The conclusion that "all employees who attend the sales training program and who attend the technical training program are in department B" does not necessarily follow from the given assumptions.
The assumptions state that all employees in department A attend the sales training and employees in department A attend the technical training. It also mentions that employees who attend both training programs are in department B. However, it does not provide any information about employees who only attend one of the training programs.
Based on the given information, we cannot conclude that all employees who attend both training programs are in department B. There could be employees from department A who attend both programs and employees from department B who only attend one of the programs.
Therefore, the conclusion cannot be determined solely based on the given assumptions. Additional information about the distribution of employees across departments and their training program attendance is needed to draw a conclusive statement about the department affiliation of employees attending both training programs.
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A square, with sides of length x cm, is inside a circle.
Each vertex of the square is on the circumference of the circle.
The area of the circle is 64 cm².
Work out the value of x.
Give your answer correct to 3 significant figures.
The value of x will be 6.383cm.
Solution to Circle Geometry problem
Point to note
The diameter of the circle is the diagonal of the squareEach half of the square formed a right angle triangleWe can use the Pythagorean theorem to find the length of the diagonal which is same as diameter
diameter² = side² + side²
diameter² = 2 * x²
diameter = √(2 * x²)
Since the diameter is equal to twice the radius, we have:
diameter = 2 * radius
radius = diagonal / 2
radius = √(2 * x²) / 2
Recall that area of the circle is given by:
area = πr²
where r is the radius
Substituting the expression for the radius, we get:
64 cm² = π * (√(2 * x²) / 2)²
64 cm² = π * (2 * x² / 4)
64 cm² = π * (x² / 2)
128 = π * x²
Solving for x, we get:
x² = 128 / π
x = √(128 / π)
x = 6.383
Therefore, the value of x is approximately 6.383cm.
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Solve 2x(3x+5)+3(3x+5)=ax 2 +bx+c
Answer:
6x² + 19x + 15
Step-by-step explanation:
2x(3x+5)+3(3x+5)
= (3x + 5) (2x + 3)
= 6x² + 9x + 10x + 15
= 6x² + 19x + 15
So, the answer is 6x² + 19x + 15
We can start by simplifying the left side of the equation using the distributive property:
2x(3x+5)+3(3x+5) = (2x)(3x) + (2x)(5) + (3)(3x) + (3)(5)
= 6x^2 + 10x + 9x + 15
= 6x^2 + 19x + 15
Now we can compare this expression with the right side of the equation, which is a polynomial in x with unknown coefficients a, b, and c:
ax^2 + bx + c
Since the two sides are equal, their corresponding coefficients must be equal as well. This gives us a system of three equations in three unknowns:
a = 6 (the coefficient of x^2)
b = 19 (the coefficient of x)
c = 15 (the constant term)
Therefore, the solution to the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c is:
2x(3x+5)+3(3x+5) = 6x^2 + 19x + 15
A restaurant put out small dishes of butter at each table.
They divided 1/6 of a pound of butter evenly between
5 dishes.
Answer:
Step-by-step explanation:
Hello!
1. Start by Plugging your numbers in. now all you have to do is 5 divided by 6! Use a calculator but anything works.
What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
The range of the given function is {y|y>9}. Therefore, option B is the correct answer.
The given function is f(x)=3x+9.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Substitute x=0, 1, 2, 3, 4,....in y=3x+9, We get
When x=0
y=9
When x=1
y=12
When x=2
y=15
When x=3
y=18
So, the range is {9, 12, 15, 18,.....}
Therefore, option B is the correct answer.
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the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 200 and 400 shoppers at the grocery store? the answer should be typed as a decimal with 4 decimal places.
This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
Using the normal distribution formula, we can calculate the z-scores for 200 and 400 shoppers:
z(200) = (200 - 505) / 115 = -2.65
z(400) = (400 - 505) / 115 = -0.91
Next, we can use a standard normal distribution table or calculator to find the area between these two z-scores. The probability is:
P(-2.65 < z < -0.91) = 0.1678
Therefore, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
To calculate the probability that there are between 200 and 400 shoppers at the grocery store, we first need to determine the z-scores for those values. We can then use a standard normal distribution table or calculator to find the area between those two z-scores. The result is the probability of interest. In this case, the probability that there are between 200 and 400 shoppers at the grocery store is 0.1678.
The probability that there are between 200 and 400 shoppers at the grocery store is 0.1678. This means that on a random day, there is a 16.78% chance that the number of shoppers at the grocery store will fall between 200 and 400.
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Factorize a2 - b2
[tex]a {?}^{2} - b {?}^{2} \\ \\ [/tex]
The factorization of the given expression, a² - b², is (a + b)(a - b)
Factorizing an expressionFrom the question, we are to factorize the given expression.
From the given information, the given expression is
a² - b²
This is a special case in the factorization of polynomials. This is called difference of two squares.
Given the expression
x² - y²
The above expression can be written in the factorized form as
(x + y)(x - y)
Check:
Check by expanding the above factored form
(x + y)(x - y)
Applying the distributive property
x(x - y) + y(x - y)
x² - xy + xy - y²
Simplify further
x² - y²
Thus,
x² - y² = (x + y)(x - y)
In the same manner,
a² - b² = (a + b)(a - b)
Hence, the factorization of a² - b² is (a + b)(a - b)
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The quadratic equation h=-16t^2+32t+2
represents the height, h (in feet), of a ball kicked after t seconds. Answer each question. Express each answer as a decimal rounded to the nearest hundredth.
How long will it take the ball to reach 18 feet?
When will the object be at 10 feet?
When will the ball hit the ground?
By solving the quadratic equations,
It will take the ball 1 second to reach 18 feet
It will take the ball 1.71 seconds to be at 10 feet
It will take the ball 2.06 seconds to hit the ground
Solving quadratic equations: Determining how long it would take the ball to reach a heightFrom the question, we are to determine how long it would take the ball to reach 18 feet
To determine how long it would take the ball to reach 18 feet, we will set h = 18 in the equation
The given equation is
h = -16t² + 32t + 2
Put h = 18
18 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 18 = 0
16t² - 32t + 16 = 0
16t² - 16t - 16t + 16 = 0
16t(t - 1) -16(t - 1) = 0
(16t - 16)(t - 1) = 0
16t - 16 = 0 OR t - 1 = 0
16t = 16 OR t = 1
t = 16/16 OR t = 1
t = 1 OR t = 1
Hence,
t = 1 second
Hence, it will take the ball 1 second to reach 18 feet
To determine how long it will take the ball to reach 10 feet, we will set h = 10
h = -16t² + 32t + 2
Put h = 10
10 = -16t² + 32t + 2
Rearrange
16t² - 32t - 2 + 10 = 0
16t² - 32t + 8 = 0
Using the quadratic formula,
t = 0.29 second OR t = 1.71 seconds
The ball will hit the ground when h = 0
Set h = 0 in the equation
h = -16t² + 32t + 2
0 = -16t² + 32t + 2
16t² - 32t - 2 = 0
Using the quadratic formula,
t = -0.06 OR t = 2.06
Since t cannot be negative,
t = 2.06 seconds
Hence, it will take 2.06 seconds for the ball to hit the ground
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The position (in meters) of a particle per respect to time (in seconds) is defined by the following function: s(t) = t^4 - 16t^3 + 72t^2 +5. Find the maximal and minimal value for the speed of the particle on domain of t being [1,7[
Answer:
Max at t=2, 128 m/s
Min at t=6, 0 m/s
Step-by-step explanation:
Given the position function of a particle with respect to time, find the minimum and maximum velocity the particle travels over the interval [1,7].
[tex]s(t)=t^4-16t^3+72t^2+5[/tex]
(1) - Find the velocity function of the particle
The velocity function is a derivative of the position function.
[tex]s'(t)=v(t)\\\\s(t)=t^4-16t^3+72t^2+5\\\\\Longrightarrow s'(t)=\frac{d}{dx}[t^4-16t^3+72t^2+5] \\\\\text{Use the derivative rules.}\\\\\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Constant Rule:}}\\\\\frac{d}{dx}[k]=0 \end{array}\right} \\\\\\\Longrightarrow s'(t)=(4)t^{4-1}-16(3)t^{3-1}+72(2)t^{2-1}+0\\\\\Longrightarrow s'(t)=4t^{3}-48t^{2}+144t\\\\[/tex]
[tex]\therefore \boxed{v(t)=4t^{3}-48t^{2}+144t}[/tex]
(3) - Take the derivative of v(t)
[tex]v(t)=4t^{3}-48t^{2}+144t\\\\\Longrightarrow v'(t)=12t^2-96t+144[/tex]
(4) - Let v'(t)=0 and solve for "t," these are the critical points
[tex]v'(t)=12t^2-96t+144\\\\\Longrightarrow 0=12t^2-96t+144\\\\\Longrightarrow 0=12[t^2-8t+12]\\\\\Longrightarrow 0=t^2-8t+12\\\\\Longrightarrow (t-6)(t-2)=0\\\\\therefore \text{The critical points are} \ \boxed{t=6 \ \text{and} \ t=2}[/tex]
(5) - Find the max/min values (in this case these values represent the particle's velocity) by plugging the critical points into v(t)
[tex]\text{Recall that} \ v(t)=4t^{3}-48t^{2}+144t \ \text{and} \ t=6, \ t=2\\\\\text{\underline{When t=6:}}\\\\\Longrightarrow v(6)=4(6)^{3}-48(6)^{2}+144(6)\\\\\Longrightarrow \boxed{v(6)=0 \ m/s}\\\\\text{\underline{When t=2:}}\\\\\Longrightarrow v(2)=4(2)^{3}-48(2)^{2}+144(2)\\\\\Longrightarrow \boxed{v(6)=128 \ m/s}[/tex]
Thus, at time, t=6, the particle's velocity is smallest, 0 m/s. And at time, t=2, the particle's velocity is greatest, 128 m/s.
Please helppp. What’s the area and circumference??!
The value of EF is 26
What is segment of a circle?A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.There is minor segment and major segment.
Since the two arcs are equal, i.e arc EF = arc CD, therefore,
chord EF = chord CD
9x-1 = 41 - 5x
collecting like terms
9x +5x = 41+1
14x = 42
divide both sides by 14
x = 42/14
x = 3
Therefore EF = 41-5x
= 41-5×3
= 41-15
= 26
therefore the value of EF is 26
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emily paints at a constant rate. she can paint square feet in minutes. what is emily's constant rate in square feet per minute?
Emily's constant rate in square feet per minute is 10. This means that she can paint 10 square feet in one minute.
To determine Emily's constant rate in square feet per minute, we need to use the given information that she can paint a certain number of square feet in a certain number of minutes. Let's say that Emily can paint x square feet in y minutes.
To find her rate, we need to divide the number of square feet painted by the number of minutes it took to paint them. So Emily's constant rate would be:
x / y = rate (in square feet per minute)
For example, if Emily can paint 200 square feet in 20 minutes, her rate would be:
200 / 20 = 10
Therefore, Emily's constant rate in square feet per minute is 10. This means that she can paint 10 square feet in one minute.
In conclusion, to determine Emily's constant rate in square feet per minute, we need to divide the number of square feet painted by the number of minutes it took to paint them. The result is the rate in square feet per minute.
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Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?
Answer:
f(x) = x^3 - 12x^2 + 6x - 8
f'(x) = 3x^2 - 24x + 6 = -30
3x^2 - 24x + 36 = 0
x^2 - 8x + 12 = 0
(x - 2)(x - 6) = 0, so x = 2, 6
Answer:
the values of x are :
x = 2
x = 6
An athlete throws a shot put with an initial vertical velocity of 40 feet per second. He releases the shot put at a height of 5.69 feet.
Use an equation that models the height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown to find the time that the shot put is in the air.
Round your answers to the nearest whole numbers.
The shot put is in the air for approximately 3 seconds.
The height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown can be modeled by the equation:
h(t) = h + vt - (1/2)gt²
where v is the initial vertical velocity in feet per second, and s is the initial height in feet.
Here, the initial vertical velocity is 40 feet per second, and the initial height is 5.69 feet. Therefore, we can plug in these values to get:
h = -16t² + 40t + 5.69
To find the time that the shot put is in the air, we need to find the value of t when h = 0, since the shot put will hit the ground when its height is 0.
Therefore, we can set the equation equal to 0 and solve for t:
0 = -16t² + 40t + 5.69
Using the quadratic formula, we get:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 40, and c = 5.69.
Plugging in these values, we get:
t = (-40 ± √(40² - 4(-16)(5.69))) / 2(-16)
Simplifying, we get:
t ≈ 3 or t ≈ 0.2
Since the shot put cannot be in the air for negative time, the only possible answer is t ≈ 3.
Therefore, the shot put is in the air for approximately 3 seconds.
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Can someone tell me the original and perpendicular slope of this question
The slope of the original line of the graph sis found to be 1 and the slope of perpendicular line is -1.
One of the line shown in the graph is passing through the points (0, -7) and (7, 0). Now we have to recall that the slope M of the line L passing from points (a, b) and (c, d) is given as,
M = (d-b)/(c-a)
Also, if the line L is perpendicular to line l, then the slope m of the line l will be given as,
m = -1/M.
So, now the slope of line L is,
M = (0-(-7))/(7-0)
M = 7/7
M = 1
Now, the slope of the perpendicular line l is,
m = -1/1
m = -1.
Hence, the slope of the perpendicular line and original lines are -1 and 1.
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a rectangular lot is 135 yards long and 100 yards wide, give the length and width of another rectangular lot that has the same perimeter but a larger area.
A 2-pint bottle of salad dressing costs $13.76. What is the price per cup?
Submit
The price per cup of salad dressing in a 2-pint bottle that costs $13.76 is $0.86.
To calculate the price per cup of salad dressing, we need to know that there are 2 cups in a pint. Therefore, there are 4 cups in a 2-pint bottle of salad dressing.
To find the price per cup, we divide the total cost of the bottle by the number of cups in the bottle.
$13.76 ÷ 4 cups = $3.44 per cup
Therefore, the price per cup of salad dressing is $0.86, which is obtained by dividing $3.44 by 4.
It is important to know the price per unit, whether it is per ounce, per pound, per liter, or per cup, to be able to compare the cost of different products accurately.
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You and your friends decide to go out to
dinner and celebrate your birthday. The
meal costs $168.34. The sales tax is 5%
and your waiter was okay so you want to
leave a 15% tip. What was the total bill?
Round to the nearest cent.
The total bill of the dinner to celebrate birthday including sales tax and tip to the nearest cent is $202.01
What was the total bill?Cost of the meal = $168.34
Sales tax = 5% of $168.34
= 0.05 × 168.34
= $8.417
Tip = 15% of $168.34
= 0.15 × 168.34
= $25.251
Total bill = Cost of the meal + Sales tax + Tip
= $168.34 + $8.417 + $25.251
= $202.008
Hence, the total bill is $202.01 to the nearest cent.
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The terminal side of theta in standard position contains the point (-2, -6). Find the exact value of sin theta.
The exact value of sin theta as required to be determined in the task content is; sin theta = -3 / 2√10.
What is the exact value of sin theta as required?It follows from the task content that the exact value of sin theta is required to be determined from the given information.
Since the given terminal side of theta is; (-2, -6) it follows that the length of the hypothenuse in the arrangement is;
= √((-2)² + (-6)²)
= √(4 + 36)
= √40
= 4√10.
Therefore, since sin theta = opposite / adjacent;
Sin theta = -6 / 4√10
sin theta = -3 / 2√10.
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a simple random sample of 50 adults was surveyed, and it was found that the mean amount of time that they spend surfing the internet per day is 54.2 minutes, with a standard deviation of 14.0 minutes. what is the 99% confidence interval (z-score
The 99% confidence interval for the population mean time spent on the internet, in minutes, is given as follows:
(48.9, 59.5).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 50 - 1 = 49 df, is t = 2.68.
The parameter values are given as follows:
[tex]\overline{x} = 54.2, s = 14, n = 50[/tex]
Then the lower bound of the interval is given as follows:
[tex]54.2 - 2.68\frac{14}{\sqrt{50}} = 48.9[/tex]
The upper bound of the interval is given as follows:
[tex]54.2 + 2.68\frac{14}{\sqrt{50}} = 59.5[/tex]
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15 Points PLEASE HELP ME OUT.
Algebra 1 honors
Answer: A C(t) = -(x-5)^2
Step-by-step explanation:
Answer:
C(t) = -x^2 + 5
Step-by-step explanation:
Notice how C(t) = 5 when t = 0. This means that (0, 5) is a point on C(t) and is the y-intercept, thus making the constant term (term without variable in standard form) 5. Next, notice how C(t) decreases as t increases and decreases. This means that C(t) is reflected over the x-axis such that it looks like an upside-down U shape. Thus, a negative must be applied to the term of the highest degree.
PROBLEM SOLVING The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period $T$ (in seconds) can be modeled by the function $T=1.1\sqrt{L}$ , where $L$ is the length (in feet) of the pendulum. Estimate the length of a pendulum with a period of $1.65$ seconds. Write your answer as a decimal.
Answer:
If $T=1.65$ seconds, then we can solve the equation for $L$ as follows:
$$
T=1.1\sqrt{L}
$$
$$
\frac{T}{1.1}=\sqrt{L}
$$
$$
\left(\frac{T}{1.1}\right)^2=L
$$
Substituting $T=1.65$, we get:
$$
L=\left(\frac{1.65}{1.1}\right)^2=2.25
$$
Therefore, the length of the pendulum is approximately 2.25 feet.
The points (7,-5) and (r,5) lie on a line with slope . Find the missing coordinate .
The missing coordinate is equal to 15.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
5/4 = (5 + 5)/(r - 7)
5/4 = 10/(r - 7)
5(r - 7) = 40
5r - 35 = 40
5r = 75
r = 75/5
r = 15.
Based on the information provided, the slope is the change in y-axis with respect to the x-axis and it is equal to 5/4.
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Complete Question:
The points (7,-5) and (r,5) lie on a line with slope 5/4. Find the missing coordinate
After heating up in a teapot, a cup of hot water is poured at a temperature of
20
3
∘
203
∘
F. The cup sits to cool in a room at a temperature of
6
9
∘
69
∘
F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between the temperature of the water and the temperature of the room, as given by the formula below:
�
=
�
�
+
(
�
0
−
�
�
)
�
−
�
�
T=T
a
+(T
0
−T
a
)e
−kt
�
�
=
T
a
= the temperature surrounding the object
�
0
=
T
0
= the initial temperature of the object
�
=
t= the time in minutes
�
=
T= the temperature of the object after
�
t minutes
�
=
k= decay constant
The cup of water reaches the temperature of
18
5
∘
185
∘
F after 1.5 minutes. Using this information, find the value of
�
k, to the nearest thousandth. Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
Enter only the final temperature into the input box.
The cup of water reaches a temperature of 173 F after 4.5 minutes.
What is temperature?Temperature is a measure of the average kinetic energy of particles in a system. It is an important physical quantity used to describe the state of a system and is widely used in science, engineering, and everyday life. Temperature is a thermodynamic property of a system that shows how much energy is available to do work. In everyday terms, temperature is a measure of how hot or cold something is.
k = -0.2416
The equation for the cooling rate of the cup of water is:
T(t) = 203- 0.2416t
After 4.5 minutes, the temperature of the cup of water can be found by substituting t = 4.5 into the equation:
T(5) = 203- 0.2416(4.5 ) = 173.08 F
Therefore, the cup of water reaches a temperature of 173 F after 4.5 minutes.
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The graph of function fis shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.
g(x)=f(x + 2)
Drawing Tools
Select
Line
Click on a tool to begin drawing.
-6
-2
Delete
Undo
8
Reset
A graph representing the function g(x) = -1/2f(x + 2) is shown in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 - 0)/(5 - 3)
Slope (m) = 4/2
Slope (m) = 2.
At data point (3, 0) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 2(x - 3)
y = f(x) = 2x - 6
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The radius of circle O is 22, and OC = 15. The diagram is not drawn to scale. What is the length of segment AB? Round the answer to the nearest tenth.
16.1
32.2
26.7
53.3
The length of the segment AB according to the given equation as required to be determined is; 32.2.
What is the length measure of the segment AB?As evident from the task content; the length measure of segment AB is required to be determined.
The assumption is such that point C is the midpoint of AB.
Therefore, on this note, the triangle OBC is a right triangle and the since radius OB = 22 and OC = 15;
CB² = 22² - 15²
CB² = 484 - 225
CB² = 259
CB = 16.1
Therefore, since C is the midpoint of AB; AB = 2 × 16.1 = 32.2.
Ultimately, the length of segment AB is; 32.2.
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In the diagram, ⨀R≅ ⨀S . Find m DE⌢ .
Answer:
60°
Step-by-step explanation:
ST = SW, since both are radii of the circle.
SW = WT, given.
STW is an equilateral triangle.
RED is an equilateral triangle.
Therefore, the measure of DE is 60°.
A store sells packages of 3 pens for $1.50, 8 pens for $4.00, and 12 pens for $6.00. Let c represent the total cost and p represent the number of pens. Write an
equation to represent this situation.
The equation for the total cost and p represent the number of pens is c = 3p + 8p + 12p
Which equation represents the situation?3 pens for $1.50
8 pens for $4.00
12 pens for $6.00
Where,
c represent the total cost
p represent the number of pens
Total cost, c = 1.50 + 4.00 + 6.00
= $11.50
Number of pens, p = 3 + 8 + 12
= 23
c = 3p + 8p + 12p
$11.50 = 23p
Hence, c = 3p + 8p + 12p is the equation that represents the situation.
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You deposit $400 in an account that pays 2.34% annual
compounded monthly. What is the balance after
interest
10 years?
A=
The balance after 10 years, considering monthly compounding, would be approximately $512.69.
To calculate the balance after 10 years, we can use the formula for compound interest:
A = [tex]P(1 + r/n)^{(nt)[/tex]
A is the final balance
P is the principal amount (initial deposit)
r is the annual interest rate (in decimal form)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the principal amount (P) is $400, the annual interest rate (r) is 2.34% or 0.0234, the interest is compounded monthly (n = 12), and the number of years (t) is 10.
Using these values, we can calculate the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
We may use the compound interest calculation to determine the balance after 10 years:
A = [tex]P(1 + r/n)^{(nt)[/tex]
The ultimate balance is A.
P stands for the initial deposit's principal.
The yearly interest rate is represented by the decimal r, while the number of times it is compounded annually is represented by n.
The number of years is t.
In the above scenario, the principle (P) is $400, the annual interest rate (r) is 2.34%, or 0.0234, the interest is compounded on a monthly basis (n = 12), and the time (t) is 10.
These numbers allow us to determine the final balance (A):
A = $400(1 + 0.0234/12)⁽¹²ˣ¹⁰⁾
A = $400(1.00195)¹²⁰
A ≈ $400(1.28172)
A ≈ $512.69
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A fair six sided die is thrown.find the possibility Of getting the following a)a3 b)a4 c) a9 d) a1 or a2
Answer:
a) 1/6. b) 1/6. c) 0. d) 1/3.
Step-by-step explanation:
it's a fair die, so probability of getting any of the 6 numbers is equal.
that is, they all have probability 1/6.
a) p(3) = 1/6
b) p(4) = 1/6
c) p(9) = 0. die only goes up to 6.
d) p(1) = 1/6. p(2) = 1/6
p(1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
a bag contains 6 red marbles, 4 blue marbles, 8 yellow marbles, 10 green marbles, & 2 white marbles. find the probability of drawing a blue marble (please help right now)
The probability of selecting a blue marble is 2/15
What is the probability of drawing a blue marbleA probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space.
In this problem, to find the probability of drawing a blue marble, let's work with the sample space.
Probability of blue marble = number of blue marbles / total number of marbles
Total number of marbles = 6 + 4 + 8 + 10 + 2 = 30
Probability of blue marble = 4 / 30
probability of blue marble = 2/15 = 0.133
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find the cosine of the angle between the planes x + y + z = 0 and x + 3y + 4z = 6.
So the cosine of the angle between the two planes is 8sqrt(78) / 78.
To find the cosine of the angle between two planes, we need to find the normal vectors of each plane and then use the dot product formula.
The normal vector of the first plane is <1, 1, 1>, and the normal vector of the second plane is <1, 3, 4>.
The dot product of these two vectors is:
<1, 1, 1> · <1, 3, 4> = 1(1) + 1(3) + 1(4) = 8
The magnitude of the normal vector of the first plane is:
|<1, 1, 1>| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)
The magnitude of the normal vector of the second plane is:
|<1, 3, 4>| = sqrt(1^2 + 3^2 + 4^2) = sqrt(26)
Therefore, the cosine of the angle between the two planes is:
cosθ = (normal vector of plane 1) · (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2)
= 8 / (sqrt(3) * sqrt(26))
= 8 / (sqrt(78))
= 8sqrt(78) / 78
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