 + 3 + 9 + 6 + 6 + 2} = 471 / 49 = 9.6122\].
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Simplify three fifths times the quantity 1 plus the square root of 16 end quantity squared minus the quantity five minus two end quantity cubed.
PLS HURRRYYYY
Answer:
-12
Step-by-step explanation:
3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =
= 3/5 * (1 + 4)^2 - (3)^3
= 3/5 * (5)^2 - 27
= 3/5 * 25 - 27
= 15 - 27
= -12
Please Solve, Thank you!
Answer:
1711
Step-by-step explanation:
[tex]4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711[/tex]
Make sure to follow order of operations!
what is (45 )(4−3 ) =
Answer:
45
Step-by-step explanation:
Do the operation in parentheses first.
(45)(4 - 3) = (45)(1) = 45
Answer:
Step-by-step explanation:
The answer is 45.
Given,
[tex](45)(4-3)\\=(45)(1)\\=45[/tex]Using subtraction and multiplication rule.
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Which expression correctly represents “three less than the product of a number and two, increased by five”?
2 n minus 3 + 5
Answer:
(2n - 3) + 5 is a correct expression.
Solve the problem bellow and reduce to lowest terms:
Find 4/7 of 1/8
A: 4/8
B: 4/56
C: 4/7
D: 1/14
Pls I need your help
Answer: D
Step-by-step explanation:
we will multiply
4/7* 1/8
we will get 1/14
Answer:
Step-by-step explanation:
After reducing 4/7 of 1/8 to the lowest terms we get 1/14. Thus, option C is the answer.
For reducing a number to its lowest terms, first, we need to simplify the numbers to a more significant number, i.e. 4/7 of 1/8 means 4/7*1/8=4/56.
Now we know that 56 is a multiple of 4 when multiplied by 14. Hence, when we get it in the lowest term we would get 1/14
Please explain how to do it too ill give brainliest
Answer:
x = 90
Step-by-step explanation:
The given diagram shows a circle with intersecting chords, KM and JL.
To find the value of x, we can use the Angles of Intersecting Chords Theorem.
According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.
Let the point of intersection of chords KM and JL be point P.
As the chords are straight lines, angle x° forms a linear pair with angle JPM.
Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.
From inspection of the given diagram:
[tex]m\overset\frown{JM}=30^{\circ}[/tex][tex]m\overset\frown{LK}=(2x - 30)^{\circ}[/tex]Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):
[tex]\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}[/tex]
As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:
[tex]\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}[/tex]
Therefore, the value of x is 90, which means that the two chords intersect at right angles.
you are sent to the local tea shop to pick up 9 drinks. You purchase 3 sweet teas and 6 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21
The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:
Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84
Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14
Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28
Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21
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n quadrilateral ABCD, AD ∥ BC. Quadrilateral A B C D is shown. Sides A D and B C are parallel. The length of A D is 3 x + 7 and the length of B C is 5 x minus 9. What must the length of segment AD be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units
Answer:
(c) 31 units
Step-by-step explanation:
Given quadrilateral ABCD has AD║BC, with AD=3x+7 and BC=5x-9, you want to know the length of AD for the quadrilateral to be a parallelogram.
Congruent sidesOpposite sides of a parallelogram are congruent, so for ABCD to be a parallelogram, we must have ...
BC = AD
5x -9 = 3x +7
2x = 16
x = 8
AD = 3x +7 = 3(8) +7 = 31
The length of AD must be 31 units if ABCD is to be a parallelogram.
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Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences. Graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2.
By finding the point where the graphs intercept, we will see that the solution of the system of equations is the point (0, 2).
How to find the solutions of a system of equations graphically?The solutions of a system of equations are the points where the graphs of the different equations intercept when graphed.
Below you can see the graph of the system:
[tex]g(\text{x}) = 3x + 2 \ \ \ \ \text{(green)}[/tex] [tex]f(\text{x}) = |\text{x} - 1| + 1 \ \ \ \ \text{(blue)}[/tex]There you can see that we have only one intersection point at x = 0, y = 2, then we can conclude that our system has only one solution, and the solution is the point (0, 2).
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The diameter of a circle is 3 miles. What is the area?
Answer:
Area = 7.065 square miles
Step-by-step explanation:
The diameter of a circle is the distance across the circle passing through its centre, and it is equal to twice the radius. Therefore, if the diameter of a circle is 3 miles, then the radius is 1.5 miles.
The formula for the area of a circle is [tex]A = \pi r^2[/tex] ([tex]A = \pi \times r^{2}[/tex])
[tex]A[/tex] is the area [tex]r[/tex] is the radius. The value of pi ([tex]\pi[/tex]) is approximately 3.14, so we will use that value.Substituting the value of the radius into this formula, we get:
[tex]A = 3.14 \times 1.5^2[/tex][tex]A = 3.14 \times 2.25[/tex][tex]A = 7.065[/tex]Therefore, the area of the circle is approximately 7.065 square miles.
________________________________________________________
The answer is:
A = 7.069 miles²
Work/explanation:
We have the diameter, but we need to find the radius. We can do that by diving the diameter by 2:
radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 miles
Now we move on to the next step - the formula.
The formula is:
[tex]\sf{A=\pi r^2}[/tex]
where:
A = areaπ = pir = radiusdiagram
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\small 1.5\ miles}\end{picture}[/tex]
Plug in the data
[tex]\sf{A=\pi \times 1.5^2}[/tex]
[tex]\sf{A=\pi\times2.25}[/tex]
[tex]\sf{A=7.069~miles^2}[/tex]
Hence, this is the areaBy first finding tan, calculate the size of angle
0.
Give your answer in degrees to the nearest
integer.
13 cm
9 cm
0
Not drawn accurately
Tan (θ) = 13/9
θ = 55.305°
Given that cos0 = 8/17 and sin0 = -15/17. What is the value of tan0?
The value of tan 0 is -15/8.
The tangent is a periodic function that is defined by a unit circle. It is the ratio of the opposite side to the adjacent side of a right-angled triangle that contains the angle in question as one of its acute angles. The value of the tangent function can be positive, negative, or zero, depending on the quadrant in which the angle is located.
The given values are
cos0 = 8/17
sin0 = -15/17
We can use the trigonometric identity of tan = sin/cos to find the value of tan 0.
Substituting the given values, we get
tan 0 = sin 0 / cos 0
= (-15/17) / (8/17)
=-15/8
Therefore, the value of tan 0 is -15/8.
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I need all the roots of the graph
Answer:
It looks to be -4, -2, 1, and 3
